Shell-Model Analysis of the Excited States ofHe4

Using a theory previously developed for the ${\mathrm{O}}^{16}$ nucleus, the energy levels of ${\mathrm{He}}^4$ were calculated using the nuclear shell model and the random-phase approximation (RPA). Though no attempt was made to optimize the parameters of the calculation, the predicted energies of the excited states compare favorably with those determined from experimental analyses. Qualitative agreement with experiment is obtained for the calculated electron inelastic-scattering form factor to the first $0^{+}$ excited state and for the integrated photoabsorption cross section. However, the prediction of the majority of the $E1\mathrm{}$ strength in the higher of the 1—, $T=1\mathrm{}$ levels does not conform to most experiments which indicate the lower level to have the stronger ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ component. The RPA produces some improvement over an ordinary shell-model calculation by decreasing the energies of the lower excited states by several hundred keV and by increasing the relative $E1\mathrm{}$ strength of the lower 1—, $T=1\mathrm{}$ level.