Symmetry Effects on Nuclear Dipole Radiation with Application to a Bound Excited State ofHe42

The effect of nuclear symmetry properties on electric dipole transitions is investigated using the independent particle model and Wigner's theory of the symmetric Hamiltonian. Methods are given for the construction of completely symmetrized wave functions for the nuclear states on this model. Symmetry selection rules are found to operate, in addition to the usual selection rules, to reduce the amount of nuclear dipole radiation. A detailed study of the ${\mathrm{He}}^4$ nucleus leads to the conclusion that if a resonant state at 21.6 Mev does exist with a strong dipole transition to the ground state, then a bound, excited state of the alpha-particle also exists. Spin-orbit and tensor forces are introduced to give a possible explanation of the angular distribution of gamma-rays when protons are captured by tritium.