Low-energy ${}^{12}$C continuum states in three-$\alpha$ model

TL;DR

This paper investigates low-energy continuum states of carbon-12 using a three-alpha model, calculating transition strengths and resonance parameters to compare with experimental data and analyze interaction model dependencies.

Contribution

It introduces phenomenological three-alpha Hamiltonians with various potentials and computes transition strengths and resonance parameters using Faddeev formalism, providing new insights into ${}^{12}$C continuum states.

Findings

Resonance energies and widths are extracted for ${}^{12}$C states.

Transition strength distributions are calculated and compared with experiments.

Interaction potential models influence the resonance parameters and spectra.

Abstract

The electric multipole strength distributions for transitions from the ${}^{12}\mathrm{C}(0_1^+)$ ground state to $3\alpha$ ($0^+$, $1^-$, $2^+$, and $3^-$) continuum states are studied in terms of $3\alpha$ model. Several sets of the $3\alpha$ Hamiltonian are introduced phenomenologically with conventional $\alpha$-$\alpha$ interaction potentials and $3\alpha$ potentials with different range parameters. The transition strength distributions are obtained from wave functions of $3\alpha$ bound- and continuum states calculated by the Faddeev three-body formalism. From these strength distributions, the resonance parameters (energy, $3\alpha$-decay width, and transition strength) of $3\alpha$ resonance states are extracted. Dependencies of these observables on interaction potential models are studied to examine the introduced interaction models. Using the transition strength distributions, excitation-energy spectra in the ${}^{12}\mathrm{C}(\alpha,\alpha^\prime)3\alpha$ reaction are calculated to compare with experimental data.