Three-body bremsstrahlung and the rotational character of the 12C-spectrum

TL;DR

This paper investigates electric quadrupole transitions in 12C using a three-alpha model, deriving cross sections and analyzing the rotational structure of the nucleus's resonant states.

Contribution

It introduces a detailed three-body calculation of 12C's continuum states and compares the rotational patterns with schematic models, providing new insights into its nuclear structure.

Findings

Reproduces experimental energy dependence of cross sections.

Predicts additional cross sections for 12C resonances.

Identifies two rotational bands with distinct alpha configurations.

Abstract

The electric quadrupole transitions between $0^+$, $2^+$, and $4^+$ states in $^{12}$C are investigated in a $3\alpha$ model. The three-body wave functions are obtained by means of the hyperspherical adiabatic expansion method, and the continuum is discretized by imposing a box boundary condition. Corresponding expressions for the continuum three-body ($3\alpha$) bremsstrahlung and photon dissociation cross sections are derived and computed for two different $\alpha-\alpha$ potentials. The available experimental energy dependence is reproduced and a series of other cross sections are predicted. The transition strengths are defined and derived from the cross sections, and compared to schematic rotational model predictions. The computed properties of the $^{12}$C resonances suggest that the two lowest bands are made, respectively, by the states $\{0^+_1, 2^+_1, 4^+_2\}$ and $\{0^+_2, 2^+_2, 4^+_1\}$. The transitions between the states in the first band are consistent with the rotational pattern corresponding to three alphas in an equal sided triangular structure. For the second band, the transitions are also consistent with a rotational pattern, but with the three alphas in an aligned distribution.