One-loop vacuum polarization at $m{\alpha }^7$ order for the two center problem

Abstract

We present calculations of the one-loop vacuum polarization contribution (Uehling potential) for the two-center problem in the NRQED formalism. The cases of hydrogen molecular ions ($Z_1=Z_2=1$) as well as antiprotonic helium ($Z_1=2$, $Z_2=-1$) are considered. Numerical results of the vacuum polarization contribution at $m{\alpha }^7$ order for the fundamental transitions $(v=0,L=0)\to (v^{\prime }=1,L^{\prime }=0)$ in H${}_2^{+}$ and HD${}^{+}$ are presented.

6 pages, 2 figues, submitted to PRA

References in corpus (3)

• Theoretical transition frequencies beyond 0.1 ppb accuracy in H${}_2^{+}$, HD${}^{+}$, and antiprotonic helium
• Relativistic corrections of mα^6(m/M) order to the hyperfine structure of the H_2^+ molecular ion
• Relativistic corrections of order mα^6 to the two-center problem

Cited by in corpus (2)

• One-loop vacuum polarization at m$\alpha$7 and higher orders for three-body molecular systems
• Precision Spectroscopy of 2S-nS Transitions in Atomic Hydrogen: A Determination of the Proton Charge Radius