The Excited States of theH3andHe4Nuclei

Abstract

Calculations were made with trial wave functions corresponding to such excited states of ${\mathrm{H}}^3$ and ${\mathrm{He}}^4$ which, in the Hartree approximation, would contain one or two particles excited into the $p$ shell. If only one particle is excited there is no state which would be completely symmetrical in space coordinates and if two particles are excited only an $S$ and a $D$ state have this property. On account of the supposed predominance of the Majorana exchange forces in the nuclear Hamiltonian, these should be the lowest excited states in ${\mathrm{H}}^3$ while in ${\mathrm{He}}^4$ the $P$ state in which only one particle would be excited in the Hartree picture lies close to these. No stable excited states are indicated for either of the nuclei when the forces are of the exchange type unless the range of force is much greater than the accepted range. Several improved forms of the $D$ state wave function were tried but they failed to lower the energy sufficiently to make the states stable.