Lamb shift of electronic states in neutral muonic helium, an electron-muon-nucleus system

Abstract

Neutral muonic helium is an exotic atomic system consisting of an electron, a muon, and a nucleus. Being a three-body system, it possesses a clear hierarchy. This allows us to consider it as a hydrogenlike atom with a compound nucleus, which is, in turn, another hydrogenlike system. There are a number of corrections to the Bohr energy levels, all of which can be treated as contributions of generic hydrogenlike theory. While the form of those contributions is the same for all hydrogenlike atoms, their relative numerical importance differs from atom to atom. Here, the leading contribution to the (electronic) Lamb shift in neutral muonic helium is found in a closed analytic form together with the most important corrections. We believe that the Lamb shift in neutral muonic hydrogen is measurable, at least through a measurement of the (electronic) i.r-2.? transition. We present a theoretical prediction for the li-2 s transitions with an uncertainty of 3 ppm (9 GHz), as well as for the 2s-2p Lamb shift with an uncertainty of 1.3 GHz.The hydrogen atom is the simplest one and the easiest to access, but its study is not free of problems. For instance, a recent determination of the proton radius by measuring the Lamb shift in muonic hydrogen [1] led to a result inconsistent with that from hydrogen spectroscopy [2] (on various determinations of the proton charge radius see, e.g., Ref.[3]). The muonic hydrogen atom is only one example of exotic "editions" of hydrogen. Due to the "proton-radius puzzle" one may wonder, in particular, whether a theory of the ordinary or muonic hydrogen atoms is adequate. To probe it one may consider various isotopes of hydrogen, including exotic ones.In particular, the muonium atom, a bound system of an electron and a positive muon, is such a system, where the quantum electrodynamics (QED) effects are about the same as in hydrogen, the nuclear recoil effects are enhanced, and the nuclear structure contributions are suppressed. (One may treat various radiative corrections to the muon line as the nuclear structure corrections.) On the contrary, the neutral muonic helium atom, a neutral three-body system, which consists of a nucleus (either an a particle or a helion, the nucleus of the 3 He atom), a muon, and an electron, is a kind of hydrogenlike atom with a compound nucleus [4][5][6], where the effective nuclearstructure effects are enhanced. The recoil contributions there are less important than in ordinary hydrogen, while the hyperline effects are enhanced. Remarkably, the effective nuclear-structure effects are under control.There are a number of exotic atoms, which are of interest because of specific relations between numerical values of their ' savely.karshenboim@mpq.mpg.de parameters. The specifics of neutral muonic helium is in certain properties of its compound nucleus. Muonic helium is a system with a well-defined hierarchial structure. Its atomic part is similar to that of an ordinary hydrogen atom, possessing an electron and a compound nucleus. Such a nucleus consists of an "internal"...

Possibility of New Precise Measurements of Muonic Helium Atom HFS at J-PARC MUSE

“…The 1s-2s transition has been measured in hydrogen [20] and muonium [21], but not yet in µ 3 He or µ 4 He. The 1s-2s transition in neutral muonic helium has been calculated [22], and is very similar to that in hydrogen. This experiment is believed to be possible.…”

“…The excitation of the 1s-2s transition in neutral muonic helium could easily be achieved via Doppler-free two-photon pulsed laser spectroscopy in a similar manner as with hydrogen or muonium. The measurements could then be performed as suggested in [22] by using a double resonance technique by either looking at the disappearance of the 1s ground state HFS transition, or the appearance of the 2s excited state HFS transition.…”

Energy levels in muonic helium

“…where the tensor representation for the angular part of the wave function is used. The basis wave function of the P-state is defined by the sum of functions in (13)- (14) in the form φ(ρ,λ)=c1φ10(ρ,λ)+c2φ01(ρ,λ). For numerical calculation, a program was written in the MATLAB system for solving the three-particle Coulomb problem in the framework of the stochastic variational method.…”

“…It should be noted that new precise measurement of hyperfine structure of muonic helium is planned at J-PARC MUSE [13] because high intensity pulsed negative muon beam gives an opportunity to improve the result (1) by two orders of magnitude. Another important energy interval that could be investigated experimentally could be the electron Lamb shift (2P-2S) [14][15]. In this work we study hyperfine structure and the electron Lamb shift in muonic helium atom using the stochastic variational approach [16][17][18].…”

Two-body corrections to the g factors of the bound muon and nucleus in light muonic atoms

“…In such a case the magnetic moment and spin of the compound nucleus is the muon one and the screening of the magnetic moment of the compound nucleus is a two-body problem of an electron and a compound nucleus. Such a hierarchy technique for the study of neutral muonic helium has been successfully applied to the hyperfine structure [8][9][10][11][12] and the Lamb shift [13,14] of the electron energy levels.…”