Abstract
We have estimated the shift and broadening of the resonance lines in the spectrum of antiprotonic helium atoms $\overline{p}{\mathrm{He}}^{+}$ implanted in solid helium $^{4}\mathrm{He}$. 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 $^{4}\mathrm{He}$ have been applied for estimating the resonance-line shift due to collisions of $\overline{p}{\mathrm{He}}^{+}$ atom with the surrounding $^{4}\mathrm{He}$ atoms. The dependence of the line shift, which has been calculated in the quasistatic limit, on the solid-$^{4}\mathrm{He}$ density is nonlinear.
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