  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.
