We study the phase structure and phase transition of cold dense QCD matter via the Dyson–Schwinger equation approach. We take the rainbow approximation and the Gaussian-type gluon model. In order to guarantee that the quark number density begins to appear at the nuclear liquid-gas phase transition chemical potential, we propose a chemical potential dependent modification factor for the gluon model. We find that for the iso-symmetric quark matter, the modification reduces the chemical potential of the phase coexistence region of the first-order phase transition. We also implement the relativistic mean field theory to describe the hadron matter, and make use of the Maxwell and Gibbs construction method to study the phase transition of \(\beta \)-equilibrium and charge neutral matter in compact stars. The results show that the phase transition will not happen in case of the Gaussian-type gluon model without any modification. The results also indicate that the upper boundary of the coexistence region should be larger than the current Nambu solution existing region. We also calculate the mass-radius relation of the compact stars, and find that the hadron-quark phase transition happens at too high chemical potential so that the maximum mass of the compact star is hardly affected by the hadron-quark phase transition.

我们通过戴森-施温格方程方法研究冷致密 QCD 物质的相结构和相变。我们采用彩虹近似和高斯型胶子模型。为了保证夸克数密度在核液气相变化学势处开始出现，我们为胶子模型提出了一个化学势相关的修正因子。我们发现，对于等对称夸克物质，修饰降低了一级相变相共存区的化学势。我们还实现了相对论平均场论来描述强子物质，并利用麦克斯韦和吉布斯构造方法来研究\(\beta \)-致密星中的平衡和电荷中性物质。结果表明，高斯型胶子模型在不作任何修改的情况下不会发生相变。结果还表明共存区域的上边界应大于当前南部解现有区域。我们还计算了致密星的质量半径关系，发现强子-夸克相变发生在过高的化学势下，致密星的最大质量几乎不受强子-夸克相变的影响。