A Fortran 90 program to solve the Hartree–Fock equations for interacting spin- 1 2 fermions confined in harmonic potentials

Abstract
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-di...

Title of program: trap.x
Catalogue Id: AEBB_v1_0

Nature of problem
The simplest description of a spin ½ trapped system at the mean field level is given by the Hartree-Fock method. This program presents an efficient approach to solving these equations. Additionally, this program can solve for time-independent Gross-Pitaevskii and Hartree-Fock equations for bosonic atoms confined in a harmonic trap. Thus the combined program can handle mean-field equations for both the fermi and the bose particles.

Versions of this program held in the CPC repository in Mendeley Data
AEBB_v1_0; trap.x; 10.1016/j.cpc.2008.04.004

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
一组受简谐势（harmonic oscillator potential）约束、通过接触势（contact potential）相互作用的弱相互作用自旋1/2费米子，是一类紧密模拟磁光阱（magneto-optic trap）中双组分费米原子稀薄气体物理特性的模型系统。本研究旨在提供一套Fortran 90计算机程序，该程序采用基组展开技术，求解受三维（原文截断）简谐势约束的自旋1/2费米子的哈特利-福克（Hartree–Fock, HF）方程。

程序名称：trap.x
目录标识：AEBB_v1_0

问题概述
受约束自旋1/2体系在平均场近似下的最简描述由哈特利-福克方法给出。本程序提供了一种高效求解上述方程的途径。此外，本程序还可求解简谐势约束下玻色原子的不含时格罗斯-皮塔耶夫斯基（Gross-Pitaevskii）方程与哈特利-福克方程。因此，本集成程序可同时处理费米子与玻色粒子的平均场方程。

本程序存放在Mendeley数据的CPC程序库中，版本为AEBB_v1_0；对应程序为trap.x；DOI：10.1016/j.cpc.2008.04.004

本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2019）