Collisional shift and broadening of the 2p-2sspectral lines in muonic helium ions

Abstract

In connection with the recently proposed Lamb-shift experiments at Paul Scherrer Institute in ${\ensuremath{\mu}}^{\phantom{\rule{0.16em}{0ex}}4}{\mathrm{He}}^{+}$ and ${\ensuremath{\mu}}^{\phantom{\rule{0.16em}{0ex}}3}{\mathrm{He}}^{+}$ by using the laser-spectroscopy method, the pressure shift and width of the $2p$-$2s$ spectral lines in muonic-helium ions were studied in the present paper within the fully quantum-mechanical close-coupling approach. The calculations of the $S$ matrix as well as of the energy-dependent shift and width were made for collisional energies $E={10}^{\ensuremath{-}5}--1$ eV. The shift and width averaged over energy were obtained for target temperatures up to 350 K. It is shown that the fine-structure effect does not exceed a few percent. The isotopic effect is very small and can be neglected for the shift at $T\ensuremath{\ge}150$ K, contrary to the width, for which the isotopic effect becomes much more pronounced at $T\ensuremath{\ge}150$ K. At density $N=2.4145\ifmmode\times\else\texttimes\fi{}{10}^{18}$ atom/cm${}^{3}$ corresponding to the target pressure 100 mbar ($T=300$ K) the predicted values of the shifts are equal to 35 (50) MHz for ${\ensuremath{\mu}}^{\phantom{\rule{0.16em}{0ex}}3}{\mathrm{He}}^{+}$ and 33 (35) MHz for ${\ensuremath{\mu}}^{\phantom{\rule{0.16em}{0ex}}4}{\mathrm{He}}^{+}$ respectively for upper (lower) values of the $2p$-$2s$ energy-level separation. At the same conditions the values of the widths are equal to 2.4 (13.6) MHz for ${\ensuremath{\mu}}^{\phantom{\rule{0.16em}{0ex}}3}{\mathrm{He}}^{+}$ and 2.0 (3.0) MHz for ${\ensuremath{\mu}}^{\phantom{\rule{0.16em}{0ex}}4}{\mathrm{He}}^{+}$.