Dice Question Streamline Icon: https://streamlinehq.com

Membership of 3^-_1, 4^-_1, and 5^-_1 States in the 12C Ground Rotational Band

Determine whether the 3^-_1, 4^-_1, and 5^-_1 states in the carbon-12 nucleus share the same intrinsic wave function as the 0^+_1, 2^+_1, and 4^+_2 states and hence constitute members of the ground rotational band formed by rotation of an equilateral triangular three-alpha intrinsic configuration.

Information Square Streamline Icon: https://streamlinehq.com

Background

The algebraic cluster model of Bijker and Iachello proposes that 12C has an intrinsic equilateral triangular three-alpha arrangement whose rotational excitations produce the ground band sequence 0+, 2+, 3-, 4±, and 5-; notably, the observed 4+_2 and 4-_1 are nearly degenerate, and a 5-_1 state has been identified, supporting this rotational picture.

In reconstructing the intrinsic density from electron-scattering form factors, the authors assume the 0+_1, 2+_1, 3-_1, and 4+_2 states share a common intrinsic state. However, they emphasize that experimental confirmation that the 3-_1, 4-_1, and 5-_1 states also belong to this same ground rotational band is currently lacking. They suggest that studies of α-decay and electromagnetic transitions, and measuring the transition form factor of the 5-_1 state, could provide evidence.

References

Next, let us consider a reasonable question of whether we can recognize the $3-_1$ state (and subsequently the $4-_1$ and $5-_1$ states) as members of the ground rotational band. We currently lack clear experimental evidence for this. Little is known about the $4-_1$ and $5-_1$ states except for their energies.

— Shape of 12C (2403.05287 - Kimura et al., 8 Mar 2024) in Subsection 'Discussions', Section 'Numerical results and discussion'