Effects of mutual excitations in the fusion of carbon isotopes

Abstract

Fusion data for 13 C+ 13 C, 12 C+ 13 C and 12 C+ 12 C are analyzed by coupled-channels calculations that are based on the M3Y+repulsion, double-folding potential. The fusion is determined by ingoingwave-boundary conditions (IWBC) that are imposed at the minimum of the pocket in the entrance channel potential. Quadrupole and octupole transitions to low-lying states in projectile and target are included in the calculations, as well as mutual excitations of these states. The effect of oneneutron transfer is also considered but the effect is small in the measured energy regime. It is shown that mutual excitations to high-lying states play a very important role in developing a comprehensive and consistent description of the measurements. Thus the shapes of the calculated cross sections for 12 C+ 13 C and 13 C+ 13 C are in good agreement with the data. The fusion cross sections for 12 C+ 12 C determined by the IWBC are generally larger than the measured cross sections but they are consistent with the maxima of some of the observed peak cross sections. They are therefore expected to provide an upper limit for the extrapolation into the low-energy regime of interest to astrophysics.

Correlation between the12C+12C,12C+Notani1, Esbensen2, Fang3 et al. 2012Phys. Rev. CSelf Cite

“…For 12 C+ 13 C and 13 C+ 13 C, the coupling effects to the excited 12 C core should also exist. For example, the 13 C(3/2 − , 3.684 MeV) included in our coupled-channels calculation can be interpreted as an oblate 12 C core with its 4.44 MeV(2 + ) state coupled to a p 1/2 valence neutron [22]. However, the resonance structures which should also exist in these two systems disappear due to the coupling of the valence neutron in 13 C. This result may not be so surprising.…”

“…Details of the calculation are presented in a separate paper [22]. Here we focus on the results shown by the solid red lines in Fig.…”

First Direct Measurement ofC12(C12Bucher1, Tang2, Fang3 et al. 2015Phys. Rev. Lett.323550View full textAdd to dashboardCite

“…For E cm ≤ 4.6 MeV, only the n 0 and n 1 channels are open. The theoretical ratio, σ ni(th) /σ pi(th) , is calculated using TALYS [29] combined with entrance channel spin populations supplied from a coupled-channels calculation by Esbensen [30]. The resonances in 12 C( 12 C,n i ) 23 Mg and 12 C( 12 C,p i ) 23 Na originate from both the molecular resonances in the entrance channel and the characteristic resonances in the final decay channels.…”

Constraining the12C+12C fusion cross section for astrophysics

“…Since the isotope systems are much easier to model due to their smooth behavior, such an upper limit could be predicted down through the astrophysical energy range. To this end, a coupled-channels (CC) calculation was done by H. Esbensen [15]. By using nuclear structure data for 12 C and 13 C, the experimental pointproton density for 12 C, and tuning the CC parameters to the 13 C+ 13 C measurement from Ref.…”

“…[20] which use the statistical model TALYS (www.talys.eu) with input from the CC calculation of Ref. [15] for the entrance channel spin populations. The agreement with experimental data provides confidence in the extrapolation to lower energies (Fig.…”