论文标题
保护近似以稀释平衡系统。配对相互作用电位
Conserving approximations to dilute equilibrium systems. Pair interaction potential
论文作者
论文摘要
我们研究了自洽的近似值，例如$φ$衍生和病毒的方法，以稀释平衡中强烈相互作用的系统。我们认为，通过一对潜在的热力学数量相互作用的一种非权威主义费物的系统由各种光谱函数表示。我们回顾了$φ$衍生的近似方案，证明了Noether和Botermans-Malfliet fermion数量密度的确切保守性，然后以$φ$描述的$φ$，我们显示了这两个数字密度的巧合。作为测试对电位的示例，我们考虑了Walecka，CD Bonn和Reid参数化的Yukawa Central Nucleon-Nucleon电位，以及相应的经典Lennard-Jones电位。 tadpole和三明治图描述的$φ$得出第二和第三个病毒系数的表达式。接下来，我们专注于对国家方程式的病毒方法。详细研究了经典，半经典和纯粹的量子方法。然后，考虑了状态病毒方程的不同外推，包括范〜der〜waal形式和排除数量模型。我们使用有效范围近似来得出第二个病毒系数的表达式，并使用实验相移比较结果与纯量子结果进行比较。注意力集中在由于核子核子散射中存在准结合状态而出现的核子核子散射长度异常值的问题，由于保利（Pauli）阻塞的作用，这可能会在此问题中破坏。我们介绍了该术语的第二个病毒系数减去第二个病毒系数的结果。我们讨论了这种程序在病毒限制中描述核问题状态方程的有效性。
We study self-consistent approximations such as the $Φ$-derivable and virial approaches to dilute strongly interacting systems in equilibrium. We consider a system of non-relativistic fermions of one kind interacting via a pair potential Thermodynamical quantities are expressed in terms of various spectral functions. We review the $Φ$ derivable approximation scheme demonstrating the exact conservation of the Noether and the Botermans-Malfliet fermion number densities, and then for $Φ$ described by the tadpole and sandwich diagrams we show the coincidence of these two number densities. As examples of test pair potentials, we consider the Yukawa central nucleon-nucleon potentials within Walecka, CD Bonn, and Reid parameterizations, and the corresponding classical Lennard-Jones potentials. Expressions for the second and third virial coefficients are derived and analyzed for $Φ$ described by the tadpole and sandwich diagrams. Next, we focus on the virial approach to the equation of state. Classical, semiclassical, and purely quantum approaches are studied in detail. Then, different extrapolations of the virial equation of state are considered including the van~der~Waals form and excluded-volume models. We derive the expression for the second virial coefficient using the effective range approximation for the scattering amplitude and compare the result with the purely quantum result using the experimental phase shifts. Attention is focused on the problem of anomalously large value of the nucleon-nucleon scattering length appearing due to the presence of the quasi-bound state in nucleon-nucleon scattering, which can be destroyed in the matter because of the action of the Pauli blocking. We present results for the second virial coefficient subtracting this term. We discuss the validity of such a procedure to describe the equation of state of the nuclear matter in the virial limit.
