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Manuscript Title: Calculation of atomic energy level values.
Authors: L.J. Radziemski Jr., K.J. Fisher, D.W. Steinhaus, A.S. Goldman
Program title: LEVEL
Catalogue identifier: AAKD_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 3(1972)9
Programming language: Fortran.
Computer: CDC 6600.
Operating system: SCOPE 3.1.2.
Program overlaid: yes
RAM: 55K words
Word size: 60
Peripherals: magnetic tape, disc, drum.
Keywords: Atomic physics, Energy level, Least squares solution, Matrix inversion, Isotopic shift, Structure.
Classification: 2.1.

Nature of problem:
An atomic energy level array consists of two sets of energy levels of different parity and transitions between them (we exclude transitions within sets). There are wide variations in the accuracies of the wave number values of observed classified transitions, and usually many more observed transitions than energy levels. The problem is to determine the best values for the levels and their uncertainties. The uncertainties are very important because these are used to determine the accuracies of wave numbers computed from the energy levels. Calculation of level isotope shifts can also be made since this is a trivial variation of the level calculation problem.

Solution method:
The normal equations obtained from the least squares formulation are partitioned to reduce the size of the matrix to be inverted to the magnitude of the smaller set of energy levels. The variance-covariance matrix is used to compute corrections to the values of the energy levels and to compute variances on the levels and on the computed wave numbers. The method of inversion produces results with round-off error beyond the significance of the data involved with this kind of physical problem. Only half of the symmetric matrix is stored, and the inverse is stored in the same location so storage requirements are minimized.

High speed core storage of 64 000 words limits the number of levels on the small side to 285 and the number of classifications to 19 000.