A calculation of the doubly differential cross section for inclusive pion - helium-4 double charge exchange at incident pion kinetic energy less than 270 MeV

Pi-nuclear scattering calculations that use multiple scattering usually require the knowledge not only of the {dollar}pi{dollar}-nucleon interaction in free space but also its modification inside a nuclear medium. A relativistic 3-Body model consisting of the pion, the {dollar}isp{lcub}rm th{rcub}{dollar}-nucleon and the residual nucleus also called the core, is developed. In this model the nucleon core separation in co-ordinate space is approximated by the separation between the center of mass of the {dollar}pi{dollar}-{dollar}isp{lcub}rm th{rcub}{dollar}nucleon subsystem called the Composite, and the core. The instant form of dynamics was employed to introduce interactions between the pion and the nucleon and between the {dollar}pi N{dollar} Composite and the Core. The Composite-Core Hamiltonian is assumed to admit no bound states. The relativistic 3-Body total Hamiltonian is then diagonalized by nested-separable eigenfunctions. This diagonalization allows the construction of an expression for matrix elements of the medium modified {dollar}pi N{dollar} scattering operator {dollar}tausb{lcub}i{rcub}{dollar} in the lab frame in terms of the CM {dollar}pi N{dollar} free space t-matrix elements. Terms that are quadratic in the {dollar}pi N{dollar} t-matrix elements in this expression are neglected.; The Sequential Single Charge eXchange (SSCX) mechanism contribution to inclusive {dollar}pi{dollar}-{dollar}sp4{dollar}He Double Charge eXchange (DCX) is calculated using only the double scattering term of the Watson multiple scattering series. The {dollar}tau{dollar}-matrix elements obtained from the 3-Body model are used for the first scattering. It contains explicit dependance upon the matrix elements of the Composite-Core scattering operator {dollar}tsb{lcub}pi N-C{rcub}{dollar}. This explicit dependance is ignored in the second scattering. The pole of the intermediate pion Green function is fixed from 3-Body model considerations and the requirement that pion be on the mass shell at the pole.; The calculated inclusive cross sections {dollar}{lcub}{lcub}dsp2sigma{rcub}over{lcub}dOmega dTsbpi{rcub}{rcub}{dollar} are compared with the Kinney et al. experimental results and essential agreement with the spectrum for incident pion kinetic energy {dollar}Tsbsp{lcub}pi{rcub}{lcub}rm In{rcub}{dollar} = 120 MeV is found. At higher values of {dollar}Tsbsp{lcub}pi{rcub}{lcub}rm In{rcub}le 270{dollar} MeV only qualitative agreement with the experiment is claimed. Zeroing {dollar}tsb{lcub}pi N-C{rcub}{dollar} changes the cross section magnitudes by {dollar}<{dollar}5%. The presence of the P33 partial wave, the choice of the appropriate width in momentum space of the Gaussian wavefunction for the ground state {dollar}sp4{dollar}He and the inclusion of both single spin flip and double spin flip amplitudes are found to be important.