Studies of quasiclassical approach applicability to true three-body decays

Abstract

Within the hyperspherical harmonics approach the three-body problem is reduced to a motion of one effective particle in a "strongly deformed" field, which is described in coupled-channel formalism. This method is especially suited to studies of phenomena characterized by genuine three-body dynamics, e.g. Borromean haloes and true three-body decays. The reduction of the hyperspherical equations set to a single-channel Schrödinger equation provides the basis for the use of the standard quasiclassical expression for calculations of widths for true three-body decays. We demonstrate that the quasiclassical approach by itself is quite precise in application to typical profiles of the three-body effective potentials. However, the reduction to single-channel formalism leads to significant overestimation of the two-proton width ${\Gamma }_{2p}$. This is demonstrated by the example of the ${}^{17}$Ne first excited $3/2^{-}$ state decay, questioning, however, the applicability of such an approximation in general.

Comments: 12 pages, 5 figures