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.

arXiv comment12 pages, 5 figures

References in corpus (15)

• Radioactive decays at limits of nuclear stability
• Two-proton radioactivity and three-body decay. III. Integral formulae for decay widths in a simplified semianalytical approach
• Three-body decay of ${}^6$Be
• Three-body structure of the low-lying ${}^{17}$Ne-states
• Two-proton radioactivity and three-body decay. IV. Connection to quasiclassical formulation
• Direct and sequential radiative three-body reaction rates at low temperatures
• Above threshold s-wave resonances illustrated by the 1/2${}^{+}$ states in ${}^9$Be and ${}^9$B
• Possibility to study a two-proton halo in ${}^{17}$Ne
• Anatomy of three-body decay I. Schematic models
• Radiative capture reaction for ${}^{17}$Ne formation within a full three-body model
• Necessary conditions for accurate computations of three-body partial decay widths
• Search for $2p$ decay of the first excited state of ${}^{17}$Ne
• Anatomy of three-body decay II. Decay mechanism and resonance structure
• Capture reactions into borromean two-proton systems at rp-waiting points
• Structure and decay at rapid proton capture waiting points