Radiative pion absorption in nuclei and soft-pion theorems

Abstract

The analogy between radiative pion absorption and muon capture is contained in a soft-pion theorem which states that the matrix elements of radiative pion absorption are those of the axial-vector current involved in muon capture. This soft-pion theorem is derived, and two methods of calculating radiative absorption rates, for pions bound in the 1S atomic orbital, from the corresponding muon capture rates are presented. The first method treats the nucleus as an elementary particle and uses electron scattering data in order to account for the vector part of the muon capture process; the second method uses nuclear photoexcitation information in order to account for the vector part of this process. Corrections to the soft-pion theorem are considered. In particular, the nuclear Fermi gas model is employed in order to estimate the corrections due to absorption of the pion and due to the nuclear Fermi motion. These corrections are found to be small. Further, corrections due to the rescattering of the pion are considered. They reduce the radiative pion absorption rate by approximately 60% in 12C.