The two-photon transition of the fully-ionized muonic boron migrating in helium

In recent experiments performed at the Paul Scherrer Institute (PSI) measurements were made of the yield of the two-photon transition of the fully-ionized muonic boron formed and quenched in a gaseous mixture of diborane B₂H₆ and helium. In the present work this yield is calculated for an idealized case of a very low diborane density when the main 2 s state decay modes competing with the two-photon transition are due to the electron transfer from helium to the μ-ion. As the rate of this transfer depends strongly on the relative velocity, a treatment is needed of the whole kinetics of processes occurring with the μ-ion in helium. Accordingly, within the optical model with a complex potential constructed before we calculate cross-sections of the elastic scattering and electron transfer. Then the time evolution of the μ-ion energy is considered and, finally, the yield is calculated. It proves that at helium pressures Torr this yield may be written in the form: ,where the factor C is greater than unity and increases rapidly with the initial energy E₀ which the μ-ion has after its formation in the diborane molecule. Thus measurement of the pressure dependence of allows E₀ to be estimated. The results obtained make it possible to suggest a similar parametrization of the PSI data. Received: 21 October 1997 / Revised: 16 January 1998 / Accepted: 2 March 1998