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Generalized seniority for favored J does not equal 0 pairs in mixed configurations

Nov, 1969
15 pages
Published in:
  • Nucl.Phys.A 137 (1969) 129-143
  • Published: 1969
DOI:
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Abstract: (Elsevier)
By assigning a pseudo-spin and pseudo-orbital angular momentum ( b -spin and c -spin) to the single-particle states in a mixed configuration of identical nucleons, it is possible to classify as B = 0 objects both the favored pair operators of the surface delta interaction (SDI) and the multipole moment operators, (the latter under suitable assumptions). The favored pair is defined for each J as the specific superposition of two-particle states acted upon by this separable interaction. The SDI is diagonal in the total B - and C -spins; the eigenvalues of a ( B , C ) multiplet are independent of the total angular momentum J, ( J = B + C ) ; and all states with B = case1 2 v are degenerate ( v = total seniority). For the case of a degenerate doublet of levels ( l j , l +2) j + 1), e.g. ( d 5 2 g 7 2 ) or ( f 7 2 h 9 2 ), the specification, B = 0, defines the fa the number of nucleons not members of favored pairs. Exact calculations for the ( d 5 2 g 7 2 ) system show that states with B < 1 2 v cluster closely about their centers of gravity; therefore, to a good approximation the SDI can be replaced by a generalized pairing interaction depending only on B and v . Possible generalizations are discussed for the case of many degenerate single-particle levels, where this generalized pairing interaction is no longer a good approximation.