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Shell-model test of the rotational-model relation between static quadrupole moments Q(2^+_1), B(E2)'s, and orbital M1 transitions

S. J. Q. Robinson·L. Zamick·A. Escuderos·R. W. Fearick·P. von Neumann-Cosel·A. Richter
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Abstract

In this work, we examine critically the relation between orbital magnetic dipole (scissors mode) strength and quadrupole deformation properties. Assuming a simple K=0 ground state band in an even-even nucleus, the quantities Q(2^+_1) (i.e., the static quadrupole moment) and B(E2)_{0_1 \to 2_1} both are described by a single parameter--the intrinsic quadrupole moment Q_0. In the shell model, we can operationally define Q_0(Static) and Q_0(BE2) and see if they are the same. Following a brief excursion to the sd shell, we perform calculations in the fp shell. The nuclei we consider ({44,46,48}Ti and {48,50}Cr) are far from being perfect rotors, but we find that the calculated ratio Q_0(Static)/Q_0(BE2) is in many cases surprisingly close to one. We also discuss the collectivity of orbital magnetic dipole transitions. We find that the large orbital B(M1) strength in {44}Ti relative to {46}Ti and {48}Ti cannot be explained by simple deformation arguments.

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S. J. Q. Robinson, L. Zamick, A. Escuderos, R. W. Fearick, P. von Neumann-Cosel, A. Richter. 2005-08-25. Shell-model test of the rotational-model relation between static quadrupole moments Q(2^+_1), B(E2)'s, and orbital M1 transitions. https://doi.org/10.1103/physrevc.73.037306

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