Absence of hindrance in a microscopic C12+C12 fusion study

Abstract

Background: Studies of low-energy fusion of light nuclei are important in astrophysical modeling, with small variations in reaction rates having a large impact on nucleosynthesis yields. Due to the lack of experimental data at astrophysical energies, extrapolation and microscopic methods are needed to model fusion probabilities. Purpose: To investigate deep sub-barrier 12 C+ 12 C fusion cross sections and establish trends for the S factor. Method: Microscopic methods based on static Hartree-Fock and time-dependent Hartree-Fock (TDHF) meanfield theory are used to obtain 12 C+ 12 C ion-ion fusion potentials. Fusion cross sections and astrophysical S factors are then calculated using the incoming wave boundary condition method. Results: Both density-constrained frozen Hartree-Fock (DCFHF) and density-constrained TDHF (DC-TDHF) predict a rising S factor at low energies, with DC-TDHF predicting a slight damping in the deep sub-barrier region (≈1 MeV). Comparison between DC-TDHF calculations and maximum experimental cross sections in the resonance peaks are good. However, the discrepancy in experimental low-energy results inhibits interpretation of the trend. Conclusions: Using the fully microscopic DCFHF and DC-TDHF methods, no S factor maximum is observed in the 12 C+ 12 C fusion reaction. In addition, no extreme sub-barrier hindrance is predicted at low energies. The development of a microscopic theory of fusion including resonance effects, as well as further experiments at lower energies must be done before the deep sub-barrier behavior of the reaction can be established.

Status on $$^{\mathbf {12}}\mathbf {C}+{}^{\mathbf {12}}{\mathbf {C}}$$ fusion at deep subbarrier energies: impact of resonances on astrophysical $$S^{*}$$ factors

“…Their simple extrapolation agrees reasonably with some recent theoretical calculations, such as CC-M3Y+Rep [10], TDWP [11] and barrier penetration model based on the global Sáo Paulo potentials (SPP) [12], see Fig. 1, as well with sophisticated coupledchannels calculations [13,14] and recent Hartree-Fock and time-dependent Hartree-Fock calculations [15]. We note that the predictions based on the CC-M3Y+Rep method are considered to be the upper limit of the 12 C+ 12 C fusion cross section [16,17].…”

“…The assigned in [8] spin 1 − for the resonance at 0.877 MeV is a mistake because a resonance with negative parity cannot be populated in the collision of two identical bosons such as 12 MeV, which is inside the Gamow window, is of a crucial importance for the 12 C − 12 C fusion rates and will play the same role as the "Hoyle" state [29] in the triple-α process of synthesis of 12 C [30]. Note that the models using the global potentials in [10,11,31,32] can predict resonances only above E = 2.5 MeV (the TDHF calculations of [15] do not take into account any possible resonant behavior in the fusion process). The THM data at low energies call for an improvement of the theoretical models.…”

Description of the asymmetric to symmetric fission transition in the neutron-deficient thorium isotopes: Role of the tensor force

“…To our knowledge, the impact of the tensor term in the potential energy surface and collective inertia required for fission has never been investigated. On the other hand, the role played by the tensor term has been investigated recently in several fusion studies [51][52][53][54][55]. The tensor interaction rearranges the position of the single particle orbitals changing the shell effects responsible for many of the properties of the quantities relevant to fission.…”

Influence of the tensor interaction on heavy-ion fusion cross sections

“…The density-constraint that is performed to the evolved densities is what provides the static collective energy which is then interpreted as the ion-ion interaction potential. The DC-TDHF approach has been applied to many systems spanning the nuclear chart and the fusion cross sec-tion results generally agree well with available experimental data [28][29][30][31][32][33][34][35][36][37][38][39]. By themselves, direct TDHF calculations have been used in recent years to investigate the impact of the tensor force on heavy-ion collisions [40][41][42][43][44], though no studies employing phenomenological nor microscopic methods for obtaining ion-ion potentials have included the tensor interaction until recently [45].…”

“…forces. 12 C + 12 C plays a significant role in nucleosynthesis and the r-process and thus the energies of focus are often in the extreme sub-barrier regime (≈ 1 MeV) [39,[56][57][58]. Figure 1 spans the entire sub-barrier region, though the large range of values prohibits a close comparison of extreme sub-barrier values.…”