The Absorption of Slowπ−Mesons byHe4Nuclei

On the assumption of central charge-independent two particle nuclear forces, the wave function ${\mathrm{}(E+K)\mathrm{}}^{-2\mathrm{}}{\mathrm{}(bE+K)\mathrm{}}^{-2\mathrm{}}$ with $E$ the binding energy, $K$ the kinetic energy, and $b=5.3\mathrm{}$ is found to be a better wave function, in the sense of a variational principle, for the ${\mathrm{He}}^4$ nucleus than the optimum Gaussian. With this wave function, the ratios of the numbers of protons to deuterons to tritons in final states resulting from the absorption of ${\pi }^{-}$ mesons from $K$ shells of mesic helium atoms are found to be 1:1.3:0.7. For reasonable values of the $\mathrm{PS}\left(\mathrm{PV}\right)\mathrm{}$ coupling constant, 20 percent of the absorptions take place directly from the $2p$ level. The number of high energy $\gamma$-rays is less than 1 percent of the number of nonradiative absorptions. Charge-exchange absorption is energetically forbidden.