Statistical Theory of Deformed Nuclei

The changes in binding energy of ${}_{114}{}^{}{}_{}{}^{}X_{}^{298}{}_{}{}^{}$ under deformation into prolate spheroidal shapes have been calculated using the statistical theory of nuclei. The density is restricted only by the requirement that each equidense surface is a spheroid. It is found that the energy is minimized when the density has an approximately uniform surface thickness around the nucleus. To first order the change in binding energy is given well by the liquid-drop model, but at large deformation the statistical theory predicts less drop in energy and, consequently, a slightly more stable nucleus.