New Approach to the Analysis of Nucleon-Deuteron Breakup Data

Abstract

We propose calculations and measurements of N+ d breakup cross sections as a function of a new set of kinematic variables. When carried out as a function of these variables, separable-potential calculations predict cross sections which exhibit a very deep destructive interference minimum over a wide range of bombarding energies. We proposed a procedure for isolating the effect of the crucial M d2 amplitude on the cross section.A basic difficulty in attempting to extract new information about the NN force from measured three-body observables is that the observables are largely determined by what is already known about the NN force from the nucleon-nucleon data. The purpose of this article is to suggest a method of selecting the kinematical situations under which to perform N+d breakup measurements to facilitate the observation of short-range effects. (These we take to include both the off-energy-shell behavior of the NN force and explicit three-body forces.) We shall also present estimates of the variation in the cross section which might be caused by these short-range effects.Since three-body breakup amplitudes depend sensitively on the three final-state NN relative energies, we suggest that the relative energies be used to parametrize the kinematics and that comparisons of data and calculations should be done for fixed values of these relative energies. If in addition the direction of one of the finalstate nucleon momenta is held fixed, the cross section can depend only on the cm. rotation angle of a momentum triangle of fixed shape about the direction of the fixed nucleon momentum. This rotation angle, or an equivalent kinematic variable, is the continuous variable against which the cross section is to be measured and calculated in this scheme. The above specification fixes four independent kinematic variables, thus defining a one-dimensional kinematic locus in three-body phase space. We have computed the breakup cross section along a particular one of these constant-relative-energy loci using the YY model, 1 where the Watson-Faddeev integral equations are solved with separable spin-dependent s-wave NN interactions. 2 The model cross section is given bywhere F K is a kinematic factor, M q is the amplitude for breakup in the quartet state {S = • §-), and M dl and M d2 are the doublet-state (S= ?) amplitudes in which the two identical nucleons are coupled to spin 1 or 0, respectively. Results from model calculations of elastic N-d scattering phase parameters 3 with different NN forces lead us to expect that M d2 is much more sensitive to the details of the NN force used in the calculations than the other amplitudes. This can be understood because wave-function antisymmetry makes a state contributing to M d2 the only one in which there is a significant probability of finding the three nucleons simultaneously close together. 3 ' 4The advantage of the above procedure is that the s-wave parts of M q , M dU and M d2 are all constant along such a locus. If we assume that the deviation between the model-predicted M d2 a...

Tensor analyzing powerAyyfordpbreakup in the symmetric constant relative energy configuration

“…8 potential are responsible for the low values of Ayy found in Fig. 1 The Coulomb interaction between the two protons, which was totally neglected in our calculations, is not expected to account for the observed disagreement.…”

“…The A yy tensor analyzing power requires that the deuteron quan-tization axis lie in the plane defined by the beam and the outgoing neutron and be perpendicular to the beam direction.The SCRE geometry was first suggested in Ref [8]. as a good candidate for studying small effects associated with off-shell properties of the NN interaction or three-body…”

Measurement of theAyytensor analyzing power for theHLow1, Stephenson2, Olmer3 et al. 1991Phys. Rev. C6060View full textAdd to dashboardCite

“…More complete calcu-2276 1991 The American Physical Society lations have brought better agreement and the effect has been largely explained [6]. The symmetric constant relative energy (SCRE) geometry, first suggested by Jain et al [7], off'ers a geometry that features a strong interference minimum in the cross section as a function of the angles of the outgoing nucleons. It was suggested [7] that this minimum would provide a window where there would be sensitivity to the weaker effects associated with off-shell amplitudes or three-body forces.…”

“…The symmetric constant relative energy (SCRE) geometry, first suggested by Jain et al [7], off'ers a geometry that features a strong interference minimum in the cross section as a function of the angles of the outgoing nucleons. It was suggested [7] that this minimum would provide a window where there would be sensitivity to the weaker effects associated with off-shell amplitudes or three-body forces. In this geometry, all three nucleons are emitted in the center-ofmass frame at relative angles of 120' and with equal kinetic energies.…”