Asymptotic normalization coefficients for α+C12 synthesis and the S factor for C12(α,γ)O16 radiative capture

Mukhamedzhanov, A M; deBoer, R J; Irgaziev, B F; Blokhintsev, L D; Kadyrov, A S; Savin, D A

doi:10.1103/PhysRevC.110.055803

: The

{}^{12}C (α, γ) {}^{16}O

reaction, determining the survival of carbon in red giants, is of interest for nuclear reaction theory and nuclear astrophysics. A specific feature of the

{}^{16}O

nuclear structure is the presence of two subthreshold bound states, (6.92 MeV,

2^{+}

) and (7.12 MeV,

1^{-}

), that dominate the behavior of the low-energy

S

factor. The strength of these subthreshold states is determined by their asymptotic normalization coefficients (ANCs), which need to be known with high accuracy. : The objective of this research is to examine how the subthreshold and ground-state ANCs impact the low-energy

S

factor, especially at the key astrophysical energy of

300 keV

. The

S

factors are calculated within the framework of the

R

-matrix method using the code. Our total

S

factor takes into account the

E 1

and

E 2

transitions to the ground state of

{}^{16}O

including the interference of the subthreshold and higher resonances, which also interfere with the corresponding direct captures, and cascade radiative captures to the ground state of

{}^{16}O

through four subthreshold states:

0_{2}^{+}, 3^{-}, 2^{+}

, and

1^{-}

. To evaluate the impact of subthreshold ANCs on the low-energy

S

factor, we employ two sets of the ANCs. The first selection, which offers higher ANC values, is attained through the extrapolation process [Blokhintsev , ]. The set with low ANC values was employed by deBoer []. A detailed comparison of the

S

factors at the most effective astrophysical energy of 300 keV is provided, along with an investigation into how the ground-state ANC affects this

S

factor. : The contribution to the total

E 1

and

E 2 S

factors from the corresponding subthreshold resonances at

300 keV

are

(71 - 74) %

and

(102 - 103) %

, respectively. The correlation of the uncertainties of the subthreshold ANCs with the

E 1

and

E 2 S (300 keV)

factors is found. The

E 1

transition of the subthreshold resonance

1^{-}

does not depend on the ground-state ANC but interferes constructively with a broad

(9.585 MeV; 1^{-})

resonance giving (for the present subthreshold ANC) an additional

26 %

contribution to the total

E 1 S (300 keV)

factor. Interference of the

E 2

transition through the subthreshold resonance

2^{+}

with direct capture is almost negligible for small ground-state ANC of

58 {fm}^{- 1 / 2}

. However, its interference with direct capture for higher ground-state ANC of

337 {fm}^{- 1 / 2}

is significant and destructive, contributing

- 27 %

. The low-energy

S_{E 2} (300 keV)

factor experiences a smaller increase when both subthfreshold and the ground-state ANCs rise together due to their anticorrelation, compared to when only the subthreshold ANCs increase. Published by the American Physical Society2024

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