HARMONIC-OSCILLATOR STATES AND ALPHA PARTICLE .1. FORM FACTOR FOR SYMMETRIC STATES IN CONFIGURATION SPACE

Recent experiments on electron scattering by helium nuclei and the information they give on the form factor of the α particle, suggest that the elementary gaussian distribution of charge in this nucleus must be modified. For this purpose we have expanded the wavefunction of the α particle in terms of a complete set of nonspurious four-particle harmonic-oscillator states that are symmetric under the exchange of the nucleons and have orbital angular momentum zero. The latter states can be derived very easily in terms of a symmetric set of relative coordinates, and we then transform them to Jacobi coordinates, for which the calculation of the form factor can be done in an elementary fashion. Numerical results are presented for an expansion of up to four quanta, showing that it is possible to find linear combinations of the harmonic-oscillator states which give a good fit to the experimental values. We also discuss general procedures for getting the coefficients in the expansion both through a variational analysis of a possible Hamiltonian, and a least square fit to the experimental form factor. © 1969.