The finite size of the carbon nucleus causes the $K$-orbit muon density within the nucleus to be smaller than the density for a point nucleus. Previously calculated muon capture rates in carbon should be reduced by about 6% for this effect. Our recalculated capture rate to the ground state of ${\mathrm{B}}^{12}$ does not differ greatly from previously calculated values. It is 7300 ${\sec }^{-1\mathrm{}}$, with an assigned theoretical error of about 10%. The result tends to support the Feynman-Gell-Mann proposal of a conserved vector current in the framework of a universal Fermi interaction. We give also various predicted correlation coefficients, which do not differ significantly from those of Wolfenstein.

The allowed and all second-forbidden matrix elements have been calculated as a function of the intermediate coupling parameter $\frac{a}{K}$. The beta-decay rate of ${\mathrm{B}}^{12}$ is predicted correctly for $\frac{a}{K}=4.5\mathrm{}$, a value which is close to that favored by other evidence. The calculated second-forbidden vector matrix element differs by 20% from the "experimental" value derived from a magnetic dipole transition rate in ${\mathrm{C}}^{12}$.

• Received 23 July 1959

DOI:https://doi.org/10.1103/PhysRev.116.1591