dorsal/arxiv
View SchemaTopics Concerning the Quadrupole-Quadrupole Interaction
| Authors | M. S. Fayache, Y. Y. Sharon, L. Zamick |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9609057 |
| URL | https://arxiv.org/abs/nucl-th/9609057 |
Abstract
We address some properties of the quadrupole-quadrupole ($Q \cdot Q$) interaction in nuclear studies. We first consider how to restore $SU(3)$ symmetry even though we use only coordinate and not momentum terms. Using the Hamiltonian $H=\sum_i (p^2/2m + m/2 \omega^2 r_i^2) -\chi \sum_{i < j}Q(i) \cdot Q(j) - \chi/2 \sum_i Q(i) \cdot Q(i)$ with $Q_{\mu}=r^2 Y_{2,\mu}$, we find that only 2/3 of the single-particle splitting ($\epsilon_{0d}-\epsilon_{1s}$) comes from the diagonal term of $Q \cdot Q$ -the remaining 1/3 comes from the interaction of the valence nucleus with the core. On another topic, a previously derived relation, using $Q \cdot Q$, between isovector orbital $B(M1)$ (scissors mode) and the ``difference'' ($B(E2, isoscalar)-B(E2, isovector)$) is discussed. It is shown that one needs the isovector $B(E2)$ in order that one get the correct limit as one goes to nuclei sufficiently far from stability so that one subshell (neutron or proton) is closed.
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"abstract": "We address some properties of the quadrupole-quadrupole ($Q \\cdot Q$)\ninteraction in nuclear studies. We first consider how to restore $SU(3)$\nsymmetry even though we use only coordinate and not momentum terms. Using the\nHamiltonian $H=\\sum_i (p^2/2m + m/2 \\omega^2 r_i^2) -\\chi \\sum_{i \u003c j}Q(i)\n\\cdot Q(j) - \\chi/2 \\sum_i Q(i) \\cdot Q(i)$ with $Q_{\\mu}=r^2 Y_{2,\\mu}$, we\nfind that only 2/3 of the single-particle splitting\n($\\epsilon_{0d}-\\epsilon_{1s}$) comes from the diagonal term of $Q \\cdot Q$\n-the remaining 1/3 comes from the interaction of the valence nucleus with the\ncore. On another topic, a previously derived relation, using $Q \\cdot Q$,\nbetween isovector orbital $B(M1)$ (scissors mode) and the ``difference\u0027\u0027\n($B(E2, isoscalar)-B(E2, isovector)$) is discussed. It is shown that one needs\nthe isovector $B(E2)$ in order that one get the correct limit as one goes to\nnuclei sufficiently far from stability so that one subshell (neutron or proton)\nis closed.",
"arxiv_id": "nucl-th/9609057",
"authors": [
"M. S. Fayache",
"Y. Y. Sharon",
"L. Zamick"
],
"categories": [
"nucl-th"
],
"title": "Topics Concerning the Quadrupole-Quadrupole Interaction",
"url": "https://arxiv.org/abs/nucl-th/9609057"
},
"schema_id": "dorsal/arxiv",
"source": {
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"variant": "snapshot-2026-03-01",
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