Two-photon decays of highly excited states in hydrogen

TL;DR

This paper compares relativistic and nonrelativistic calculations of two-photon decay rates in highly excited hydrogen states, analyzing dependence on quantum number and multipole contributions up to n=100.

Contribution

It provides a comprehensive comparison of calculation methods and derives an analytical formula for E1M1 decay in the nonrelativistic limit.

Findings

Relativistic and nonrelativistic results are compared for n up to 100.

Higher multipole contributions are quantified for ns states.

Analytical formula for E1M1 decay is derived.

Abstract

The relativistic and nonrelativistic approaches for the calculations of the two-photon decay rates of highly excited states in hydrogen are compared. The dependence on the principal quantum number (n) of the ns, nd, and np initial states is investigated up to n = 100 for the nonresonant emissions. For the ns states together with the main E1E1 channel the contributions of higher multipoles (M1M1, E2E2, E1M2) are considered. For the np states the E1M1 and E1E2 channels are evaluated. Moreover, the simple analytical formula for the E1M1 decay is derived in the nonrelativistic limit.