Systematics of the Quadrupole–Quadrupole Interaction and Convergence Properties

Abstract

Our main concern in this work is to show how higher shell admixtures affect the spectrum of a Q. Q interaction. We first review how, in the valence space, the familiar SU(3) result for the energy spectrum can be obtained using a coordinate space Q. Q interaction rather than the Elliott one which is symmetric in r and p. We then reemphasize that the Elliott spectrum goes as L(L + 1) where L is the orbital angular momentum. While in many cases this is compatible with the rotational formula which involves I(I+ 1 ), where I is the total angular momentum, there are cases, e.g., odd-odd nuclei, where there is disagreement. Finally, we consider higher shell admixtures and devise a scheme so as to obtain results, with the Q. Q interaction, which converge as the model spaces are increased. We consider not only ground state rotational bands but also those that involve intruder states.

Effects of the spin-orbit and tensor interactions on M1 excitations in light nuclei

“…The calculated T = 1 and T = 2 isovector orbital strengths (i.e. scissors modes) [16] are at much higher energies ≈ 19 M eV . With a Q · Q interaction, the T = 1 and T = 2 orbital strengths are degenerate.…”

“…In Table I we present the single-particle energies obtained for the (x, y) interaction with x = 1, y = 1 in both a small space and a large space. By the former we mean that the 16 O core is inert. In the large space, we allow 2hω excitations in the shell model diagonalization and we set the lowest state to zero [11].…”

“…Studies of 8 Be and 10 Be were previously carried out by Fayache, Zamick and Sharma [15,16]. The study was limited to the x = 1 y = 1 case, but the quadrupole-quadrupole interaction was also studied.…”

“…As shown by Fayache et.al. [16], with a Q · Q interaction one could obtain analytic results for the isovector orbital strength B l in 10 Be. The results were:…”