Precision measurements of low energy deuteron photodisintegration confront theory (Dated: October 30, 2006)

Transcription

1 Precision measurements of low energy deuteron photodisintegration confront theory (Dated: October 30, 2006) APS/123-QED Angular distributions of the d( γ, n)p cross section have been measured at beam energies of 3.5, 4.0, 6.0 and 10 MeV. The High Intensity γ-ray Source (HI γs) provided the nearly monoenergetic beams, while neutrons were detected using a segmented array of 88-detectors. Analysis of the these data reveal a striking discrepancy with current low energy models of the nucleon-nucleon (NN) interaction. The most prominent feature of the discrepancy lies in an observed front-back (polar angle) asymmetry in the center of mass photo-neutron yield that is not represented in the theory. The magnitude of this difference systematically rises as the γ-ray energy falls toward threshold. The source of this disagreement is not yet understood. PACS numbers: Valid PACS appear here The study of deuteron photodisintegration has provided great insight into the nature of the strong interaction. This includes the development and testing of realistic meson exchange potentials, the role of meson exchange (MEC) and isobar (IC) currents, and the question of relativistic effects[1]. More recently the interaction has been studied using the techniques of effective field theory where powercounting provides information on the accuracy of the calculations. At higher energies (E γ 20 MeV) there are considerable data and agreement with theory is generally acceptable. However, the quantity and quality of experimental data rapidly falls as the energy approaches the deuteron photodisintegration threshold (2.22 MeV). Below 10 MeV there are only a handful of d(γ, n)p measurements[2 10]. Of those, only half include data taken below E γ =6 MeV and all had quite limited angular coverage (a typical set-up employed 2 4 detector cells distributed azimuthally at a one or two polar angles). This notable deficit is largely due to the historical lack of clean, sufficiently intense γ-ray beams in that energy range, and the difficulties associated with detecting low-energy neutrons (the recoil protons typically have insufficient energy to make it out of the target). In addition, the inverse n-p capture reaction in the near-threshold region plays a key role in Big Bang nucleosynthesis calculations and is often referred to as the Baryometer of the universe. Understanding this reaction at these very low energies is therefore of great interest. As will be seen below, the results reveal severe discrepancies between these experimental results and state-of-the-art theoretical predictions, indicating that our understanding of this most fundamental nuclear process is incomplete. The present work was performed at the High Intensity γ-ray Source (HI γs) located at the Duke Free- Electron Laser Laboratory (DFELL) on the campus of Duke University. This facility [11] produces nearly 100% linearly polarized γ-rays which are nearly mono-energetic (de/e < 2% in the present case) by Compton backscattering free-electron laser photons from highly relativistic electrons in the Duke storage ring. The polarization vector is in the horizontal plane, which we label as φ = 90. The neutron detector (BLOWFISH) consists of 88 BC-505 liquid scintillator cells distributed on the surface of an imaginary 4 cm (16 ) radius sphere centered on the target. The cells are divided among 8 arms equally distributed in φ, 11 cells to an arm, and cover a solid angle of roughly 1/4 of 4π. The choice of scintillator allows pulse-shape discrimination (PSD) to enhance neutral particle ID, and the detector frame is free to rotate about the beam-axis to aid in the reduction of systematic errors. After being collimated to a 2.5 cm diameter spot size, the beam impinged upon a thin-walled deuterated target. At higher energies ( MeV) the target cell was filled with D 2 O and identical H 2 O targets were used to study background and systematic effects. A deuterated scintillating target was employed at the lowest energies of 3.5 and 4.0 MeV. This active target was used to detect the recoiling protons from the photodisintegration and provided an additional signal for distinguishing good events from background. Data at 4.0 MeV were obtained using both the active and passive targets. The active targets were deemed unnecessary at the higher energies. Following careful ADC and TDC calibration, cuts on the PSD parameter, active target signals (when applicable), energy and timing information were made to provide an initial signal/background separation. The resulting cleaned data were then fitted to a function parametrizing the neutron time-of-flight (ToF) response plus background. The fit allowed the remaining background to be removed and the resulting neutron ToF peak was then integrated over an appropriate interval to determine a true neutron yield

2 2 for each detector cell. The accurate separation of signal from background involved the development of a detailed Monte Carlo simulation within the GEANT3 framework[12]). The external GCALOR simulation package [13] was integrated through its GEANT interface to provide correct nx cross sections for neutrons with kinetic energies below 20 MeV. In addition to the expected attenuation and smearing of the recoil neutron distribution due to scattering in the target and detector material, the neutron yields were found to be more sensitive to energy threshold and time-of-flight (ToF) cuts than anticipated. The reason for this is somewhat subtle and centers on the details of how neutron detection works in a scintillator. At low neutron energies (below a few MeV), the relatively rapid change in the np scattering cross section combines with the very non-linear light-output response (LOR) of a scintillator to low energy recoil protons (and other charged recoil particles) to make neutron detection efficiency a strong function of the incident neutron kinetic energy, detector energy threshold, and ToF cut. Extensive followup has shown that these systematic phenomena are now well understood[14], but it underscored the requirement for careful monitoring of cell gains over the course of the experiment, an accurate measurement of the LOR for the cells (ours came from a dedicated measurement in 2002 [15]), and the need for a detailed, well-tested simulation. It should be noted that these systematic issues and sensitivities are inherent in any neutron detection device using a (liquid) scintillator and are in no way unique to our set-up. However, there is a notable lack of discussion of these phenomena in the literature. When such issues were addressed they were typically handled using techniques extrapolated from higher energy studies that we found do not apply at lower energies. The large solid angle coverage of the BLOWFISH was critical to the identification and understanding of these phenomena. Indeed some of these effects are manifestly impossible to isolate from data taken using the common two or four cell apparatus with cells distributed azimuthally in multiples of 90. The center-of-mass (CoM) d( γ, n)p differential cross sections were extracted from the experimental neutron yields by parametrizing the cross section as a series of associated Legendre polynomials (ALPs) coupled with a φ-dependent piece:[25] σ(θ,φ) = c 00 + l c lm Y lm(θ,φ). (1) m l where, m 0 0,±1 0,±1,±2 0,2 0,2. The Y lm are trigonometric forms of the spherical harmonics: Y lm(θ,φ) = { P m l (cosθ)cos(mφ) : m 0 P m l (cosθ)sin( m φ) : m < 0 (2) where θ (φ) is the polar (azimuthal) angle. Of the 13 terms in this expansion, only nine terms contain information about the underlying d( γ, n)p interaction [16]: c 00 is a measure of the total cross section, while c lm, l = {1... 4},m = {0, 2}, parametrize the angular distribution of the differential cross section. The four remaining parameters (c 1±1,c 2±1 ) violate the symmetry of the photodisintegration reaction and were added to monitor for potential systematic contributions associated with the experimental apparatus or beam characteristics. Equation 1 was normalized by the magnitude of the isotropic term (c 00 ) as a concession to the fact that ours was not an absolute cross section measurement but instead parametrized the shape of the differential cross section. Of the four non-physical parameters, only c 11 was found to be inconsistent with zero in a few of the data sets. The exact value varied, but appeared correlated with a particular set of beam tune parameters (i.e. a baseline configuration for a given γ-ray beam energy). Investigation with the Monte Carlo showed that the measured deviation could be easily understood as an effect of the beam position shifting 1 2 mm off the nominal beam axis. It is worth noting that when we simulated an exaggerated transverse shift of the beam axis by 10 mm (generating a c 11 value 5 the maximum observed) there was no statistically significant impact on the value of the other extracted parameters no doubt a benefit of the the orthogonality of the ALP basis functions. The values for the eight nuclearphysics coefficients are presented in Table I. Remove the Asym discussion altogether? The physics asymmetry (Σ(θ)) may be computed from the extracted cross sections (σ(θ, φ)) using: Σ(θ) = σ(θ,φ = 90 ) σ(θ,φ = 0 ) σ(θ,φ = 90 )+σ(θ,φ = 0 ) (3) Figure 2 present the extracted physics asymmetry at θ = 90 vs. incident γ-ray energy. This representation of the data has the advantage of inheriting the smallest associated systematic errors. This was due to the cross section ratio implicit in the asymmetry calculation providing (at least) a first order cancellation of run-to-run and cell-to-cell variations in neutron detection efficiencies. However, detailed analysis [14] proved that the second order effects play

3 3 REMOVE the old coeffs column before submission Leg. Coeff. 3.5 MeV 4.0 MeV 6.0 MeV 10.0 MeV Old Coeff. c 10 (a 1 ) 0.23 ± ± ± ± 9 p 2 c 20 (a 2 ) ± ± ± ± p 3 c 22 (e 2 ) 2 ± ± ± 6 70 ± 5 p 4 c 30 (a 3 ) ± ± ± ± p 6 c 32 (e 3 ) 0.04 ± ± 8-0 ± ± 2 p 5 c 40 (a 4 ) ± ± p 7 c 42 (e 4 ) ± 1 4 ± 4 p 8 TABLE I: Normalized associated Legendre polynomial coefficients for the d( γ, n)p differential cross section. The 3.5 and 4.0 MeV run-sets were fit with the highest order multipole coefficients c 4m fixed at zero. All coefficients have been normalized such that c The associated uncertainties are a combination of the fit-errors and the systematic uncertainties summed in quadrature Data (fit) Arenhovel - - c 1 0 c 2 0 c 2 2 c 3 0 c 3 2 c 4 0 c 4 2 Parameter Index 10.0 MeV 6.0 MeV 4.0 MeV 3.5 MeV c 1 0 c 2 0 c 2 2 c 3 0 c 3 2 c 4 0 c 4 2 Parameter Index FIG. 1: Normalized associated Legendre polynomial expansions for the CoM d( γ, n)p differential cross section for E γ =10.0, 6.0, 4.0, and 3.5 MeV are presented (circles) vs. Arenhövel s potential model predictions [17, 18] ( s). The 3.5 and 4.0 MeV run-sets were fit with c 4m fixed at zero. All coefficients have been normalized such that c a significant role even in an asymmetry measurement. One reflection of those complications were the rather large errors assigned to the lower energy data-sets. Those errors were considerably larger than the (statistically dominated) errors reported in a concurrent measurement that followed our experimental approach at HI γs [2]. Modeling the systematic behavior of the 2- and 4-detector configurations used to collect those data in the current simulation indicates that those data would be more susceptible to threshold, ToF, and secondary neutron scattering artifacts. Unfortunately, the limited solid-angle coverage, and lesser systematic controls coupled with significantly lower statistics suggest that the true systematic uncertainties associated with those data should be much larger than were estimated at the Σ (θ=90 ) Present work Tornow et al. (2003) del Bianco et al. (1981) Arenhövel (NORMAL+MEC+IC+REL) E γ [MeV] FIG. 2: Neutron asymmetry in d( γ, n)p vs incident γ-ray energy at θ = 90 in the CoM frame. The solid diamonds are the present work, open circles are Tornow [2], open triangle is from del Bianco [10], and the solid line is a theoretical calculation from Arenhövel [17]. See text for discussion of the errors. time. Attempts to reconcile the discrepancy with the Tornow group were unsuccessful. Nevertheless, the present asymmetry data were found to be in reasonable agreement with potential model calculations by Arenhövel [17], with the possible exception of an emerging systematic over-prediction of the neutron asymmetries as E γ moves toward threshold. At the high end, our data are in good agreement with an older measurement at E γ =9.9 MeV [10]. The χpt EFT calculations [19] generate asymmetries nearly identical to Arenhövel over the energy range of interest. End of Asym discussion The same data are plotted along with ALP coefficients computed from Arenhövel s potential model [17, 18] in Figure 1. There is reasonable agreement at higher energies, but a progressively larger

4 4 disagreement in parameters c 10 and c 30 appears as the γ-ray energy approaches threshold. Those terms are proportional to cos(θ) and encode much of the front-back (i.e. polar angle) asymmetry in the CoM cross section. c 32 is also proportional to cos(θ), but is additionally linked to the azimuthal asymmetry through a cos(2φ) factor. (c 32 also exhibits a growing discrepancy between data and Arenhövel as E γ approaches threshold, but it is considerably less pronounced.) The present data are also in marked disagreement with a 1987 measurement by Stephenson et al. [4]. The latter data comprise the most extensive data set in this energy region and claim the highest precision. Figure 3 present their LAB-frame differential cross section ratios (σ(θ)/σ(90 )) against results drawn from our data. The Partovi/Argonne V14 curves are from [4]. The current figure adds a calculation by Arenhövel (dashed line), and includes additional data from [6]. In general, the data tend to lie closer to the Partovi/AV14 calculations, but the overall agreement is not very satisfactory. See Schiavilla plot, understand difference in arenhovel s curves choosing initial values for the parameters randomly distributed over the range [ 1,1]. Every fitting trial converged to the same set of values. Additional trials were run with various coefficients fixed at zero. Again, while the overall χ 2 increased (as one would expect), the free parameters all converged to same values as in the general fit no doubt a reflection of the orthogonality of the terms in the associated Legendre polynomial expansion. FIG. 4: Ratios of the extracted expansion coefficients (c l0 /c l2 ) v.s. E γ. The dashed lines reflect constant ratios predicted by fundamental spin-coupling constraints. The solid curve reflects a calculation by Arenhövel [17]. The 6 MeV c 30 /c 32 data point is omitted as the associated coefficients are so close to zero that the ratio is ill-defined. σ(45)/σ(90) σ(135)/σ(90) σ(155)/σ(90) E γ (MeV) FIG. 3: Energy dependence of σ(θ)/σ(90 ) for the d(γ, n)p reaction in the LAB frame. The present results are plotted as solid diamonds, the open squares are from [6], and the solid triangles are from [4]. The solid line represents a calculation from Partovi [20] which is indistinguishable from the Argonne AV14 model [21] (see [4]). The dashed line reflects a recent calculation by Arenhövel [17]. A large effort was made to understand the source of these discrepancies and discount any potential problems with either the detector apparatus or the analysis procedure[14]. A few of the most stringent checks are described below. The stability of the fitting procedure was tested by FIG. 5: c 10 /c 30 as a function of E γ. The dashed lines reflects the constant ratio predicted by fundamental spincoupling constraints. The solid curve reflects a calculation by Arenhövel [17]. The 6 MeV data point is omitted as the associated coefficients are so close to zero that the ratio is ill-defined. Ratios extracted from Stephenson [4] and Smit [9] are presented for comparison. The d( γ, n)p differential cross section may also be expanded in terms of the reduced transition matrix elements (TMEs) contributing to the reaction. The formalism of Ref. [16] was used to generate expressions which relate the Legendre polynomial expansion coefficients to the amplitudes and phases of the TMEs. The associated Racah algebra leads to some quite fundamental relationships between several of the coefficients. In particular the following four general expressions should hold: c 10 /c 30 = 1, c 20 /c 22 = 2, c 30 /c 32 = 6, c 40 /c 42 = 12. (4) Figures 4 and 5 present the ratios computed from

5 5 the present data. The agreement is quite striking. The ratio c 10 /c 30 may also be computed for the Stephenson data provided the c 40 contribution to the azimuthal cross section (small, but unmeasured in that experiment) is accounted for using either Arenhövel s calculation (green points in Figure 5) or from our data (blue). It is interesting to note that the resulting Stephenson ratios are systematically and significantly different from -1. Moreover there appears to be a clear downward trend from -1 starting at 10 MeV. This trend is supported by the independent data of Smit and Brooks [9] which give a ratio of about -2.3 for E γ = 2.75 MeV. So, the early data appear consistent with one another, and generally agree with calculations better than the present data. But, the present data generate coefficients which appear to satisfy general constraints extremely well, much better than the other data where comparisons are possible. One potential explanation for this discrepancy may be that the energy dependence of the neutron detector efficiencies was not correctly accounted for in the older data. We found that the details of the LOR function and precise monitoring of the PMT gains were critical to accurately reproducing the measured PH and ToF spectra over the full solidangle coverage of the BLOWFISH in the simulation. Common parametrizations that were contemporary with the earlier data (i.e. Cecil et al.[22], and others based on the same world data) were found to perform very poorly at these low energies. Note that this failure was not a fundamental error in the parametrization, but a reflection of the lack of accurate neutron data over that energy range. An updated LOR parametrization based on our follow-up measurements has been published in Pywell et al.[23]. In conclusion, the unexpected forward-backward asymmetry evident in our data (represented in parameters c 10 and c 30 ) is in marked disagreement with current theoretical models. Such non-spherical components must arise from the E2 and/or M2 transition elements, the most probable being an interference between the p- and d-wave terms, i.e. between E1 and E2 radiation. Preliminary investigation of the present data within the TME framework suggests the (dominant) E1 p-wave strength is in quite good agreement with theory. However, the E2 strength is in violent disagreement with theory at the two lowest energies. Calculations suggest a factor of 30 times greater than the theoretical prediction at 3.5 MeV. A theoretical explanation of this observation is lacking. [1] H. Arenhövel and M. Sanzone, Few Body Syst. Suppl. 3 (1991) 1. [2] W. Tornow et al., Mod. Phys. Lett. A 18 (2003) 282. [3] E. Schreiber et al., Phys. Rev. C 6106 (2000). [4] K.E. Stephenson et al., Phys. Rev. C 35 (1987) [5] V. Likhachev et al., Nucl. Phys. A 628 (1998) 597. [6] Y. Birenbaum et al., Phys. Rev. Lett. 61 (1988) 810. [7] A. de Graeve et al., Nucl. Phys. A 530 (1991) 420. [8] A. de Graeve et al., Phys. Lett. B 227 (1989) 321. [9] F. Smit and F. Brooks, Nucl. Phys. A 465 (1987) 429. [10] W. del Bianco et al., Phys. Rev. Lett. 47 (1981) [11] V.L. et al., Phys. Rev. Lett. 78 (1997) [12] CERN, GEANT Detector Description and Simulation Tool, [13] C. Zeitnitz and T. Gabriel, GCALOR Simulation Package, University of Mainz (Zeitnitz), and Oak Ridge National Laboratory (Gabriel), [14] B. Sawatzky, A Measurement of the Neutron Asymmetry in d( γ, n)p Near Threshold, Ph.D. dissertation, University of Virginia, [15] J. Ives, Simulation and measurement of the response of the BLOWFISH detector to low-energy neutrons., M.Sc. thesis, University of Saskatchewan, [16] H. Weller et al., 50 (1992) 29. [17] H. Arenhövel, Private communication, [18] H. Arenhövel, W. Leidemann and E.L. Tomusiak, 28 (2000) 147. [19] Proceedings of 22nd International Symposium on Weak and Electromagnetic Interactions in Nuclei, World Scientific, Singapore, [20] F. Partovi, Annals of Physics 27 (1964) 79. [21] R. Wiringa, R. Smith and T. Ainsworth, Phys. Rev. C 29 (1984) [22] R. Cecil, B. Anderson and R. Madey, Nucl. Instrum. Methods 161 (1979) 439. [23] R. Pywell et al., Nucl. Instrum. Methods A 565 (2006) 725. [24] G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic Press, Inc., San Diego, 1985). [25] The sign convention of the ALPs follows Arfken [24].