Calculating the nuclear mass in the very high angular momentum regime

Macroscopic-microscopic methods are applied in the high-spin regime to calculate the nuclear binding energy (“mass”) as a function of proton number, neutron number, and angular momentum. Masses at high spin are calculated using the cranked Nilsson-Strutinsky model together with two different liquid drop models, the Lublin-Strasbourg drop model and the finite range liquid drop model. When comparisons are made with experimental data, a similar agreement between theory and experiment is obtained as for ground-state masses.

Figure 1

Experimental (top panel) and theoretical (middle panel) microscopic energies and their difference (lower panel) for some well-established high-spin bands in $A=109$–$158$ nuclei. The LSD model and a diffuse surface ($r_0=1.16$ fm, $a=0.6$ fm) has been used when calculating the first and second terms, respectively, of Eq. (3). Calculated states where all valence nucleons have their spin vectors aligned with the axis of rotation (terminating states) are encircled.

Figure 2

Difference in total energy between theory and experiment for the highest spin states of 10 nuclei with masses in the range A=20–194. In the lower panel, the same parameters as in Fig. 1 have been used whereas the FRLDM model has been used for the static liquid drop energy in the upper panel and the rigid moment of inertia has been calculated with a sharp surface in the middle panel.

Figure 3

Same difference as in the lower panel of Fig. 2 for six additional nuclei in the mass range A=72–175.

Figure 4

Calculated deformations of high-spin states for eight nuclei from Figs. 2 and 3, shown in the same spin interval as in those figures. Spin increases when going from right to left.