Multi-Electron Coefficients of Fractional Parentage

for p, d, and f Electrons

This is the home page of the multi-electron coefficients of fractional parentage for p, d, and f electrons. It is intended
as a permanent resource of the CFP data, and provides it in two different formats: regular-text format and PostScript
format. Any portion, or the whole database (in either format) can be downloaded (as compressed files) from this site.

In the PostScript format the CFP-data is one complete document, tabulating the numerical values of the fractional
parentage coefficients from the respective complete minimal subsets of multi-electron CFPs for p, d, and f electrons.
Since the complete document is almost 2,900 pages long, it is broken into 36 separate PostScript files, where each individual file covers certain range of pages from the complete document. To view the brief description of the contents
(ranges) of the PostScript files, and/or download a particular file, go to the PostScript Format Database.

In the regular-text format the CFP-data is organized in a slightly different fashion, and can be thought of as being
composed of different blocks (with respect to body-number and electron type). This internal organization reflects
the different functional purpose of the regular-text database. It is intended primarily as data-input to computer
programs that seek to utilize the numerical values of the multi-electron fractional parentage coefficients in automated
computations. Hence, besides tabulating the CFPs, the regular-text files also feature some tag-lines (markers), that
can serve as cues to a reading subroutine. To view the brief description of the contents (ranges) of the regular-text
files, and/or download a particular file, go to the Regular-Text Format Database.

Basic Definitions and Terminology

Notation: An individual coefficient of fractional parentage is defined (both in the regular-text and
PostScript format databases) via five descriptors:

body-number

daughter-term configuration the configuration to which
the spectroscopic term of the daughter state belongs

daughter-term label the Nielson&Koster label for the
spectroscopic term of the daughter state

first parent-term label the Nielson&Koster label for
the spectroscopic term of the first parent state

second parent-term label the Nielson&Koster label
for the spectroscopic term of the second parent state

The complete minimal subset of multi-electron CFPs for a given electron type is defined as a subset
of the full set of multi-electron CFPs, which satisfies the following requirements:

Completeness:

symmetry transformations

Minimality: For any CFP that belongs to the minimal complete subset of the CFPs for a given
electron type, there is no symmetry transformation that can relate it to any other CFP from the
minimal subset, except for the identity transformation, which relates it back to itself.

As a consequence of Pauli's exclusion and the electron-hole duality principles, the complete set of multi-electron coefficients of fractional parentage (for a given electron type) exhibit a six-fold symmetry.

Tag-Conventions Within the Regular-Text Database

In order to facilitate the automated reading/processing of the regular-text files, several types of tag-lines are defined.

References

BUTLER, P. H., 1975, ``Coupling Coefficients And Tensor Operators for Chains Of Groups,''
Phil. Trans. Roy. Soc. London A., 277 pp 545--85

DONLAN, V. L., 1970, ``Tables of Two Particle Fractional Parentage Coefficients for the pⁿ, dⁿ, and fⁿ
Configurations,'' Ohio, Wright-Patterson Air Force Base, Air Force Materials Laboratory Technical Report
AFML-TR-70-249.

EDMONDS, A. R., 1996, ``Angular Momentum in Quantum Mechanics,''
Princeton, NJ: Princeton University Press.

JUDD, B. R., 1963, ``Operator Techniques In Atomic Spectroscopy,''
New York: McGraw-Hill Book Company, Inc.

JUDD, B. R., 1967, ``Second Quantization And Atomic Spectroscopy,''
Baltimore, MD: The Johns Hopkins Press.

JUDD, B. R., 1968, ``Group Theory In Atomic Spectroscopy,''
New York, NY: Academic Press.

NIELSON, C.W. and KOSTER, G.F., 1963, "Spectroscopic Coefficients for the pⁿ, dⁿ, and fⁿ Configurations",
Cambridge, MA: The M. I. T. Press

PRESS et al, 1992, ``Numerical Recipes in C,''
Cambridge, England: Cambridge University Press.

RACAH, G., 1942, ``Theory Of Complex Spectra. I,''
Phys. Rev., 61 pp 134--45