Variational Theory of the Alpha-Particle

The energy of the normal state of the alpha-particle is calculated with the use of an elaborate variational method, in which a fixed set of nuclear constants in the general symmetric Hamiltonian has been adopted. The result agrees well with an earlier, independent calculation, and allows the convergence limit to be determined with considerable precision. Comparison with previous work on ${\mathrm{H}}^3$ indicates that the binding energies of both ${\mathrm{H}}^3$ and ${\mathrm{He}}^4$ can be very nearly accounted for with the use of a single set of constants satisfying the conditions imposed by the triplet state of ${\mathrm{H}}^2$; but the value of $g$ (ratio of Heisenberg to Majorana forces) required is lower than usually supposed, and will give somewhat too low an energy for the singlet state of ${\mathrm{H}}^2$. The same methods are employed to calculate the excited singlet and triplet states of the alpha-particle, and yield the results which have already been stated. No excited state is stable. A virtual excited state is shown to exist near the energy of dissociation into four particles.