Nonstatic Nuclear Forces of the Triplet State in Momentum Space

Abstract

The nucleon-nucleon scattering in the uncoupled triplet states is described by the one­ boson-exchange model in conjunction with the Schrodinger equation in momentum representa­ tion. The nonstatic matrix elements due to the exchange of rc, (J), p and an isoscalar scalar meson are obtained. The nonstatic nuclear forces in momentum space are discussed in detail in connection with the LS force and the velocity-dependent term in coordinate space. Also the behavior of 3P0 phase shift at 25"'-'50 MeV is especially discussed. The meson coupling constants are adjusted to fit the experimentally determined phase shifts. The phase shifts obtained from our momentum-space calculations are in reasonable quantitative agreement with those obtained from the phase-shift analysis. § I. Introduction Analysis of the experimental data on nucleon~nucleon scattering at high energies has made it clear that there exists a strong nonstatic force. Investigation of the nonstatic effects such as the LS, the quadratic LS and the velocity­ dependent forces, is indispensable in order to determine nuclear forces. The semi­ phenomenological potentials with the above~mentioned nonstatic effects have already been obtained by several authors. 1 ) However, it is an open question whether the nonstatic effects are determined uniquely at small inter~nucleon distances. In an ordinary procedure to obtain the nonstatic nuclear forces, we first derive the nuclear potential in momentum representation, then transform it into coordinate representation. In this procedure, however, some of the nonstatic effects are left out of account. In order to give a complete description of the nonstatic interaction, the recoil effects and the retardation effects must be taken into account. Thus, we start with relativistic covariant interaction and treat the problem in momentum space throughout so that we are able to take the nonstatic effects and nonlocality into account as accurately as possible. Momentum~space calculations in conjunction with the Schrodinger equation have not been performed throughly compared to coordinate-space calculations. However, momentum-space calculations are advantageous in dealing with the nonstatic effects and nonlocality, and make it possible to obtain essential understanding of the nonstatic nuclear forces 2 a), 2 b) (hereafter we refer to Ref. 2a) as I). In I, we analyzed nuclear forces in the singlet states in order to discuss the problems of the repulsive core