The scissors mode, a magnetic dipole excitation-mainly orbital is usually discussed in terms of a transition from a J = 0 + ground state to a J = 1 + excited state. This is understandable because it follows from the way the experiment is performed-e.g. inelastic electron scattering. Here however, we start with the excited 1 + state and consider all possible transitions to J = 0 + ,1 + and 2 + states with final isospins. There is a larger transition to the 0 + 2 state than to ground. This has a much richer structure.We note that the "sum of sums" is independent of the interaction.
Wave functions arising form a pairing Hamiltonian E(0) i.e. one in which the interaction is only between J=0 + T=1 pairs, lead to magnetic dipole and Gamow-Teller transition rates that are much larger than those from an interaction E(Jmax) in which a proton and a neutron couple to J=2j. With realistic interactions the results are in between the 2 extremes. In the course of this study we found that certain M1 and GT matrix elements vanish with E(0). These are connected to seniority and reduced isospin selection rules. We find the surprising result that the M1 strength to the "single j scissors" is larger for a J=0 T=1 pairing interaction than it is for Q.Q.
We obtain wave functions for two protons and two neutrons in the gg/2 shell expressed as column vectors with amplitudes D (Jp,Jn). When we use a quadrupole-quadrupole interaction (Q ■ Q) we get, in many cases, a very strong overlap with wave functions given by a single set of unitary 9 -j coefficients-U9j = (O'j ) I I . * * V ( j j JB 10'j ) JpU j) ln)')-Here Jb = 9 for even I T = 0 states. For both even and odd T = 1 states we take JB equal to 8 whilst for odd 7, T = 0 we take JB to be 7. We compare the Q ■ Q results with those of a more realistic interaction.
Calculations of B(E2)'s and quadrupole moments in the shell g 9/2 region below 100 Sn are hampered by the fact that the inclusion of the g 7/2 configuration leads to model spaces that are too large to handle. Understanding the impact of specific orbit space functions in large-scale shell-model (LSSM) calculations helps to shed light on the validity of the results that are obtained. We therefore examine lighter nuclei if the f − p region where one can easily include all the orbitals, f 7/2 , p 3/2 , p 1/2 and f 5/2 . We perform such calculations but then take a step back and exclude the f 5/2 orbital. By comparing the two calculations we can hope to get insight into the importance of the missing spin-orbital partner in other regions.
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