Calculation of transition probabilities and ac Stark shifts in two-photon laser transitions of antiprotonic helium

Numerical ab initio variational calculations of the transition probabilities and ac Stark shifts in two-photon transitions of antiprotonic helium atoms driven by two counter-propagating laser beams are presented. We found that sub-Doppler spectroscopy is, in principle, possible by exciting transitions of the type (n, L).(n - 2, L - 2) between antiprotonic states of principal and angular momentum quantum numbers n n similar to - 1 similar to 35, first by using highly monochromatic, nanosecond laser beams of intensities 104-105 W/cm(2), and then by tuning the virtual intermediate state close (e. g., within 10-20 GHz) to the real state (n - 1, L - 1) to enhance the nonlinear transition probability. We expect that ac Stark shifts of a few MHz or more will become an important source of systematic error at fractional precisions of better than a few parts in 10(9). These shifts can, in principle, be minimized and even canceled by selecting an optimum combination of laser intensities and frequencies. We simulated the resonance profiles of some two-photon transitions in the regions n = 30-40 of the (P) over bar He-4(+) and (P) over bar He-3(+) isotopes to find the best conditions that would allow this.