Resonant enhancement of field-induced annihilation rate for ($\pi^+\pi^-$) atom: a possibility to measure np-ns energy splitting

Some possibilities are discussed for measuring the np-ns energy splitting in (pi sup + -pi sup -) atoms in experiments with relativistic particle beams, using the electromagnetic field control of annihilation process. Significant resonant enhancement of annihilation probability may be observed in an oscillating field. The resonance provides much more spectacular changes in the decay rate than corresponding decay rate changes in a steady field. The position of resonance on the frequency axis gives an additional and more accurate information on the np-ns transition energy, than the data on the ratio between the field-free and dc-field-induced annihilation rates. Numerical results are presented for the states n=2 and n=3.