Anatomy of three-body decay III: Energy distributions

Abstract

We address the problem of calculating momentum distributions of particles emerging from the three-body decay of a many-body resonance. We show that these distributions are determined by the asymptotics of the coordinate-space complexenergy wave-function of the resonance. We use the hyperspherical adiabatic expansion method where all lengths are proportional to the hyperradius. The structures of the resonances are related to different decay mechanisms. For direct decay all inter-particle distances increase proportional to the hyperradius at intermediate and large distances. Sequential three-body decay proceeds via spatially confined quasistationary two-body configurations. Then two particles remain close while the third moves away. The wave function may contain mixtures which produce coherence effects at small distances, but the energy distributions can still be added incoherently. Two-neutron halos are discussed in details and illustrated by the 2 + resonance in 6 He. The dynamic evolution of the decay process is discussed. : 21.45.+v, 31.15.Ja, 25.70.Ef PACS IntroductionNuclear resonances and excited states can be very complicated many-body structures with a number of different decay modes. The simplest decay, perhaps beside γ-emission, is breakup into two particles as exemplified by nucleonand α-emission, and binary fission [1]. The deceivingly simple breakup into

Resonances in three-body systems with short and long-range interactions

“…The same analog 2 + state has been found in 6 Li and 6 Be at (1.67,0.54) MeV and (3.04,1.16) MeV, respectively [ 4]. Realistic detailed calculations using the (complex scaled) adiabatic expansion method concerning the 2 + resonance in 6 He can be found in [ 5,6]. In Figs.…”

“…Accurate calculation of these eigenvalues is the first and essential requirement needed to obtain reliable radial wave functions. 6 Be and 6 …”

“…First computed radial wave function (thick curves) for the 2 + resonance in 6 Be and the corresponding asymptotics (thin curves). such a kind of potential the solutions are known to go asymptotically as in Eq.…”

Energy Distributions from Three-Body Decaying Many-Body Resonances

“…The wave function and the complex energy of the resonance are then defined. Coordinate and momentum space angular wave functions are identical for a given total energy and an asymptotically large value of [11]. To obtain the energy (E ) distribution of the particle we integrate the square of the resonance wave function over unobserved momenta.…”

“…This stability condition is difficult to reach when both three-body background continuum states are populated simultaneously with resonances in one or more of the two-body subsystems. At sufficiently large distances we can precisely identify these structures as components in the complex scaled wave functions related to different adiabatic potentials [11]; e.g., sequential decay proceeds through a potential approaching the corresponding complex two-body energy E 2b [10], whereas no intermediate structure is present for direct decay to the continuum.…”