Auger transition rates for metastable states of antiprotonic heliumHe+p¯

The rates of Auger transitions of antiprotonic helium ${}^4$He${}^{+}\overline{p}$ and ${}^3$He${}^{+}\overline{p}$ are calculated by using a variational scattering method with an elaborate three-body trial function. The shift of the energy levels of these systems due to the coupling with the Auger-decay channels is also obtained from this calculation. Thus an improvement is made over the previously calculated nonrelativistic energies. Together with the relativistic corrections calculated elsewhere, the theoretical transition wavelength between the states $\mathrm{}(n,l)=(37,34)\mathrm{}$ and $\mathrm{}(38,33)\mathrm{}$ of ${}^4$He${}^{+}\overline{p}$, for example, is significantly improved to be 713.593 nm, which compares well with the experimental value 713.578$\pm$0.006 nm. The calculated Auger lifetime of the level (38,33) is 3.2 ps, as compared with the value 4.1$\pm$0.2 ps deduced from the measured line broadening. Auger rates are calculated also using Fermi’s golden-rule formula with a regular Coulomb function with no phase shift for the Auger electron. The results agree fairly well with the accurate variational results.