Quadrupole collectivity of summed magnetic dipole orbital strength using schematic interactions

Abstract

We perform shell-model calculations in Ne for the summed magnetic dipole orbital strength and spin strength with a schematic interaction consisting of single-particle splitting, an isospin-conserving pairing interaction, and a quadrupole-quadrupole interaction. We consider four channels: orbital excitations to J = 1+ T= 1 states, and then to J = 1+ T = 2 states; spin excitations to J= 1+ T = 1 states, and then to J=1+ T =2 states. For the orbital T~T channel, the summed M1 strength varies quadratically with the size of the quadrupole interaction x for small values of this parameter when degenerate singleparticle energies are used. Using realistic single-particle splitting does not destroy the quadrupole collectivity. The other three channels respond in different manners. We also consider linear-energyweighted sum rules for which analytic results are obtained. The relevance of this work to experiments on orbital strengths and their relations to quadrupole excitations is discussed.

Sum rules in the proton-neutron interacting boson model: Generalized treatment and specific applications

“…The EW magnetic dipole sum rule has been worked out already within the nulcear shell model, properly [22,23] as well as in the IBM-2 [13,14,24,25]. In the present paper, we start &om the more general results, described earlier, and stress a few aspects that have only been very brieBy addressed in the former papers.…”

“…Comparing expressions (22), (26), and (27), one finds, equating terms in g2, g2, and g g" the interesting results 1 = --(0~+lng Io+, )r. ", 1 (ox In&. los ) 5 from which we obtain the quite simplified expression for the NEW sum rule as (28) ) B(M1;0+~m 1~+) = --(gg") f = --(g-g-)' (oi IL-.…”

“…2 &(g-g-)'~"(oi lndloi)+& (46) with The erst term on the right-hand side follows from the contribution of the quadrupole interaction and is proportional to the expectation value of the proton-neutron quadrupole force in the ground state [22]. The latter is a measure of the quadrupole deformation energy which can also be related to the corresponding binding energy in a quadrupole deformed mean field such as the Nilsson model [23].…”

Scissors Modes and Spin Excitations in Light Nuclei IncludingΔN=2 Excitations: Behaviour of8Be and10Be

“…We note that the Zheng Zamick sum rule [28] is able to handle the divergent behaviour between 8 Be and 10 Be. This sum rule involves the difference between isoscalar and isovector summed B(E2) strength, whereas corresponding expressions by Heyde and de Coster [32] based on the I.B.A.…”

“…A simple self-consistent Nilsson model was shown to give the second plateau at twice the energy of the first plateau [28,32]. That is to say the high energy rise was equal to the low energy rise.…”