Trinucleon round State Calculations with Graz Separable Potentials*

The results of trinucleon bound state calculations using with the recent version (Graz II) of Graz separable N IV potentials are presented. Graz II potentials frt not only the latest phenomonological phases rather accurately in the energy range 0 6OOAfeV(Z&), but. also provide a correct description of the deuteron data (l&,pd, Q, q). Their of&shell behavior is similar to that of the Paris potential, The results of calculations reported here are discussed and compared with those obtained for Graz I separable potentials and Yamaguchi forces used by Doleschall, and Site&o and Karchenko. The results show that Graz II potentials provide no improvement when compared with aforementioned forces used in a trinucleon system. The ‘Sr Graz 11 force seems to be unreasonably weak. Submitted to Physical Review C * Work supported by the Department of Energy under contract number DEAC03-76SFOO515. Recently a new version (Graz II) ‘-’ of the Graz separable potentials (GPX I)s-4 for the NN system was proposed. The construction of Graz II forces arose from the need to overcome the shortcomings of extant separable force models, which provide a technically convenient descripticn of the N N forces when used in a Faddeev-type calculation of a few-body system. The advantages of the Graz II forces over the Graz I, Doleshall,” and Piepere separable forces arc discussed in detail in Refs. 1 and 2. The o&shell behavior was studied by means of Noyes -Kowalski’ half-off-shell function and compared with Reid-soft-core’ and Paris” potential. A reasonable agreement between the separable and local forces was found only for the case of Graz II potentials. It is known that separable forces which reproduce low energy two-nucleon observables t,end to overbind the trinucleon system (triton for example by 3 4MeV).” The investigation of the problem of three nucleons serves as a source of additional information on the interactions between nucleons. In contrast to the problem of two nucleons at low energies the three-nucleon motion problem proves to be very sensitive to the form (off-shell behavior) of the two-particle potential. Therefore it is quite important to find a potential representing -the interaction between nucleons which, besides explaining the known experimental data of the deuteron bound state and two nucleon scattering will describe correctly the motion of threenucleons. Since the Graz II separable potentials achieved significant improvement in fitting the on-shell two-nucleon data according to the recent N-N phase shift analysisr2-” and also care has been taken in constructing a reasonable off-shell behavior, it became interesting to use these forces within a trinucleon system. In this paper we report on several trinucleon bound state calculations with different separable forces, The forces used are listed in Table I. Below analytic formulae for these forces are given (numerical values for the corresponding parameters can be found in references as indicated in Table I). The forces TNPSK, SNPSK, SNPDO and SNNDO are rank one separable forces of Yamagucbi type: