Microscopic Descriptions of ¹²C+α for the Oxygen-16 States in the Stellar Alpha-Capture Rate Evaluation

We report the first calculations of low-lying excited 0⁺ states in ¹⁶O and their rotational bands within a no-core shell-model framework. Such descriptions pose a challenge as a result of the cluster and collective nature of these states, but become feasible in the no-core symplectic shell model (NCSpM). The model utilizes the almost perfect symmetry of nuclear dynamics, the symplectic symmetry that preserves equilibrium shapes. It uses an inter-nucleon interaction deduced in the symplectic effective field theory, with only four parameters. The NCSpM yields the low-lying positive-parity energy spectrum of ¹⁶O, electric quadrupole transition strengths, and the ground-state rms radius, in a reasonable agreement with experiment. We use the NCSpM wave functions of the first two excited 0⁺ states, their rotational bands, and the low-lying 1^- and 3^- states in ¹⁶O to project onto ¹²C+α cluster wave functions. Using the cluster wave functions, we calculate alpha partial widths and asymptotic normalization coefficients. Our results are in good agreement with available experimental data and point to the importance of collectivity to reproduce the data. These results are crucial to further improving the evaluation of the  ¹²C(α, γ)¹⁶O reaction rate at astrophysical temperatures. This rate is also of cosmological importance and may further inform studies of the masses of black holes produced by pulse pair instability supernovae.