The properties of the low-energy <math><mmultiscripts><mrow><mi>C</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>12</mn></mrow></mmultiscripts><mo>+</mo><msup><mrow></mrow><mrow><mn>12</mn></mrow></msup><mi>C</mi></math> molecular resonances, which potentially enhance the fusion reaction rate at low temperatures, have been investigated by a full-microscopic nuclear model employing various nuclear energy density functionals. We show that some density functionals plausibly describe the observed high-spin <math><mmultiscripts><mrow><mi>C</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>12</mn></mrow></mmultiscripts><mo>+</mo><msup><mrow></mrow><mrow><mn>12</mn></mrow></msup><mi>C</mi></math> molecular resonances and predict many <math><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math> and <math><msup><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msup></math> resonances at low energies, which enhance the reaction rate. We also discuss how the uncertainty in the nuclear energy density functionals propagates to that of the reaction rate.

Japan

Yasutaka Taniguchi

Masaaki Kimura

Impact of the molecular resonances on the Fusion Reaction Rate

The <math><mmultiscripts><mrow><mi>C</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>12</mn></mrow></mmultiscripts><mo>+</mo><msup><mrow></mrow><mrow><mn>12</mn></mrow></msup><mi>C</mi></math> fusion reaction plays a vital role in the explosive phenomena of the universe. The resonances in the Gamow window rule its reaction rate and products. Hence, the determination of the resonance parameters by nuclear models is indispensable as the direct measurement is not feasible. Here, for the first time, we report the resonances in the <math><mmultiscripts><mrow><mi>C</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>12</mn></mrow></mmultiscripts><mo>+</mo><msup><mrow></mrow><mrow><mn>12</mn></mrow></msup><mi>C</mi></math> fusion reaction described by a full-microscopic nuclear model. The model plausibly reproduces the measured low-energy astrophysical S-factors and predicts the resonances in the Gamow window. Contradictory to the hindrance model, we conclude that there is no low-energy suppression of the S-factor.

Fusion -factor From a Full-microscopic Nuclear Model

The existence of <math><mmultiscripts><mrow><mi>C</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>12</mn></mrow></mmultiscripts><mo>+</mo><msup><mrow></mrow><mrow><mn>16</mn></mrow></msup><mi>O</mi></math> molecular resonances at sub-barrier energy has been a significant problem in nuclear astrophysics because they strongly affect the <math><mmultiscripts><mrow><mi>C</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>12</mn></mrow></mmultiscripts><mo>+</mo><msup><mrow></mrow><mrow><mn>16</mn></mrow></msup><mi>O</mi></math> fusion reaction rate in type Ia supernovae and heavy stars. However, experimental surveys have been limited to 4 MeV and cannot access the deep sub-barrier energy due to a very small fusion cross section. Here we predict a couple of resonances with <math><msup><mrow><mi>J</mi></mrow><mrow><mi>π</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math>, <math><msup><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msup></math>, and <math><msup><mrow><mn>4</mn></mrow><mrow><mo>+</mo></mrow></msup></math> in the deep sub-barrier energy based on the antisymmetrized molecular dynamics calculation that reproduces the known resonances and low-lying spectrum of <math><mmultiscripts><mrow><mi>Si</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>28</mn></mrow></mmultiscripts></math>.