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Manuscript Title: Energy eigenvalues and bound-bound transitions of hydrogen atoms in a magnetic field using cylindrical basis functions.
Authors: S.M. Kara
Program title: CPOLAR
Catalogue identifier: AAHK_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 20(1980)221
Programming language: Fortran.
Computer: CDC 7600.
Operating system: SCOPE.
RAM: 71K words
Word size: 60
Keywords: Atomic physics, Structure, Magnetic field, Hydrogen, Eigenvalues, Eigenvectors, Energy, Bound-bound transitions, Oscillator strength, Wavelength.
Classification: 2.1.

Nature of problem:
Calculates energy eigenvalues and corresponding eigenvectors of a hydrogen atom in a uniform static magnetic field and also determines the bound-bound transition probabilities, wavelengths and oscillator strengths. The wavefunctions are represented by a basis of cylindrical functions.

Solution method:
All integrals are calculated analytically and the eigenvalues and eigenvectors are found using routines from the NAG library. The eigenvalues are calculated using the method of bisection and corresponding eigenvectors by inverse iteration.

Restrictions:
Only transitions involving the first two states of each parity and m are considered, but the program requires only a simple modification to include more if desired. The dipole velocity formulation of the bound- bound transition probabilities is calculated only for delta m = 0 transitions i.e. only the nabla o matrix element is calculated.

Running time:
To calculate eigenvalues and eigenvectors of a basis consisting of 128 terms, for two different parity and m sets, and all possible transitions between the first and second states of each of the two sets the dipole length and velocity formulations, takes about 20 s CPU time depending on how many eigenvalues are being calculated (a maximum of 10).