Radiative pion capture has been studied theoretically and experimentally for many years and for information on earlier achievements see Ref. [1]. In particular, the $\pi^- + d \rightarrow \gamma + n + n$ reaction has attracted a lot of attention, because this process can be used to extract the neutron-neutron scattering length. This issue is discussed in detail in Ref. [2], where also important references to earlier and more recent theoretical calculations can be found.

Recently, we have calculated capture rates for the $\mu^- + d \rightarrow \nu + n + n$, $\mu^- + ^3$He$ \rightarrow \nu + ^3$H, $\mu^- + ^3$He$ \rightarrow \nu + n + d$, $\mu^- + ^3$He$ \rightarrow \nu + n + n + p$ [3] and $\mu^- + ^3$H$ \rightarrow \nu + n + n + n$ [4] reactions. It is clear that the pion radiative capture can also be treated within our momentum space framework. In this contribution, the $\pi^- + ^2$H$ \rightarrow \gamma + n+n$, $\pi^- + ^3$H$ \rightarrow \gamma+n+n+n$, $pi^- +^3$He$ \rightarrow \gamma+n+d$ and $\pi^- + ^3$He$ \rightarrow \gamma + n+n+p$ capture reactions are studied with realistic nucleon-nucleon and three-nucleon potentials under full inclusion of final-state interactions. We assume that the full initial state consists of the atomic K-shell pion wave function and the initial nucleus state. Our calculations are performed with traditional nuclear forces and a simple single-nucleon transition operator but they represent a solid base for future calculations with input from chiral effective field theory. We plan further investigations of pion radiative capture processes using the transition operator from Ref. [5].

References:

[1] Helmut W. Baer, Kenneth M. Crowe, Peter Truoel, Adv. Nucl. Phys. 9, 177 (1977).

[2] Anders Gardestig, J. Phys. G36, 053001(2009).

[3] J. Golak et al., Phys. Rev. C90, 024001 (2014)

[4] J. Golak et al., Phys. Rev. C94, 034002 (2016).

[5] Harold W. Fearing et al., Phys. Rev. C62, 054006 (2000).