Total eigenphase description of multiparticle quantum systems

This paper presents a formalism for studying semianalytically the development of a multiparticle quantum-mechanical system outward from its center of mass, casting its dynamics in terms of hyperspherical coordinates which emphasize collective motions of all constituents. The formalism expresses the system’s devleopment through an R matix which varies with the system’s hyperradius R, incorporating a greater amount of the dynamics as R grows. Eigenvalues of the R matrix are further transformed into R-dependent phases whose R variation elucidates interactions between alternative degrees of freedom. An initial application to the ${}_{}{}^1{}_{}{}^{}$ ${\mathit{S}}^{\mathit{e}}$ states of helium reveals details of interactions hitherto concealed within numerical treatments.