Vacuum polarization in muonic atoms: the Lamb shift at low and medium Z

Abstract

In muonic atoms the Uehling potential (an effect of a free electronic vacuum polarization loop) is responsible for the leading contribution to the Lamb shift causing the splitting of states with Delta n = 0 and Delta l \neq 0. Here we consider the Lamb shift in the leading nonrelativistic approximation, i.e., within an approach based on a certain Schrodinger equation. That is valid for low and medium $Z$ as long as (Z alpha)^2 >> 1. The result is a function of a few parameters, including kappa = Z alpha m_ mu/m_e, n and l. We present various asymptotics and in particular we study a region of validity of asymptotics with large and small kappa. Special attention is paid to circular states, which are considered in a limit of n >> 1.

References in corpus (2)

• Light Fermion Finite Mass Effects in Non-relativistic Bound States
• The Uehling correction to the energy levels in a pionic atom

Cited by in corpus (9)

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• Vacuum polarization in muonic and antiprotonic atoms: the fine structure at medium Z
• $K$-series X-ray yield measurement of kaonic hydrogen atoms in a gaseous target
• Relativistic recoil effects for energy levels in a muonic atom within a Grotch-type approach: An application to the one-loop electronic vacuum polarization
• Relativistic recoil effects in a muonic atom within a Grotch-type approach: General approach
• Relativistic recoil effects to energy levels in a muonic atom: a Grotch-type calculation of the second-order vacuum-polarization contributions
• The Uehling correction in muonic atoms exactly in Zα