Atomic few-body systems with muonium

Abstract

Properties of some few-body systems which include one positively charged muon µ + and two electrons e − are discussed. In particular, we consider the negatively charged muonium ion Mu − (or µ + e − 2 ) and four-body MuPs (or µ + e − 2 e + ) systems each of which has only one stable bound (ground) state. The problem of annihilation of the electron-positron pair(s) in the MuPs system is investigated. The hyperfine structure splitting of the ground state in the MuPs system evaluated with our expectation value of the muon-positron delta-function is ∆ ≈ 23.05758 M Hz. Another group of interesting four-body neutral systems investigated in this study includes the p + µ + e − 2 , d + µ + e − 2 and t + µ + e − 2 'quasi-molecules'. These quasi-molecules are formed in large numbers when positively charged muons slow down in liquid hydrogen, or in liquid deuterium and/or tritium. The properties of these systems are unique, since they occupy an intermediate position between actual two-center molecules and one-center atoms. PACS number(s): 32.10.Fn, 31.15.A-and 31.15.VeIn this communication we report the results of our analysis of some three-and fourbody systems each of which include one positively charged muon µ + and two electron e − .Briefly, we can say that each of these few-body systems contains muonium Mu (or µ + e − ), or muonium ion Mu − (or µ + e − 2 ). Recently, there is an increasing experimental interest to such few-body systems (see discussions and references in [1] - [5]). This can be explained by rapidly growing experimental abilities to detect and isolate similar few-particle systems.Moreover, by using the modern experimental techniques one can investigate some of the bound state properties of these systems. Another reason follows from the fact that the µ + muon has positive electric charge and relatively small particle mass. This means that all atomic and molecular few-body systems which contain one positively charged muon and two electrons have very special electron density distribution which differs substantially from electron density distributions in 'similar' atomic and molecular systems. In reality, such systems can be considered as a separate class of bound systems which are neither atoms, nor molecules. In some cases, the positively charged muon plays a role of central particle which stabilize a few-electron structure, e.g., in the Mu − ion and MuPs system (see below).Formally, all few-body systems with positively charged muon are unstable, but their lifetime τ (≈ 2 · 10 −6 sec) significantly exceeds the mean time(s) of atomic transitions and decay processes τ tr ≤ 1 · 10 −11 sec. In other words, these few-body quasi-atomic systems can be created and stabilized in their bound state(s) substantially faster than the decay of the µ + muon can occur.As follows from the above, it is important to predict the overall stability of the few-body systems which include muonium Mu (or muonium ion Mu − ) and investigate their basic properties. These problems are considered in our study. In particular, below we consid...

Photoionization treatment of encompassed plasma-implanted exotic atoms

“…In fact, such systems can be thought of as a separate class of bound systems that are neither atoms nor molecules. The calculation of some matrix elements of such two-, three-, or four-particle systems involves the disappearance of electron-positron pairs in the structure, and the analysis of hyperfine structure has been performed [17]. There are indeed numerous experimental studies on muonic systems, and the motivations behind each of them are quite diverse and purposeful.…”