PROGRAM SUMMARY
Title of program:
RACAH
Catalogue identifier:
ADQP
Ref. in CPC:
149(2002)39
Distribution format: tar gzip file
Operating system: Linux 6.1+
High speed store required:
30MK words
Number of lines in distributed program, including test data, etc:
85798
Keywords:
Angular momentum, Complex atom, Configuration state function,
jj-coupling, LS-coupling, LS-jj transformation, LSJ and jjJ
spectroscopic notation, Nonrelativistic, Relativistic,
Subshell state, General purpose, Rotation group.
Programming language used: Maple V, Release 6 and 7
Other versions of this program:
Cat. Id. Title Ref. in CPC ADNM RACAH 135(2001)219 ADOS RACAH 139(2001)314 ADRW RACAH 153(2003)422
Nature of physical problem:
For open-shell atoms and ions, a reliable classification of the level
structure often requires the knowledge of the LS-jj transformation
matrices in order to find the main components of the wave functions as
well as their proper spectroscopic notation. Apart from the
transformation of individual (sub-)shell states, matrices of much larger
complexity arise for the transformation of symmetry-adapted
configuration state functions which are constructed from the coupling of
two or more open shells.
Method of solution:
LS-jj transformation matrices are provided for all (sub-)shell states
with orbital angular momenta l<=3 in the framework of the RACAH program
[2]. These matrices are then utilized to transform symmetry-adapted
configuration state functions (CSF), including the coupling of two open
shells. Moreover, a simple notation is introduced to handle such
symmetry functions interactively and to transform even atomic states
which are given as a superposition of CSF.
Restrictions:
The program presently supports all shell states with l<=3, i.e. up to
open f-shells, in LS-coupling and with j<=7/2, i.e. up to open f7/2- and
g7/2-subshells, in jj-coupling. For the transformation of configuration
state functions, the coupling of two open LS-shells or, correspondingly,
four jj-subshells are also supported. In jj-coupling, however, a
standard order [cf. Section 2.2] is always assumed for the coupling
sequence of the individual shells. Several simplifications are used on
the basis of this standard order.
Unusual features:
Apart from the "interactive access" to the LS-jj transformation matrix
elements between (sub-)shell states in LS- and jj-coupling, a complete
transformation of the coupling scheme can be carried out also for
configuration respectively atomic state functions, just by typing a few
lines at MAPLE's prompt. To simplify the handling of the program, a
short but very powerful notation has been introduced which help the user
to construct stepwise symmetry-adapted functions of different
complexity. But although the program presently supports only shell
states in LS- and jj-coupling, the same notation can be extended also to
incorporate further coupling schemes in the future. The main commands
of the present extension are described in detail in Appendix B; for a
quick reference on the current capabilities of the RACAH program, we
refer the reader to Ref. [3] and to a list of all available commands in
the file Racah-commands.ps which is appended to the code.
Typical running time:
The program replies promptly on most requests. Even large tabulations
of LS-jj transformation matrices can be carried out in a few (tens of)
seconds.
References:
[1] Maple is a registered trademark of Waterloo Maple Inc.
[2] S. Fritzsche, Comp. Phys. Commun. 103 (1997) 51; G. Gaigalas,
S. Fritzsche, B. Fricke, Comp. Phys. Commun. 135 (2001) 219.
[3] S. Fritzsche, T. Inghoff, T. Bastug and M. Tomaselli, Comp. Phys.
Commun. 139 (2001) 314.