Equally Spaced Levels with T=1 two-body Matrix elements

TL;DR

This paper explores generating equally spaced and rotational spectra in nuclear models using only T=1 two-body matrix elements, revealing a new partial dynamical symmetry with specific interactions.

Contribution

It demonstrates that equally spaced and rotational spectra can be achieved with only T=1 matrix elements, introducing a novel partial dynamical symmetry in nuclear structure models.

Findings

Equally spaced spectra obtained with T=1 interactions.

Discovery of a new partial dynamical symmetry.

Spectra can resemble vibrational or rotational patterns.

Abstract

If one examines two-body matrix elements from experiment one notices that not only J=0 T=1 lies low but also J=1T=0 and J=J_{max} =2j T=0. It is sometimes thought that one needs both T=1 and T=0 two-body matrix elements to get equally spaced spectra of even I states i.e. vibraitonal spectra. We here attempt to get equally spaced levels with only those that have T=1 (even J).As an example we perform single-j calculations (f_{7/2}) in ^{44} T and ^{46} Ti. We then shift gears and decide to play around with the input two particle matrix, elements (not worrying about experiment) to generate interesting spectra e.g. rotaional spectra with and then without T=0 two-body matrix element. Of special interest is a new partial dynamical symmetry found when the "123", the "1234" etc.,interactions are used.