SHELL EFFECTS ON THE SPACING OF NUCLEAR LEVELS

Recent measurements of resonances in slow neutron total cross sections yield good estimates of the average level spacing, D, in medium and heavy nuclei. These spacings show large variations, by factors of 10³ to 10⁵, in the region of magic numbers of nucleons. There are also variations by smaller factors between nuclei with even and odd numbers of protons or neutrons. The even–odd effect is a co-operative phenomenon; it can be approximately treated by redefining the ground state to be used for a Fermi gas model. After this correction the gas model should predict D with reasonable accuracy since it is required only to define the density of a complete set of states. The magic number variations are shown to be fitted by an improved approximation to the single-nucleon level density. This is obtained from the observed sequence of single-particle spins and the assumption that the energy interval between spin subshells is constant. Fifty-two observed spacings are fitted by a two-parameter formula with an average uncertainty factor 3. Many of the larger remaining differences between observation and the predictions of the model are qualitatively explicable as expected departures from this uniform spacing hypothesis.