Energy difference betweem oblate and prolate solutions

Last modification: 1996/3/21

A figure ( GIF file of 14KB or PS file of 323KB ) shows the energy difference between the oblate and the prolate solutions of the HF+BCS with SIII. The abscissa is the neutron number N, while the ordinate is the energy of the oblate solution subtracted by that of the prolate solution. A circle is put only when both solutions exist for each nucleus. The circles belonging to the same isotope chain are connected by a line to guide the eyes. The atomic number Z can be known from the direction of the hand in each circle.

The energy difference is small near major-shell closures but large in the middle of the major shells. Apart from this shell fluctuation, one can see some overall trends. For each of the three major shells of neutrons divided by N=50, 82, 126, and 184, the largest energy difference is 4.70 MeV (¹²⁴Sm, delta=-0.25, 0.37), 6.58 MeV (¹⁶⁴Gd, delta=-0.22, 0.31), and 11.05 MeV (²⁵⁴No, delta=-0.17, 0.26), respectively; as the nucleus becomes heavier, the energy difference increases while the size of deformation decreases. For nuclei with N < 50, the changes along isotope chains are not so regular as in heavier nuclei and the oblate solutions often have lower energies than prolate ones. For nuclei with N > 50, oblate ground states are very rare and found only in nuclei very close to shell magics. The dominance of prolate deformations for N >50 may be attributed to the change of the nature of the major shells from the harmonic-oscillator shell to the Mayer-Jensen shell.