Relativistic corrections of m\alpha^6 order to the ro-vibrational spectrum of H_2^+ and HD^+ molecular ions

The major goal of the high-precision studies of ro-vibrational states in the hydrogen molecular ions is to provide an alternative way for improving the electron-to-proton mass ratio, or the atomic mass of electron. By now the complete set of relativistic and radiative corrections have been obtained for a wide range of ro-vibrational states of H_2^+ and HD^+ up to order R_\infty\alpha^4. In this work we complete calculations of various contributions to the R_\infty\alpha^4 order by computing the relativistic corrections to the binding energy of electron.Comment: 4 pages, 1 figur

Proposed method for laser spectroscopy of pionic helium atoms to determine the charged-pion mass

Metastable pionic helium ($\pi{\rm He}^+$) is a three-body atom composed of a helium nucleus, an electron occupying the $1s$ ground state, and a negatively charged pion $\pi^-$ in a Rydberg state with principal- and orbital angular momentum quantum numbers of $n\sim \ell+1\sim 16$. We calculate the spin-independent energies of the $\pi{\rm ^3He}^+$ and $\pi{\rm ^4He}^+$ isotopes in the region $n=15$--19. These include relativistic and quantum electrodynamics corrections of orders $R_{\infty}\alpha^2$ and $R_{\infty}\alpha^3$ in atomic units, where $R_{\infty}$ and $\alpha$ denote the Rydberg and fine structure constants. The fine-structure splitting due to the coupling between the electron spin and the orbital angular momentum of the $\pi^-$, and the radiative and Auger decay rates of the states are also calculated. Some states $(n,\ell)=(16,15)$ and $(17,16)$ retain nanosecond-scale lifetimes against $\pi^-$ absorption into the helium nucleus. We propose to use laser pulses to induce $\pi^-$ transitions from these metastable states, to states with large ($\sim 10^{11}$ s$^{-1}$) Auger rates. The $\pi{\rm He}^{2+}$ ion that remains after Auger emission of the $1s$ electron undergoes Stark mixing with the $s$, $p$, and $d$ states during collisions with the helium atoms in the experimental target. This leads to immediate nuclear absorption of the $\pi^-$. The resonance condition between the laser beam and the atom is thus revealed as a sharp spike in the rates of neutrons, protons, deuterons, and tritons that emerge....(continued)Comment: 25 pages, 3 tables, 11 figure

Calculation of the relativistic Bethe logarithm in the two-center problem

We present a variational approach to evaluate relativistic corrections of order \alpha^2 to the Bethe logarithm for the ground electronic state of the Coulomb two center problem. That allows to estimate the radiative contribution at m\alpha^7 order in molecular-like three-body systems such as hydrogen molecular ions H_2^+ and HD^+, or antiprotonic helium atoms. While we get 10 significant digits for the nonrelativistic Bethe logarithm, calculation of the relativistic corrections is much more involved especially for small values of bond length R. We were able to achieve a level of 3-4 significant digits starting from R=0.2 bohr, that will allow to reach 10^{-10} relative uncertainty on transition frequencies.Comment: 19 pages, 5 tables, 7 figure

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~L-1~35, first by using highly monochromatic, nanosecond laser beams of intensities 10^4-10^5 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 \bar{p}^4He^+ and \bar{p} ^3He^+ isotopes to find the best conditions that would allow this.Comment: 18 pages 2 tables 12 figures, submitted to Phys. Rev.