标题： 一个简单的示意图模型用于解释$^{12}$C+$^{12}$C 融合反应中的截面亏损 显示英文标题

标题： A simple schematic model for a cross section deficit in $^{12}$C+$^{12}$C fusion reactions

摘要： 在天体物理能量下，观察到了在$^{12}$C+$^{12}$C 融合反应中的截面亏缺现象，在这种情况下，融合截面在非共振区域被抑制，与$^{12}$C+$^{13}$C 系统的融合截面相比。 我在此构建了一个简单的示意图模型来模拟这一现象。 该模型由基于高斯正交系综（GOE）的随机矩阵哈密顿量组成，该哈密顿量在离散基态表示中耦合到一个入口通道哈密顿量。 我展示了当 GOE 配置的能级密度和衰减宽度都很大时，透射系数几乎为1，实现了强吸收区。 另一方面，当这些参数较小时，透射系数随能量显著变化。 在这种情况下，模型中的共振能量处的透射系数达到1，这与截面亏缺的实验发现一致。 显示英文摘要

摘要： A cross section deficit phenomenon has been observed in $^{12}$C+$^{12}$C fusion reactions at astrophysical energies, at which fusion cross sections are suppressed in the off-resonance regions as compared to fusion cross sections for the $^{12}$C+$^{13}$C system. I here construct a simple schematic model which simulates this phenomenon. The model consists of a random matrix Hamiltonian based on the Gaussian Orthogonal Ensemble (GOE), which is coupled to an entrance channel Hamiltonian in the discrete basis representation. I show that the transmission coefficients are almost unity when both the level density and the decay widths of the GOE configurations are large, realizing the strong absorption regime. On the other hand, when these parameters are small, the transmission coefficients are significantly structured as a function of energy. In that situation, the transmission coefficients at resonance energies reach unity in this model, that is consistent with the experimental finding of the cross section deficit.