Shift and broadening of resonance lines of antiprotonic helium atoms in solid helium

TL;DR

This study estimates the resonance line shift and broadening of antiprotonic helium atoms in solid helium, finding negligible broadening from collective motion and a nonlinear density-dependent line shift due to collisions.

Contribution

It introduces a method to analyze resonance line shifts and broadening in solid helium using response functions and pair-correlation functions, highlighting the negligible effect of collective motion.

Findings

Broadening from collective motion is negligible.

Resonance line shift depends nonlinearly on helium density.

Collision effects cause the observed line shift.

Abstract

We have estimated the shift and broadening of the resonance lines in the spectrum of antiprotonic helium atoms $\bar{p}\mathrm{He}^{+}$ implanted in solid helium $^4$He. The application of the response function for crystalline helium has enabled determination of the contributions from the collective degrees of freedom to the shift and broadening. It occurs that the broadening due to the collective motion is negligible compared to the natural line width. The available pair-correlation functions for crystalline $^4$He have been applied for estimating the resonance-line shift due to collisions of $\bar{p}\mathrm{He}^{+}$ atom with the surrounding $^4$He atoms. The dependence of the line shift, which has been calculated in the quasistatic limit, on the solid-$^4$He density is nonlinear.