Odd-Jpairing in nuclei

Abstract

We point out a simplicity that arises when we use an interaction in which only an energy with odd J is non-zero. The emphasis is on J = Jmax and in particular J = 9 + in the g 9/2 shell. It is noted that high overlaps can be deceptive. In many cases a single set of unitary 9-j coefficients gives either an exact or a very good approximation to the wave function of a non-degenerate state. The many degeneracies that occur in these calculations are discussed and explained.

Analytical and numerical calculations for the asymptotic behavior of unitary9jcoefficients

“…As was noted in [1] at first glance U (2, j) seems to fall of exponentially with j. This suggests a form Ae −αj (2) For this form ln(|U (2, j)|) = ln(A) − αj.…”

“…In previous works [1,2] Zamick and Escuderos addressed the problem of maximum j-pairing. In the course of these studies they found that results simplified by the fact that a certain coupling matrix element was very small.…”

“…with J p and J n both even [1,2]. In this work we will first conduct numerical studies to much higher angular momenta and with greater precision for the unitary 9j coefficients using Mathematica.…”

“…But as one went to higher shells this U 9j becomes rapidly smaller. Indeed behavior was parametrized as Aj m e −αj [2,3]. The consequence of a very weak coupling is that for small total angular momentum I the lowest 2 states for a maximum J pairing interaction are (jj) 2j (jj) 2j (jj) Jp (jj) Jn I and (jj) 2j (jj) (2j−2) (jj) Jp (jj)…”

Shell model calculations ofB(E2)values, static quadrupole moments, andgfactors for a number ofN=Znuclei

“…Besides the references already mentioned, we add Refs. [11]- [17]. Also, to a large extent, one can regard earlier studies of properties in the f 7/2 shell as precursors to analogous studies in the g 9/2 shell.…”