Role of the shape deformation in 12C + 12C fusion at sub-Coulomb energies

Le Hoang Chien ,Vy Nguyen Ha Thach,Anh Bui

doi:10.32508/stdjns.v2i4.818

Abstract

The fusion cross section of 12C+12C system at the energies of astrophysical interest is calculated in the framework of barrier penetration model taking into account the deformed shape of interacting nuclei. In particular, the quadrupole surface deformation of both projectile and target nuclei has been included during the fusion process. The real and imaginary parts of nucleus-nucleus interactions performed using the Woods-Saxon square and Woods-Saxon functions, respectively have been carefully tested by 12C-12C elastic scattering data analysis before employed to evaluate the astrophysical S factors (the fusion cross sections). The optical model results of elastic angular distributions are consistent with the experimental data. Within the barrier penetration model, the real part of the obtained optical potential gives a good description of the non-resonant astrophysical S factor. It turns out that the taking into account of quadrupole deformation of 12C nuclei increases the astrophysical S factor at energies below Coulomb barrier.

Highlights

Study of 12C+12C fusion at low energies is important to understand the carbon burning stage in the massive stars
The stars themselves increase their temperature to 108 K at which two 12C nuclei gain enough energy to fuse into each other and generate heavy elements such as 20Ne, 23Na, 23Mg. Such typical condition in the stars corresponding to the thermal energy less than 1.5 MeV is not achieved in the experiments at the present time because the fusion cross section is estimated to be very small, in the order of 10-10 mb
We focus on two important problems relevant to the 12C+12C fusion at energies below the Coulomb barrier

Summary

Introduction

Study of 12C+12C fusion at low energies is important to understand the carbon burning stage in the massive stars (at least eight times of solar mass). The stars themselves increase their temperature to 108 K at which two 12C nuclei gain enough energy to fuse into each other and generate heavy elements such as 20Ne, 23Na, 23Mg. Due to gravitational collapse, the stars themselves increase their temperature to 108 K at which two 12C nuclei gain enough energy to fuse into each other and generate heavy elements such as 20Ne, 23Na, 23Mg Such typical condition in the stars corresponding to the thermal energy less than 1.5 MeV is not achieved in the experiments at the present time because the fusion cross section is estimated to be very small, in the order of 10-10 mb. During the last four decades, 12C+12C fusion at low energies still attracts a lot of experimental and theoretical efforts [2,3,4,5,6,7,8,9,10,11,12]

Methods

Results

Conclusion