Quadrupole corrections to matrix elements of transitions in resonant reactions of muonic molecule formation

Abstract

The calculated resonant formation rates of the muonic molecules ddµ and dtµ are presented. The approach developed earlier for calculating the transition matrix elements in the dipole approximation has been extended to include the quadrupole terms in the multipole expansion of the interaction operator. The calculated dependence of the dtµ formation rates on the energies of the incident tµ muonic atoms shows that the effect of including the quadrupole correction is to reduce the magnitude of the peak rates by about 20–30% at the different temperatures, compared to those calculated in the dipole approximation. The dependence on temperature for the ddµ formation rates is obtained with the differences between the presented and previous calculations being less than 5%.