Interaction of Alpha-Particles

The properties of the forces between alpha-particles are discussed on the basis of a Heitler-London analysis augmented by a "van der Waals" calculation. The results are in some respects unfavorable to the alpha-particle model of the nucleus inasmuch as they contradict the assumptions often made when this model is applied. Thus, for instance, it is pointed out that there are no attractive van der Waals forces beyond the range of the exchange forces, the range of the second-order forces being no greater than that of the first-order forces. The forces between alpha-particles are not additive. The range of the forces is approximately equal to that of the forces between elementary nuclear particles. The Heitler-London forces are repulsive if the usual choice of a symmetric Hamiltonian is made. The details of the forces are first worked out in connection with a simple fictitious example (§1) in terms of which these various features are most easily discussed. Calculations for the alpha-particle, for which a $\psi$-function of the Gauss type is assumed, are made in §§2 and 3. Finally (§4) the results are used in an examination of the problem of the scattering of alpha-particles in helium. It appears that the scattering of the $S$ waves can be explained only partially by means of the present interaction, its fault being the failure to produce resonance at the correct energy.