Energy Distributions from Three-Body Decaying Many-Body Resonances

Abstract

We compute energy distributions of three particles emerging from decaying many-body resonances. We reproduce the measured energy distributions from decays of two archetypal states chosen as the lowest 0 and 1 resonances in 12 C populated in decays. These states are dominated by sequential, through the 8 Be ground state, and direct decays, respectively. These decay mechanisms are reflected in the ''dynamic'' evolution from small, cluster or shell-model states, to large distances, where the coordinate or momentum space continuum wave functions are accurately computed.

Three-body decays andR-matrix analyses

“…To have a clean simulation we therefore select unnatural parity states and ignore the 4 + contribution. The structure and decays of 12 C are recently investigated and described in [7,[17][18][19]. The 2 + energy is E 2r = 2.7 MeV above the threshold for separation into two free α-particles and the width is 2r = 1.5 MeV.…”

“…Then the Breit-Wigner approximation for the sequential part is fairly accurate. Examples of this are rather abundant among the natural parity states of 12 C. We have in earlier publications discussed prominent examples like the Hoyle state and the second 0 + resonance in 12 C [7,19]. When E 3r is too small compared to 2r distinction is meaningless because the degrees of freedom are completely entangled.…”

“…With the realistic resonance parameters the distributions reproduce the measured results for the 1 + state; see Refs. [7,19,21]. We next attempt to investigate the connection to the basic assumption in the R-matrix formalism, i.e., the two-step process of two consecutive sequential decays.…”

“…Parity conservation prevents the state from decaying sequentially by α emission to the narrow 0 + ground state of 8 Be. In the literature, the three characteristic peaks from the breakup of this state have been described as signatures of both sequential [4][5][6] and direct [3,7] breakup.…”

Three-body properties of low-lying12Be resonances

“…1, each adiabatic potential corresponds to a very specific asymptotic configuration, i.e., bound 11 Be (either in the ground state or in the excited state) plus a neutron, 11 Be populating a twobody resonance plus a neutron, or the three constituents in the continuum. This is because the observable final-state momenta of each of the emerging particles precisely are reflected in the coordinate wave function at asymptotic large distances [8,45]. The probability of decaying through a given channel is then the probability of occupying the adiabatic potential describing that channel at large distance.…”