Photoelectric Cross Section of the Deuteron

Abstract

Photoelectric cross section curves for a Majorana-Heisenberg potential of the type $V=-V_0{e}^{-\frac{r^2}{a^2}}$ and a velocity dependent potential determined by $J_0=-\left(\frac{2B}{a}\right)e^{-\frac{(r+\rho )}{a}}$ are compared with a cross section curve for a square hole Majorana force calculated by Breit, Condon and Stehn. In each case the values of the constants used are those which have been determined as the best for accounting for the binding energies of ${\mathrm{H}}^2$, ${\mathrm{H}}^3$, and ${\mathrm{He}}^4$. Results show that the cross section values for the first two potentials differ considerably from the third but very little from each other. A general formula for the area under the cross section curve, which holds for exchange as well as for ordinary forces is derived. For exchange forces $\int \sigma \left(\nu \right)d\left(h\nu \right)\cong \left(\frac{\pi e^{2}h}{2Mc}\right)(1+a\alpha )$ and this depends only on $a$, the range of interaction, $\alpha$, being defined by $\frac{{\alpha }^2{\hslash }^2}{M}=\epsilon$, the binding of energy the deuteron. The addition of a long range repulsive force to the velocity dependent interaction is found to decrease the cross section for this potential type considerably. The classical equivalent of the velocity dependent potential operator is determined.