Nucleon-Nucleon t-matrix Effective Interaction for (p, 2p)Reactions

Abstract

Abstract. In (p, 2p) reactions the p-p interaction is the main knockout interaction which acts in its full glory. Recent finite range (p, 2p) calculations used a parametrized spin-isospin dependent finite range tNN (r) -effective interaction operator which is a function of the distance between the nucleons alone. In the present work we have evaluated the nucleon-nucleon (N -N ) t-matrix effective interaction using the Reid soft core N -N interaction potential. In this we find that the proper t-matrix effective interaction is not only a function of spin and isospin of the interacting nucleons but is a strong function of the relative orbital angular momentum, L also. The radial behaviour of the tL(r) is also found to be very unconventional in that it is found to go to zero at r = 0 while in the conventional usage the t(r) is taken to peak at r = 0 because of its representation in terms of Yukawa functions. This very different behaviour of our calculated N -N t-matrix effective interaction operator is expected to make large changes in the Finite Range (FR-DWIA) predictions for (p, 2p) reaction cross sections. Besides this it is hoped that the marked differences one obtains in the behaviour of these tL(r)'s from different realistic N -N interactions through their resulting fits obtained for the (p, 2p) reactions will provide us a tool to select the proper N -N interaction out of the many available in literature. IntroductionFor a long time the medium energy (p, 2p) reactions on light medium mass nuclei were considered to be very good tools to obtain the absolute proton spectroscopic factors in those target nuclei. These expectations grew further with the recent advancements made in this field due to the incorporation of the sophisticated relativistic finite range methodology and the development of related computer programs [1,2,3,4,5,6]. For performing these advanced calculations one requires not only the scalar and vector components of the optical potentials which in the Dirac phenomenology fit the proton elastic scattering data but also requires the proper p-p t -matrix effective interaction, t( r). The conventional finite range distorted wave impulse approximation FR-DWIA calculations employ the meson exchange model t-matrix effective interaction by Love and Franey or Horowitz [7,8,9] or others in the same category [10,11] where the direct and exchange contributions to the amplitude are parametrized separately in terms of a number of Yukawa type functions in the first-order Born approximation. Thus far, the use of the Dirac phenomenology in the present relativistic finite range-distorted wave impulse approximation (RFR-DWIA) has not resulted much improvement in agreements with the data in comparison to the non-relativistic FR-DWIA formalisms. The existing studies of the sensitivities of the analyzing power to both the zero range (ZR) and finite range (FR) approximations on 40 Ca