Study of the Q.Q Interaction- Single Particle Behavior to Elliott's Rotations

TL;DR

This paper investigates the effectiveness of the quadrupole-quadrupole (Q.Q) interaction in shell model calculations, demonstrating its ability to produce spectra resembling Elliott's rotational model without momentum terms, across different shell spaces.

Contribution

It shows that Q.Q interaction can yield useful single particle and collective spectra in shell model calculations, emphasizing the importance of single particle energies.

Findings

Q.Q interaction produces J(J+1) spectra with B(E2) values differing from the rotational model.

Spectra include both even and odd J states, starting from J=0.

Results are consistent in single j shell and full S-D shell spaces.

Abstract

We perform shell model calculations using a quadrupole-quadrupole interaction (Q.Q).We show results in single j shell spaces and the full S-D shell . We show that one gets useful results with Q.Q in both spaces.. We emphasize the importance of the choice of single particle energies in order to obtain the results of Elliott using a Q.Q interaction without the momentum terms. We show a J(J+1) spectrum for a ground state band but with B(E2)'s different from the rotational model. We also show excited J(J-1), J((J-1) and J(J+3) spectra.We find spectra starting with J=0 which have both even J and odd J members.