Measurements of the Drell-Hearn-Gerasimov Integrand for the Deuteron

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1 Measurements of the Drell-Hearn-Gerasimov Integrand for the Deuteron Blaine orum * (University of Virginia) Rob ywell (University of Saskatchewan) Brad Sawatzky (Temple University) Henry Weller * (Duke University) for the GDH Collaboration May 11, 9 bstract We are proposing to measure the integrand of the Drell-Hearn-Gerasimov integral for the deuteron from as close to threshold as proves possible to the maximum photon energy available at HIGS where the only contributing reaction is expected to be d γ, n p. These measurements will complement measurements made elsewhere of the corresponding integrals for the nucleons, making possible a determination of the source of any violations of the Drell-Hearn-Gerasimov Sum Rule that may emerge for the nucleons. They will also provide another polarization observable to complement measurements using linearly polarized photons and measurements of induced neutron polarization. The measurements will use the polarized target currently under development and the Blowfish detector. For the initial measurements beam energies of 8, 1, and 16 MeV will be employed. * Spokesperson

2 Introduction We are proposing to measure the integrand of the Drell-Hearn-Gerasimov integral for the deuteron from as close to threshold as proves possible to the maximum photon energy available at HIGS where the only contributing reaction is expected to be d( γ, n) p. These measurements will complement measurements made elsewhere of the corresponding integrals for the nucleons, making possible a determination of the source of any violations of the Drell-Hearn-Gerasimov Sum Rule that may emerge for the nucleons. They will also provide another polarization observable to complement measurements using linearly polarized photons and measurements of induced neutron polarization. The measurements will use the polarized target currently under development and the existing Blowfish detector. For the initial measurements beam energies of 8, 1, and 16 MeV will be employed. Motivation Spin-dependent Compton scattering of a photon with energy from a nucleon can be expressed as Born ( ) = (,, κ) M e ( ε ', ') ( ε, ˆ) ( α, β)( / ) ( ', k' ) (, kˆ) 3(,, 1, 1)( / M) ( ) ( ) ( ) ( ˆ) + e k k M + ε ε α β α β { } 3( 1 1)( + ε ', k' ε, k, ε ', k' ε, k α, β, α, β / M In the forward scattering limit ( ) f ( ) ε ' ε + ig( ) ( ε ' ε) where 4 f ( ) = f ( ) + f '( ) + O( ) α f ( ) = M f ' = α + β electric and magnetic polarizabilities 4 ( ) = ( ) + '( ) + ( ) g g g O g ( ) g ' ακ = M ( α + β ) = γ = M forward spin polarizability 3 ) 4

3 In 1954 M. Gell-Mann, M. Goldberger, and W. Thirring [1] showed that g' 1 γ = 4π 1/ 3/ 3 where 1/ ( 3/ ) is the total inelastic cross section when the target nucleon spin and the incident photon helicity are anti-parallel (parallel). Similarly, S. B. Gerasimov [] and, independently, S. D. Drell and. C. Hearn [3] showed in 1966 that, under the very reasonable assumption that g =, g ακ 1 d 1/ 3/ = = d, M 4 π the so-called Gerasimov-Drell-Hearn Sum Rule. Thus, the amplitudes for Compton scattering are related to integrals over the amplitudes for all inelastic processes. The GDH sum rule is customarily written 1/ 3/ 4 κ d = Sαπ, M where is the threshold photon energy for inelastic processes, M (κ ) is the mass (anomalous magnetic moment) of the target, and S is the spin of the target. t LEGS we measured the GDH integral for photon energies up to 4 MeV. These measurements will complement measurements from JLB. Measurements of the GDH integrand are also being pursued at Mainz ( MeV Eγ 8 MeV ) and Bonn ( 7 MeV Eγ 9 MeV ) [4]. Their results indicate that the GDH sum rule for the proton is confirmed while the situation for the neutron remains unclear[5]. This is due in no small part to the fact that in their experimental configurations they cannot isolate π and π + events unambiguously. In the fall of 6 we measured the GDH integrand at LEGS ( 18 MeV Eγ 4 MeV ) using the newly developed HD target. dded to the previously available Spin SYmmetry (SSY) detector was a time projection chamber to permit accurate determination of both the charge and momentum of reaction products, that is pions. nalysis of these data is currently underway. The GDH sum rule for a nucleon is κ d = π α m π

4 where π is the threshold energy for pion production from the nucleon, is the total inelastic photon cross section when the nucleon and photon angular momenta are parallel (anti-parallel), and m ( κ ) is the mass (anomalous magnetic moment) of the nucleon. Of course, one cannot measure to infinite photon energy so the LHS should be written max d = d + d π π max In testing the sum rule one must account for the unmeasured piece of the integral using a theoretical calculation. One question, therefore, is whether this correction is in fact correct. We can address this question by first noting that if the sum rule is valid then the difference between the sum rule value of the integral and the measured piece must equal the integral from to. max It was pointed out by Hosada and Yamamoto [6,7] and Gerasimov [] that these arguments could be applied equally well to the deuteron. That is, the deuteron could be treated as the object of the sum rule rather than simply as a source of neutrons. The resultant "GDH'' sum rule is given by d d κ d d = 4π α md where is the threshold not for pion production ( 145 MeV) but for photodisintegration (. MeV), and md ( κ d) is the mass (anomalous magnetic moment) of the deuteron. The sum rule values for the proton, neutron, and deuteron are Target κ GDH p μ b n μ b d μ b The GDH integral for the deuteron can be separated into three pieces d d d d d d d d max π d = d d d.6 b + + = π μ max The first term on the RHS will be measured at HIγ S; the second term was measured at LEGS and elsewhere. For the high photon energies relevant to the third (unmeasured) piece we note that to the order of.1% the deuteron can be treated as the sum of a neutron plus a proton plus trivial corrections. Thus, if the sum rule is valid then the sum

5 of the unmeasured pieces of the GDH integral for the neutron and proton must equal the unmeasured piece of the deuteron. dding these to the measured pieces of the deuteron GDH integral should yield a value in agreement with the sum rule prediction. If such agreement is observed, then we can conclude that the sum rule is valid and calculating the "unmeasured" pieces of the neutron and proton integrals will be a test of nucleon models. If no agreement is observed, then something is wrong with the sum rule. erhaps the assumption of unsubtracted dispersion relations? The forward spin polarizability is customarily written g' ( α β ) S + d 3 γ = = π Thus, in measuring the GDH integrand we will also measure the forward spin 3 polarizability. It should be noted, however that the strong 1 weighting means that only data obtained with the lowest photon energies make any significant contribution. separate proposal entitled Detailed Study of Deuteron hotodisintegration in the Energy Range 1 13 MeV has also been submitted. That proposal focuses on significant discrepancies observed between theory and experiment in d( γ, n) p, d( γ, n) p, and d( γ, n ) pfor photon energies of about 1-13 MeV. t this energy and others the proposed measurements of the GDH integrand will provide complementary polarization data to existing measurements of d( γ, n) p and d( γ, n) p. Combined, they will provide a stringent test our understanding of this most fundamental nuclear system. M Experiment Figure 1 shows the calculation of H. renhovel et al. [8] of the cross section differences entering the GDH Sum Rule. The GDH integral is clearly dominated by the near-threshold, E γ < 5 MeV region. However, precisely measuring deuteron photodisintegration in this region requires a scintillating target to ensure that neutrons detected in the Blowfish correspond to a nuclear event in the target. This capability will not be initially available in the polarized target. Therefore, initial measurements will be made with higher incident photon energies where a scintillating target is not required. Butanol CHOH 4 9 -based hydrogen/deuterium targets contain substantial amounts of carbon and oxygen. To avoid the need to eliminate neutrons ejected from the oxygen or carbon from those detected in the Blowfish initial measurements will be made at photon energies below MeV. The photon energies at which we plan to run are 8, 1, and 16 MeV. 16 MeV is the photon energy for which the cross section difference is most positive. Because the

6 Figure 1: The cross section difference entering the GDH Sum Rule integral. ote that the abscissa scale is logarithmic so the area under the curve is proportional to the contribution to the sum rule integral. total cross section is falling rapidly above E γ 4 MeV, 16 MeV is also close to where the cross section asymmetry ( ) ( ) Moreover, it is an energy at which we have data on d( γ, n) = + is expected to be largest. p [9]. 1 MeV is in the middle of the region where significant disagreements exist between theory and experiment [1,11]. 8 MeV is the energy at which the asymmetry is predicted to be zero. finite value for the asymmetry would give a clear indication of the magnitude of any discrepancy between theory and experiment. While the forward spin polarizability will be measured later when lower beam energies and a scintillating target are used, the data we will obtain during this initial run will not make an appreciable contribution to the forward spin polarizability integral. Figure shows the integrand and clearly demonstrates that beam energies of greater than 6 MeV do not contribute to determining the forward spin polarizability The Blowfish detector [1], with its associated electronics and data acquisition system, is in place and ready for use. new simulation package will be required since the target (and beam) will be oriented perpendicular to the detector axis of symmetry; in previous experiments the beam entered along the axis. The existing 5-paddle beam

7 Figure : The integrand in the expression for the deuteron forward spin polarizability. ote that the integral is determined solely by data taken with photon energies below 6 MeV. monitor, cross calibrated with a sodium iodide detector will be used to monitor the beam flux. The target is nearing completion but work remains. The heat exchangers are currently at CER being affixed to the target cylinder. The only components that remain to be ordered are the microwave guides required to carry the polarizing rf power to the target cell. Some target monitors which have been purchased remain to be configured. Based on Don Crabb s experience we anticipate that the target will be moved to HIGS for final installation towards the end of 9. The experiment proposed here could be run in spring 1. Since this will be the first use of this target we have based count rate estimates on 6 conservative estimates of parameters. We assume that the beam flux will be 5 1 photons per second through a cm collimator. The target length will be 4 cm; the polarized deuteron density will be.8 times that of water; the deuteron polarization was assumed to be 4%. The neutron detection efficiency was assumed to be about 15%. With these assumptions, including time for reversing the target polarization, we estimate that five days of two-shift operation will be required.

8 References 1. M. Gell-Mann, M. Goldberger, and W. Thirring, hys. Rev. 95 (1954) S.B. Gerasimov, Sov. J. ucl. hys. (1966) S.D. Drell and.c. Hearn, hys. Rev. Lett. 16 (1966) K. Helbing, roc. Third Int. Symp. On the GDH Sum Rule and its Extensions, orfolk, US (4) S. Hoblit et al., hys. Rev. Lett. 1 (9) M. Hosada and K. Yamamoto, rog. Theor. hys. 36 (1966) M. Hosada and K. Yamamoto, rog. Theor. hys. 36 (1966) H. renhovel, W. Leidemann, and E. Tomusiak, Few-Body Syst. 8 () 147; private communication 5 and later. 9. M. Blackston, h.d. thesis, recision Measurements of Deuteron hotodisintegration using Linearly olarized hotons of 14 and 16 MeV, Duke University, R. Schiavilla, hys. Rec. C7 (5) 341; private communication, B. orum et al., Detailed Study of Deuteron hotodisintegration in the Energy Range 1 13 MeV, roposal to HIGS C, B. Sawatzky, h.d. dissertation, Measurement of the eutron symmetry in d γ, n p near Threshold, University of Virginia, 5.