Hyperfine structure and -pair annihilation in the muonium–positronium MuPs and positronium hydrides

Abstract

The hyperfine structure of the ground states in a number of positronium hydrides (TPs, DPs, 1 HPs) and MuPs (µ + e − 2 e + ) is determined with the use of highly accurate variational wave functions.We also evaluate the probabilities of various processes in the MuPs system, including the (e − , e + )-pair annihilation and its conversion into the charge conjugate system µ + e − 2 e + → µ − e − e + 2 . * Electronic address: afrolov@uwo.ca

Positron annihilation in the MuPs system

“…Its numerical value is the probability to find all three corresponding particles at one spatial point with spatial radius αa 0 ≈ a 0 137 . Our best numerical treatment to-date for the δ +−− value gives ≈ 3.68652 · 10 −4 , and therefore, Γ (1) 1γ ≈ 3.9314(20)·10 −1 sec −1 for the ground state in the MuPs system. Analysis of the second one-photon annihilation in MuPs is significantly more complicated (see discussion in [1]).…”

“…Our best numerical treatment to-date for the δ +−− value gives ≈ 3.68652 · 10 −4 , and therefore, Γ (1) 1γ ≈ 3.9314(20)·10 −1 sec −1 for the ground state in the MuPs system. Analysis of the second one-photon annihilation in MuPs is significantly more complicated (see discussion in [1]). To evaluate the corresponding annihilation rate Γ (2) 1γ one needs undertake an extensive QED consideration [7].…”

“…In this study we restrict ourselves to the discussions of the positron annihilation and hyperfine structure splitting. The muonium-positronium conversion and other interesting problems [1] are not considered here.…”

Internal structure and positron annihilation in the four-body MuPs system

“…The corresponding annihilation rates are very small, but in some theoretical considerations oneand zero-photon annihilations play a noticeable role. An approximate formula for zerophoton annihilation rate Γ 0γ takes the form (see, e.g., [3]):…”

“…Analysis of the second one-photon annihilation of the (e + , e − )−pair in the MuPs system is more complicated (see discussion in [3]). An approximate expression for the Γ (2) 1γ rate is written in the form which is similar to Eq.…”