The finite range simple effective interaction including tensor terms

TL;DR

This paper investigates the effectiveness of a finite range simple effective interaction in predicting single particle level crossings in isotopic chains without tensor terms, highlighting the need for tensor contributions in certain shell closure cases.

Contribution

It demonstrates that the finite range simple effective interaction can predict some level crossings without tensor terms, but emphasizes the necessity of including tensor terms for accurate shell gap predictions.

Findings

Successfully reproduces the crossing at N=46 with K(ρ₀)=240 MeV

Shows tensor terms are essential for accurate shell gap predictions in certain isotopes

Highlights limitations of the central-only interaction in shell structure modeling

Abstract

The prediction of single particle level crossing phenomenon between $2p_{3/2}$ and $1f_{5/2}$ orbitals in $Ni$- and $Cu$-isotopic chains by the finite range simple effective interaction without requiring the tensor part is discussed. In this case the experimentally observed crossing could be studied as a function of nuclear matter incompressibility, $K(\rho_0)$. The estimated crossing for the neutron number $N$=46 could be reproduced by the equation of state corresponding to $K(\rho_0)$=240 MeV. However, the observed proton gaps between the $1h_{11/2}$ and $1g_{7/2}$ shells in $Sn$ and $Sb$ isotopic chain, and the neutron gaps between the $1i_{13/2}$ and $1h_{9/2}$ shells in $N$=82 isotones, as well as the shell closure properties at $N$=28 require explicit consideration of a tensor part as the central contribution is not enough to initiate the required level splittings.