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Manuscript Title: A Fortran 90 program to solve the Hartree-Fock equations for interacting spin-½ Fermions confined in Harmonic potentials
Authors: Hridis Kumar Pal, Alok Shukla
Program title: trap.x
Catalogue identifier: AEBB_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 179(2008)267
Programming language: mostly Fortran 90.
Computer: PCs - SUN, HP Alpha, IBM.
Operating system: Linux, Solaris, Tru64, AIX.
Keywords: Trapped Fermi gases, Hartree-Fock Equation Numerical Solutions.
PACS: 02.70.-c, 02.70.Hm, 03.75.Ss, 73.21.La.
Classification: 7.7.

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.

Solution method:
The solutions of the Hartree-Fock equation corresponding to the fermi systems in atomic traps are expanded as linear combinations of simple-harmonic oscillator eigenfunctions. Thus, the Hartree-Fock equations which comprise a set of nonlinear integro-differential equations, is transformed into a matrix eigenvalue problem. Thereby, its solutions are obtained in a self-consistent manner, using methods of computational linear algebra.

Running time:
The run times of example jobs are from a few seconds to a few minutes. For jobs involving very large basis sets, the run time can extend into hours.