Variational calculation of antiprotonic helium atoms

A few per cent fraction of antiprotons stopped in helium survives for an enormous time (up to tens of microseconds) in comparison with the usual lifetime ($10^{-12}s$) of these particles in matter. The explanation is that antiprotons are captured in the metastable antiprotonic helium atoms $^{3,4}\! H\! e\bar pe$ carrying an extremely large total angular momentum $L\sim 30-40$. Initial populations, level lifetimes and very precise values of the transition energies were obtained in experiments on the resonant laser--induced annihilation. Analogous long-lived systems were observed in experiments with negative kaons and pions. The purpose of this report is to present the results of calculation of eigenenergies, radiative transition rates, energy-level splitting due to relativistic interactions and Auger decay rates of antiprotonic helium atoms within the variational approach.