A Hartree-Fock-like variational calculation which is specifically directed toward the treatment of axial and triaxial deformations in light nuclei is presented. By choosing Cartesian harmonic-oscillator wave functions to be the trial wave functions and taking the oscillator length parameters $b_x[={\left(\frac{\hslash }{m{\omega }_x}\right)}^{\frac{1}{2}}]$, $b_y$, $b_z$ in each major oscillator shell to be the variational parameters, the capacity for deformation is built into the wave functions from the outset and a substantial reduction in the calculational effort is achieved. These variational wave functions are not strictly orthogonal, but the effects of this approximation appear to be relatively unimportant. A realistic two-body effective interaction is employed which depends on the average density of the nucleus under consideration. It is constructed from nuclear matter theory and has been shown to contain the most important physical aspects of the Brueckner $G$ matrix. The shapes of the intrinsic states of $4n$ nuclei are found to be more complicated than simple spheroids or ellipsoids, often exhibiting large hexadecapole moments. Ground-state properties including binding energies, rms charge radii, and multipole moments are calculated and found to be in accord with experimental results and earlier calculations.

[NUCLEAR STRUCTURE $\mathrm{sd}-,pf$-shell nuclei; calculated binding energies, radii, moments, density distributions. Variational method. Density-dependent interaction.]

• Received 30 August 1973

DOI:https://doi.org/10.1103/PhysRevC.9.1882