XL. The binding energies of three- and four-particle nuclei.

Abstract

The binding energies of the nuclei H³, He³ and He⁴ are calculated, using the standard variation method with a simple two-parameter wave-function of a new form. Purely central interactions of the Yukawa and exponential types are considered. It is found that, when the nuclear parameters are chosen to fit the low-energy scattering and deuteron data, reasonable values are obtained for the three-particle nuclei, but the a-particle binding energy is too high. This result is in agreement with the calculations of Rarita and Present for the exponential potential, and those of Svartholm for the Yukawa potential. In contrast with Svartholm's method of calculation, the potential and kinetic energies of the nuclei are obtained explicitly. In the case of the a-particle, the Yukawa potential yields exceptionally high values for these quantities, and results also in a very concentrated nucleus. The exponential potential, on the other hand, does not give rise to such high values for the potential and kinetic energies nor does it concentrate the nucleus to the same extent as the former potential†.