ABSTRACT
At the end of last section it was pointed out that the quasi-spin scheme is not sufficiently general to describe correctly nuclear spectra. In ground states, ( S + ) N | 0 〉 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203739716/ff034a11-a369-4bc6-a470-f8cf1794dcb5/content/eq2134.tif"/> , with seniority ν = 0, the operator S + https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203739716/ff034a11-a369-4bc6-a470-f8cf1794dcb5/content/eq2135.tif"/> in (22.1) gives rise to mixing of configurations where nucleons are in several j-orbits. Yet this mixing is restricted by the equal amplitudes of the various S j + https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203739716/ff034a11-a369-4bc6-a470-f8cf1794dcb5/content/eq2136.tif"/> in (22.1). It turns out, as will be explained in the following, that this gives an over simplified description of eigenstates of the shell model Hamiltonian. The quasi-spin scheme is indeed a generalization of seniority in a single j-orbit to the case of several orbits. It seems, however, that also a generalization of the quasi-spin scheme is needed.
