2 - The pairing force and seniority  pp. 33-51

The pairing force and seniority

By David M. Brink and Ricardo A. Broglia

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Evidence for pairing correlations

The nucleus 208Pb is well described by the independent particle model in terms of closed shells in both neutrons and protons. The absence of low-lying states supports this hypothesis. The shell model would then describe the low-lying levels of 207Pb in terms of the states of a single neutron hole. The observed energies, angular momenta and parities are in good accord with this picture, although small admixtures of more complicated configurations must be invoked to account for some fast electromagnetic decays (see Sections 9.1 and 9.2). The next step is to interpret the levels of 206Pb in terms of two holes, which are combinations of the single-hole states of 207Pb, interacting through a residual interaction. The dramatic effect of the internucleon force is shown by the fact that there is only one excited state below 1.2 MeV, compared with the five we would get in the independent hole approximation (see Fig. 2.1). This becomes even more striking in 204Pb, where the independent hole picture predicts about thirty levels within 1 MeV of the ground state, whereas again only one is observed (Mottelson (1996)).

Another indication of the importance of the residual interaction among nucleon pairs is the well-known difference in physical properties between even and odd nuclei. For example, studies of cosmic abundances show that nuclei with even proton and neutron numbers are much more abundant, and thus more stable, indicating stronger binding energies.