ЭЛЕМЕНТАРНЫЕ ЧАСТИЦЫ И ПОЛЯ
THE RATIO Rdp OF THE QUASI-ELASTIC nd ^ p(nn) TO THE ELASTIC np ^ pn CHARGE-EXCHANGE-PROCESS YIELDS AT THE PROTON EMITTING ANGLE 0pMb = 0° OVER 0.55-2.0-GeV NEUTRON BEAM ENERGY REGION. EXPERIMENTAL RESULTS
© 2009 V. I. Sharov1)*, A. A. Morozov1), R. A. Shindin1), V. G. Antonenko2), S. B. Borzakov3), Yu. T. Borzunov1), E. V. Chernykh1), V. F. Chumakov1), S. A. Dolgii1), M. Finger4)'5), M. Finger, Jr.4), L. B. Golovanov1), D. K. Guriev1), A. Janata4), A. D. Kirillov1), A. D. Kovalenko1), V. A. Krasnov1), N. A. Kuzmin6), A. K. Kurilkin1), P. K. Kurilkin1), A. N. Livanov1), V. M. Lutsenko6), P. K. Maniakov1), E. A. Matyushevsky1), G. P. Nikolaevsky1), A.A. Nomofilov1), Tz. Panteleev3)'7), S. M. Piyadin1), I. L. Pisarev4\
Yu. P. Poluninp>, A. N. Prokofiev8), V. Yu. Prytkov1), P. A. Rukoyatkin1), M. Slunecka4),5), V. Sluneckova4\ A. Yu. Starikov1), L. N. Strunov1), T. A. Vasiliev1), E. I. Vorobiev1), I. P. Yudin6), I. V. Zaitsev1), A. A. Zhdanov8), V. N. Zhmyrov4)
Received May 20, 2008; in final form, December 29, 2008
New experimental results on ratio Rdp of the quasi-elastic charge-exchange yield at the outgoing proton angle dPl\ab = 0° for the nd — p(nn) reaction to the elastic np — pn charge-exchange yield, are presented. The measurements were carried out at the Nuclotron of the Veksler and Baldin Laboratory of High Energies of the JINR (Dubna) at the neutron-beam kinetic energies of 0.55, 0.8, 1.0, 1.2, 1.4, 1.8, and 2.0 GeV. The intense neutron beam with small momentum spread was produced by breakup of deuterons which were accelerated and extracted to the experimental hall. In both reactions mentioned above the outgoing protons with the momenta pp approximately equal to the neutron-beam momentum p„jbeam were detected in the directions close to the direction of incident neutrons, i.e., in the vicinity of the scattering angle #Pjlab = 0°. Measured in the same data-taking runs, the angular distributions of the charge-exchange-reaction products were corrected for the well-known instrumental effects and averaged in the vicinity of the incident-neutron-beam direction. These corrected angular distributions for every of nd — p(nn) and np — pn charge-exchange processes were proportional to the differential cross sections of the corresponding reactions. The data were accumulated by Delta—Sigma setup magnetic spectrometer with two sets of multiwire proportional chambers located upstream and downstream of the momentum analyzing magnet. Inelastic processes were considerably reduced by the additional detectors surrounding the hydrogen and deuterium targets. The time-of-flight system was applied to identify the detected particles. The accumulated data treatment and analysis, as well as possible sources of the systematic errors are discussed.
PACS:13.75.Cs, 25.40.Kv, 25.60.Bx, 25.10.+s
1. INTRODUCTION
1) Joint Institute for Nuclear Research, Veksler and Baldin Laboratory of High Energies, Dubna, Russia. , . -+11+
2)Russian Scientific Center "Kurchatov Institute", Moscow. lhls paper presents new expenmental n^ufe °n
3) Joint Institute for Nuclear Research, Frank Laboratory of the ratio Rdp of the charge-exchange quasi-elastic Neutron Physics, Dubna, Russia. differential cross section for the reaction nd — p(nn)
4)joint Institute for Nudear ^earc^ Mekpw Lab°ratory at the outgoing proton angle dp,lab = 0° to the elastic
5)fNuclearproblems Dubna, Russia. charge-exchange differential cross section for the
5)Charles University, Faculty of Mathematics and Physics,
Praha CZechRepublic np — pn reaction. Ihe intense quasi-monochromatic
6)Joint Institute for Nuclear Research, Laboratory of Particle neutron beam was produced by breakup of the Physics, Dubna, Russia. -
7)Institute for Nuclear Research and Nuclear Energy, Bulgar- 8)Petersburg Nuclear Physics Institute, Russian Academy of ian Academy of Sciences, Sofia. Sciences, Gatchina.
E-mail: sharov@sunhe.jinr.ru
deuterons accelerated by the Nuclotron of the Veksler and Baldin Laboratory of High Energies (VBLHE) at the Joint Institute for Nuclear Research (JINR, Dubna). The measurements were carried out at the neutron-beam kinetic energies of 0.55, 0.8, 1.0, 1.2, 1.4, 1.8, and 2.0 GeV.
In both nd ^ p(nn) and np ^ pn reactions the outgoing (scattered) protons with the momenta pp approximately equal to the neutron-beam momentum Pn,beam were detected in the directions close to the direction of incident neutrons, i.e., in the vicinity of the scattering angle dp>\ab = 0°. Thus we have considered such outgoing proton as the former beam neutron which was scattered at dp>cM = 0° and got the electric charge in the charge-exchange process.
The yields of the quasi-elastic and elastic scattering were measured with the D2 and H2 targets over the spectrometer angular acceptance 0 < p < 2n and 0 <9 < 30 mrad. They were corrected having taken into account the detector efficiencies and other well-known instrumental effects. These corrected yields were proportional to the corresponding differential cross sections.
The measurements were performed within the program of the JINR project Delta—Sigma experiment [1-3] (see also [30] in arXiv:0706.2195 [nucl-th]). The goal of this experimental program is to determine the imaginary and real parts of the all np ^ ^ np forward (9n,cM = 0)and backward (9n,cM = n) elastic-scattering amplitudes over the 1.2-3.7-GeV energy region. For this purpose the energy dependences of a sufficient data set of the np spin-dependent observables have to be obtained for the direct reconstruction of the np amplitudes (see, for example, [4]). In this highest energy interval of free polarized neutron beams such measurements are possible now only at the Nuclotron.
At the forward (9n,cM = 0) and backward (9n,cM = n) angles five complex invariant amplitudes a, b, c, d, and e from the amplitudes representation [5] which are the functions of the angle 9n,cM and energy En,cM, satisfy the following equations:
a(0) - b(0) = c(0) + d(0), e(0) = 0, (1.1)
a(n) - b(n) = c(n) - d(n), e(n) = 0. (1.2)
Therefore only three complex amplitudes are independent in these directions. The forward and backward scattering amplitudes are connected by the angular symmetry conditions [5] which differ for the isospin states I = 1 and I = 0. We assume that the I = 1 amplitudes are known. Consequently for the direct reconstruction of the np forward (or/and backward) amplitudes, altogether, at least six independent np
observables at either the forward or backward directions are needed (see below Eqs. (1.3)—(1.8)). Two np observables are well known, one of them is the spin-independent np total cross section aotot, the second one is the np ^ np differential cross section at On,cm = n
The research program Delta—Sigma foresees the measurements of total-cross-section differences AaL,T(np) and spin correlation parameters Aookk(np ^ np) and Aoonn(np ^ np) at On,cm = n for the longitudinal (L, along the incident nucleon momentum k) and transverse (T, along the perpendicular n to the k) beam and target polarization directions, respectively. The AaL,T(np) observables together with aotot (np) are linearly related to the imaginary part of the forward scattering amplitudes via three independent optical theorems [5]:
^otot = —lm[a(0) +6(0)], (1.3)
-A<7r = ^Im[c(0)+d(0)], (1.4)
-AaL = ^lm[c(0)-d(0)], (1.5)
where K is the CM momentum of the incident neutron. These three observables unambiguously determine the imaginary parts of all the three amplitudes.
The AaL,T(np) observables are to be measured in transmission experiments. Measurements of the -AaL(np) energy dependence were carried out at 10 different values of the polarized-neutron-beam energy from 1.2 to 3.7 GeV [6—11]. The L-polarized neutron beam at the Synchrophasotron facility of the JINR VBLHE and the Dubna L-polarized proton target were used. New measurements of the Aol,T(np) are expected in the near future when the new high-intensity source of polarized deuterons to be put in operation at the Nuclotron. This device will be based on the CIPIOS [12] equipment imported to Dubna from the Indiana University Cyclotron Facility.
The Aookk(np ^ np) and Aoonn(np ^ np) values are to be defined in the backward direction. These observables could be measured simultaneously with the corresponding AaL,T(np ^ np) experiments. The backward np observables are connected with the invariant amplitudes as follows [4]:
^(vr) = ^(|a|2 + |6|2 + |C|2 + |d|2), (1.6)
da
^¡AoonniTT) = l-[\a\2 - \b\2 - |c|2 + |d|2), (1.7)
da dñ
Aookk(n) = Re a*d + Re b*c. (1.8)
Using the known imaginary parts of the forward amplitudes transformed into the backward direction, the np differential cross section and the two spin correlation parameters A00kk(np) and A00nn(np) at $cm = n are sufficient to obtain the real parts of all the three amplitudes. But in contrast to the optical theorems at d = 0°, the scattering amplitudes in the backward direction are related to the np scattering observables by bilinear equations. Each of them may have, in principle, an independent ambiguity in the sign. The total ambiguity is then eightfold at most, and any independent experiment decreases it by a factor of two.
To reduce the total ambiguity in the scattering-amplitude determination, the Delta—Sigma Collaboration performed the measurements of the ratio Rdp = (da/dü)(nd — p(nn))/(da/dü)(np — pn) for the charge-exchange processes on the deuterium and hydrogen targets. A high-intensity unpolarized neutron beam was scattered either in the liquid D2 and H2 or solid CD2 and CH2 targets. The results of the experiments under discussion are listed below.
Following the theory developed in [13—18] the differential cross section for nd — p(nn) chargeexchange reaction at 0Pt\ab = 0p,cM = 0° within the impulse approximation, can be written as follows:
(da/dü)(nd ^ p(nn)) = = (2/3)(da/dQ)SD(np ^ pn),
(1.9)
Sections 2 and 3 describe the method of measurements and the essen
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