Qiujian Ye Triangle Universities Nuclear Laboratory, Duke University

Transcription

1 Double Polarized Compton Scattering On 3 He target at HIγS Qiujian Ye Triangle Universities Nuclear Laboratory, Duke University Abstract This article describes recent work on the design of a double polarized Compton Scattering experiment on polarized 3 He, which will be proposal at the High Intensity Gamma Source(HIγS) at the Duke Free Electron Laboratory. Theoretical calculations show that neutron spin polarizabilities(γ 1,γ,γ 3,γ 4 ) can be extracted from double polarized Compton Scattering from 3 He. The proposed experiment will be carried out at a photon energy of 15 MeV. Geant4 simulations show the feasibility of identifying elastic Compton Scattering events from other processes by using the HINDA detector system and the sensitivity to extract of neutron spin polarizabilities. This experiment will allow for the first time extraction of the neutron spin polarizabilities and improve our knowledge of nucleon structure. 1

2 PHYSICS MOTIVATION Introduction Understanding the nucleon structure is one of the major goals of nuclear physics. Electric and magnetic polarizabilities of the nucleon are quantities which describe the response of the nucleon to an external electromagnetic field. These two polarizabilities are named α E and β M, indicating the ability of the nucleon to produce induced dipole moments under the external electric and magnetic field. Another set of fundamental quantities related to the nucleon s structure are nucleon spin polarizabilities, which investigate the stiffness of the nucleon spin. These quantities can be studied by low energy Compton Scattering on nucleons. In low energy Compton scattering, the zero-order term of photon energy in Compton amplitude related to the static properties of the nucleon such as its charge and mass, while the first-order term contains contributions from the anomalous magnetic moment of the nucleon, and the second-order term includes the information of α E and β M. Nucleon spin polarizabilities(γ 1,γ,γ 3,γ 4 ) appear at the third-order in the Compton amplitude. Double polarized Compton Scattering asymmetries from 3 He target have been shown to be sensitive to neutron spin polarizabilities [1]. The extraction of neutron spin polarizabilities is more challenging than that of the proton spin polarizabilities, because no stable free neutron targets exist in nature. Further neutron has no charge, so the Thomson term disappears resulting in a low cross section. One way to extract neutron polarizabilities is via double polarized Compton Scattering from 3 He. The details will be discussed in the next section. Compton Scattering at Low Energy The main interactions of photon passing through matter are: photoelectric effect, Compton Scattering(including Thomson and Rayleigh Scattering) and Pair Production. Moreover, gamma ray can interact with 3 He nucleus through the following processes: Quasi-free scattering, photodisintegration and other processes. Double Polarization Asymmetry from Compton Scattering on a nucleon Spin polarizabilities of the nucleon can be probed directly via circularly polarized photons Compton scattering from a polarized nucleon target. Fig. 1 shows the sensitivity of double polarization asymmetry to neutron spin polarizabilty γ 1 as a function of photon energy in the and for various photon scattering angles in the. The photon is always circularly polarized, and A and A corresponds to the target spin being perpendicular and parallel to the incident photon momentum direction in the reaction plane, respectively. The black curve is the asymmetry predicted from a fourth-order chiral perturbation theory [3, 4], and the red (blue) curve corresponds to varying γ 1 by 1% (+1%), leaving all other polarizabilty values fixed. The black dotted curve is the Born term only which includes the pion pole contribution. Fig. is the corresponding asymmetry results showing sensitivity to neutron spin polarizability γ, and Fig. 3 and Fig. 4 are similar results showing sensitivity to neutron spin polarizability γ 3 and γ 4, respectively. All the calculations are carried out for a free polarized neutron target, and the neutron electric and magnetic polarizability

3 values of α = 1, β = (all in units of 1 4 fm 3 ) are used in all these calculations. Fig. 5 shows the sensitivity of the double polarization asymmetries to the neutron electric and magnetic polarizabilities. The red curve corresponds to α = 1, β = 4, and the blue curve is for α = 8, β = 6 (all in units of 1 4 fm 3 ). These results show that the perpendicular asymmetry A is most sensitive to the neutron spin polarizabilties γ 1 and γ at a photon scattering angle of 9 in the frame. The parallel asymmetry A is sensitive to the neutron spin polarizability γ 1, γ, γ 4 at a photon scattering angle of 1 when the incident photon energy is relatively large, 1 MeV. While sensitivity to neutron α, β is shown in Fig. 5, these spin-dependent asymmetries are much more sensitive to the unknown neutron spin polarizabilities γ i. Therefore, the spindependent compton scattering of circularly polarized photons from a polarized neutron target will allow sensitive probe of the neutron spin polarizabilities. The corresponding results for proton are shown in Fig. 6-Fig. 9. One sees clearly that these double polarization asymmetries are more sensitive to spin polarizabilities in the case of neutron than that of proton. This is because the Born contribution dominates the Compton scattering in the case of the proton. A q=1 º 4 q=9 6 º q=155 º A q=1 º q=9 º q=155 º w FIG. 1: Compton scattering double polarization asymmetry as a function of photon energy in MeV for different photon scattering angle in the. 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. Since there is no stable free neutron target in nature, effective neutron target, i.e. nuclear targets, deuteron and 3 He nucleus 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 [5, 6]. The details will be discussed in the next section. 3

4 A q=1 º -.5 q=9 º q=155 º A q=1 º q=9 º q=155 º w FIG. : Compton scattering double polarization asymmetry as a function of photon energy in MeV for different photon scattering angle in the. The sensitivity to neutron spin polarizability γ 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 º q=1 -.1 q=9 º q=155 º A q=1 º q=9 º q=155 º w FIG. 3: Compton scattering double polarization asymmetry as a function of photon energy in MeV for different photon scattering angle in the. 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. 4

5 A q=1 º -.5 q=9 º q=155 º A q=1 º q=9 º q=155 º w FIG. 4: Compton scattering double polarization asymmetry as a function of photon energy in MeV sfor different photon scattering angle in the. 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. A Θ Θ Θ 155 A Θ Θ Θ 155 Ω FIG. 5: Compton scattering double polarization asymmetry as a function of photon energy for different photon scattering angle in the. The sensitivity to neutron electric and magnetic polarizability α,β 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. 5

6 A Θ Θ Θ 155 A Θ Θ Θ 155 Ω FIG. 6: Compton scattering double polarization asymmetry as a function of photon energy for different photon scattering angle in the. The sensitivity to proton spin polarizability γ 1 is shown by the difference between red (blue) curve and the black curve (see text for details) A Θ Θ Θ 155 A Θ Θ Θ 155 Ω FIG. 7: Compton scattering double polarization asymmetry as a function of photon energy for different photon scattering angle in the. The sensitivity to proton spin polarizability γ is shown by the difference between red (blue) curve and the black curve (see text for details). 6

7 A Θ Θ Θ 155 A Θ Θ Θ 155 Ω FIG. 8: Compton scattering double polarization asymmetry as a function of photon energy for different photon scattering angle in the. The sensitivity to proton spin polarizability γ 3 is shown by the difference between red (blue) curve and the black curve (see text for details). A Θ Θ Θ 155 A Θ Θ Θ Ω FIG. 9: Compton scattering double polarization asymmetry as a function of photon energy for different photon scattering angle in the. The sensitivity to proton spin polarizability γ 4 is shown by the difference between red (blue) curve and the black curve (see text for details). 7

8 Double Polarization Asymmetry from Compton Scattering on a polarized 3 He As discussed previously, one can also extract the neutron spin polarizabilities from polarized Compton scattering from a polarized 3 He target at the elastic kinematics as demonstrated by a recent next-to-leading order chiral perturbation theory calculation []. Further, the calculation shows [7] that sensitivities to the proton spin polarizabilities are highly suppressed in the double-polarization observables. The amplitude for Compton scattering from polarized 3 He is a sum of one-body and two-body parts: T γ 3 He = A 3 He i t i, A 3 He i i=1...6 = A 1B i + A B i. Here, t i are invariants constructed out of the photon momentum and polarization vectors. A 1B i (A B i ) are one-body and two-body Compton structure functions. Calculation [7] shows that A B i, i = are negligible at O(Q 3 ). Moreover, in a polarized 3 He target the spins of the two protons are mostly anti-aligned shown in Fig. 1, therefore the neutron carries the major contribution to the nuclear spin. Hence, we expect that A 3 He i A n i, which supports the idea that Compton scattering on 3 He is an ideal avenue to extract neutron spin polarizabilities. Experimentally, one has to suppress backgrounds during the experiment using the FEL beam RF structure as demonstrated successfully in the 16 O Compton scattering experiment [8] at HIγS. Fig. 11 shows the diffentital cross-section (DCS) calculated by Choudhury et al. [] for elastic Compton scattering from 3 He as a function of the scattered photon angle for an incident photon energy of 1 MeV (1 MeV) in the left (right) panel in the center-of-mass frame. In Fig. 11, the red curve is the result at the next-to-leading order, but without the two-body contribution. The blue curve is the result at the next-to-leading order with two-body contribution. The green curve is the calculation including the proton Thomson term only. For details, see Ref. []. Fig. 1 shows the calculated sensitivities of the unpolarized DCS to α n (left) and β n (right) for incident photon energy of 1 MeV (1 MeV) in the upper (lower) planel. FIG. 1: Polarized 3 He target as an effective polarized neutron target The spin dependent differential cross section difference z and x are defined as following: 8

9 z = dσ dσ dω dω x = dσ dσ, dω dω (1) where z (x) refers to the target spin along the incident photon momentum direction (transverse to it) in the scattering plane. The photons are always circularly polarized. The corresponding spin dependent asymmetries are defined as: A z = A x = dσ dσ dω dω dσ + dσ dω dω dσ dσ dω dω dσ + dσ dω dω, () Fig. 13 shows the sensitivities of z to the neutron spin polarizabilities, γ i (i = 1 4) (in the order from left to right and top to bottom) by varying the corresponding spin polarizabilities. Fig. 14 is the corresponding plot for x. These calculations are for photon energy ω cm = 1 MeV in the center of mass frame (ω = 15 MeV in the frame). While z is most sensitive to γ 1, γ and γ 4 at forward Compton scattering angles, x is most sensitive to γ 1 at angles between 1-1 degrees, and to γ 4 over a relatively large angular range. Fig. 15 (Fig. 16)shows the corresponding sensitivities of A z (A x ) to the neutron spin polarizabilities γ i (i = 1 4). Since there is no stable free neutron target, one should carry out the double polarized Compton scattering from a polarized 3 He target to form z ( x ) and A z (A x ). These measurements allow for the extraction of two combinations of the neutron spin polarizabilities γ i (i = 1 4). Moreover, from γd scattering data [7], we can extract the combination of γ 1 and γ 3. If combining all the information, we can at least extract two spin polarizabilities and provide constraints on the other two. Taking into account the energy dependence of the sensitivity to the neutron spin polarizabilities, we plan to carry out the polarized elastic Compton scattering experiment at HIγS with 15 MeV photon energy (below π production threshold). Experimental Data No experimental data for individual neutron spin polarizabilities, one constrain for γ i is the neutron backward spin polarizability, which was determined as γ n π = γ 1 + γ + γ 4 = (58.6 ± 4.) 1 4 fm 4 [9]. 9

10 9 8 7 IA O(e ) O(e Q) IA O(e ) O(e Q) d σ/dω (nb/sr) d σ/dω (nb/sr) c. m. angle(deg) c.m. angle(deg) FIG. 11: Calculations of DCS at 1 MeV (left) and 1 MeV (right) in the center of mass frame. dσ / dω (nb/sr) α (n) = fm 3 α (n) = 1 4 fm 3 α (n) = α (n) = 1 4 fm 3 α (n) = fm 3 dσ / dω (nb/sr) β (n) = 1 4 fm 3 β (n) = β (n) = 1 4 fm 3 β (n) = fm 3 β (n) = fm c.m. angle(deg) c.m. angle(deg) 4 5 dσ / dω (nb/sr) 15 dσ / dω (nb/sr) c.m. angle(deg) c.m. angle(deg) FIG. 1: Calculations of elastic Compton scattering from 3 He DCS sensitivities to α n (left) and β n (right) for ω = 1 MeV (upper panel) and 1 MeV (lower panel) in the center of mass frame. 1

11 Z Z γ i (n) = -γ i (O(e Q)) γ i (n) = -γ i (O(e Q))/ γ i (n) = γ i (n) = γ i (O(e Q))/ γ i (n) = γ i (O(e Q)) FIG. 13: Sensitivities of z to neutron spin polarizabilities, γ i at ω=15 MeV in the frame. X X FIG. 14: Sensitivities of x to neutron spin polarizabilities, γ i at ω=15 MeV in the frame. Other Processes Quasi-free Scattering Another interaction between photon and 3 He is Quasi-free Scattering: γ + 3 He γ + p + d (3) γ + 3 He γ + p + p + n (4) 11

12 Asymmetry in Z Asymmetry in Z γ i (n) = -γ i (O(e Q)) γ i (n) = -γ i (O(e Q))/ γ i (n) = γ i (n) = γ i (O(e Q))/ γ i (n) = γ i (O(e Q)) FIG. 15: Sensitivities of A z to neutron spin polarizabilities, γ i at ω=15 MeV in the frame. Asymmetry in X Asymmetry in X FIG. 16: Sensitivities of A x to neutron spin polarizabilities, γ i at ω=15 MeV in the frame. The Kinetic of quasi-free Compton Scattering can be calculated by implementing the fermi momentum of proton(deuteron) inside the 3 He and the Cross Section of γp and γd interactions. The differential cross section of the Quasi-free scattering can be calculated by the following procedure: The Cross Section of reaction: γ + 3 He γ + p + d (5) 1

13 can be calculated by reaction γ + p γ + p (6) γ + d γ + d (7) but now proton(deuteron) has fermi momentum, so Lorentz transformation is applied to calculate Cross Section in the rest frame of the proton(deuteron). It is then transformed back to the frame to obtain the quasi-free Cross Section. In order to verify that the above method is correct, the same method has been applied to the reaction γd γnp and the MC simulation result has been compared to other theory calculations. From Fig. 17 and Fig. 18, our simulation results are consistent with other calculations. FIG. 17: Monte Carlo simulation of reaction γd γnp, fitted by Gauss Distribution FIG. 18: Calculation of cross section γd γnp [1], the incident E γ is 1MeV Photodisintegration of 3 He Both the two-body and three-body break-up channels of 3 He have been studied, These processes are known as photo-disintegration of 3 He: γ + 3 He p + d (8) γ + 3 He p + p + n (9) Discussion As discussed above, double polarized Compton scattering process 3 He(γ,γ) 3 He contains information on neutron spin polarizabilities, and are required to be separated from quasi-free scattering and photodisintegration of 3 He and background events. One way to identify elastic Compton Scattering is to simultaneously detect both the scattered gamma ray (by using NaI(Tl) Detectors) and 3 He particle (by using 3 He Detectors). However, the problem 13

14 is that in most cases the scattered 3 He particles (incident gamma energy should below pion production threshold) do not gain enough kinetic energy to pass through target cell, which is construed with Pyrex Glass and its wall thickness is 1 mm. The kinematics of the 3 He elastic Compton scattering for an incident photon energy of 1 MeV are listed in Table I. TABLE I: Compton Scattering on 3 He at E γ =1 MeV Scattered Gamma(degree) E(Scattered Gamma)(MeV) E(Scattered 3 He)(MeV) For an 13 MeV incident gamma, recoiling 3 He kinetic energy is 9.8 MeV at the scattered gamma angle of 14 degree. However, Monte Carlo simulation shows the minimum kinetic energy for 3 He passing through target cell is 1 MeV, as shown in Fig. 19. So in this case we can not identify the elastic compton scattering since the detection of recoiling 3 He is impossible. FIG. 19: MC Simulation of 1 MeV 3 He passing through 1 mm Pyrex Glass Another way to specify elastic scattering is by only detecting the scattered gamma ray with high energy resolution NaI Detector to separate elastic events from other processes. 14

15 The scattered gamma ray from quasi-free scattering on 3 He is important for this experiment. The usual approach to quasi-free scattering is introducing the concept of fermi momentum of nucleon inside nucleus: one photon hits a 3 He nucleus can be treated as the photon hits a proton or neutron (or deuteron), which is then knocked out off the nucleus, the residual nucleon being unperturbed and keeping the same momentum it had before the collision. When the kinetic energy of the spectator nucleon is zero, the scattered gamma ray can reach its maximum energy. Monte Carlo Simulations have been done for two-body and three body quasi-free scattering. The kinematics of three reactions at 1 MeV with a 3 % energy spread ( E/E = 3 %) photon beam are shown in Fig.. FIG. : Energy distribution of scattered gamma for elastic and quasi-free scattering As shown in Fig., if the energy resolution of the NaI detector is good enough, the elastic Compton Scattering can be separated from quasi-free processes. Whereas, backgrounds also come from gamma interactions with the surrounding material. Geant4 simulation is required to help the design the experiment and reduce the background and extract the Compton Scattering cross section. THE PROPOSED EXPERIMENT The Experiment Overview We propose a double polarized Compton Scattering from polarized 3 He at the High Intensity Gamma Source (HIγS) Facility. The polarized 3 He target is based on the principle of spin-exchange optical pumping technique. A solenoid design is implemented to provide uniform magnetic field for 3 He target system. We plan to use the HIγS NaI Detector Array (HINDA) consists of eight NaI detectors for the photon detection. The good energy resolution of the HINDA is sufficient to separate the elastic Compton Scattering from 15

16 the quasi-free processes. Target collimators are implemented to shield photons from the incoming and outgoing target windows. The asymmetry will be formed by flipping the target spin polarization from time to time to minimize systematic false asymmetries. In this experiment, the polarized 3 He target apparatus is proposed for a longitudinal asymmetry configuration. We are planning to measure three angles asymmetry simultaneously and further a fit of the asymmetries at different angles can help the extraction of the spin polarizabilities. The experiment is proposed at an incident gamma energy of 15 MeV. The details of the experiment will be discussed in the next section. Experimental Setup The layout of the experiment is shown in Fig. 1. A vacuum beam pipe is planned to be placed in front of target cell in order to reduce backgrounds from gamma interactions with air. Eight NaI detectors are allocated at three different angles 4,6,14 with respect to the incident photon beam, layout details are shown in Table II. Good shielding for the detector system, especially PMTs is required to ensure the detectors work in a good condition. Since magnetic fields are one of the most important influences on PMTs. It is common practice to shield PMTs with a mu-metal screen which cover around the PMTs tubes. Because of the small cross section( nb), the NaI detectors are proposed to placed closely to the target cell. The practical limitation is how to locate the eight NaI detectors close to the target without interfering with each other and the solenoid. When we place detectors closer to the target, more backgrounds will be seen by the detectors. However, for Compton Scattering experiment we do not need to worry about that, details will be discussed later. The accepted distance from the target to each NaI detector front face is 6 cm (Note:it is not necessary to have the same distance for each detector). TABLE II: Detectors Layout DetectorID Theta(deg) Phi(deg) Gamma Beam at HIγS We will use the gamma beam from the Duke Free-Electron Laser Laboratory (DFELL), which can provide a high-flux gamma of /sec with 1% circular polarization 16

17 FIG. 1: Experimental setup overview and 3.% spread beam energy. The integrated luminosity is defined by: L = ρ v t (1) where ρ is the target thickness, v is incident photon flux, t is the total time. And if the beam time is 5 hours, L = cm =.99 Pb 1. Polarized 3 He Target Since the lifetime of free neutrons is less than 15 minutes, stable free neutron target does not exists, it decays. However, as discussed before polarized 3 He can be treated as an effective polarized neutron. The polarized 3 He target design is similar to that used in Hall A at Jefferson Lab [11]. The target thickness is atoms/cm with polarization 5%. In our recent test, the highest polarization of 3 He we have achieved is 6%. Solenoid Design A single-layer solenoid is applied to provide the holding field for 3 He target system, here we discuss the concept design. Scattered photons attenuate when they pass through material, given by formula: I = I e µx (11) 17

18 For Mylar µ = 1 cm /g, and Copper µ = 5 1 cm /g. If Copper wire and Mylar are used (the support material) for the solenoid, we should have 1 mm thick Copper(ρ= 8.96 g/cm 3 ) and cm thick Mylar( ρ= 1.39 g/cm 3 ). Plug in (13), we have I =.94 I, which means 9% photons pass through the solenoid. In the experiment, the required magnetic field is 1 gauss along the beam direction, and the magnetic field should keep uniform in the target region including pumping chamber, transfer tub and target cell. Simulation by COMSOL has been applied in order to investigate the field uniformity. Simulation parameters are list in Table III (the qualified wire is AWG 18). Simulation results show that the solenoid have good performance in providing uniform TABLE III: Solenoid Geometry Length(cm) r in (cm) r out (cm) Current N A 1 magnetic field. D magnetic field map are shown in Fig., and B-distributions in Target center are shown in Fig. 3 and Fig. 4(the gradient of Bz is 17.1 mg/cm(smaller than 3 mg/cm), for Bx the gradient is even small shown in Figure 11(scalars are different). From above discussion, the solenoid can provide the required uniform magnetic field. And it FIG. : COMSOL simulation of Solenoid B-field will reduce 1% events, but not introduce more effective background(because for nuclear Compton scattering, the scattered gamma energy spectrum is a peak which is near the incident gamma energy, but other processes cannot produce so high energy gamma, so we can easily make a cut to exclude these events). 18

19 Magnetic Flux Density B (x =, y = ) Bz(G) Z(m) FIG. 3: Solenoid B field distribution along the z-axis Magnetic Flux Density B (y =, z = ) Bx(G) X(m) FIG. 4: Solenoid B field distribution along the x-axis Target collimator design The design of the target collimator can be found in Fig. 5. The goal of the target collimator is to shield photons generated from the target windows, which are considered as the major background. The angular acceptance effect for the target collimator is shown in Fig. 6. Target collimators are also implemented in Geant4 simulations. HINDA System Compton Scattering experiments are difficult because of low cross sections and the requirement of high energy resolution. Besides high intensity photon beam and long running time, the experiment also requires high energy resolutions, high efficiency and large acceptance detectors. HIγS NaI Detector Array(HINDA) consists of eight 1.5 in. 1.5 in.nai core detectors. Surrounding the core is an active shield of eight 1. long NaI(Tl) crystals. And each detector contains 6 lead collimator and 6 borated paraffin, which can help reduce neutron backgrounds. One NaI detector design is shown in Fig. 7. The electronics for each NaI detector have two different setups: CLEAN (anticoincidence between the shield and the core) and CONIC (coincidence between the shield and the 19

20 FIG. 5: Target collimators layout (in Green) core). CLEAN model can reduce the background from the environment, while CONIC model is used to isolate the first escape peak from the core [13], result is shown in Fig. 8. The energy resolution of NaI detector has been tested at HIγS [14], in this test the energy resolution is.9% at 15.1MeV. DAQ The experiment will use TUNL as the data acquisition system(daq). TUNL is modified from the Online Data Acquisition (CODA) system of continuous electron beam accelerator facility (CEBAF) at Jefferson Laboratory. Estimated Counts Rate An estimate of the count rate in each NaI detector is discussed below. Average values(different target-detector distances and target s finite volume) are used to roughly represent the count rate in all detectors.the count rate in the NaI detector is given by: N = dσ () v ρ Ω (1) dω where dσ () is the differential cross sectionat angle, v is the photon beam intensity, ρ is dω the target thickness and Ω is the solid angle. From above discussion, we know that:

21 FIG. 6: Angular acceptance effect of the target collimator 1)Photon beam intensity v = /s )Target thickness ρ = cm 3)Differential cross section, dσ = 15 nb/sr (average from dω 5 to 145 ) 4)solid angle Ω = msr Using above values, we obtain an average rate of 3.39 counts/hour in each NaI detector. The estimate counts for the experiment are list in Table IV. TABLE IV: Raw count rate of each detector Scattered Angle(degree) Parallel(counts/hour) Anti-Parallel(counts/hour) MONTE CARLO SIMULATION Geant4 overview Geant4 (GEometry ANd Tracking) is a platform for the simulation of the passage of particles through matter, by using Monte Carlo methods[6]. It provides a complete tool for 1

22 FIG. 7: A NaI detector assembly with the core detector, shield detector and front lead collimator detector simulation including particle source,detector geometry, materials, physics process and event track, visualization and user interface. Simulation Description The Geant4 simulation code used in this experiment was first wrote by [15]. Later the simulation was modified for elastic Compton Scattering on polarized 3 He.The modified parts include: Geometry and Event Generators which are described below. Physics list: This simulation code contains Geant4 modular physics list, including electromagnetic, optical, photolepton-hadron, hadronic, transportation. Geometry: Target Cell (pumping chamber,transfer tube and target chamber), target collimators, a solenoid which provide magnetic field for the polarized target, a stand for the solenoid and detectors support. Details are shown in Fig. 1. Event generator: Physics event generators have been developed to simulate 3 He(γ,γ) 3 He(elastic scattering), 3 He(γ,γ)pd and 3 He(γ,γ)ppn (Quasi-free) reactions and two-body and three-body photodisintegration of 3 He. All these reactions are defined in a vertex generator, and the position of the interaction points are selected uniformly in the restricted to the size of target cell. Since our target is a 4-cm long gas target, so the Z coordinate of the scattering point is also selected uniformly inside the target cell.

23 FIG. 8: 41 AmBe spectrum in HINDA [13] Finite Volume Target We are planning to layout the detectors close to the target, due to the large size of the NaI detectors, each detector will cover a range of scattered angles. And our polarized 3 He target is about 4 cm long, which can not be treated as point source. The angular acceptance of the NaI detectors has been simulated for finite target and point-like target (photons are shot randomly in all directions), the result is shown in Fig. 9. The angular coverage for each NaI detector 15- degree. Detector Properties Detector Geometry Two types of detector geometry have been setup: one is in-beam, the other is scattering, shown in Fig. 3. In-beam simulation runs are used to determine the smearing function in order to account for light collection, attenuation and P.M.T response, the smearing functions are determined by comparison with data. The smearing function at 45 MeV has been extracted in [13], a value of.6% is determined, and the result is shown in Fig. 31. More work is required to determine the smearing parameters at other energies. Scattering simulation are used to simulate the real experiment and extract cross sections from data. Geant4 simulations of these two setups are shown in Fig. 3 and Fig. 34. A NaI missing 3

24 5 Counts 15 Point Target 4 cm Target Energy Deposition(MeV) FIG. 9: Simulation of the effect of finite target energy spectrum is created to produce the number of detected photons.fig. 33 and Fig. 35 shows the simulated missing energy spectrum, which is convoluted with the Gaussian that is used to fit the experimental spectrum. Detection Efficiency Two types of efficiency are generally referred, when talking about the detection efficiency: absolute and intrinsic detection efficiency. Their relationship can be expressed as: ε abs = events registered events entering detector events entering on detector events emitted by source = ε int ε geom (13) If one interaction is enough to produce a detectable electric pulse, the efficiency is: ε int = 1 e µ(e)l where µ is the attenuation coefficient of photons, L is the length of the detector. For each NaI detector ε int 1, the detection efficiency is determined by geometric and electronic efficiency. If the gamma-ray peak is summed from one width above the center to two widths below, the detection efficiency has been found around 6 % for photon energies between MeV and 1 MeV. Energy Deposition By using the parameter.6 % to smear our simulation result, the combined distribution of energy deposited in 4 NaI detectors positioned symmetrically at =45 with respect the 4

25 FIG. 3: In-beam and scattering setup photon beam is shown in Fig. 36. The energy of the incident photon beam is 1 MeV( with E/E =3.%) for this simulation. Background Study Background from Quasi-free Processes As discussed before, the contamination from Quasi-free scattering can be easily separated. In addition, since NaI detector does not discriminate neutron and gamma, neutrons from 3-body photodisintegration of 3 He is another source of background. Calculation [16] shows the maximum kinematics energy of neutron is 73. MeV, which does not contribute to the elastic scattering region. Background from Target Window When a photon beam passes through the target,the beam interacts with the target cell and support materials around the target, scattered gammas can enter and deposit energy in the HINDA system, which can be simulated by Geant4. However, Geant4 does not include the nuclear Compton Scattering reaction from the materials in its database. Since the target cell is made of Pyrex glass, which is primarily made of Oxygen-16 (53.96%) and Silicon- 8(37.7%). According to equation(4), the energies of the scattered photons on Oxygen and 3 He differ by (E r) Element (E r)3 He (shown in ) If we assume the energy resolution of our NaI detector is.6%, the energy difference at 4 degree and 6 degree are too small to be 5

26 FIG. 31: In-beam test result for HINDA NaI detector at beam energy 45 MeV [13] TABLE V: Energy difference at E γ =15 MeV Scattered Angle(degree) (E r) Oxygen (E r)3 He(MeV) (E r) Silicon (E r)3 He(MeV) observed, while it should be possible to detect a difference of MeV. This may be the major background in our experiment, but as discussed before this kind of background are mostly reduced by using target collimators. Background from Nitrogen In the experiment, nuclear Compton Scattering from Nitrogen is another source of background. And reference target filled with nitrogen is helpful to measure this background contribution. 6

27 FIG. 3: Simulation of NaI detector in-beam configuration Counts Missing Energy/MeV FIG. 33: Simulated missing energy spectrum SIMULATION RESULT Projection on asymmetries As discuss before, the double polarized Compton Scattering experiment involves circularly polarized photons and a polarized target, by measuring the asymmetry we can investigate the 4-spin polarizabilities of the target neutron. When the target is polarized along the beam direction(parallel or anti-parallel), the corresponding observable is called Parallel polarization asymmetry and is defined as: A = N N N + N 1 P t P b (14) where and denote the polarization of target. When the target is polarized perpendicular to the beam direction, in this case the observable 7

28 FIG. 34: Simulation of NaI detector scattering configuration COUNTS missing energy /MeV FIG. 35: Simulated missing energy spectrum is perpendicular polarization asymmetry and is defined as: A = N N N + N 1 P t P b (15) where and denote the polarization of target. After comparing the longitudinal asymmetry and transverse asymmetry, we decide to study the longitudinal asymmetry because of the better uncertainty and sensitivity. The statistical uncertainty of the longitudinal asymmetry is: δa = δn ( N + δn (N + N ) ) ( N 1 (16) (N + N ) ) P t P b where if δn = N, δn = N, the uncertainty is: N N 1 δa = (17) (N + N ) 3 P t P b 8

29 35 COUNTS Beam Energy 1 MeV 3 3 He(γ,γ) He events 3 He(γ,γ)pd events 3 He(γ,γ)ppn events E deposited (MeV) FIG. 36: Energy deposition in NaI detector from reactions 3 He(γ,γ) 3 He, 3 He(γ,γ)ppn and 3 He(γ,γ)pd at 45 In simulating the asymmetry results, we used the parameters list in Table VI. The asymmetry result for the elastic Compton Scattering is shown in Fig. 37. And the difference of differential cross section result is also shown in Fig. 38. For reference, the projected results are list in Table VII, Table VIII, Table IX. TABLE VI: List of Parameters used for simulation Parameter Value Photon Flux photons/s Photon Circular Polarization 1% Target Density nuclei/cm Effective Target Length 4 cm Target Polarization 5% Total Running Time 1 hours TABLE VII: Projected counts at E γ =15 MeV Scattered Angle(degree) Parallel(counts) Anti-Parallel(counts)

30 TABLE VIII: Projected longitudinal asymmetry at E γ =15 MeV Scattered Angle(degree) Asymmetry Uncertainty TABLE IX: Projected Helicity-dependent differential cross section difference at E γ =15 MeV Scattered Angle(degree) DXS difference(nb/sr) Uncertainty(nb/sr) Extraction of Spin Polarizabilities By measuring differential cross sections in the parallel and anti-parallel case, the longitudinal asymmetry can be obtained. From theoretical calculation[3], spin polarizabilities can be extracted by fitting the experimental results to theoretical calculations. Before extracting spin polarizabilities from experiment, the first step is to determine the value for α and β, which are known as electric and magnetic polarizabilities. By using the theoretical values of γ i as starting value for a fit, replace γ i with γ i + δ i by introducing the fitting parameters δ i, the value of spin polarizabilities can be determined by a chi-square minimization: χ = 4 i=1 ( y i f(γ 1, γ, γ 3, γ 4 ) σ i ) (18) where y i is the experimental data with errors σ i, and f(γ 1, γ, γ 3, γ 4 ) is the theoretical prediction. In order to determine the value of γ i, we expand χ in Taylor series around the minimum γ i : χ (γ i ) = χ (γ min i ) + 1 χ (γ γi i γi min ) (19) Since the variance of γ i is related to the second derivative of χ according to σ = 1 χ γ i 1 () so we have χ (γ i ) = χ (γi min ) + 1 σ (γ i γi min ) (1) A function of the form above with 3 parameters, χ (γ min i ), σ and γi min, was fit to spindependent differential cross section difference and the longitudinal asymmetry respectively in Fig. 39 and Fig. 4. The fitting results from spin-dependent differential cross section difference are listed in Table X and fitting results from the longitudinal asymmetry are list 3

31 Asymmetry in Z Asymmetry in Z γ i (n) = -γ i (O(e Q)) γ i (n) = -γ i (O(e Q))/ γ i (n) = γ i (n) = γ i (O(e Q))/ γ i (n) = γ i (O(e Q)) FIG. 37: The incident gamma beam at energy of 15 MeV with flux /s and 1% circular polarization. The target thickness is atoms/cm with 5% polarization. The 3 He target spin is parallel to the incident photon momentum direction. The running time is 1 hours. in Table XI: Combining both the A and the Σ z measurements, the neutron spin polarizabilities extracted from the proposed elastic Compton Scattering are: γ 1 = 4.14 ±.7 γ = 3.1 ±.59 γ 3 = 1.1 γ 4 = -1.6 ±.6 All are in units of 1 4 fm 4. The statistical sensitivity to each neutron spin polarizability σγ 1 γ 1, σγ γ and σγ 4 γ 4 are: 16.9%, 19.1% and.6%, respectively. TABLE X: Fitting results from spin-dependent differential cross section difference (units in 1 4 fm 4 ) Parameters Extraction results Uncertainty γ γ γ γ

32 Z Z γ i (n) = -γ i (O(e Q)) γ i (n) = -γ i (O(e Q))/ γ i (n) = γ i (n) = γ i (O(e Q))/ γ i (n) = γ i (O(e Q)) FIG. 38: Difference of differential Cross Section. The incident gamma beam at energy of 15 MeV with flux /s and 1% circular polarization. The target thickness is atoms/cm with 5% polarization. The 3 He target spin is parallel to the incident photon momentum direction. The running time is 1 hours. TABLE XI: Fitting results from longitudinal asymmetry (units in 1 4 fm 4 ) Parameters Extraction results Uncertainty γ γ γ γ Note: In reality, one combination of γ 1, γ and γ 3 can be extracted from the longitudinal asymmetry. If the transverse asymmetry is measured, another linear combination of γ 1, γ and γ 4 can be obtained.moreover, from γd scattering[3], we can extract the combination of γ 1 and γ 3. If we combine all the information we can at least extract two spin polarizabilities and provide constrains on the other two. 3

33 χ 8 χ γ γ χ γ 4 FIG. 39: Fitting for spin-dependent differential cross section difference. The calculated values of the function χ for different values of γ i. The solid curve is the fitting result χ χ γ γ χ γ 4 FIG. 4: Fitting for the longitudinal asymmetry. The calculated values of the function χ for different values of γ i. The solid curve is the fitting result. Beamtime request Consider the background contribution to the true Compton Scattering from 3 He, the longitudinal asymmetry can be written as: A = N P N A N P + N A N B 1 P t P b () 33

34 where N P and N A refer to the number of gamma events recorded by detectors (including true events and background), N B is background gamma counts. For the purpose of estimating the background contribution due to target windows and N, we assume that 8% of the events recorded in the elastic scattering region will be true Compton Scattering from 3 He, and % will come from the target windows and N. This is certainly an exaggeration estimation of the background, but using this it allows us to get a conservative estimate of the beam-time. And if we assume that the background running time is given T back and 1 (a = T total T back a T back ) of full target running, we see that: Target Run: N P = (NP true + N B ) ± NP true + N B, N A = (NA true + N B ) ± NA true + N B. Background Run: N B a ± N B a Total background: N B ± an B where NP(A) true is the true Compton Scattering events from 3 He, and N B background during the target run period. If assume N true A =.85 N true P The statistical uncertainty can be expressed by:, we should have N B = 1 4 ((Ntrue P + N true A is the total )/) =.5Ntrue δa = 1 (N P t P b (N P + N A N B ) A N B ) δnp + (N P N B ) δna + (N P N A ) δnb = 1 (N true P t P b (N true + N true A ) (NP true + N B ) + (NP true ) (NA true + N B ) + (NP true NA true) an B P A ) where δn P = N true P + N B, δn A = N true A + N B. And δn B = an B δa = = ( a) 1.85 P t P b N true P 1.85 P t P b 1.83 ( T total T back +.5 T back ) n true P (per hour) For comparison, the theoretical calculated uncertainty is given by: δa = 1 (N true P t P b (N true + N true A ) (δnp true ) + (NP true ) (δna true) (3) so P δa theory = δa = δa theory A ) 1.85 P t P b Ttotal ( T total n true P (per hour) P. (4) ) (5) T total T back T back Calculate the derivative of equation(7), we reach the minimum value of δa min 1.1δA theory when T back = T total. If we want to maintain the statistical uncertainty, the running time for 3.14 He target is 1 hours and running time for reference target is 6 hours, in total we need at least 16 hours running time for this experiment. 34

35 SUMMARY The proposed experiment is a challenge experiment, which requires high intensity beam (5 1 7 /sec) or higher at the upgraded energy (E γ = 15 MeV), a high pressure polarized 3 He target and a high efficiency and energy resolution NaI detectors system. We present studies for the new design of a double polarized Compton Scattering on polarized 3 He. The proposed experiment will allow for the first time extraction of all four neutron spin polarizabilities. We expect it become availe in the future. 35

36 [1] R.P.Hildebrandt, H.Griesshammer, and T.R.Hemmert,nucl-th/3854. [] Choudhury et al. Phys. Rev. Lett. 98, 333 (7). [3] J.A. McGovern, Phys. Rev. C 58, 113 (1998), J. McGovern, private communication. [4] K.B. Vijay Kumar, J.A. McGovern, and M.C. Birse, Phys. Lett. B 479, 167 (). [5] B. Blankleider and R.M. Woloshyn, nmphys. Rev. C 9, 538 (1984). [6] J.L. Friar et al., Phys. Rev. C 4, 31 (199). [7] D. Choudhury, private communications. [8] B. A. Perdue et al., Phys. Rev. C 7, 6435 (4). [9] K.Kossert et al.,eur.phys.j. A16,59(3). [1] M.I.Levchuk et al,few Body System 16,191-15(1994). [11] J.S. Jensen, Ph.D. Thesis, California Institute of Technology, (unpublished), availe from P.L. Anthony et al., Phys. Rev. D, (1996). [1] J. Allison, K. Amako, J. Apostolakis, H. Araujo, P. Arce Dubois and M. Asai et al., IEEE Trans Nucl Sci 53 (1) (Feb 6), pp [13] P.P. Martel et al, Nuclear Instrumentation and Methods, TUNL XLVIII 8-9 pp [14] S.S. Henshaw et al, Nuclear Instrumentation and Methods, TUNL XLVIII 8-9 pp [15] A.Teymurazyan et al, Nuclear Instrumentation and Methods, TUNL XLVIII 8-9 pp [16] R.Skibinski, Jagiellonian University, private communication (9). [17] S.Pomme, Applied Radiation and Isotopes 65 (7) [18] Bernard, V., Kaiser et al, Phys.Rev.Lett.,67,

37 Appendices Compton Scattering at Low Energy The Compton Scattering amplitude T γn can be written as [7]: T γn = e {A 1ˆε ˆε + A ε ˆkˆε ˆk + ia 3 σ (ˆε ˆε) [ ] +ia 4 σ (ˆk ˆk)ˆε ˆε + ia 5 σ (ˆε ˆk)ˆε ˆk (ˆε ˆk )ˆε ˆk [ ] +ia 6 σ (ˆε ˆk )ˆε ˆk (ˆε ˆk)ˆε ˆk } where A 1... A 6 are the Compton structure function, they are functions of the photon energy ω. ˆε, ˆε are the incoming and outgoing photon polarizations and ˆk, ˆk are the momentum direction of incoming and outgoing photon. If Taylor expanding the invariant amplitudes around, one can express A i as A 1 = Z M (α + βcos)ω + O(ω 4 ) A = Z ω M + βω + O(ω 4 ) A 3 = ω M [Z(Z + κ) (Z + κ) cos] + A π 3 + (γ 1 (γ + γ 4 )cos)ω 3 + O(ω 5 ) A 4 = (Z + κ) ω + γ M ω 3 + O(ω 5 ) A 5 = (Z + κ) ω M Z(Z + κ)ω A 6 = M + A π 5 + γ 4ω 3 + O(ω 5 ) + A π 6 + γ 3 ω 3 + O(ω 5 ) At O(Q 3 ), the neutron polarizabilities can be obtained [18]: α = fm 3 β = fm 3 γ 1 = fm 4 γ =. 1 4 fm 4 γ 3 = fm 4 γ 4 = fm 4 The amplitude T γn is used to calculate the differential cross section by using: dσ dω cm = M 16π s T γn (6) 37

38 Solid Angle Calculation Disk Source Consider the geometry with a disk source (with radius R s ) parallel to a detector with circular aperture with radius R d, and the distance between them is d. The solid angle is given by Ω = 4π ω 4 where ω = R d d, φ = Rs d ; {1 34 (ω + φ ) (ω4 + φ φ ω ) 35 + φ 6 16 (ω6 + 3 } 4 φ ω (φ + ω )) (7) Line Source Consider the geometry with a line source (with length L) situated in a plane parallel to a detector with circular aperture with radius R d, and the distance between midpoint of the linear source and the the detector s symmetry axis is d in [17]. The solid angle subtended by the line source is given by [17]: Ω = 4πd L ln( 1 + ( R d L/d (L/d) d ) L/d + (8) 4 + 4(R d /d) + (L/d) ) Simulation Result In the HINDA system, each NaI Core has a circular entrance with radius R d = cm, with distance 7 cm (between the center of target cell and the front face of NaI core). First, we calculate the Solid Angle for a point source to each NaI detector is msr. And if we treated our 3 He target as a 4cm-long line (in order to compare with the calculation in [17]), the solid angle given by (4) is 16.9 msr, about 93.7% of that for point source. We simulated the point source and a 4 cm-long line source in Geant4 shown in Fig. 41, the ratio of finite target to point source is 94.9%, which is consistent with the calculation results. 38

39 3 5 Counts 15 Point Source 4 cm line source Energy Deposition(MeV) FIG. 41: Simulation results for point source and line source 39