Energy levels for a three-dimensional bounded harmonic oscillator are obtained for intermediate distances of the boundary. Energy levels are found to depend on the dimensionless parameter ${\rho }_0=\left(\frac{\omega M}{\hslash }\right)R^2$. ${\rho }_0$ is the ratio of the strength of the oscillator levels ($\hslash \omega$) to that of the square well levels ($\frac{{\hslash }^2}{M{R}^2}$).

Adding a spin-orbit energy 30 times the Thomas value, nuclear energy levels are worked out for the two mass regions at $A=50\mathrm{} \mathrm{and} 90$. For ${\rho }_0=6\mathrm{}$, good agreement with the experimental level sequence is obtained.

• Received 14 March 1958

DOI:https://doi.org/10.1103/PhysRev.115.1681