## Abstract

Shell model calculations are performed for magnetic dipole excitations in ^{8}Be and ^{10}Be, first with a quadrupole-quadrupole interaction (Q • Q) and then with a realistic interaction. The calculations are performed both in a 0p space and in a large space which includes all 2ℏω excitations. In the 0p with Q • Q we have an analytic expression for the energies of all states. In this limit we find that in ^{10}Be the L = 1 S = 0 scissors mode with isospin T= 1 is degenerate with that of T = 2. By projection from an intrinsic state we can obtain simple expressions for B(M1) to the scissors modes in ^{8}Be and ^{10}Be. We plot cumulative sums for energy-weighted isovector orbital transitions from J = 0^{+} ground states to the 1^{+} excited states. These have the structure of a low-energy plateau and a steep rise to a high-energy plateau. The relative magnitudes of these plateaux are discussed. By comparing ^{8}Be and ^{10}Be we find that contrary to the behaviour in heavy deformed nuclei, B(M1)_{orbital} is not proportional to B(E2). On the other hand, a sum rule which relates B(M1) to the difference (B(E2)_{isoscalar} - B(E2)_{isovector}) succeeds in describing the difference in behaviours in the two nuclei. The results for Q • Q and the realistic interactions are compared, as are the results in the 0p space and the large (0p + 2ℏω) space. The Wigner supermultiplet scheme is a very useful guide in analyzing the Shell model results.

Original language | English (US) |
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Pages (from-to) | 123-154 |

Number of pages | 32 |

Journal | Annals of Physics |

Volume | 251 |

Issue number | 1 |

DOIs | |

State | Published - Oct 10 1996 |

## All Science Journal Classification (ASJC) codes

- General Physics and Astronomy

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