用Fortran 90程序求解简谐势中自旋1/2费米子的Hartree-Fock方程
A Fortran 90 program to solve the Hartree-Fock equations for interacting spin-1/2 Fermions confined in Harmonic potentials
摘要：
一组弱相互作用的自旋为1/2的费米子，受谐振子势的约束，通过接触势相互作用，是一个模型系统，它很好地描述了磁光阱中两组分费米子原子的稀气体物理。在目前的工作中，我们的目的是提出一个Fortran 90计算机程序，使用基组扩展技术，解决Hartree-Fock（HF）方程的自旋1/2 $ Fermions confined by a three-dimensional harmonic oscillator potential, and interacting with each other via pair-wise delta-function potentials. Additionally, the program can also account for those anharmonic potentials which can be expressed as a polynomial in the position operators $ x，$ $ y $, and $ z$。限制HF（RHF）和非限制HF（UHF）方程都可以求解给定数量的费米子，它们之间存在排斥或吸引相互作用。这种系统的UHF解决方案的选择，也使我们能够研究可能的磁性物理的两个组件的限制原子费米气体，与不平衡的人口。使用我们的代码，我们还证明了这样的系统具有壳结构，并遵循Hund的规则。
英文摘要：
A set of weakly interacting spin-1/2 Fermions, confined by a harmonic oscillator potential, and interacting with each other via a contact potential, is a model system which closely represents the physics of a dilute gas of two-component Fermionic atoms confined in a magneto-optic trap. In the present work, our aim is to present a Fortran 90 computer program which, using a basis set expansion technique, solves the Hartree-Fock (HF) equations for spin-1/2$ Fermions confined by a three-dimensional harmonic oscillator potential, and interacting with each other via pair-wise delta-function potentials. Additionally, the program can also account for those anharmonic potentials which can be expressed as a polynomial in the position operators $x,$ $y$, and $z$. Both the restricted-HF (RHF), and the unrestricted-HF (UHF) equations can be solved for a given number of Fermions, with either repulsive or attractive interactions among them. The option of UHF solutions for such systems also allows us to study possible magnetic properties of the physics of two-component confined atomic Fermi gases, with imbalanced populations. Using our code we also demonstrate that such a system exhibits shell structure, and follows Hund's rule.
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