Formation spectra of pionic atoms in the Green's function method

Abstract

We study the formation spectra of deeply bound pionic atoms in the ($d, 3$He) reactions using the Green's function method, stimulated by recent developments in experimental techniques. The Green's function method is considered to be a better theoretical formalism than the effective number approach to evaluate the formation rate of unstable systems. We compare the calculated results by the Green's function method with those by the effective number approach in various cases. We find that the differences between the results obtained by both methods are reasonably small and we can reaffirm that the effective number approach is a good theoretical method for the analyses of the previous experimental data with typical binding-energy errors of $\Delta \hbox {B.E.} \gtrsim 20$keV for the deeply bound pionic atoms. On the other hand, we think that theoretical results using the Green's function method will be necessary in the near future to deduce precise information on the pion properties in nuclei from analyses of the pionic atom data with better accuracy than before.