On the Photodisintegration of the Deuteron (Pseudoscalar Meson Theory)

Abstract

There are many difficulties in the meson theory at the present stage of its development. The singularities of nuclear potentials are the most serious ones in the deuteron problem. In order to overcome these points many attempts have been made repeatedly. Recently van Hove and Araki have shown that if the relativistic effects are taken into account the singularities are reduced to 1/r for the pseudoscalar meson theory. Thus we can find the solution of the deuteron problem, and, for example, the scattering cross-section of the neutron by the proton can be evaluated unambiguously. The photodisintegration of the deuteron is the same problem as the scattering. Its cross-section depends on the nuclear potential as much as the scattering cross-section does. Although many authors treated this problem to test the meson theory, it is necessary to consider it from the new theoretical standpoint on account of the recent discovery of π meson and the precise experimental results. The purpose of this paper is to work out the total cross-section of the photodisintegration of the deuteron for the pseudoscalar meson theory by making use of the above mentioned new nuclear potentials. In §1 we discuss the general theory of the cross-section of the photodisintegration of the deuteron. In §2 we consider the photoelectric effect which corresponds to the transition from the initial 3S state to the final 3P state. As stated above, we should decide exactly the solution of the Schrödinger equation of the deuteron for the new potential, but for simplicity we neglect the tensor forces and obtain the initial state function by the variational method and the final one by replacing the new potential with the square well potential. In §3 the photomagnetic effect which comes from 3S →1S transition is computed. In this case the initial and final states are also derived by the same method as before. In §4 numerical results are shown for various values of 3P state potential and compared with the recent experimental results.