The Scattering of Thermal Neutrons by Deuterons

The cross section for the scattering of very slow neutrons by deuterons is calculated by numerical methods. Polarization is completely neglected and the wave equation for the process is set up in such a form as to take correctly into account exchange effects between the incident neutron and the neutron initially in the deuteron. This wave equation is then replaced by an integral equation the solution of which is correctly symmetrized and has the right asymptotic value to describe the scattering process. The numerical integration is performed by replacing the integral equation by a finite set of simultaneous linear algebraic equations. The work is greatly simplified by the use of a sum of two Gauss functions to approximate the ground state deuteron wave function. It is assumed throughout this paper that the interactions between like and unlike particles are equal and are of the general form $V_{\mathrm{ij}}=-\left[\right(1-g-g_1-g_2)P_{\mathrm{ij}}+g{P}_{\mathrm{ij}}{Q}_{\mathrm{ij}}+g_1+g_2{Q}_{\mathrm{ij}}]J\left(r_{\mathrm{ij}}\right),$ where the symbols have their usual meanings and where $J\left(r_{\mathrm{ij}}\right)$ is a Gauss function. The calculation is carried out for two sets of $g$'s. For the first set, $g_1=g_2=0\mathrm{}$, $g=0.2\mathrm{}$, the cross section is found to be equal to 4.57×${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$, and for the second set of $g$'s, $g_2=2\mathrm{}$, $g=0.22-g_2$, $g_1=0.25-0.8\mathrm{}{g}_2$, the value of the cross section is found to be equal to 6.91×${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$. The experimental value is at least 20 percent smaller than the first of these values.