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TMF, 1970 Volume 4, Number 2, Pages 208–215 (Mi tmf4145)

The Elliott scheme and its generalization

G. N. Afanas'ev


Abstract: A study is made of the symmetry propertiea of the quadrupole interaction in the field of a spherically symmetric oscillator. The noninvarlance group of the Hamiltonian describing this interaction is found to be $SO(3,2)$ for a two-dimensional and $Sp(3,3)$ for a three-dlmonslonal operator. It is shown that if vibrations of the generalized model are present at all in the standard model with pairing and quadrupole forces they only appear as a result of competition between these forces.

Received: 29.12.1969


 English version:
Theoretical and Mathematical Physics, 1970, 4:2, 784–789


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