Fusion cross sections for 12C + 12C, 12C + 13C and 13C + 13C at low energies

doi:10.1016/0375-9474(82)90316-5

Nuclear Physics A

Volume 384, Issues 1–2, 9–16 August 1982, Pages 257-272

https://doi.org/10.1016/0375-9474(82)90316-5 Get rights and content

Abstract

Fusion cross sections for ¹²C + ¹²C and ¹²C + ¹³C have been measured by the total-γ-ray- yield method over the c.m. energy intervals 4.2–7.0 MeV and 3.1–6.7 MeV, respectively. Comparing the present ¹²C + ¹²C fusion cross sections with those obtained previously by various methods, the discrepancies between data are clarified. The fusion cross sections for ¹²C + ¹³C agree with those of Dayras et al. and confirm the unusual energy dependence below the interaction barrier. The fusion cross sections for the ¹²C + ¹³C and ¹³C + ¹³C systems are found to be enhanced with respect to the ¹²C + ¹²C system more than the increase in the nuclear radius suggests. The enhancement, which is larger for ¹²C + ¹³C than for ¹³C + ¹³C, is attributed to the attractive action of the valence neutron of the ¹³C nucleus. A new resonance has been observed in the ¹²C + ¹²C system at E_c.m. ≈ 5.22 MeV.

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Constraining the 12C+12C astrophysical S-factors with the 12C+13C measurements at very low energies
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Citation Excerpt :
The total fusion cross sections over the full energy range measured in this work are converted from the measured cross sections of the 12C(13C,p)24Na channel based on the statistical model calculations, and hence a reliable branching ratio of the proton channel with a quantified uncertainty is needed. The experimental branching ratio is obtained by comparing the 12C(13C,p)24Na cross sections to the two sets of measured total fusion cross sections [17,18] (Fig. 4). Two different statistical model codes, Talys [26] and Empire [27], are used to calculate the branching ratio (see Fig. 4).
We use an underground counting lab with an extremely low background to perform an activity measurement for the ${}^{12}C +^{13} C$ system with energies down to $E_{c . m .} = 2.323$ MeV, at which the ¹²C(¹³C,p)²⁴Na cross section is found to be 0.22(7) nb. The ${}^{12}C +^{13} C$ fusion cross section is derived with a statistical model calibrated using experimental data. Our new result of the ${}^{12}C +^{13} C$ fusion cross section is the first decisive evidence in the carbon isotope systems which rules out the existence of the astrophysical S-factor maximum predicted by the phenomenological hindrance model, while confirming the rising trend of the S-factor towards lower energies predicted by other models, such as CC-M3Y+Rep, DC-TDHF, KNS, SPP and ESW. After normalizing the model predictions with our data, a more reliable upper limit is established for the ${}^{12}C +^{12} C$ fusion cross sections at stellar energies.
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^†: On leave of absence from the University of Burdwan, Burdwan 713104, West Bengal, India.

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Nuclear Physics A

Abstract

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Theoretical exploration of S-factors for nuclear reactions of astrophysical importance

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Study of the hindrance effect in sub-barrier fusion reactions