Quantitative information as to the nature of intranuclear forces has been obtained by considering the hydrogen and helium isotopes, using a Hamiltonian of the exchange type based on the neutron-proton model with interactions between all the particles. The interactions between like particles are taken to be the same for protons and for neutrons except for the small Coulomb force between protons which accounts for at least half of the difference in the binding energies of ${\mathrm{He}}^3$ and ${\mathrm{H}}^3$. It is not inconsistent with existing experimental evidence to assume the range of such forces to be about the same as the range of neutron-proton forces. By making these assumptions and by using simple attractive potentials, it is found that the forces between like particles are given by a potential with depth not greater than 30 $m{c}^2$ and with an effective radius of action which must be less than 2.8×${10}^{-13\mathrm{}}$ cm to be consistent with experimental data for the binding energies. A more accurate determination of the constants based on assuming a close correlation of the three- and four-body problems with "equivalent" two-body problems gives the depth of the proton-neutron potential as 74 $m{c}^2$ and of the like-particle potentials as 26 $m{c}^2$ and a range of 2.2×${10}^{-13\mathrm{}}$ cm for the forces. reasons for believing in the reliability of the "equivalent" two-body method for determining approximate binding energies for three- and four-body problems are discussed. It is shown furthermore that if the exchange operators multiplying the neutron-proton interaction potentials are assumed to be linear combinations of the Majorana and Heisenberg types, it is possible to explain the large scattering of neutrons on protons at low velocities. The proportion of the Heisenberg to the Majorana operator in the linear combination necessary to obtain the correct scattering is about one-fifth. It is then shown that in the three- and four-body problems such an operator can to a good approximation be represented by an equivalent Majorana operator and that because of this fact the results obtained for nuclear energies and for the magnitude and range of the forces (in which Majorana operators were used) remain the same except that the depth of the potential for like particles is increased from 26 to 41 $m{c}^2$. The latter value yields a scattering intensity for protons in hydrogen which agrees qualitatively with the experimental results.

• Received 16 August 1935

DOI:https://doi.org/10.1103/PhysRev.48.906