Nuclear Single-Particle Wave Functions

An approximate single-particle nuclear wave function is derived by solving an appropriate single-particle Schrödinger equation in a Hartree approximation with two-body central forces. The result of the first iteration is obtained in analytic form by means of the Thomas approximation in analogy with the Hulthén deuteron function. Because the wave function exhibits the correct asymptotic form for large particle separation, while maintaining the expected smooth behavior at small separations, it obtains significant improvement in the accuracy of the normalization over previously used functions for light nuclei. Comparison is made with the single-particle momentum distribution of ${\mathrm{He}}^4$ obtained from recent ($p, d$) pickup experiments, and applications to the analysis of various inelastic scattering processes are discussed.