Scissors Modes and Spin Excitations in Light Nuclei including $\Delta N$=2 excitations: Behaviour of ${}^{8}Be$ and ${}^{10}Be$

Abstract

Shell model calculations are performed for magnetic dipole excitations in ${}^{8}Be$ and ${}^{10}Be$ in which all valence configurations plus $2\hslash \omega$ excitations are allowed (large space). We study both the orbital and spin excitations. The results are compared with the `valence space only' calculations (small space). The cumulative energy weighted sums are calculated and compared for the $J=0^{+}$ $T$=0 to $J=1^{+}$ $T$=1 excitations in ${}^{8}Be$ and for $J=0^{+}$ $T$=1 to both $J=1^{+}$ $T$=1 and $J$=$1^{+}$ $T$=2 excitations in ${}^{10}Be$. We find for the $J=0^{+}$ $T$=1 to $J=1^{+}$ $T$=1 isovector {\underline {spin}} transitions in ${}^{10}Be$ that the summed strength in the {\underline {large}} space is less than in the {\underline {small}} space. We find that the high energy energy-weighted isovector orbital strength is smaller than the low energy strength for transitions in which the isospin is changed, but for $J=0^{+}$ $T$=1 to $J=1^{+}$ $T$=1 in ${}^{10}Be$ the high energy strength is larger. We find that the low lying orbital strength in ${}^{10}Be$ is anomalously small, when an attempt is made to correlate it with the $B(E2)$ strength to the lowest $2^{+}$ states. On the other hand a sum rule of Zheng and Zamick which concerns the total $B(E2)$ strength is reasonably satisfied in both ${}^{8}Be$ and ${}^{10}Be$. The Wigner supermultiplet scheme is a useful guide in analyzing shell model results. In ${}^{10}Be$ and with a $Q\cdot Q$ interaction the T=1 and T=2 scissors modes are degenerate, with the latter carrying 5/3 of the T=1 strength.

Comments: 51 pages, latex, 9 figures available upon request