Correlation between the12C+12C,12C+

M. Notani

¹

,

H. Esbensen

²

,

X. Fang

³

et al.

Abstract

The fusion cross section for 12 C+ 13 C has been measured down to Ec.m.=2.6 MeV at which the cross section is of the order of 20 nb. By comparing the cross sections for the three carbon isotope systems, 12 C+ 12 C, 12 C+ 13 C and 13 C+ 13 C, it is found that the cross sections for 12 C+ 13 C and 13 C+ 13 C provide an upper limit for the fusion cross section of 12 C+ 12 C over a wide energy range. After calibrating the effective nuclear potential for 12 C+ 12 C using the 12 C+ 13 C and 13 C+ 13 C fusion cross sections, it is found that a coupled-channels calculation with the Incoming Wave Boundary Condition (IWBC) is capable of predicting the major peak cross sections in 12 C+ 12 C. A qualitative explanation for this upper limit is provided by the Nogami-Imanishi model and level density differences among the compound nuclei. It is found that the strong resonance found at 2.14 MeV in 12 C+ 12 C exceeds this upper limit by a factor of more than 20. The preliminary result from the most recent measurement shows a much smaller cross section at this energy which agrees with our predicted upper limit.

Constraining the12C+12C fusion cross section for astrophysics

“…The details of the experiment can be found in Ref. [13]. The results show good agreement with the previous measurement from Ref.…”

“…This correlation holds true across the entire measured energy range, except the unusually strong resonance reported by Spillane [10]. The reason for this has been explained as due to the relatively lower level density in the compound nucleus for 12 C+ 12 C compared to 12 C+ 13 C and 13 C+ 13 C [13,14]. As a result, the isotope fusion systems provide an upper limit for the 12 C+ 12 C system.…”

“…This suggests that if these resonances exist, they must be present due to some unknown phenomenon that is not present for the resonances observed at higher energies. A more likely explanation is that such large resonances in the 12 C+ 12 C system do not exist and the observation by Spillane was influenced by a beam-induced background reaction that was not taken into account [13,17]. Indeed, a more recent low-energy measurement [17] was unable to confirm the existence of this resonance in the proton channel (Fig.…”

“…The main background source in the total neutron yield was due to 12 C+ 13 C→ 24 Mg+n where 13 C was naturally present in the target at 1.1%. To measure the neutron yield from this reaction, a 13 C beam was used, and the yield curve was measured across the same energy range in the center-of-mass.…”

“…[12], 12 C+ 13 C from Ref. [11], and 12 C+ 13 C from ND [13]. and 13 C+ 13 C cross sections were known to display much smoother behavior below the Coulomb barrier [11,12].…”