Quadrupling in the Shell Model

A nonunitary Lorazo transformation of the space of the one-particle states is generalized to isospin-dependent transformations. The generators of the ten-dimensional quasispin algebra for protons and neutrons depend on two sets of the dynamical parameters. This algebra is spectrum generating for the generalized pairing and quadrupling Hamiltonian. We suggest a new fourth operator based on the quadrupling interaction, which-in the special case of the definite weights of the T = 0 and T = 2 quadrupling forces-is essentially equivalent to the one introduced by Hemenger and Hecht. However, our definition has physical motivation.

[1]  B. Lorazo.  Collective pairing states and non-unitary representations of the quasi-spin group , 1975 .

[2]  B. Lorazo.  Parameter-dependent quasispin group , 1975 .

[3]  I. Talmi.  On a group-theoretical mistreatment of generalized seniority , 1975 .

[4]  B. Lorazo,et al.  Validity of the Talmi's mass formula for single closed shell nuclei , 1974 .

[5]  Y. Smirnov,et al.  A new projected basis in the theory of five-dimensional quasi-spin , 1973 .

[6]  M. Yamamura,et al.  Quadrupling and pairing in the shell model , 1972 .

[7]  J. Eichler.  Multiple transfer of T = 1 pairs and quadruples in heavy ion collisions , 1971 .

[8]  E. Olivieri,et al.  Effective four-body interaction in light nuclei , 1971 .

[9]  A. Bose,et al.  Connection Between Symplectic, Quasispin, and Generalized Bogoliubov Groups , 1971 .

[10]  K. Hecht,et al.  Five-dimensional quasispin toward a complete classification of the isospin characteristics of shell-model states in the seniority scheme , 1970 .

[11]  H. Lipkin,et al.  ON THE APPLICATION OF THE GROUP Sp(4) OR R(5) TO NUCLEAR STRUCTURE. , 1969 .

[12]  K. Hecht.  Five-dimensional quasi-spin the n , T dependence of shell-model matrix elements in the seniority scheme , 1967 .

[13]  B. H. Flowers,et al.  A four-body operator in nuclear spectroscopy , 1965 .

[14]  K. Hecht.  Five-Dimensional Quasispin. Exact Solutions of a Pairing Hamiltonian in theJ−TScheme , 1965 .

[15]  J. C. Parikh.  THE ROLE OF ISOSPIN IN PAIR CORRELATIONS FOR CONFIGURATIONS OF THE TYPE (j)N , 1965 .

[16]  V. Soloviev.  Effect of quadrupole correlations in light nuclei , 1960 .