Measurements were performed for the photodisintegration cross section of the deuteron for photon energies from 1.6 to 2.8 GeV and center-of-mass angles from 37° to 90°. The measured energy dependence of the cross section at θc.m. = 90° is in agreement with the constituent counting rules

Belz, J. E.

et al.

Kuhn, S. E.

Potterveld, D. H.

van den Brand, J.F. J.

White, J. L.

Zeidman, B.

English

Old Dominion University

Old Dominion University ODU Digital Commons Physics Faculty Publications Physics 1995 Two-Body Photodisintegration of the Deuteron up to 2.8 GeV J. E. Belz D. H. Potterveld S. E. Kuhn Old Dominion University, skuhn@odu.edu J.F. J. van den Brand J. L. White See next page for additional authors Follow this and additional works at: https://digitalcommons.odu.edu/physics_fac_pubs  Part of the Elementary Particles and Fields and String Theory Commons, and the Quantum Physics Commons Original Publication Citation Belz, J. E., Potterveld, Kuhn, S., . . . Vandenbrand, J. F. J., White, J. L., & Zeidman, B., et al. (1995). Two-body photodisintegration of the deuteron up to 2.8 GeV. Physical Review Letters, 74(5), 646-649. https://doi.org/10.1103/PhysRevLett.74.646 This Article is brought to you for free and open access by the Physics at ODU Digital Commons. It has been accepted for inclusion in Physics Faculty Publications by an authorized administrator of ODU Digital Commons. For more information, please contact digitalcommons@odu.edu. Authors J. E. Belz, D. H. Potterveld, S. E. Kuhn, J.F. J. van den Brand, J. L. White, B. Zeidman, and et al. This article is available at ODU Digital Commons: https://digitalcommons.odu.edu/physics_fac_pubs/459 VOLUME 74, NUMBER 5 PHYSICAL REVIEW LETTERS 30 JANUARY 1995 Two-Body Photodisintegration of the Deuteron up to 2.8 GeV J.E. Belz, 1·* D.H. Potterveld, 2 P. Anthony, 3 R.G. Amold, 4 J. Arrington, 1 D. Beck, 5 E.J. Beise, 1·t P.E. Bosted, 4 H.-J. Bulten, 6 M. S. Chapman,7 K. P. Coulter, 2·* F. Dietrich,3 R. Ent, 7·§ M. Epstein, 8 B. W. Filippone, 1 H. Gao, 1 R. A. Gearhart,9 D. F. Geesaman,2 J.-O. Hansen,7 R. J. Holt, 2-11 H. E. Jackson,2 C. E. Jones, 6·1 C. E. Keppel, 4 E.R. Kinney, 10 S. Kuhn, 11·** K. Lee,7 W. Lorenzon, 1-tt A. Lung, 4·** N.C.R. Makins,7 D.J. Margaziotis, 8 R.D. McKeown, 1 Z.E. Meziani, 11 R.G. Milner,7 B. Mueller, 1 J. Napolitano,1 2 J. Nelson,?.§* T.G. O'Neill, 1•91 V. Papavassiliou, 2 G. G. Petratos, 9 -1111 S. E. Rock, 4 R. E. Segel, 13 M. Spengos, 4 Z. M. Szalata, 4 L. H. Tao, 4 K. van Bibber,3 J. F. J. van den Brand, 6 J. L. White, 4 and B. Zeidman 2 1California Institute of Technology, Pasadena, California 91125 2 Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 3 Lawrence Radiation Laboratory, Livermore, California 94550 4Department of Physics, The American University, Washington, D.C. 20016 5Department of Physics, University of Illinois, Urbana, Illinois 61801 6Department of Physics, University of Wisconsin, Madison, Wisconsin 53706 7 Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 8Department of Physics, California State University, Los Angeles, California 90032 9 Stanford Linear Accelerator Center, Stanford, California 94309 10 Department of Physics, University of Colorado, Boulder, Colorado 80309 11Stanford University, Stanford, California 94305 12Department of Physics, Rensselaer Polytechnic Institute, Troy, New York 12180 13 Northwestern University, Evanston, Illinois 60201 (Received 18 May 1994; revised manuscript received 24 August 1994) Measurements were performed for the photodisintegration cross section of the deuteron for photon energies from 1.6 to 2.8 GeV and center-of-mass angles from 37° to 90°. The measured energy dependence of the cross section at Bc.m. = 90° is in agreement with the constituent counting rules. PACS numbers: 25.20.Dc, 12.38.Qk, 24.85.+p, 25.10.+s One of the most intriguing issues in nuclear physics is whether perturbative quantum chromodynamics (pQCD) is applicable to exclusive nuclear reactions at energies of a few GeV. While it is widely believed that pQCD is applicable at sufficiently high energies, the reason that exclusive reactions appear to be well described by the constituent counting rules [1,2) remains uncertain. Exclusive photo-reactions in few-body systems are well suited to address this question because large momentum transfers to the constituents can be obtained with photon energies of only a few GeV [3]. Previous studies [4,5) of deuteron photodisintegration suggested the onset of asymptotic scaling near a photon energy of 1.5 GeV, although agreement with the constituent counting rules was observed only over a small energy interval from 1.4 to 1.8 GeV. Furthermore, the data from 0.8 to 1.6 GeV were consistent with another QCD-based approach, the reduced nuclear amplitude analysis [6] discussed below. Here we report data up to a photon energy of 2.8 Ge V as a test of the asymptotic models. For a pQCD description of these reactions to be valid, the amplitudes must be dominated by short range processes involving hard gluon exchanges between quarks. Thus the observation of constituent counting rule behavior in reac-tions on the deuteron is particularly surprising, consider-ing that the nucleon-nucleon interaction has a hard core. Thus far, experimental observation of scaling according 646 0031-9007 /95 /74(5)/646(4)$06.00 to the constituent counting rules has been limited to sys-tems involving free hadrons and mesons, but not nuclei. Exclusive photo-reactions for the proton appear to scale according to the constituent counting rules above 2 Ge V [7]. Furthermore, high energy nucleon-nucleon reactions appear to scale according to the constituent counting rules above energies larger than the nucleon masses [8]. Thus data above a photon energy of 2 Ge V are crucial. The constituent counting rules [1,2) predict that the differential cross section du/ dt should scale with energy as l/sn- 2 , where s is the square of the center-of-mass energy and n is the total number of pointlike constituents involved in both the initial and final st.ates of the reaction. For the yd -+ pn reaction, we expect that when scaling is achieved, the cross section will have the form du h(0c_m.) - ---dt s 11 (I) where a calculation of the function h(0c.m.) requires a model of the dynamics. Traditionally, experimental evi-dence for asymptotic scaling in exclusive reactions con-sists of two tests: (i) whether the data obey the constituent counting rules [1,2) and Ci) whether hadron helicity con-servation [9] is satisfied. No polarization data exist for high energy photo-reactions to date, and all investigations have focused on cross section measurements. Because the momentum transfer per quark is rela-tively small (<1 GeV 2 /c 2 ) for existing elastic e-d scat-© 1995 The American Physical Society VOLUME 74, NUMBER 5 PHYSICAL REVIEW LETTERS 30 JANUARY 1995 tering data, the counting rules are not expected to apply. Brodsky and Chertok introduced the reduced nuclear am-plitudes (RNA) approach [10] to circumvent the problem. Indeed the counting rules do not work for the existing e- d cross section which extends up to 4 GeV [11]. In the RNA analysis, the amplitude is described in terms of quark interchange between the two nucleons; further-more, the soft components responsible for quark binding within the nucleons are removed by dividing out the em-pirical nucleon form factors so that the RNA approach is expected to provide a better description of reactions at intermediate energy. Following its dramatic agreement with the elastic e- d scattering cross section [11] from I to 4 (GeV /c)2, Brodsky and Hiller [6] applied the RNA approach to the yd-+ pn reaction. In this case, one has du dflc.m. where the FN('iN) are the nucleon form factors evaluated at the average four-momentum transfer to the outgoing nu-cleons, pf is the transverse momentum, and /(Oc.mJ is the reduced nuclear amplitude. If the RNA approach applies, the angular dependence is given by the nucleon form factors and the energy independent function / 2 (0c.m.). Presently, the reaction yd -+ pn provides the only other test of the RNA approach over a wide range of momen-tum transfers. As an alternative to the QCD-based models, T.-S. H. Lee [12] and S. I. Nagomyi et al. [13] have performed meson-exchange calculations for the yd-+ pn reaction. Although traditional meson-exchange models [12,14,15] describe the data rather well below a photon energy of I Ge V, the extension of these models to higher energies is problematic because of the large number of heavy resonances that can contribute and the need to include relativistic effects. The present experiment was performed in End Station A at the Stanford Linear Accelerator Center, using a technique similar to that of earlier work [5]. Electron beams from the NPI injector were accelerated to energies from 1.6 to 2.8 GeV and passed through a removable copper radiator 0.086 cm thick to produce a beam of bremsstrahlung photons. The uncollimated photons and remaining electron beam then passed through a 15 cm long cryogenic liquid deuterium target, as shown in Fig. 1. Charged particles from the target were detected in the 8 Ge V / c spectrometer by an array of plastic BREMSSTRAHLUNG SPEb~~o~~TER I RADIATOR ----E~-~-1.f2:aG;V----► ~ .. ----··r•"•---0=:)-~-----D2 n--_ TARGET FIG. 1. The target region showing the bremsstrahlung radia-tor, the deuterium target, and the spectrometer pivot. scintillators and a set of ten wire chambers. Protons were easily separated from deuterons (produced in the Al target windows) with a time-of-flight system. Both e+ and 7r+ trigger rates were negligible. In addition to photo-protons from d( y, p )n, there were several sources of background protons: electrodisintegra-tion of the deuterium target, events from the target win-dows, and photo-reactions with pion production, such as d(y,p)n7r 0 • Contributions from the target windows were removed by subtracting the results obtained with a liq-uid hydrogen target of identical dimensions. The yield from electrodisintegration was measured by repeating the procedure without the radiator present. This background was subtracted from the photodisintegration yield with an energy-dependent weighting function to account for the modification of the electron beam's flux and energy distri-bution by the radiator. Events with pion production were excluded by accepting only the photo-protons with the highest momenta. Finally, the bremsstrahlung photon's energy was calculated from the proton's momentum and scattering angle. The overall normalization of the inci-dent photon flux was calculated to within 3% with the thick-target bremsstrahlung computer codes of Matthews and Owens [16], and independently with a code devel-oped at Caltech [ 17]. The solid angle of the spectrometer was calibrated to 3% using the I H (e, e 1 p) and I H (e, e1 p) reaction, and is consistent with detailed simulations of the spectrometers [ 18]. The measured cross sections appear in Table I. It is convenient to discuss the results in terms of the quantity s 11 du/ dt, which should approach a constant value at fixed Oc.m. according to the constituent count-ing rules. This quantity is plotted versus E-y in Fig. 2(a) for the Oc.m. = 90° data, along with lower energy mea-surements. The data are consistent with the scaling be-havior suggested by the previous measurements [ 4,5] above E-y = 1.0 GeV. Fitting the available data above E-y = 1.15 GeV with the form du/dt oc l/sn yields n = TABLE I. Average photon energy, center-of-mass angle, and center-of-mass cross section and total uncertainty. Statistical and systematic errors have been added in quadrature. E-y 0c.m. da/df! Uncertainty (GeV) (deg) (nb/sr) (nb/sr) 1.522 84.2 3.8 0.5 1.539 52.5 5.6 0.7 1.543 36.7 10.9 1.1 1.934 88.3 1.0 0.2 1.956 52.6 1.6 0.3 1.961 36.7 3.3 0.5 2.321 89.4 0.27 0.05 2.343 52.6 0.43 0.08 2.344 36.8 1.2 0.2 2.721 89.4 0.08 0.02 2.748 36.8 0.5 0.1 647 VOLUME 74, NUMBER 5 PHYSICAL REVIEW LETTERS 30 JANUARY 1995 1.0 0.5 3.0 2.5 2.0 1.5 1.0 0.5 • PRESENT WORK c EXPERIMENT NE8.: \¾-J _ -!_: .. V .. --r >-....:_··· (a) ec.m.= 53' \ " \ ',, (b) Bc.m.= 37' (c) 0.0 ~-~~-~--~-~--~ o.o 0.5 1.0 1.5 2.0 2.5 3.0 E7 (GeV) FIG. 2. s 11d(T/dt vs E-y for (a) Bc.m. = 90°, (b) Bc.m. = 53°, and (c) 80 .m. = 37°. The present work is plotted as circles, and earlier data are plotted as squares [5] and crosses [19-22]. The dashed curve represents the reduced nuclear amplitudes analysis, the dotted line is the QGS model, the dot-dashed line is from [13], and the solid line is a traditional meson-exchange calculation, as discussed in the text. 11.2 ± 0.2, in good agreement with the counting rules. The dashed line in Fig. 2(a), representing the RNA analy-sis, was calculated from Eq. (2) using a value of j2(0c.mJ chosen to agree with a data point at Ey = 0.8 GeV. This curve falls below the high Ey data, and does not reach an asymptotic limit at these energies. The dot-dashed line, taken from [13], was calculated without including subnucleonic degrees of freedom, and is in good agreement with the data above Ey = 0.6 GeV. Nevertheless, the calculation is normalized to the data at 1 Ge V, and the energy dependence is determined by an arbitrary parameter. Recently, Kondratyuk et al. [23] have applied a quark-gluon string model (QGS) and Regge phenomenology to the reaction yd--+ pn (dotted line). The calculation at 90° is constrained by data at other angles, although there are a large number of free parameters. The model exhibits scalinglike behavior over a limited region of s, however, there is strong disagreement with the data at the highest energy. The solid line represents Lee's meson-exchange calculation [12], which is a traditional calculation that reproduces the measured NN phase shifts up to 2 Ge V and is also constrained by photo-meson production data. Below 500 MeV the calculation gives a reasonable description of 648 the data, but above I Ge V the calculation disagrees with both the energy and angular dependence. At the other two angles the calculation is off scale. The data at 0c.m. = 53°, shown in Fig. 2(b), are also consistent with the quark counting rules. A fit to the scal-ing behavior from 1.54 to 2.34 GeV gives n = 10.6 ± 0.6. The data are also consistent with the QGS model (dotted line). The dashed line represents the RNA calcu-lation with the same normalization as the 90° data. Be-cause calculations of .f2 (0c.m.) are not yet reliable, we choose .f2 (0c.mJ = constant and concentrate on the energy dependence of the fixed-angle cross sections. At 0c.m. = 37° the quantity s 11do-/dt is a rising func-tion of energy [Fig. 2(c)]. and a fit to the scaling behav-ior gives n = 9.5 ± 0.4. Both the RNA calculation and QGS calculation predict too large a cross section. The 37° data all correspond to transverse momenta of less than 1 (Ge V / c )2 to the outgoing neutron. The lack of scal-ing behavior here is consistent with a threshold in the ap-plicability of scaling behavior at a pf of approximately 1 (GeV/c)2. The results reported here demonstrate that at 0c.m. = 90° the cross section for the process yd--+ pn is in good agreement with the constituent counting rule predictions for incident photon energy greater than 1.5 GeV. Al-though this is qualitatively similar to measurements of other electromagnetic processes on elementary systems at energies of several Ge V, it is in sharp contrast to elastic electron-deuteron scattering where the asymptotic region has not yet been reached and the data are well described by the RNA approach. The present data disagree with the RNA approach at all three reaction angles. Whether the observed scaling at intermediate energy in exclusive reac-tions is indeed attributable to pQCD is still under debate [24]. Further insight into this question may be obtained with cross section measurements at higher energy [25] and from measurements of polarization observables in this reaction [26]. This work was supported in part by the U.S. De-partment of Energy, Nuclear Physics Division, under Contracts No. W-31-109-ENG-38 (Argonne), No. DE-FG02-86ER40269 (Colorado), No. W-7405-ENG-48 (LLNL), No. DE-AC02- 76ER03069 (MIT), No. DE-AC03- 76SF00515 (SLAC), No. DE-FG03-88ER40439 (Stanford), and by the National Science Foundation under Grants No. PHY-9014406 and No. PHY-9114958 (AU) 9115574 (Caltech), No. PHY-9101404 (CSLA), No. PHY-9213517 (Northwestern), No. PHY-9208119 (RPI), and No. PHY-9101404 (Wisconsin). *Present address: Department of Physics, University of Colorado, Boulder, CO 80309. tPresent address: Physics Department, University of Maryland, College Park, MD 20742. *Present address: Department of Physics, University of VOLUME 74, NUMBER 5 PHYSICAL REVIEW LETTERS 30 JANUARY 1995 Michigan, Ann Arbor, MI 48109. §Present address: Continuous Electron Beam Accelerator, Newport News, VA 23606. IIPresent address: Department of Physics, University of Illinois, Urbana, IL 61801. 'llpresent address: Physics Division, Argonne National Laboratory, Argonne, IL 60439. **Present address: Old Dominion University, Norfolk, VA 23529. ttPresent address: Physics Department, University of Pennsylvania, Philadelphia, PA 19106. **Present address: Caltech, Pasadena, CA 91125. §§Present address: SLAC, Stanford, CA 94309. llllpresent address: Physics Department, Kent State University, Kent, OH 44242. [l] V.A. Matveev, R.M. Muradyan, and A.N. Tavkhelidze, Lett. Nuovo Cimento 7, 719 (1973). [2] S. J. Brodsky and G. Farrar, Phys. Rev. Lett. 31, 1153 (1973). [3] R.J. Holt, Phys. Rev. C 41, 2400 (1990). [4] J. Napolitano et al., Phys. Rev. Lett. 61, 2530 (1988). [5] S.J. Freedman et al., Phys. Rev. C 48, 1864 (1993). [6] S. J. Brodsky and J. R. Hiller, Phys. Rev. C 28, 475 (1983). [7] R. L. Anderson et al., Phys. Rev. D 14, 679 (1976). [8] J. Ralston and B. Pire, Phys. Rev. Lett. 49, 1605 (1982). [9] S. J. Brodsky and G. P. Lepage, Nucl. Phys. A353, 247c (1981). [ 10] S. J. Brodsky and B. T. Chertok, Phys. Rev. D 14, 3003 (1976). [11] R. Arnold, B. T. Chertok, E. B. Dally, A. Grogorian, C. L. Jordan, W. P. Schiiltzs, R. Zdarko, F. Martin, and B. A. Mecking, Phys. Rev. Lett. 35, 776 (1975); R. Arnold et al., Phys. Rev. Lett. 58, 1723 (1987). [12] T.-S. H. Lee, Argonne National Laboratory Report No. PHY-5253-TH-88; T.-S. H. Lee, in Proceedings of the International Conference on Medium and High Energy Nuclear Physics, Taipai, Taiwan, 1988 (World Scientific, Singapore, 1988), p. 563. [13] S. I. NagornyI, Yu. A. Kasatkin, and I. K. Kirichenko, Sov. J. Nucl. Phys. 55, 189 (1992). [14] H. Arenhovel and M. Sanzone, Photodisintegration of the Deuteron-A Review of Theory and Experiment, Few Body Systems Supplement 3 (Springer-Verlag, Berlin, 1991). [15] J.M. Laget, Nucl. Phys. A312, 265 (1978). [16] J. L. Matthews and R. 0. Owens, Nucl. Instrum. Methods 111, 157 (I 973). [17] J.E. Belz, Ph.D. thesis, California Institute of Technol-ogy, 1994 (unpublished). [18] N. 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Two-Body Photodisintegration of the Deuteron up to 2.8 GeV

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Two-Body Photodisintegration of the Deuteron up to 2.8 GeV

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