On the geometrical shape of the single particle spin-orbit potential

Abstract

A good description of the single particle shell model states near the Fermi surface, after including core polarization correction, can be obtained by taking identical geometrical shapes for both central and spin orbit potential thus reducing the number of free parameters in the scattering analysis. This bary centric approach also reproduces the charge distribution admirably. PACS: 21.10.PcThe physical picture behind the nuclear structure studies through nuclear reactions is describable in terms of an average one-body potential. Though the replacement of the interactions among the nucleons by the average potential is a drastic simplification, yet it is a common practice. This one-body potential consists of mainly two parts -a central potential of realistic nature (Woods-Saxon type), and a spin-orbit potential necessary for description of spin dependent interactions. The simplest approach is to write down the forms that are allowed by general invariance arguments [1]. Greenlees and Pyle [2] established in a systematic and careful analysis of the proton elastic scattering cross-sections and polarization data over a wide mass region between 4~ and 2~ that the radius parameter rso of the spin orbit potential is smaller than that of the central part of the Woods-Saxon potential used. This difference of radial extent has been interpreted by Greenlees, Pyle and Tang [3] in terms of the short range character of the nucleon-nucleon spin-orbit interaction. This difference of geometry in central and spin-orbit potential was further high lighted in the work of Rost [4]. In the case of 2~where the single particle picture has maximum validity, Rost obtained better Z 2 for both neutron and proton states, by using different radius parameters for central and spin-orbit potential. Rost's suggestion of using r~o=0.75r o is now widely accepted in calculating the single particle energies and wave functions for a wide range of nuclei and has been found to be crucial for the evaluation of the shell gap in the super heavy region [5]. In a recent reevaluation [6] of parameters of the Woods-Saxon potential which generates the single particle spectrum near the Fermi surface of 2~ results were obtained in tune with the earlier findings. It has also been proven [7] that even in lower shell region one can generate the requisite level bunching effect by altering only the strengths of central and spin-orbit potentials. However, in the present work we will show that this difference in geometrical shape is not the only solution for obtaining a reliable spectrum of single particle states of closed shell nuclei. It has been conclusively shown that there is another way of getting a unique set of Woods-Saxon parameters, identical in geometry for both the central and spin-orbit components, which gives good Z2-fit with the observed single particle spectra of 2~ We first calculate the bary centers of the different spin-orbit doublets (SOD) for the proton and neutron states in 2~ from the observed single particle spectra [6]. The binding energies of the...

Utility of a global set of potential parameters from the orbit radii measurements of valence nucleons

“…As the single particle shell model gets its maximum support in the lead region [13,14], we have optimized the potential parameters of WoodsSaxon shape for the doubly closed shell nucleus 2~ both for protons and neutrons. The method has been elaborated earlier [15]. Then we have interpolated the central potential for the lower mass nuclei assum-…”