Compton Scattering from Nucleon and Nuclear Targets

Transcription

1 Compton Scattering from Nucleon and Nuclear Targets M.W. Ahmed 1, C.W. Arnold 2, T. Averett 3, M. Blackston 1, X.Z. Cai 4, J.R. Calarco 5, J.G. Chen 4, T. Clegg 2, D. Crabb 6, D. Dutta 1, G. Feldman 7, H. Gao 1, A. Gasparian 8, W. Guo 4, C. Howell 1, H. Karwowski 2, M. Kovash 9, K. Kramer 1, Y.G. Ma 4, R. Miskimen 10, A.M. Nathan 11, B. Norum 6, R. Pedroni 8, C.B. Wang 4, H.W. Wang 4, H.R. Weller 1, S. Whisnant 12 Y. Wu 13, W. Xu 4, Y. Xu 4, A. Young 14, X. Zong 1 1 TUNL & Duke University 2 TUNL & University of North Carolina, Chapel Hill 3 College of William & Mary 4 Institute of Applied Physics, Shanghai, Chinese Academy of Science 5 University of New Hampshire 6 University of Virginia 7 George Washington University 8 North Carolina A&T State University 9 University of Kentucky, Lexington 10 University of Massachusetts, Amherst 11 University of Illinois, Urbana-Champaign 12 James Madison University 13 DFELL & Duke University 14 TUNL & North Carolina State University, Raleigh Abstract The High Intensity Gamma Source (HIγS) at Duke Free Electron Laboratory opens a new window to the study of fundamental quantities related to the structure of the nucleon through Compton scattering from both polarized and unpolarized nucleon and nuclear targets. These studies allow for the extraction of the neutron electromagnetic polarizabilities with unprecedented accuracy, and will provide data for the first time on currently unknown quantities such as the spin polarizabilities of the neutron. Compton scattering from the helium isotopes will allow for a precision determination of the 3 He and 4 He polarizabilities. These studies will comprise precision tests of effective field theories, lattice QCD calculations and predictions from the standard model of nuclear physics. In order to carry out this important and extensive Compton Scattering program at HIγS, a collaboration involving physicists from 13 Universities has made a detailed study of the requirements of an experimental program to achieve these goals. They have concluded that a large acceptance photon detection system is required. We request the support of such a detection system (HINDA) from the NSF through the agency s MRI program. 1

2 INTRODUCTION Understanding the structure of the nucleon from the underlying theory of strong interaction in terms of quark and gluon degrees of freedom is a fundamental and challenging task in physics. The experimental and theoretical investigation of the structure of the nucleon has been more intense than ever in the last two decades or so, largely due to progress and breakthroughs achieved both in experiments and theories. With the development in polarized beam, recoil polarimetry, and polarized target technologies, polarization experiments have provided more precise data on quantities ranging from electromagnetic form factors of the nucleon from elastic electron-nucleon scattering to spin structure functions probed in deep inelastic lepton-nucleon scattering. At the same time, significant theoretical progress has been made in describing these data and in providing new insight in understanding the structure of the nucleon in areas ranging from effective field theories to lattice QCD. The newly discovered Generalized Parton Distributions (GPDs)[1, 2], which can be accessed through deeply virtual Compton scattering and deeply virtual meson production, connect the nucleon form factors and the nucleon structure functions probed in the deep-inelastic scattering experiments. The GPDs provide new insights into the structure of the nucleon, and possibly provide a complete map of the nucleon wave-function. Nucleon polarizabilities comprise another set of fundamental quantities related to the structure of the nucleon, describing the response of the nucleon to external electromagnetic fields. These quantities can be accessed through low energy Compton scattering experiments. Compton scattering from nucleons at low energy is specified by low-energy theorems up to and including terms linear in photon energy. These terms are completely determined by the static properties of the nucleon, i.e. the nucleon charge, mass and its anomalous magnetic moment. At next to leading order in photon energy there appear new structure constants which are related to the dynamic response of the nucleon s internal degrees of freedom. The electric (α) and magnetic (β) scalar polarizabilities, which describe the response of the nucleon to external electric and magnetic field, respectively, enter in terms which are second order in photon energy. At the third order four new parameters, γ 1 to γ 4, the spin polarizabilities, appear. While spin polarizabilities do not have as intuitive a physical interpretation as the electric and magnetic polarizabilities, they are nevertheless just as fundamental. The closest analogy in classical physics that one can make to spin polarizabilities is the Faraday rotation in which the linear polarization of incoming light is rotated going through a spin polarized medium. In the last two decades or so significant efforts have been devoted to Compton scattering measurements from the proton in order to extract the proton electric (α) and magnetic (β) polarizabilities. The most precise information on these two quantities are from the recent Mainz experiment [3]: α = [11.9 ± 0.5(stat.) 1.3(syst.) ± 0.3(mod.)] 10 4 fm 3, β = [1.2±0.7(stat.)±0.3(syst.)±0.4(mod.)] 10 4 fm 3. While the proton electric and magnetic polarizabilities are known relatively well, our knowledge of the neutron polarizabilities is much poorer than that of the proton due to the lack of free neutron targets in nature. The neutron electric and magnetic polarizabilities have been extracted from experiments using deuterium targets. The first experiment with a deuterium target was low-energy neutron scattering from heavy nuclei [4]. In recent years, coherent elastic Compton scattering by the deuteron, and the quasi-free Compton scattering from the deuteron are commonly used. The most precise information on the neutron s electric (α n ) and magnetic polarizabilities (β n ) is from the quasifree Compton scattering experiment carried out at Mainz [5]: α n = 2

3 12.5±1.8(stat) (syst)±1.1(model), β n = (stat) (model) 1.1(model), in units of 10 4 fm 3. Compared to the nucleon electric and magnetic polarizabilities, very little is known about nucleon spin polarizabilities (γ i, i = 1 4). The only quantities which have been extracted so far are the forward and backward spin polarizabilities, γ 0 and γ π. The forward and backward spin polarizabilities are two independent linear combinations of γ 1, γ 2 and γ 4. In order to determine all four spin polarizabilities separately, two additional measurements which are sensitive to the nucleon s spin polarizabilities are needed. Unpolarized Compton scattering differential cross-section measurements are not sensitive to the nucleon spin polarizabilities. Double-polarization asymmetries from circularly polarized photons Compton scattering off a polarized nucleon target have been shown to be sensitive to the nucleon spin polarizabilities [6, 7]. Single spin observables and double-polarization observables from Compton scattering on nucleon and nuclear targets are being proposed with the upgraded HIγS photon energy and high-intensity photon flux. These new experiments will advance our knowledge of the nucleon polarizabilities greatly, therefore providing stringent tests of theories. COMPTON SCATTERING AT LOW ENERGIES The general amplitude for Compton scattering based on parity, charge conjugation, and time reversal symmetry can be written [9] in terms of six structure dependent functions A i (ω, θ), i = 1,...6 as: T = A 1 (ω, θ) ɛ ɛ + A 2 (ω, θ) ɛ ˆk ɛ ˆk (1) +ia 3 (ω, θ) σ ( ɛ ɛ) + ia 4 (ω, θ) σ ( ˆk ˆk) ɛ ɛ + ia 5 (ω, θ) σ [ ( ɛ ˆk) ɛ ˆk ( ɛ ˆk ) ɛ ˆk ] ia 6 (ω, θ) σ [( ɛ ˆk ) ɛ ˆk ( ɛ ˆk) ɛ ˆk ], where ω(= ω ) denotes the photon energy in the center-of-mass frame, θ is the center-ofmass scattering angle of the photon, ɛ, ˆk ( ɛ, ˆk ) are the polarization vector and direction of the incident (final) photon, and σ represents the spin (polarization) vector of the nucleon. Following the general conventions, the six structure dependent functions, A i (ω, θ) (i = 1,..., 6) are separated into the pion-pole ( anomalous ) contributions and the remaining ( regular ) terms: A i (ω, θ) = A i (ω, θ) π0 pole + A i (ω, θ) reg (2) One can now carry out a low energy expansion of the six regular structure functions in powers of photon energy: A 1 (ω, θ) reg c.m. = Q e2 M N + 4π(α E + cos θβ M )ω 2 (3) + 4π M N (α E + β M )(1 + cos θ)ω 3 + O(ω 4, 1 M N 3 ), 3

4 A 2 (ω, θ) reg c.m. = Q e2 ω 4πβ MN 2 M ω 2 4π (α E + β M )ω 3 + O(ω 4 1, 3 ), (4) M N M N A 3 (ω, θ) reg c.m. = [ Q(Q + 2κ) (Q + κ) 2 cos θ ] e 2 ω (5) 2MN 2 +4π[γ 1 (γ 2 + 2γ 4 ) cos θ]ω 3 + O(ω 4 1, 3 M ), N A 4 (ω, θ) reg c.m. = (Q + κ)2 e 2 ω + 4πγ 2 ω 3 + O(ω 4 1, 3 ), (6) M N 2M 2 N A 5 (ω, θ) reg c.m. = (Q + κ)2 e 2 ω + 4πγ 4 ω 3 + O(ω 4 1, 3 ), (7) M N A 6 (ω, θ) reg c.m. = 2M 2 N Q(Q + κ)e2 ω + 4πγ 2MN 2 3 ω 3 + O(ω 4, 1 3 ). (8) M N Where the charge of the nucleon is Q = (1 + τ 3 )/2, its anomalous magnetic moment is κ = (κ s + κ v τ 3 )/2, and the mass of the nucleon is M N. For each structure function the leading order terms in the ω expansion are given by model-independent Born contributions for scattering from a spin 1/2 point particle with an anomalous magnetic moment and are fixed by low energy theorems of current algebra. The higher order terms in ω are model dependent quantities and the comparison between data and theoretical predictions provides sensitive tests of the validity of the theoretical approaches. The more familiar electric (α E ) and magnetic (β M ) polarizabilities enter the amplitude at the O(ω 2 ) and measure the response or deformation of the system to quasi-static electric and magnetic fields. The γ i (i = 1,.., 4), which enter the amplitude at the ω 3 order are the so-called spin polarizabilities. They determine independently the response of a microscopic target with spin 1/2 to a quasi-static electromagnetic field when the spin degree of freedom is involved. For example, an induced dipole p s can be constructed by p s = γ 3 ( S B), where S denotes the spin of the target. The forward and backward spin polarizabilities (γ 0 and γ π ) are linear combination of the γ i : γ 0 = γ 1 γ 2 2γ 4 (9) γ π = γ 1 + γ 2 + 2γ 4 Both γ 0 and γ π can be obtained in a model dependent way by relying on a multipole analysis of single-pion-photoproduction data. Recently, the backward spin polarizability γ π = γ 1 + γ 2 + 2γ 4 has been extracted by the LEGS group for the first time from unpolarized Compton scattering data from the proton [10]. However, the extracted value γ π = ( 27.1 ± 2.2) 10 4 fm 4 contradicts the predictions of standard dispersion theory [11 13] as well as those of chiral perturbation theory [9, 14, 15]. The theoretical prediction for γ π from chiral effective field theory is fm 4 [9]. The LEGS result is also in disagreement with the TAPS result γ π = ( 36.1±2.2) 10 4 fm 4 [3]. The most recent Mainz experiment [16] using the LARA detector extracted a backward polarizability value ranging from (-35.9 to -40.9) 10 4 fm 4 depending on the parameterization used for the photomeson amplitudes, which is in agreement with 4

5 the earlier result from Mainz [3]. The new data confirm the previous observation that there is a systematic discrepancy between Mainz results and LEGS results. The clarification of the situation will benefit from double polarization Compton scattering experiments [17] in which circularly polarized photons are scattered off a polarized proton target. The neutron backward spin polarizability was determined to be γ n π = (58.6 ± 4.0) 10 4 fm 4 [18]. A sum rule exists for γ 0, which was originally discovered by Gell-Mann, Goldberger and Thirring (GGT) [19]: γ 0 = 1 dω 4π 2 ν 0 ω [σ (ω) σ 3 + (ω)]. (10) Where ν 0 is the pion production threshold, and σ (ω), σ + (ω) are the total photoabsorption cross-sections when the total helicity of the photon-nucleon system is 1/2 and 3/2 along the photon momentum direction, respectively. The GGT sum rule is closely related to the Drell-Hearn-Gerasimov (DHG) sum rule [20], which has gained enormous renewed interest in recent years both experimentally and theoretically [21], and which is given by: πe 2 κ 2 2M 2 N dω = ν 0 ω [σ (ω) σ + (ω)]. (11) The following results on γ 0 were reported [22] based on the multipole analysis of the photopion production data: γ fm 4 (proton) (12) fm 4 (neutron) γ 0 The most recent extraction of the proton forward spin polarizability is from the Mainz GDH experiment [23], and the extracted value of γ 0 based on the Mainz data and the dispersion analysis is γ 0 = [ 1.01 ± 0.08(stat) ± 0.10(syst)] 10 4 fm 4 [24]. COMPTON SCATTERING FROM DEUTERIUM AND NUCLEON POLARIZ- ABILITIES In the past ten years, great progress has been made in studies of the proton polarizabilities through Compton scattering [3, 26], facilitated largely by the advent of high duty-cycle tagged photon facilities. Investigations of the neutron polarizabilities, however, have lagged behind, primarily due to the lack of free neutron targets. Typically these measurements are performed on deuterium, using either the quasi-free D(γ, γ n)p reaction or the elastic scattering D(γ, γ)d reaction. In the case of the proton, the electric (α p ) and magnetic (β p ) polarizabilities enter at order ω 2 (where ω is the photon energy) in the Compton cross section, due to an interference with the leading Thomson amplitude. For a free neutron (as in the quasi-free reaction), there is no Thomson term (the neutron is uncharged), so the polarizabilities enter at order ω 4 and are much harder to determine. Moreover, strong model dependences in the analysis can hinder the extraction of α n and β n. In elastic Compton scattering on deuterium, the Thomson term is recovered, so the polarizability extraction is similar (in principle) to the proton case, except for the fact that only the sum of the proton and neutron polarizabilities (α N = αp+αn and β 2 N = βp+βn ) can be unambiguously deduced from the data. But with the 2 5

6 improved knowledge of the proton values available today, extracting the values of α n and β n is mostly limited by the quality of the deuteron Compton scattering data. Only three measurements of the differential cross section for the D(γ, γ)d reaction have been performed to date. Lucas et al. at Illinois [27] measured 4 angles at 49 MeV and 2 angles at 69 MeV. Lundin et al. at Lund [28] covered only a limited range of forward and backward angles at 55 and 66 MeV. Hornidge et al. at Saskatoon [29] extended the energy range up to 95 MeV and obtained a five-point angular distribution. Typical statistical uncertainties in the differential cross sections were around 10% for the MeV data and 7% for the 95 MeV data. The sensitivity to α N and β N (which we refer to as the isoscalar nucleon polarizabilities) increases with incident photon energy, but this poses a daunting experimental problem. The loosely bound deuteron has a two-body breakup threshold only 2.23 MeV below the elastic peak, so that the beam and the γ ray detector (usually NaI) must have sufficiently good resolution to separate the elastic and inelastic contributions in the scattered photon spectrum. The largest existing anti-coincidence shielded NaI detectors have about 2% energy resolution, so E γ = 100 MeV is effectively a practical upper limit for performing these experiments by detecting the scattered photon. More common anti-coincidence shielded 10 by 10 NaI detectors with 3% resolution are adequate for incident energies E γ 70 MeV. Thus, the lower-energy experiments are easier to do, but at the cost of sacrificing some sensitivity to the polarizabilities. On the theoretical side, a new industry of effective field theory (EFT) has arisen in the past ten years (starting with the development of chiral perturbation theory) and great attention has been focused on Compton scattering calculations for the proton and deuteron. Using this formalism, it is possible to make predictions for the D(γ, γ)d cross section which are in fair agreement with the data at MeV [30]. At MeV, the data are more sparse and somewhat scattered, so it is difficult to make a meaningful statement about the comparison. However, at 95 MeV, the agreement between data and theory is not very good, especially at the backward angles [31]. A fit to these data [29], in which the polarizabilities are free parameters, yields a result in which β N actually equals or exceeds α N, which is in striking contrast with the proton polarizability values (α p = 12 and β p = 2 in units of 10 4 fm 3 ). Thus far, the back-angle points in the 95 MeV data set have eluded a theoretical explanation, and so it will be particularly important to reproduce these experimental points in an independent measurement. Clearly, improved data are required in order to make better comparisons with the increasingly precise results coming from modern EFT calculations being carried out by various theoretical groups. Recently, there have been a series of EFT calculations ( [32 35]) which collectively suggest three experimental approaches to the problem of determining the isoscalar nucleon polarizabilities. These calculations have been performed using EFTs where the pions have been integrated out. Such pionless theories have been shown to be highly successful for systems whose characteristic momenta are below the pion mass. We are proposing to perform all three measurements in order to obtain a precise, reliable and consistent value of these quantities and therefore of the neutron polarizabilities. One of the recent papers [34] recommends that future high-precision deuteron Compton scattering experiments be performed at MeV photon energy where the nucleon polarizability effects are appreciable and the pionless effective field theory is most reliable. These authors, in fact, state that a measurement (of the absolute value of the cross section) with a 3% error will constrain the isoscalar electric polarizability to an error fm 3, 6

7 or about 25% of the expected value of fm 3. There are, in fact, two separate considerations here. One is the absolute value of the cross section. As pointed out in Ref. [34], there is a 12% effect on this quantity at 30 MeV when using α N =10β N =12 as opposed to setting α N and β N equal to zero. If the results of Chiral Perturbation Theory (namely, α N =10β N ) are accepted, then a 3% measurement of the absolute value of the cross section will indeed determine both α N and β N to within 25%. The second consideration comes from examining the shape of the angular distribution of the differential cross section. Rupak has performed some preliminary calculations [33] of the differential cross section σ(θ) at 50 MeV, as shown in Fig. 1. Using a model-independent sum rule to constrain α N + β N essentially fixes the forward-angle cross section. The backangle cross section is sensitive to α N β N, and clearly there is sensitivity to three different combinations of this difference, as seen in Fig. 1. Even so, the data from [27] shown in the figure are not sufficiently precise (with 10% error bars) to make a significant determination of the polarizabilities. However, a 3% statistical uncertainty measurement will determine both α N and β N to an accuracy of fm 3. We are therefore proposing to perform a precision measurement of the absolute differential cross section ( 5%) and of the angular distribution (five angles with 3% statistics) at an incident γ-ray energy of 50 MeV. At this energy, the effect in the absolute cross section is about 25%, so that a 5% measurement will determine α N = 10β N to an accuracy of fm 3, which is significantly better than the theoretical error [34]. To perform these experiments, elastically scattered photons will be detected simultaneously in four NaI detectors (which will be upgraded to 16 when this proposal is funded) mounted at azimuthal angles φ = 0, 90, 180, 270 (left, up, right, down). A frame to hold the NaI detectors has been constructed at HIγS and has aptly been dubbed the eggbeater due to its appearance. The eggbeater has already been utilized in a Compton-scattering commissioning run on oxygen. [36] The eggbeater frame can be rotated in the azimuthal angle φ so that detector locations (horizontal and vertical) can be interchanged in order to reduce systematic errors. The arms of the eggbeater allow variation of the polar angle θ between 90 and 150 in the backward hemisphere (or between 90 and 30 in the forward hemisphere). Thus, a complete set of θ and φ angles can be investigated in a manner consistent with reducing systematic effects in the polarized photon asymmetry as much as possible. The unpolarized cross sections will be obtained from the yields of the four detectors at different azimuthal angles by summing them. The very low cross section ( nb/sr) for this reaction below 100 MeV has been the principal hindrance in all of the previous experiments. With the presently anticipated HIγS photon flux of Hz in a beam having 3-to-5% energy spread and a liquid deuterium target of 20.0 cm length, counting rates of counts/hour (per detector) can be achieved. Assuming a background contribution from target cell walls of 25% of the yield, it would require collecting empty-target data for about a quarter of the time of the full-target running in order to collect reasonable statistics for background subtraction. Even with this time allocated for background subtraction, a measurement of the cross section with 2% accuracy (at one angle) would require a foreground yield of about 2600 counts in two detectors, which can be achieved in 33 hours. The upgraded array will allow us to measure four angles simultaneously, and to have four detectors at each angle in the up, down, left and right orientations, as required for linear polarization asymmetry measurements. Since the HIγS beams are 100% polarized (linear at present, linear and circular following the upgrade), the measurements of the cross section discussed above will simul- 7

8 taneously produce measured values of the linear analyzing power, Σ(θ). [Note that Y (φ=0+180) Y (φ=90+270) Σ =. In this case, Rupak and Griesshammer [32] have performed Y (φ=0+180)+y (φ=90+270) pionless EFT calculation. Their results, as a function of energy at an angle of θ=120 are shown in Fig. 2. In this case we are proposing to measure Σ(120 ) in 10 MeV steps from 30 to 70 MeV. As can be seen in Fig. 2, a measurement of Σ(120 ) at the 1% level will determine α N to an accuracy of 10% of its value which is about fm 3. Although there is some question about the accuracy of the pionless EFT calculations at and above 50 MeV, new EFT calculations are underway which include pion degrees of freedom, and which are expected to be valid at energies up to pion-threshold [37]. Preliminary reports of the results of these calculations indicate that the present predictions are, in fact, quite accurate up to MeV. [37] These measurements will require running for 120 hours in order to obtain 1% statistics at each energy if a flux of Hz is used. Four energy points (in addition to the one at 50 MeV above) can be obtained in about 500 hours of beam time. The detector system being requested in this proposal will allow us to make measurements at five angles simultaneously, which will improve the accuracy of our result by more than a factor of 2, significantly reduce systematic errors in measurements of the angular dependence of cross sections and analyzing powers, and reduce the beam time needed by a factor of five. The third experiment we are proposing is based on a recent study of the spin-dependent cross sections and asymmetries in deuteron Compton scattering performed using EFT [35]. In this work, Compton scattering amplitudes were calculated up to order (Q/Λ) 2 in lowenergy power counting. The authors considered numerous single and double polarization asymmetries [35]. They found that the single-spin asymmetry Σ y = σ Jy=+1 σ Jy= 1 σ Jy=+1 +σ Jy= 1, where the photon beam is unpolarized and the deuteron target is polarized in the J y = ±1 states exhibited a large sensitivity to the values of α N and β N. For example, the value of Σ y at 90 and E γ = 50 MeV changed by 26% when α N and β N were changed from being equal to zero to their nominal CHPT values (α N =10β N =12). This implies that a 2% measurement of Σ y will determine α N at the 7% level of accuracy. This work will utilize the frozen-spin polarized deuterium target which is presently being constructed for the measurement of the GDH sum-rule integrand of the deuteron at HIγS. [38] The same authors [35] also found that the double polarization asymmetry = σ A σ p σ A +σ p varied by 30% at back angles for a beam energy of 70 MeV. Therefore, a 3% measurement of will determine α N at the 10% level of accuracy. Since the HIγS beam is naturally polarized, our plan is to measure as well as Σ y - which will be formed by averaging over the two polarization states of the beam. The frozen-spin polarized deuterium target construction project is being led by Drs. Blaine Norum and Don Crabb of the University of Virginia in collaboration with researchers at TUNL. This target will be about 10 cm long and will provide about nuclei/cm 2. A beam of γ/s will produce 25 counts per hour per detector. A 2% analyzing power measurement can be obtained in about hours using two detectors, including background measurements. An array of 16 detectors will make it possible to measure eight angles at the 2% level in less than 100 hours of beam time. The uncertainties being demanded in these measurements require detailed attention to sources of systematic error, as well as to obtaining adequate counting statistics to achieve the desired statistical accuracy. In the case of the absolute cross section measurements, the primary contributions to the systematic errors are the beam intensity measurements, the detector efficiencies and solid angle, and the target thickness. Beam intensities at HIγS have so far been measured using low intensity beams and zero- 8

9 degree detection in order to calibrate secondary devices which could be used with the full intensity. In addition, atomic Compton scattering from Cu targets has been used to measure the beam intensities by placing well collimated detectors at angles where the scattered flux had an intensity which could be measured directly. Simulations (EGS4) have been used to compare to the measurements, which were also checked against the zero-degree results above. Overall, the results of these studies indicated that the beam intensities could be measured to an accuracy of 3%. A new technique has been developed which will allow us to measure the beam intensities to an accuracy of 1%. This method will employ a system of precision times 10 attenuators located inside the storage ring area where the beam first emerges. This location of the attenuators will assure that there is no unwanted background in the target room area. As many as six attenuators can be inserted, thereby reducing the flux by six orders of magnitude, making zero-degree measurements possible. Our ability to make precise measurements of the attenuation values of these blocks has already been demonstrated by work done on several materials in collaboration with researchers from LANL [40]. Furthermore, we are planning to use the same detector(s) to measure the beam intensity at zero degrees as we will use to measure the Compton scattered γ rays. That way, the detector efficiency only enters once in the determination of the absolute cross section. The efficiency of large NaI detectors is a quantity which has been studied in great detail at TUNL for several decades. The reference point for these measurements is the MeV resonance in 13 N observed via the 12 C(p,γ) reaction, since the number of photons per proton is well-known [41] for a thick-target yield. We will use the TUNL FN-tandem accelerator to measure these efficiencies, and duplicate the geometry including the extended target (which we will simulate by moving the 12 C foil to duplicate the length of our deuterium target). This will provide us with a direct measure of the product of the efficiency and the solid angle of these detectors. The efficiencies at other energies will be obtained using a GEANT simulation, being certain to reproduce the measured values at 15.1 MeV. Overall, we are confident that we can achieve an accuracy of 2% or better for this quantity. The thickness of our liquid deuterium target will be determined by careful measurements of the cell geometry and the monitoring of the target cell pressure and temperature during the experiment. Following the method of [42] we expect to be able to determine our target thickness to an accuracy of 1%. The combination of uncertainty in beam intensity (1%), detector efficiency and solid angle (2%), target thickness (1%), and peak fitting/background subtraction uncertainties (2%) should allow us to make an absolute cross section measurement at the 5 6% level of accuracy. Measurements of the shape of the differential cross section will be dominated by the statistical accuracy ( 3% for our measurements). The use of 20 identical detectors in a well defined geometry will essentially eliminate instrumental asymmetries. This will, in an early stage of the program, be verified directly by measuring one 5 point angular distribution with a single detector, rotated to five different positions, and comparing the results to that obtained when 5 different detectors are used. Detectors will also be interchanged to measure their relative efficiencies and to remove instrumental asymmetries. Systematic errors in analyzing power measurements are much easier to deal with than are those in cross section measurements. In the case of Σ(θ), the use of four detectors at each scattering angle (located at φ = 0, 90, 180, 270 ) makes it possible to cancel most systematic errors, especially since these detectors will be rotated into and out of each other s position. Our pilot experiment on 16 O [36] achieved a 5% uncertainty, which was entirely 9

10 due to counting statistics. We are confident that we can obtain 1% uncertainties, given adequate statistics. For the double polarization measurements of (θ), we will also cancel systematic errors by frequent reversals of the direction of polarization of the beam (on the order of every few minutes). Again, obtaining 3% uncertainties should not be a problem as long as we are able to obtain the necessary counting statistics. In summary, we are proposing a comprehensive experimental program which will determine the isoscalar electric and magnetic polarizabilities of the nucleon. There will be several experimental approaches to this program, which are designed to be complementary and which will provide consistency checks on our results. We are proposing to: Perform a careful measurement of the differential cross section and the analyzing power at an incident energy of 50 MeV. EFT calculations and a model independent sum rule will be used to determine the separate values of α N and β N from the differential cross section to an accuracy of 10%. At the same time, an accurate ( 5%) measurement of the absolute cross section will determine the polarizability to an accuracy of 20%. This result depends upon the theoretical result that α N = 10β N, and, especially when combined with the above result, will test this theoretical relationship. The 100% linearly polarized HIγS beam will be used with unpolarized targets to measure the analyzing power as a function of energy to a precision of 1%. This will be done at 4 angles, simultaneously, using the upgraded detector system requested in this proposal. EFT calculations indicate that these data will enable us to determine α N and β N to an accuracy of 10%. A frozen-spin polarized deuterium target to measure the target analyzing power to an accuracy of 3%. This should give an independent measure of the isoscalar polarizability to an accuracy of 7%. Together, these measurements are expected to provide neutron polarizability measurements for both α n and β n to an accuracy of better than 5%. Presently, the best values have considerably larger errors with, for example, a 14% statistical uncertainty, a 7% systematic uncertainty and a 9% model uncertainty in α n. In the case of β n the statistical uncertainty alone is presently 65% [39]. Consistency between the three proposed measurements will add confidence to our results, while testing some of the fundamental results of Chiral Perturbation Theory and Effective Field Theory. NUCLEON SPIN POLARIZABILITIES FROM DOUBLE-POLARIZATION COMP- TON SCATTERING Spin polarizabilities of the nucleon can be probed directly via circularly polarized photons Compton scattered from a polarized nucleon target. Because the Thompson amplitude is real and the spin-dependent amplitudes are complex, it is necessary to use circularly polarized incident photons to obtain a cross section asymmetry linear in γ i at O(ω 3 ). Therefore, we propose the use of circularly polarized photons incident on the target, where the spin polarization of the target is either along the beam direction, or in the scattering plane transverse to the beam direction. 10

11 Hildebrandt et al. [7] studied the sensitivity of the spin-dependent Compton scattering cross section to the spin-polarizabilities of the proton in an O(p 3 ) calculation. The results from their calculations are reproduced here in Figs Here we briefly summarize our conclusions from an examination of these calculations. For longitudinal target polarization, the effect of the pion-pole term (chiral anomaly) in the cross section asymmetry is dominant, and the spin-polarizability effect from nucleon structure is distinctly weaker. Nevertheless, at photon energies of approximately 100 MeV and lab angles near 110 there is significant sensitivity to the polarizabilities. For the transverse target polarization, the spin-polarizability effect is significant and comparable to the pion-pole term. This sensitivity is appreciable at lab angles greater than 70, and photon energies of approximately 100 MeV. Spin-Dependent Compton Scattering Experiment on the Proton Based on the theoretical considerations presented previously, the proposed experimental setup at HIγS is as follows: Photon detection over a range in lab angles from 60 up to approximately 180. Because the largest physics asymmetry is seen with transverse target polarization, the detector elements should be in the plane of the target polarization. Incident photon energies ranging from approximately 30 MeV (almost no spin polarizability effect) up to 140 MeV. The photon polarization should be circular. Data taking with longitudinal and transverse target polarizations. Polarized proton targets The UVa group is currently building a frozen-spin (butanol) polarized target for the GDH experiment at HIγS. This target will be similar to one under construction for JLab Hall B. The Hall B target has a length of 2.5 cm, density of 1.5 g/cm 3, and a dilution factor of 7.4, which gives polarized protons per cm 2. The polarization is 90%. Although the GDH experiment doesn t require transverse polarization, this feature has been engineered into the GDH target design. It is a great advantage to use a polarized scintillating target. Having a signal from the target that would tag a Compton (or π 0 ) event is a great advantage for reducing backgrounds in these experiments. This possibility was seriously considered for the Spin-Compton [43] and the polarized pion threshold photoproduction experiments at Mainz [44] several years ago. However, the huge flux of low energy photons in the Mainz bremsstrahlung beam made use of the scintillating target problematic. Even with low-z beam hardeners to reduce the low energy photon flux, the anticipated minimum ionizing background load in the scintillator was over 1 MHz. Fortunately, because of the nearly monochromatic character of the HIγS beam, the low energy backgrounds will be greatly reduced, making the HIγS beam ideal for the use of a polarized scintillating target. Presently, the UVa group and the JMU group are planning to build a Phase 2 target, which will be a scintillating-frozen-spin target. Here we briefly describe some of the properties of these targets as constructed by PSI, and how data analysis with the target might proceed. The PSI polarized scintillating target 11

12 is described in detail in Ref. [45]. The PSI group has constructed targets with polarizations of 84%, with scintillator block sizes up to 5 mm by 18 mm by 18 mm. If the beam enters the target along the 18 mm axis, this gives target protons per cm 2. The minimum proton energy that can be detected in these targets is approximately 1.5 MeV. Recently, progress has been made in improving the transparency of the polarized scintillator, which has been relatively poor up till now. To use the scintillating target effectively it will be important to reject quasi-free Compton scattering events 12 C(γ, γp) from Compton events on hydrogen. A Fermi gas model program was developed to study how these events might be separated. Quasi-free Compton scattering on 12 C was modeled by Compton scattering from an initial state nucleon with momentum k randomly selected from within a Fermi sphere, with energy given by E = k 2 + m 2 0 V 0. The Fermi momentum k f = 221 MeV/c was taken from analysis of quasi-elastic electron scattering on 12 C, and the binding potential V 0 was adjusted to fit the proton binding energy for 12 C, giving V 0 = 41.7 MeV. This potential depth is in good agreement with quasielastic electron scattering data. The effects of Pauli blocking in the scattering process were modeled by requiring that the proton scatter above the Fermi sea in the nuclear potential frame. Light output in the scintillator is estimated at 3000 photons per MeV of electron ionization energy loss. This light output is 30% of the photon yield usually quoted, to account for attenuation in the scintillator. The light collection efficiency and the quantum efficiency of the photodetector are estimated at 10% and 15%, respectively. Low energy protons are less efficient at producing scintillation light than electrons, and equivalent electron energies, calculated using Madey s empirical expressions, were used to calculate light production in the scintillator. PSI has reported energy resolutions approximately 25% worse than normal plastic scintillators in the identical configuration. Although it is unclear if this effect is because of reduced light output which has already been taken into account, or because of some other effect, to be conservative a multiplying factor of 1.25 is applied to the calculated energy resolutions in the scintillating target. The target size was taken as 18 mm in the z (beamline) direction, 18 mm in the x (horizontal direction) and 5 mm in the y (vertical direction), and proton stopping distances were calculated using energy-range tables from NIST. Energy resolution in the NaI detector was taken as 3% (FWHM). The NaI detector has a size of 10 x 12, and is positioned 1 m from the target. Figure 8 shows a scatter plot of measured binding energy in the scintillating target, defined as BE = E i E f T p, versus measured proton kinetic energy T p for 100 MeV Compton scattering at 90 in the x (horizontal) plane. In the 2-dimensional plot the free Compton events at BEy0 MeV and T p y 9 MeV can be easily identified and separated from the quasi-free events. There will be an appreciable background rate in the scintillating target from pair production, approximately 400 khz at an incident photon flux of 107 Hz. However, it should be possible to limit the trigger rate from these events by running a discriminator threshold sufficiently high that many of the minimum ionizing events fall below threshold, but not so high that proton events are lost. For example, at backward Compton scattering angles the proton kinetic energy is 7 times the minimum ionizing signal, and at angles as far forward as 55 degrees the proton kinetic energy is still twice minimum ionizing. In summary, our Monte-carlo studies indicate that the scintillating target should perform very well in a spin-dependent Compton scattering experiment. In a scatter plot of binding energy versus proton kinetic energy the Compton scattering events from the proton are clearly separated from those on 12 C, giving a target dilution factor of 1. We plan to construct 12

13 a prototype target and test it in the actual beam at HIγS. It has been proposed that light collection in the PSI target can be improved over the old design by using semiconductor devices directly coupled to the polarized scintillator operating at 100 mk. The detector that seems most promising in this application is the silicon photomultiplier (SiPM). These detectors have active areas of 1 mm 2, and 1000 pixels. An array of ten of these devices mounted along the 18 mm by 5 mm side of the scintillating target should give light collection efficiencies at the 10% level. We have obtained samples of the SiPMs from the Russian group at DESY, and plan to construct a room temperature, non-polarized prototype of a target that can be used in beam tests at HIγS. Optimal use of the scintillating target will also require use of a GHz flash ADC for timing and pulse-height information. When used at PSI in a pion-proton experiment, the ADC and TDC resolution could be greatly increased once appropriate software algorithms were developed. For example, ADC gates can be optimized, double-pulsing detected and removed, baselines subtracted, and constant-fraction software utilized to optimize timing. CODA support is now available for commercial PCI fast ADC cards running on Linux PCs. Rate calculations and Projections Cross section estimates are presented using the scintillating target. For these estimates we assume protons per cm 2 in the target, with a polarization of 84%, and 100% detection efficiency for recoil protons. For the photon flux we assume photon/s, with 100% circular polarization. The proposed detector geometry consists of ten NaI detector elements, each 10 in diameter by 12 thick, arrayed in two arcs, five on beam left and five on beam right, at angles of approximately 30, 60, 90, 120, and 150 degrees. The efficiency of the NaI s is taken as 60%, and they are positioned 80 cm from the target. With 16 NaI detectors as requested in this proposal, larger angular coverage is feasible or less beam time is needed for the same angular coverage in order to achieve the same statistical uncertainties. Our studies indicate that sensitivity to the polarizabilities is maximized by measuring the helicity-dependent cross sections, not just the asymmetry. Also, the most effective test of the model-dependent calculations used to extract the polarizabilities is by measuring helicity-dependent cross sections. For these reasons we plan to measure cross sections in the experiment. The HIγS group expects that it will be possible to measure the photon flux at the 3% level. In addition to taking production data at beam energies just below and above pion production threshold, we also plan to take data at a beam energy of 30 MeV as a way to test the systematic errors in the experiment. At 30 MeV theoretical uncertainties in the Compton cross sections are expected to be very small. Figure 9 and Fig. 10 show the helicity-dependent cross sections for a longitudinal polarized target at C.M. photon energies of 120 and 140 MeV, respectively. These beam energies, which correspond to lab energies of 136 MeV and 162 MeV, are approximately 7 MeV below and 15 MeV above pion production threshold. Also shown are the projected error bars for a measurement at HIγS assuming 100 hours of beam time at each energy. Fig. 11 and Fig. 12 show the cross sections for a transverse polarized target at C.M. photon energies of 120 and 140 MeV, respectively. The projected error bars shown in the figure are also for a 100 hour measurement. Fig. 9 and Fig. 11 demonstrate that there is considerable sensitivity to the spin polarizabilities in the helicity-dependent cross sections below pion threshold, particularly at backward angles with the longitudinal polarization, and at mid to backward angles with transverse polarization. Above pion threshold the sensitivity to the 13

14 spin polarizabilities greatly increases. Fig. 10 and Fig. 12 demonstrate a sensitivity to the S.P. s in both the longitudinal and transverse cross sections over the entire angular range covered by the detector array. To estimate how accurately the individual spin polarizabilities might be measured in an experiment at HIγS, we utilize the property that at forward angles the longitudinal cross section difference is sensitive to γ π = γ 1 + γ 2 + 2γ 4. Furthermore, at 90 o in the C.M. the longitudinal polarization cross section difference is sensitive to γ 1 + γ 3, and at 90 o in the C.M. the transverse polarization cross section difference is sensitive to γ 4. For this analysis we will assume that γ 0 is fixed from the Mainz GDH experiment with an error of ±13% and neglect uncertainties in α and β. Values for γ 1, γ 2, γ 3, and γ 4 are taken from Gellas et al. [14]. With these assumptions, the mid- to backward angle helicity-dependent cross sections at 120 and 140 MeV CM were used to estimate the errors inγ 1, γ 2, γ 3, and γ 4. The results show that we can anticipate errors at the level of ±12%, 10%, 45%, and 5% forγ 1, γ 2, γ 3, and γ 4, respectively. Given that this analysis only uses statistics from 4 of the 16 detectors, we believe that the error estimates presented here are conservative. In summary, we propose data taking at beam energies of approximately 30 MeV, 130 MeV and 160 MeV. The two highest energies have a strong sensitivity to the four spin polarizabilities, which can be extracted from the data with an accuracy at the level of ±10%. The 30 MeV data will provide an important test of systematic errors in the experiment when compared against theoretical calculations of Compton scattering. Approximately 100 hours per target polarization are required at 130 MeV and 160 MeV. Approximately 50 hours are needed at 30 MeV, giving a total beam time of 450 hours. We believe that this is a conservative estimate of the beam time required, and that by using additional detectors and/or moving the detectors somewhat closer to the target, a refined error analysis will indicate that comparable errors can be obtained with reduced beam time. Spin-Dependent Compton Scattering on the Neutron The static-spin polarizabilities of the nucleons have been calculated by several groups [8, 9, 14, 15]. The earlier calculations were performed at order p 3 and ω 3, and were only sensitive to the isoscalar spin polarizabilities, so the calculated values were the same for the neutron and the proton. More recently [14, 15], the first nonvanishing contributions to the isovector part of the spin polarizabilities were calculated in a p 4 order calculation using heavy baryon chiral perturbation theory (HBCHPT). The results indicate that overall these corrections are almost an order of magnitude smaller than the isoscalar values with the exception of γ 1. The values of the neutron and proton spin polarizabilities obtained in Ref. [14] are presented in Table I. Note that the values given here correspond to the structure part only, since the non-structure pole term contributions have been removed. Finally, we note that there are some differences between the values of the neutron and proton spin polarizabiliites presented in Refs. [14] and [15]. However, the authors of Ref. [15] state that these difference are due to the fact that the authors of Ref. [14] chose not to include a particular one-particle-reducible diagram in their definition of the polarizabilities. They go on to say that if this term is included, then the two calculations are in agreement-which is reassuring. Note that we are proposing to extract the values of the static spin polarizabilities for the proton and the neutron. Future experiments will attempt to meaure the dynamic (energy dependent) spin polarizabilities. As discussed in Ref. [7], the energy dependence of the 14

15 Proton HIγS uncertainty Neutron HIγS uncertainty γ1 P = γ1 n = γ2 P = γ2 n = γ3 P = γ3 n = γ4 P = γ4 n = TABLE I: The calculated spin polarizabilities (Ref.15) along with the anticipated statistical uncertainties expected from these measurements. All quantities are in units of 10 4 fm 4. The neutron projection is based on the quasifree Compton scattering events from 3 He only. four leading spin polarizabilities of the proton and neutron should provide profound insight into the dispersive behavior of the internal degrees of freedom of the nucleon, caused by relaxation effects, baryonic resonances and mesonic production thresholds. Since there is no free neutron target in nature, effective neutron targets, i.e. nuclear targets, deuteron and 3 He are commonly used for the study of the neutron. A polarized 3 He nucleus is very useful in probing the neutron electromagnetic and spin structure because of the unique spin structure of the 3 He ground state. It is dominated by a spatially symmetric S wave in which the proton spins pair off and the spin of the 3 He nucleus is carried by the unpaired neutron [46, 47]. The experiment that we are proposing is a Compton scattering experiment from a polarized 3 He target at the quasifree kinematics, i.e. the kinematics corresponding to circularly polarized photons scattering off the nucleons inside 3 He. Coincidence measurements of the scattered photons and recoil neutrons will be carried out. The advantages for detecting both the neutron and the photon in coincidence are background suppression, maximum sensitivities to the neutron spin polarizabilities, and the suppression of the proton contribution. The disadvantage is the small Compton scattering cross-section due to the suppression of the Thompson amplitude to the process and the relatively low neutron detection efficiency. Fig. 13 shows the sensitivity of the double polarization asymmetry to the neutron spin polarizability γ 1 as a function of incident photon energy for various photon scattering angles in the lab. The photon is always circularly polarized, and A (A ) corresponds to the target spin being perpendicular (parallel) to the incident photon momentum direction in the reaction plane. The black curve is the asymmetry predicted from a fourth-order chiral perturbation theory [6, 15], and the red (blue) curve corresponds to varying γ 1 by fm 4 (red) ( fm 4 (blue)), leaving all other polarizability values fixed. The black dotted curve is the Born term which only includes the pion pole contribution. Fig. 14 is the corresponding asymmetry result showing sensitivity to neutron γ 2, and Fig. 15 and Fig. 16 are similar results showing sensitivity to neutron γ 3 and γ 4, respectively. All calculations are carried out [6] for a free polarized neutron target, and the neutron electric and magnetic polarizability values of α = 12, β = 2 are used in all these calculations. These results show that the perpendicular asymmetry A is most sensitive to the neutron spin polarizabilities γ 1 and γ 3 at a photon scattering angle of 90 in the lab frame. The parallel asymmetry A is most sensitive to the neutron spin polarizability γ 4 at a photon scattering angle of 10 when the incident photon energy is relatively large, 100 MeV. One can also extract the neutron spin polarizabilities from elastic polarized Compton scattering off a polarized 3 He target. The advantage is a much larger Compton scattering cross-section and a relatively straightforward theoretical calculation of the Compton scatter- 15

16 ing process. The complication is that the extraction of the neutron spin polarizabilities will be sensitive to our knowledge of the proton spin polarizabilities, which will be determined experimentally at HIγS (see previous section). Since there is no free neutron target, one should carry out both measurements: polarized elastic Compton scattering and polarized quasielastic Compton scattering from a polarized 3 He target. These measurements will allow the extraction of the neutron spin polarizabilities in two different ways. This will help reduce theoretical uncertainties in extracting the neutron properties using an effective polarized neutron target, i.e. a polarized 3 He nuclear target. Ideally, one should also carry out the same measurements (quasifree and elastic) from a polarized deuteron target. We plan to carry out the polarized elastic 3 He Compton scattering experiment at HIγS using a 140 MeV γ-ray beam. We propose a double polarization Compton scattering experiment of circularly polarized photons from a polarized 3 He nuclear target at the quasifree and elastic kinematics using the High Intensity Gamma Source (HIγS) at the Duke Free Electron Laser Lab. The scattered photons and the knockout neutrons will be detected in coincidence for the proposed coincidence quasifree measurements. Only the scattering photons will be detected for the elastic measurements. We plan to use the upgraded 16 NaI detectors (requested in this proposal) for photon detection, and the Blow Fish detector for detecting the neutrons. The polarized 3 He target is a high-pressure target based on the spin-exchange optical pumping technique. The double polarization asymmetry will be formed by flipping the circular polarization of the incident photon beam. The target spin direction will be reversed from time to time to minimize effects due to systematic false asymmetries. In this experiment, we will align the target spin parallel and perpendicular to the incident photon momentum direction in the scattering plane to measure both the parallel asymmetry (A ) and the perpendicular asymmetry (A ). A High-Pressure Polarized 3 He Gas Target The polarized 3 He target is based on the principle of spin exchange between optically pumped alkali-metal vapor and noble-gas nuclei[48]. The design is similar to that used in electron scattering experiments in Hall A at Jefferson Lab (JLab) [49]. Traditionally, Helmholz coil systems have provided magnetic holding field for the target. But, a mumetal-shielded sine-theta coil (STC) has potential advantages over the Helmholtz coils, primarily from its compact geometry and from the improved B-field uniformity. Preliminary studies [50] have shown that such a STC could improve the planned experiment to study Compton scattering from polarized 3 He at HIγS. The projected results shown later are based on a STC for providing the target holding field. A central feature of the target will be sealed glass target cells, which will contain a 3 He pressure of about 10 atmospheres. The target cells will have two chambers, an upper chamber in which the optical pumping and spin-exchange collision take place, and a lower chamber, through which the photon beam will pass. In order to maintain the appropriate number density of alkali-metal (Rb) the upper chamber will be kept at a temperature of C using an oven constructed of high temperature resistant plastic, for example Torlon. With a density of atoms/cm 3, and a lower cell length of 40 cm, the target thickness will be 1 = atoms/cm 2. Due to the fact that the HIγS photon beam spot size is significantly larger than the electron beam size, the diameter of the HIγS target cell will be much larger than that of the 3 He target at JLab. Fig. 17 shows the schematics of the polarized 3 He target setup. Fig. 18 shows a picture 16

17 of the first HIγS polarized 3 He target Kansas on the test stand in our polarized target lab. The initial measurement from Kansas shows a target relaxation time of 18 hours. Kansas has an overall volume which is a factor of 2.5 of a typical polarized 3 He target used in Hall A experiments at Jefferson Lab. The time evolution of the 3 He polarization can be calculated from a simple analysis of spin-exchange and 3 He nuclear relaxation rates [51]. Assuming the 3 He polarization P3 He = 0 at t = 0, P3 He(t) =< P Rb > ( γse γ SE + Γ R ) (1 e (γ SE+Γ R )t ), (13) where γ SE is the spin-exchange rate per 3 He atom between the Rb and 3 He, Γ R is the relaxation rate of the 3 He nuclear polarization through all channels other than spin exchange with Rb, and P Rb is the average polarization of a Rb atom. Our target will be designed to operate with 1/γ SE = 8 hours. From Eq. (1) it is clear that there are two things we can do to get the best possible 3 He polarization maximize γ SE and minimize Γ R. Maximizing γ SE means increasing the Rb number density, which in turn means more laser power. The number of photons needed per second must compensate for the spin relaxation of Rb spins. In order to achieve 1/γ SE = 8 hours, about 50 Watts of usable laser light at a wavelength of 795 nm are needed. By usable, we essentially mean light that can be readily absorbed by the Rb. It should be noted that the absorption line of the Rb will have a full width of several hundred GHz at the high pressures of 3 He at which we will operate. Furthermore, since we will operate with very high Rb number densities that are optically quite thick, quite a bit of light that is not within the absorption linewidth is still absorbed. Currently, a new technique is being tested to improve the rubidium polarization. Normally, the diode lasers of this wavelength emit a light spectrum that is 1-2 nm wide. Since the rubidium can only absorb a very narrow portion of that spectrum, most of the power of the laser is wasted. A series of gratings are being used to narrow the line width of the diode laser output. While some laser power is lost, the line width is narrow enough so that almost all of the light is absorbed by the Rb atoms and the overall laser absorption efficiency is 2-3 times higher. The rate at which polarization is lost, which is characterized by Γ R, will have two principle contributions under the photon beam environment. From experience, target cells with an intrinsic rate of Γ cell = 1/50 hours can be produced. This has two contributions: relaxation that occurs during collisions of 3 He atoms due to dipole-dipole interactions [52], and relaxation that is presumably due largely to the interaction of the 3 He atoms with the walls. Finally, relaxation due to magnetic field inhomogeneities are held to better than Γ B = 1/100 hours [53]. Collectively, under operating conditions, we would thus expect Γ R = Γ cell + Γ B = 1/50 hours + 1/100 hours = 1/33 hours. (14) Thus, according to Eq. 1, the target polarization cannot be expected to exceed P max = γ SE γ SE + Γ R = (15) Realistically, Rb polarization is less than 100% in the pumping chamber, which will reduce the polarization to about 50-55%. 17

18 The construction and filling of the target cells have been accomplished with great care to achieve 1/Γ cell equal to hours. Cells are constructed from aluminosilicate glass, GE 180. The cells will be filled to a high density of about 10 amg 3 He. The length of the cell is 40 cm, and the diameter is 2.5 cm. The end windows are approximately 150 µ thick and the side wall is approximately 1 mm thick. A beam of laser light coming out of the diode laser is essentially unpolarized. A polarizing beam splitter can be used to make it linearly polarized and then, by passing it through a quarter wave plate, the laser light can be made to be circularly polarized. The circularly polarized laser light optically pumps the Rb vapor in the pumping chamber to polarize the Rb atoms, which then spin-exchanges with 3 He gas to polarize the 3 He nuclei. Polarization will be monitored using the NMR technique of adiabatic fast passage (AFP) [54]. The signals are calibrated by comparing the 3 He NMR signals with those of water. Further, the polarization will also be monitored during the experiment by EPR. The Detectors For the photon detection, we plan to use a photon detection array which consists of 16 NaI detectors (requested in this proposal). Each NaI detector is a cylinder with 10 diameter and 12 length. The energy resolution for a NaI detector is 2%. We propose to use such a photon detection array for the proposed Compton experiment. For the proposed coincidence measurements, the kinetic energy of the neutron is from 2.7 MeV to 22.0 MeV. The Blowfish array with BC-505 liquid scintillators will allow the detection of these neutrons. The Blowfish setup needs to be reconfigured in order to be compatible with a high-pressure polarized 3 He target and to match the acceptance of the photon detectors. The neutron detection efficiency is expected to be between 20% and 35%. The experimental setup for the proposed longitudinal asymmetry measurement is shown in Fig. 19. Projected Measurements from elastic Compton scattering process In projecting the asymmetry results, we assumed a photon flux of /sec for a photon energy spread of 10 MeV at an incident photon energy of 140 MeV and a target thickness of atoms/cm 2 with a target polarization of 45%. The circular polarization of the photon beam is taken to be 100%. A solid angle acceptance of 0.2 sr was assumed for each scattering angle bin. A total beam time of 350 hours was assumed in the projection with 100 and 250 hours for the perpendicular and longitudinal target spin orientation, respectively. The projected results for the elastic Compton scattering are shown in Fig. 20 and Fig. 21. The projected results show clearly the high precision that HIγS measurements will achieve even with a modest photon flux ( /sec), therefore providing the much needed sensitivity in probing the neutron spin polarizabilities. Projected Measurements from Quasifree Compton Scattering Process In projecting the asymmetry results, we assumed a photon flux of /sec for an incident photon energy of 140 MeV with an energy bin size of 10 MeV and a target thickness 18

19 of atoms/cm 2 with a target polarization of 45%. The circular polarization of the photon beam is taken to be 100%. A neutron detection efficiency of 25% was used. A total beam time of 1500 hours was used in projecting the results with 500 (1000) hours for the perpendicular (longitudinal) target spin orientation. The projected results are shown in Fig. 22 and Fig. 23. Anticipated results on Neutron Spin Polarizabilities The nucleon spin polarizabilities have been calculated by several groups [14, 15, 55] at the next-to-leading order (NLO) in chiral perturbation theory. Predictions on all four neutron spin polarizabilities at NLO in heavy-baryon chiral perturbation theory by Kumar, McGovern and Birse [15] are: γ 1 = [ 21.3]τ ( τ 3 ) (16) γ 2 = 2.3 ( τ 3 ) γ 3 = [10.7]τ ( τ 3 ) γ 4 = [ 10.7]τ ( τ 3 ) γ 0 = 4.5 ( τ 3 ) γ π = [ 42.7]τ ( τ 3 ), where τ 3 = 1 for neutron, and the term in brackets are the third-order anomalous contribution. The values of the neutron spin polarizability are γ 1 = 25.0, γ 2 = 0.1 γ 3 = 10.3, γ 4 = 13.0, γ 0 = 0.9, and γ π = One can see that the rather large absolute polarizability values for γ 1, γ 3, γ 4 and γ π are due to the anomalous contribution. Several authors [9, 24] define the nucleon spin polarizabilities differently from those of Kumar, McGovern and Birse [15] and Ji et al. [55] by removing the pion pole contribution. The corresponding neutron spin polarizabilities values obtained at the NLO in heavy-baryon chiral perturbation theory [15] using the definition of Refs. [9, 24] are therefore: γ 1 = 3.7, γ 2 = 0.1 γ 3 = 0.4, γ 4 = 2.3, γ 0 = 0.9, and γ π = 8.3. The only experimental information on neutron forward spin polarizability γ 0 was estimated using the VPI-FA93 multipole analysis [22]: γ fm 4 (17) The predicted neutron forward spin polarizability range between -0.7 and 2.0 [24]. The predicted γ π (neutron) value from hyperbolic Dispersion Relation is 9.2 [24], which is very close to the aforementioned value of 8.3. The predicted values of γ π (neutron) range between 6.3 and 13.7 (see review by Drechsel, Pasquini and Vanderhaeghen [24]). The only available information on γ π (neutron) was γπ n = (58.6 ± 4.0) 10 4 fm 4 [18] obtained from the quasifree Compton scattering on deuteron, which includes the pion pole contribution. L vov and Nathan [25] derived a sum rule for γ π from a backward angle dispersion relation. Their predicted values for γπ p and γπ n is 39.5 ± 2.4, and 52.5 ± 2.4, respectively. The proposed measurements from coincidence quasielastic scattering have the following statistical sensitivity to the individual neutron spin polarizability γ 1, γ 2, γ 3, and γ 4 : 0.42, 0.49, 0.53, and 0.35, respectively, in the unit of 10 4 fm 4. The proposed experiment will provide a statistical error of 1.0 in the unit of 10 4 fm 4 in the determination of both the 19

20 neutron γ π and the neutron γ 0. Recently, calculations [34, 35, 56] of double polarized elastic Compton scattering of circularly polarized photons from a polarized deuteron target have been carried out. In the incident photon energy regime relevant to the proposed measurements, the perpendicular double polarization asymmetry is shown [56] to be sensitive to the neutron spin polarizability, γ 1. Currently, calculations [57] of double polarized elastic Compton scattering from a polarized 3 He target is underway. More sensitivity to the neutron spin polarizabilties are anticipated by employing a polarized 3 He target because of its unique ground state spin structure. Theoretical uncertainties in extracting the neutron spin polarizabilities from elastic and quasifree Compton measurements are different. Therefore, two independent extractions of neutron spin polarizabilities can be carried out. These measurements will allow the extraction of the individual neutron spin polarizabilities for the first time. These projected results show clearly the high impact of the projected HIγS measurements in probing the neutron spin polarizabilities. Achieving the desired intensity of the photon flux is essential to the success of the proposed quasifree Compton scattering program. COMPTON SCATTERING FROM THE HE ISOTOPES: A MEASUREMENT OF THE ELECTRIC POLARIZABILITY OF 3 HE AND 4 HE Introduction We propose to make a measurement of the electric polarizability α E of the helium isotopes 3 He and 4 He using elastic Compton scattering of linearly polarized monochromatic photons with energies between E γ = 3 and 12.5 MeV. We see this as part of a program to systematically measure the polarizabilities, both electric and magnetic, of the free and bound nucleon and the light nuclei through mass 4. We propose to start with 3 He since the polarizabilities are two orders of magnitude larger than for nucleons, making a measurement feasible with the present HIγS beam flux. This will be followed by a similar measurement on 4 He. Our measurements will provide early experience with Compton scattering experiments, allowing us to better plan for future Compton scattering experiments on the nucleon at HIγS. The situation in the light nuclei has been reviewed by Friar in 2002[58]. The 3 He polarizability has been experimentally investigated by two independent methods: scattering of 3 He by high Z nuclei and from the energy weighted sum rule for total photonuclear absorption (see references 54 and 55 in Friar s review; reference 55 uses the world s photonuclear data prior to 1974). The relation between σ 2 and the electric polarizability α E is: σ 2 = σabs de γ E 2 γ = 2π2 hc (α E + β M ) where β M is the magnetic polarizability. In the analysis of the data β M is generally neglected relative to α E. These two very different methods give results differing by a factor of 2. Calculations using the Lorentz integral transform method[59] coupled with an expansion of the wave functions in correlated hyperspherical harmonics[60] and an effective interaction[61] have resulted in predictions of the electric polarizabilities for both 3 He and 4 He. In 3 He, Leidemann and Orlandini[62] have calculated a value of α E = fm 3 for the electric polarizability. This value is in crude agreement with the experimental value of 20

21 0.130 fm 3 compiled by Rinker[63] (and quoted by Friar[58]) from the world s photonuclear data. It is a factor of almost 2 below the value of fm 3 obtained from the scattering of 3 He by lead[64]. Although the compiled photonuclear data are in reasonable agreement with theory, we stress two points. The data used by reference [63] show a considerable spread in cross section. Hence the agreement is fortuitous. Second, as pointed out earlier, it is really the case from the photonuclear analysis that α E + β M = fm 3. Thus if β M is not negligible, the apparent agreement with theory is not as good. There are no direct measurements to date of α E for 3 He. The electric polarizability α E of 4 He has also been calculated by Orlandini [65] and Leidemann [62] as part of their work on the mass 4 system. They have found a value of α E = fm 3 for the electric polarizability of 4 He. As in the case of 3 He, experimental values for this quantity have been inferred from measurements of total photon absorption using the known relation between the energy weighted sum rule σ 2 of the photoabsorption and the polarizability given above. In the case of 4 He there are considerably more data than for 3 He, probably because of the obvious difficulties with obtaining an adequate 3 He target, However, the history of measurements of the photodisintegration of 4 He is marked by serious discrepancies between different measurements of the same channels. Factor of 2 discrepancies abound in the literature.[66] More recent measurements have not resolved this. In the case of both 3 He and 4 He, published data on σ 2 rely on measurements of the various disintegration channels 3,4 He(γ, p), 3,4 He(γ, n), 4 He(γ, pn), etc. in order to sum them to form σ abs, the total absorption cross section. This method clearly limits the measurement of α E + β M to values of E γ in excess of 6 MeV for 3 He and 20 MeV for 4 He. Inference of α E requires that one neglects β M, a reasonable assumption unless an accuracy of better than 5% - 10% is required. The larger uncertainty comes from the discrepancies in published values for the individual cross sections for the various channels. The status of the (γ, p) and (γ, n) cross section measurements on 4 He up to 1980 was reviewed by Calarco et al..[66] This paper showed that values published prior to 1980 disagreed with each other by up to factors of order 2. Subsequent measurements have continued to be plagued by similar disagreements. For example, if one uses the total photodisintegration data from Erdas et al.[67] or Arkatov et al.[68], who measured σ 2 of 73± and 72± fm 2 /MeV respectively, then, neglecting β M yields α E equal to 0.072±0.004 and 0.073±0.004 fm 3, in agreement with the calculations cited earlier. However, their individual values of the (γ, p) and (γ, n) cross sections are not in agreement with more recent measurements nor with the best averaged data cited by Calarco et al..[66] Other published data (see ref [66]) would lead to serious disagreement with Orlandini s and Leidemann s calculations. Thus we propose to do a direct measurement of α E by measuring the cross section for elastic photon scattering at 90 as a function of E γ using linearly polarized photons. We will show that the energy dependence of the cross section can give a direct measurement of α E. 21

22 Compton Scattering with Polarized Photons The static polarizability, α E, of a nucleus describes the response of a nucleus to a static electric field, whereas the dynamic polarizability, α Eν, describes the response of a nucleus to a time varying electric field[69]. Both polarizabilities should be accessible by means of a Compton scattering experiment. Our measurement will be done at sufficiently low energies such that an expansion of the Compton scattering amplitude is valid (low energy is also desirable for the current HIγS beam). The amplitude for Compton scattering, up to O(ω 4 ), is:[69] ( Z 2 e 2 ) ˆɛ 1 ˆɛ 2 M + 4πω2 (α E + ω 2 α Eν ) + 4πω 2 β Mˆɛ 1 ˆk 1 ˆɛ 2 ˆk 2 where e is the quantum of electric charge, ˆɛ 1 is a unit vector along the polarized electric field of the incident photon, ˆk 1 is a unit vector along its momentum and ˆɛ 2 and ˆk 2 are the corresponding unit vectors for the scattered photon. M is the mass of the target and ω is the energy of the incident photon. In the absence of α E, α Eν and β M, this reduces to the leading term proportional to Z 2 e 2 /M, the amplitude for Thomson scattering. The cross section for Compton scattering of linearly polarized photons on a nuclear or nucleon target is then given by, after summing over the polarization of the scattered photon but not averaging over the incident polarization:[70] dσ dω = 1 2 ( Z 2 ) 2 ( α M 1 Mω2 α E Z 2 α ) 2 ( 1 (ˆɛ1 ˆk 2 ) 2) 2Mω2 β M Z 2 α ˆk 1 ˆk 2 where α is the fine structure constant and α E = α E + ω 2 α Eν, containing both the static and dynamic contributions If ˆk 1 is taken to be along ẑ and ˆɛ 1 is taken to be along ˆx, that defines a coordinate system such that ˆk 2 is at the polar angle ϑ with respect to ˆk 1 and azimuthal angle ϕ with respect to the plane defined by ˆk 1 and ˆɛ 1. In this coordinate system the cross section can be written as: dσ dω = 1 2 ( Z 2 ) 2 ( α M 1 Mω2 α E Z 2 α ) 2 (1 sin 2 ϑcos 2 ϕ) 2Mω2 β M Z 2 α cosϑ Now, if we restrict our detectors to a scattering angle of ϑ = 90, the term in β M vanishes (except for finite acceptance effects). Furthermore, the cross section vanishes (again, except for finite acceptance effects) for detectors placed at ϑ = 90 colinearly with the direction of incident linear polarization ˆɛ 1, left and right in our case since the linear polarization vector at HIγS is oriented in the horizontal plane. The Compton scattering cross section in the low energy limit for the horizontally polarized HIγS beam with detectors oriented at 90 in both ϑ and ϕ can thus be shown to be[70] dσ dω = 1 2 ( Z 2 ) 2 [ α 1 M ( ) ( 2MαE M ω 2 2 αe 2 + Z 2 α Z 4 α 2 2Mα ) ] Eν ω 4 Z 2 α This expression is plotted as a function of energy in Figure 24 for various values of α E. 22 (18)

23 Currently, the dynamic polarizability of 3 He has not been measured (nor for any other nucleus). Following the formalism of reference[69] using a simple harmonic oscillator model, we calculate an estimate for α Eν, the dynamic electric polarizability, of fm 3 /MeV 2 for 3 He. This is small compared to the static polarizability of fm 3. However, the dynamic polarizability is multiplied by ω 2, making it important for higher energies. Thus, at low energies, the cross section for Compton scattering can be approximated as a polynomial function that varies with even powers of the γ-ray energy, with coefficients that depend on the static and dynamic electric polarizabilities. Thus a measurement of the cross section at ϑ = 90 up and down relative to a horizontally polarized incident photon flux at several points in the relevant energy range as a function of ω 2 will give us the polynomial shape of the cross section, allowing the electric polarizabilities of 3 He (and 4 He) to be extracted. Proposed Experiment As mentioned previously, the first measurements will be carried out on 3 He. We plan to do our measurement at several beam energies between 3 and 12.5 MeV. There will be three experimental setups with three 4500 psi gas bottles placed successively in the γ-ray beam. 10 x 10 NaI detectors will be placed directly above and directly below each bottle to measure the Compton scattered γ-rays. Shielding will be used to keep γ-rays scattered from the ends of the bottles from entering the detectors. A Monte Carlo code is currently being used to determine the best choice of energies for the extraction of α E and α Eν. In order to make a 3% cross section measurement, we will need about 10 3 counts at each energy point. This corresponds to about 50 hours of beam time per point at higher energies and about 25 hours per point at lower energies. These estimates assume a beam intensity of 2 x 10 7 with an energy resolution of 5-10%, a 15 cm long effective length for our gas cells, detector efficiencies of 0.57, and solid angle of 50 msr, corresponding to the back face of the NaI being 1 m away. Overall, about 200 hours of beam time will be needed for the measurement. For 4 He, we are considering gas cells identical to those just described for 3 He as well as a 40 cm long liquid He cell of sufficient diameter to accept the collimated flux. Spectra from the NaI detectors will be accumulated in singles mode and the counts will be extracted using line shape fits to these spectra. The polarizability will be obtained by a polynomial fit the the cross section as a function of ω 2. Error Analysis The statistical contribution to the overall uncertainty is about 3%. The principle contributions to the overall uncertainty come from two sources: NaI efficiency and integrated beam flux. Since the overall scale of the cross section, as determined by the intercept at E γ = 0, is independent of the polarizability which determines the slope, this need not be known absolutely to better than, say, a few percent, assuming we would like to know the absolute cross section to that level. However, what is critical is the relative efficiency and flux integration as a function of photon energy. Any systematic variation with energy translates 23

24 directly as a systematic change of the slope, hence of the polarizability. If there is a systematic change and it can be measured, then a correction can be applied. The uncertainty on that correction then becomes the systematic error in the measurement. THE HIγS NAI DETECTOR ARRAY (HINDA) Large NaI detectors have been used at TUNL for several decades, primarily in the study of radiative capture reactions. TUNL researchers have a great deal of experience with operating these detectors in order to maximize their resolution and performance, while minimizing the background and pulse-pile up problems in very hostile environments encountered, for example, in studies of the capture of fast neutrons [71]. More recently, four large NaI detectors have been utilized in the first Compton scattering experiment at HIγS. This four-detector system, called the Eggbeater (see Fig. 25), was used to measure the analyzing powers in the case of Compton scattering from 16 O. In this case the time structure of the HIγS beam along with the so-called Giant Peak Power Pulse mode of operating the HIγS [72] made it possible to reduce beam uncorrelated backgrounds by a factor of A paper reporting these results has been accepted for publication in Physical Review C [73]. The present proposal is requesting the creation of a 16 detector array of 10 by 12 NaI detectors. Even with the intense beams of HIγS, the small cross sections in Compton scattering reactions along with the demands for high precision data, makes it essential to have a detector array which offers high efficiency, reasonably good energy resolution, and large acceptance. The essential requirements of a detector system for the proposed experiments are: High efficiency Good (2-3%) energy resolution for gamma-rays between 40 and 100 MeV. Large acceptance Flexibility in the geometrical configuration of the individual detectors. The arrangement, for example, will be entirely different for the longitudinal asymmetry configuration in the 3 He( γ, γ) 3 He experiment with circularly polarized beams for which we want to cover all azimuthal angles at forward scattering angles where the effects to neutron spin polarizabilities are largest (see Fig. 19), compared to linearly polarized beams where it is essential to have left, right, up and down detectors at each scattering angle (similar to the Eggbeater arrangement, but at four scattering angles simultaneously). TUNL presently possesses four high-quality 10 and one 10 or 10 by 12 NaI detectors. If the gamma-ray peak is summed from one width above the centroid to two widths below, it is found that the efficiency is 57% for photon energies between 20 and 100 MeV. The resolution of these detectors, has been measured to be 3% at 20 MeV [71], and is expected to be close to 2% at higher energies [71]. Two additional detectors became available from collaborators recently. We are therefore requesting funds to purchase nine (9) 10 by 12 NaI detectors in order to construct the HIγS NaI Detector Array (HINDA). The HINDA will provide counting rates which will allow us to perform the measurements described in this proposal in the number of hours anticipated for this program. In addition to more 24

25 than doubling the statistics of our measurements, the ability to make measurements at twice as many angles simultaneously will greatly reduce the systematic errors in the angular distributions of cross sections and analyzing powers. This is extremely important for the success of this program, since most of the sensitivity to several important physical parameters we are measuring is contained in the angular dependence of the observables. ACKNOWLEDGMENT We thank D. Choudhury, H.W. Griesshammer, T.R. Hemmert, R. Hildebrandt, J.A. McGovern, D.R. Phillips for stimulating discussions. We also thank J. McGovern and R. Hildebrandt for carrying out various calculations at the proposed kinematic settings of this proposal. [1] X. Ji, Phys. Rev. Lett. 78, 610 (1997); Phys. Rev. D 55, 7114 (1997). [2] A.V. Radyushkin, Phy. Lett. B380, 417 (1996); Phys. Lett. B385, 333 (1996); Phys. Rev. D 56, 5524 (1997). [3] V. Olmos de Leon et al., Eur. Phys. J. A 10, 207 (2001). [4] J. Schmiedmayer, P. Riehs, J.A. Harvey, N.W. Hill, Phys. Rev. Lett. 66, 1015 (1991); L. Koester et al., Phys. Rev. C51, 3363 (1995). [5] K. Kossert et al., Phys. Rev. Lett. 88, (2002). [6] J. McGovern, private communication. [7] R.P. Hildebrandt, H. Griesshammer, and T.R. Hemmert, nucl-th/ [8] V. Bernard, N. Kaiser, and U.-G, Meissner, Int. J. Mod. Phys. E 4, 193 (1995). [9] T.R. Hemmert, B.R. Holstein, J. Kambor, and G. Knöchlein, Phys. Rev. D 57, 5746 (1998). [10] J. Tonnison et al., Phys. Rev. Lett. 80, 4382 (1998). [11] A.I. L vov and A.M. Nathan, Phys. Rev. C 59, 1064 (1999). [12] D. Drechsel, G. Krein, and O. Hanstein, Phys. Lett. B 420, 248 (1998). [13] D. Babusci, G. Giordano, A.I. L vov, G. Matone, and A.M. Nathan, Phys. Rev. C 58, 1013 (1998). [14] G.C. Gellas, T.R. Hemmert, and U.-G. Meissner, Phys. Rev. Lett. 85, 14 (2000). [15] K.B. Vijay Kumar, J.A. McGovern, and M.C. Birse, Phys. Lett. B 479, 167 (2000). [16] M. Camen et al., Phy. Rev. C 65, (2002). [17] F. Wissmann, Proceeding of the Symposium on the Gerasimov-Drell-Hearn Sum Rule and the Nucleon Spin Structure in the Resonance Region, p193, Editors: D. Drechsel &L. Tiator, World Scientific, [18] K. Kossert et al., Eur. Phys. J. A16, 259 (2003). [19] M. Gell-Mann, M.L. Goldberger, and W.E. Thirring, Phys. Rev. 95, 1612 (1954). [20] S.D. Drell and A.C. Hearn, Phys. Rev. Lett. 16, 908 (1966); S. Gerasimov, Sov. J. Nucl. Phys. 2, 430 (1966). [21] Proceedings of the Symposium on the Gerasimov-Drell-Hearn Sum Rule and the Nucleon Spin Structure in the Resonance Region, Mainz, Germany, June 14-17, 2000, Editors: D. Drechsel & L. Tiator, World Scientific; Proceedings of the Second International Symposium on the Gerasimov-Drell-Hearn Sum Rule and the Spin Structure of the Nucleon, Genova, 25

26 Italy, 3-6 July 2002, Editors: M Anghinolfi, M Battaglieri & R De Vita, World Scientific. Proceedings of the Third International Symposium on the Gerasimov-Drell-Hearn Sum Rule and its Extensions, Old Dominion University, Virginia, U.S.A., June 2-5, 2004, Editors: S. Kuhn and J.P. Chen, World Scientific. [22] A.M. Sandorfi, C.S. Whisnant, and M. Khandaker, Phys. Rev. D 50, R6681 (1994). [23] J. Ahrens et al. [GDH Collaboration], Phys. Rev. Lett. 87, (2001). [24] D. Drechsel, B. Pasquini and M. Vanderhaeghen, Physics Report 378, 100 (2003). [25] A.I. L vov and A.M. Nathan, Phys. Rev. C 59, 1064 (1999). [26] B.E. MacGibbon et al., Phys. Rev. C 52, 2097 (1995). [27] M.A. Lucas, Ph.D. Thesis, University of Illinois at Urbana-Champaign, [28] M. Lundin et al., Phys. Rev. Lett. 90, (2003). [29] D.L. Hornidge et al., Phys. Rev. Lett. 84, 2334 (2000). [30] S.R. Beane, M. Malheiro, D.R. Phillips, U. van Kolck, Nucl. Phys. A656, 367 (1999). [31] S.R. Beane et al., nucl-th/ (2002). [32] H.W. Griesshammer and G. Rupak, Phys. Lett. B529, 57 (2002). [33] G. Rupak, private communication (2003). [34] Jiunn-Wei Chen, Xiangdong Ji, and Yingchuan Li, nucl-th/ [35] Jiunn-Wei Chen, Xiangdong Ji, and Yingchuan Li, Phys. Rev. C 71, (2005); nuclth/ [36] B. A. Perdue, M. W. Ahmed, A.P. Tonchev, H. R. Weller, G. Feldman, V.N. Litvinenko, I.V. Pinayev, B.E. Norum, B.D. Sawatzsky, R. M. Prior, M. C. Spraker, submitted to PRC, June (2004). [37] D.R. Phillips, Ohio University, private communication (2004). [38] Don Crabb, University of Virginia, private communication (2004). [39] K. Kossert et al., Phys. Rev. Lett. 88, (2002). [40] Calvin E. Moss, Christen M. Frankle, Vladimir N. Litvinenko, and Henry R. Weller, NIM A 505, 374 (2003). [41] R. E. Marrs, E. G. Adelberger, K. A. Snover, and M. D. Cooper, Phys. Rev. Lett. 35, 202 (1975). [42] J. Alcorn, et al., Nucl. Instru. Method A522, (2004). [43] Letter of intent to MAMI, Spin Dependent Compton Scattering: Measuring the Spin Polarizabilities of the Proton, R. Miskimen contact person, [44] Proposal to Mainz, Measurement of Polarized Target Asymmetries in Threshold Neutral Pion Photo-production on the Proton: Test of Chiral Dynamics, contact persons: M. Pavan, R. Beck, A.M. Bernstein. [45] B. van den Brandt, et al., contribution to SPIN 2002, Sept. 2002, Brookhaven NY. [46] B. Blankleider and R.M. Woloshyn, nmphys. Rev. C 29, 538 (1984). [47] J.L. Friar et al., Phys. Rev. C 42, 2310 (1990). [48] M. A. Bouchiat, T. R. Carver and C. M. Varnum, Phys. Rev. Lett. 5,373 (1960) N. D. Bhaskar, W. Happer, and T. McClelland, Phys. Rev. Lett. 49, 25 (1982) W. Happer et al., Phys. Rev. A29, 3092(1984) [49] J.S. Jensen, Ph.D. Thesis, California Institute of Technology, 2000 (unpublished), available from P.L. Anthony et al., Phys. Rev. D, (1996). [50] C.W. Arnold, and T.B. Clegg, private communications. 26

27 [51] T.E. Chupp et al., Phys. Rev. C36, 2244(1987) [52] N. R. Nersbury et al., Phys. Rev. A48, 4411 (1993) [53] G. D. Cates et al., Phys. Rev. A38,5092 (1988) [54] A. Abragam, Principles of Nuclear Magnetism (Oxford University Press, New York, 1961). [55] X. Ji, C.-W. Kao, and J. Osborne, Phys. Rev. D 61, (2000). [56] D. Choudhury and D.R. Phillips, nucl-th/ [57] D. Choudhury and D.R. Phillips, private communication. [58] James L. Friar, e-print Archive: nucl-th/ (and references therein). [59] V.D. Efros, W. Leidemann and G. Orlandini, Phys. Lett. B338, 130 (1994). [60] Yu.I. Fenin and V.D. Efros, Sov. J. Nucl. Phys. 15, 497 (1972). [61] N. Barnea, W. Leidemann and G. Orlandini, Phys. Rev. C 61, (2000). [62] W. Leidemann, in Proc. XVIII th European Conf. Few Body Problems in Physics, Few-Body Problems in Physics 02, Springer-Verlag, [63] G.A. Rinker, Phys. Rev. A 14, 18 (1976) (and references therein). [64] F. Goeckner, et al., Phys. Rev. C 43, 66 (1991). [65] G. Orlandini, private communication. [66] J.R. Calarco, B.L. Berman, and T.W. Donnelly, Phys. Rev. C 27, 1866 (1983). [67] F. Erdas, et al., Nuovo Cimento 64B, 406 (1969). [68] Yu. Arkatov, et al., Yad. Fiz. 12, 227 (1970) (Sov. J. Nucl. Phys. 12, 123 (1971)); Yad. Fiz. 19, 1172 (1974) (Sov. J. Nucl. Phys. 19, 598 (1974)). [69] B.R. Holstein, et al., Phys. Rev. C 61, (2000). [70] B. Holstein, private communication. [71] H. R. Weller and N. R. Roberson, Rev. of Mod. Phys., Vol 52, No. 4, 699 (1980); H. R. Weller and N. R. Roberson, IEEE Transactions on Nuclear Science, Vol. NS-28, 1268, (1980). [72] M.W. Ahmed, G. Feldman, V.N. Litvinenko, S.O. Nelson, B.E. Norum, B. Perdue, I.V. Pinayev, B. Sawatzky, A.P. Tonchev, Y. Wu and H.R. Weller, Nucl. Instrum. Meth. A510, 440 (2004). [73] B.A. Perdue, M.W. Ahmed, A.P. Tonchev, H.R. Weller, G. Feldman, V.N. Litvinenko, I.V. Pinayev, B.E. Norum, B.D. Sawatzky, R.M. Prior, and M.C. Spraker, to appear in Phys. Rev. C. 27

28 25 Diff. Cross Section (nb/sr) alpha = 10 beta = 5 alpha = 7.5 beta = 7.5 alpha = 5 beta = Asymmetry Angle (deg) FIG. 1: Differential cross section (top panel) and photon beam asymmetry (bottom panel) for elastic Compton scattering from deuterium at 50 MeV. The calculation is from Rupak [33] and the data are from Lucas et al. [27]. Three curves are shown, corresponding to three different values of the polarizability difference α N - β N, where the sum has been held fixed. 28

29 FIG. 2: The photon beam asymmetry at 120 for elastic Compton scattering from deuterium as a function of incident photon energy. The calculation is from Rupak [33]. Three curves are shown, corresponding to three different values of the polarizability difference α N - β N, where the sum has been held fixed (see text). The projection data points are shown as crosses. 29

30 FIG. 3: Predictions for the proton cross-sections. Dotted curves: spin polarizabilities not included. Dotdashed: quadrupole polarizabilities not included. FIG. 4: Proton longitudinal asymmetry. Dotted curves: spin polarizabilities not included. Dotdashed: quadrupole polarizabilities not included 30

31 FIG. 5: Difference of longitudinal cross-sections. Dotted curves: spin polarizabilities not included. Dotdashed: quadrupole polarizabilities not included FIG. 6: Transverse asymmetry. Dotted curves: spin polarizabilities not included. Dotdashed: quadrupole polarizabilities not included 31

32 FIG. 7: Transverse cross section difference. Dotted curves: spin polarizabilities not included. Dotdashed: quadrupole polarizabilities not included FIG. 8: Scatter plot of measured binding energy in scintillating target versus measured proton kinetic energy. FIG. 9: Projected measurements as a function of photon angle at a center-of-mass energy of 120 MeV for a longitudinally polarized scintillation target. 32

33 FIG. 10: Projected measurements as a function of photon angle at a center-of-mass energy of 140 MeV for a longitudinally polarized scintillation target. FIG. 11: Projected measurements as a function of photon angle at a center-of-mass energy of 120 MeV for a transversely polarized scintillation target. FIG. 12: Projected measurements as a function of photon angle at a center-of-mass energy of 140 MeV for a transversely polarized scintillation target. 33

34 A qlab=10 º qlab=90 60 º qlab=155 º A qlab=10 º qlab=90 º qlab=155 º wlab FIG. 13: Compton scattering double polarization asymmetry as a function of photon energy in MeV for different photon scattering angle in the lab. The sensitivity to neutron spin polarizability γ 1 is shown by the difference between red (blue) curve and the black curve (see text for details). The upper panel is the A, and the lower panel is the A. A qlab=10 º qlab=90 º qlab=155 º A qlab=10 º qlab=90 º qlab=155 º wlab FIG. 14: Compton scattering double polarization asymmetry as a function of photon energy in MeV for different photon scattering angle in the lab. The sensitivity to neutron spin polarizability γ 2 is shown by the difference between red (blue) curve and the black curve (see text for details). The upper panel is the A, and the lower panel is the A. 34

35 A º qlab= qlab=90 º qlab=155 º A qlab=10 º qlab=90 º qlab=155 º wlab FIG. 15: Compton scattering double polarization asymmetry as a function of photon energy in MeV for different photon scattering angle in the lab. The sensitivity to neutron spin polarizability γ 3 is shown by the difference between red (blue) curve and the black curve (see text for details). The upper panel is the A, and the lower panel is the A. A qlab=10 º qlab=90 º qlab=155 º A qlab=10 º qlab=90 º qlab=155 º wlab FIG. 16: Compton scattering double polarization asymmetry as a function of photon energy in MeV for different photon scattering angle in the lab. The sensitivity to neutron spin polarizability γ 4 is shown by the difference between red (blue) curve and the black curve (see text for details). The upper panel is the A, and the lower panel is the A. 35

36 FIG. 17: Schematics of the spin-exchange polarized 3 He target. For clarity, only one set of Helmholtz coils are shown. FIG. 18: Kansas on the target test stand in the lab. 36

37 FIG. 19: The experimental setup for the proposed quasifree Compton scattering asymmetry measurements from a high-pressure polarized 3 He target. The upper (lower) panel is for the longitudinal (transverse) asymmetry configuration. 37

38 FIG. 20: The projected perpendicular asymmetry measurement at HIγs on elastic scattering of circularly polarized photons from a polarized 3 He target, as a function of photon scattering angle in the laboratory frame. The incident photon beam is circularly polarized at an energy of 140 MeV with a flux of /sec. The 3 He target spin is aligned perpendicular to the incident photon momentum direction in the scattering plane. The running time is 500 hours with 100% efficiency. FIG. 21: The projected parallel asymmetry measurement at HIγs on elastic scattering of circularly polarized photons from a polarized 3 He target, as a function of photon scattering angle in the laboratory frame. The incident photon beam is circularly polarized at an energy of 140 MeV with a flux of /sec. The 3 He target spin is aligned parallel to the incident photon momentum direction in the scattering plane. The running time is 500 hours with 100% efficiency. 38

39 FIG. 22: The anticipated sensitivity to the neutron spin polarizability γ i, i = 1 4 from a coincidence double polarization asymmetry measurement from a polarized 3 He target at quasifree Compton scattering kinematics, as a function of photon scattering angle in the laboratory frame. The incident photon beam is circularly polarized at an energy of 140 MeV with a flux of /sec. The 3 He target spin is aligned perpendicular to the incident photon momentum direction in the scattering plane. The running time is 500 hours with 100% efficiency. The theory curves are calculations from McGovern for a free polarized neutron. FIG. 23: The projected sensitivity to the neutron spin polarizability γ i, i = 1 4 from parallel asymmetry measurement. The assumed photon flux and running time is the same as in Fig. 22. The theory curves are calculations from McGovern for a free polarized neutron. 39

40 FIG. 24: A plot of the Compton scattering cross section with γ-ray energy. The curve with α E = fm 3 is the cross section using the theoretical value for α E [62], the curve with α E = fm 3 corresponds to the experimental value from reference [63], and the curve with α E = fm 3 corresponds to the experimental value from reference [64]. For each curve, α Eν is set to fm 3 /MeV 2. The data points shown represent what error bars would look like from a 3% HIγS measurement. FIG. 25: The Eggbeater NaI setup used in the 16 O Compton scattering experiment. 40