Effects of the Spin-Orbit and Tensor Interactions on the $M1$ and $E2$ Excitations in Light Nuclei

Abstract

The effects of varying the spin-orbit and tensor components of a realistic interaction on $M1$ excitation rates and $B(E2{)}^{\prime }s$ are studied on nuclei in the $0p$ and $1s-0d$ shells. Not only the total $M1$ but also the spin and orbital parts separately are studied. The single-particle energies are first calculated with the same interaction that is used between the valence nucleons. Later this stringent condition is relaxed somewhat and the $1s$ level is raised relative to $0d$. For nuclei up to ${}^{28}Si$, much better results i.e stronger $B(M1)$ rates are obtained by increasing the strength of the spin-orbit interaction relative to the free value. This is probably also true for ${}^{32}S$, but ${}^{36}Ar$ presents some difficulties. The effects of weakening the tensor interaction are also studied. On a more subtle level, the optimum spin-orbit interaction in the lower half of the $s-d$ shell, as far as $M1$ excitations are concerned, is substantially larger than the difference $E(J=3/2^{+}{)}_1-E(J=5/2^{+}{)}_1=5.2MeV$ in ${}^{17}O$. A larger spin-orbit splitting is also needed to destroy the triaxiality in ${}^{22}Ne$. Also studied are how much $M1$ orbital and spin strength lies in an observable region and how much is buried in the grass at higher energies. It is noted that for many nuclei the sum $B(M1{)}_{orbital}+B(M1{)}_{spin}$ is very close to $B(M1{)}_{total}$, indicating that the summed cross terms are very small.

39 pages, revtex 3.0

References in corpus (5)

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• Self weakening of the tensor interaction in a nucleus
• Scissors Modes and Spin Excitations in Light Nuclei including $\Delta N$=2 excitations: Behaviour of ${}^{8}Be$ and ${}^{10}Be$
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