Pseudo-mirror nuclei with A=100 and A=130

Abstract

A striking similarity in the level structures of pairs of even-even nuclei with A = 100 and A = 130 is pointed out. This agrees with Casten's method of classifying nuclear energy levels as a function of N,N,,, where N, and N,, are the numbers of valence proton and neutron pairs. It is shown that this is the natural consequence of the underlying basis of the single particle states of a pseudo-SU(3) model, and that pairs of nuclei in these two mass regions with the same N,N, can be seen as 'pseudo-mirror' nuclei. In a series ( 1-51 of recent experiments at Daresbury Laboratory the way in which the deformations of nuclei vary with Z and N in the light, rare-earth region (A - 130) has been mapped out. The results are summarised in figure 1 which shows E~, the quadrupole deformation derived from Grodzins' phenomenological formula (6,7), as a function of neutron number on either side of the N= 82 closed shell. The striking contrast in the way changes on the two sides of the figure, with the abrupt transition between N = 88 and 90 and a smooth transition for N< 82, is now understood in terms of the 2 = 64 subshell closure and the dominant role (8,9) of the n-p interaction as the mechanism driving towards deformation. Casten (lo-131, in a series of recent papers, has attempted to unify the energy systematics of all the even-even nuclei in a single scheme. He finds a considerable simplification of the known energy systematics if E(4:)/E(2:) is plotted as a function of N,N,, where N,N, is the product of the number of neutron bosons (N,,) and proton bosons (NI) counted from the nearest neutron and proton closed shells respectively. This scheme is underpinned by a theoretical model (14) in which the n-p interaction has a monopole plus quadrupole form. Casten's basic postulate is that nuclei with the same value of N,N, will have the same E(4:)lE(2:) ratio and their structures will be similar. He finds that if careful account is taken of subshell closures then various properties of the nuclei in different mass regions, including the A - 130 region, lie on smooth curves as a function of N,N,,. These properties include E(2;), E(4:)/E(2:), B(E2; 2:-0;) and the quadrupole moments of the first excited 2' states. The new data ( 1-51 on the light rare-earth nuclei fit smoothly into these systematics. Further we may now compare the data on the nuclei in the light, rare-earth region with data on the neutron-rich nuclei with A-100. Figure 2 shows the energy systematics of the light, even-even, cerium and neodymium isotopes. They are matched with the level schemes of the even-even molybdenum and zirconium