rcewriteup

一套应用很广的光谱程序

 
 
                        PROGRAM RCE MOD 20
           LEAST-SQUARES FITTING OF ATOMIC ENERGY LEVELS
 
 
                         Robert D. Cowan
                 Los Alamos National Laboratory
                          February 1978
        (revised August l986, January 1991, and August 1993)
 
 
CONTENTS
    I.  Introduction                                          2
   II.  Source Programs                                       2
  III.  Input (TAPE2E)                                        3
   IV.  Input (INE20)                                         4
    V.  Dimensions                                            8
   VI.  Running RCG and RCE (single parity)                   8
  VII.  Output                                                8
 VIII.  Running RCN, RCN2, RCG, and RCE (single parity)       9
   IX.  Formats for ELEMID and CONFIG                        10
    X.  Units                                                10
   XI.  Rerunning RCE or RCG (output file PARVALS)           11
  XII.  Running both parities together                       11
 XIII.  RCE output files LEVELS1, LEVELS2, and LEVELS3       12
  XIV.  Notes regarding convergence problems                 13
   XV.  Notes regarding Tables I and II                      15
 
 
 
 
 
 
I. Introduction
        RCE is a FORTRAN 77 program for CRAY-1 or CYBER 205 or
similar computers.  Similarly to RCN, RCN2, and RCG, it has been
adapted to run also on VAXs, SUNs, IBM RISCs, and Macintosh
Centris computers, and should be easily adaptable also to Apollos,
Hewlett-Packards, PCs, etc.
        The basic purpose of RCE is to adjust the values of various
theoretical parameters so as to produce computed atomic energy
levels in the best possible (least-squares-wise) agreement with
experimentally known level values.  Levels whose energies are not
known experimentally can be omitted from consideration.  Any of
the parameters can be held fixed at specified values, or groups of
parameters can be forced to vary in such a way that the ratios of
the values within a group remain fixed relative to each other.
        The fitting process is carried out by an automatic iterative
procedure until the parameter values no longer change from one
iteration cycle to the next (by more than 0.03), or for a
specified maximum number of cycles.  The iteration can be carried
out in any one of the seven angular-momentum coupling schemes
available in program RCG; final eigenvectors are printed in this
representation, and also in either the LS or JJ representation
(see Sec. VII).
        The basic theory involved is discussed in R. D. Cowan, The
Theory of Atomic Structure and Spectra (University of California
Press, Berkeley, 1981), especially Sections 16-3 to 16-5,
hereinafter referred to as TASS.
 
 
II. Source Programs
        The program assumes that the coefficient matrices for each
value of J and for each parameter are contained in a binary input
file TAPE2E, precomputed by program RCG.  The experimental levels
(term values) T, together with (optional) estimated parameter
values and various control information must be provided as a BCD
input file INE20 (read internally as unit 10); this file can,
except for the experimental level values, be obtained in basic
form as output from RCG (a file named OUTGINE--short for
OUTrcgINrce).
        The following brief discussion of the function of each
subroutine provides a rough outline of the basic calculational
procedure.
        MAIN  Handles all input (including, for each J, transfer of
the [LS-JJ or other] transformation matrix from TAPE2 to TAPE5,
and transfer of coefficient matrices from TAPE2 to TAPE4).  It
also handles the iteration control and most output.
        EIGEN  Called by MAIN.  Reads coefficient matrices from
TAPE4, calculates the energy matrix (for each J) for current
values of the parameters, and calls subroutine TRED2 to
diagonalize the energy matrix and thereby obtain computed energy
levels
        ORDER  Called by EIGEN (and also by MAIN) to arrange the
computed eigenvalues and vectors in the order of largest
eigenvector component (i.e., so as to make the eigenvector matrix
such that the eigenvector components of largest magnitude tend to
lie on the diagonal); vectors not having clearly dominant
components are arranged so that the corresponding eigenvalues lie
in the same numerical order as do the remaining energy levels.  [A
test number CRIT can be chosen to be zero, so that no vector will
be considered to have a dominant component.  Then all eigenvalues
will be correlated with experimental level values in numerical
order.]
        CALCX  Called by MAIN to modify the parameter values X so as
to improve the agreement between eigenvalues (W) and energy levels (T).
        LSS  Linear system solver called by CALCX.
        TRED2/TQL2  Suite of matrix-diagonalization programs.
        WR  Program to compact a two-dimensional array (dimensions
IA x IA) containing a matrix of size IM (IM.LE.IA) into a one-
dimensional array of size IM*IM or IM*(IM+1)/2.
        RD  Program to accomplish the inverse of WR.
        CLOCK  Program to obtain CPU time in minutes (for
information only).  This program contains sections appropriate for
a CRAY, VAX or Macintosh, SUN, or IBM RISC; a section appropriate
to another type of computer can be added, or the output time
simply set to zero.
        OUT8  Writes on TAPE8 (external file name LEVELS1) a summary
of the final results: experimental level, eigenvalue, Lande g-
value, dominant configuration, and the percentage composition of
the level (three largest components if an input constant CRIT1 is
zero, or a unique component plus the two largest remaining
components if CRIT1 is greater than zero) in each of two coupling
representations.  Levels are arranged in the order of increasing J
value, and for given J in order of increasing energy.
        SORT8TO7 and SORT  Sort the information on TAPE8 in the
order of increasing eigenvalues, and write it on the OUTPUT file
and on a file TAPE7 (external file name LEVELS2).  Also, sort the
information on TAPE7 in the order of dominant configuration, and
write it on a file TAPE12 (external file name LEVELS3).
        SORT2/ORDERI  Sort numbers in one table in numerically
increasing order, and similarly rearrange numbers in other tables.
 
 
III. Input (TAPE2E)
        Details of the TAPE2E binary file will not be given here,
but can be deduced from subroutine RCEINP of program RCG, where
this file is written, or from RCE MAIN, where the file is read.
Briefly, this file contains (for each of one or more "CSETS"
--i. e., for each of one or more sets of electron configurations
of interest):
        (1)  A record including a serial number for the CSET, the
number of values of J, the total number of parameters, the number
of configurations, and the number of parameters for each
configuration and for each pair of interacting configurations.
   For  each J-value:
       (2)  The value of J, the matrix size, the transformation
matrix from the primary to the secondary coupling representation,
the serial number of the configuration for each matrix row, and
brief basis-state labels in both of the representations.
        (3)  The energy-coefficient matrix for each parameter, and
the Lande g-value matrix, all in the primary representation.
 
 
IV. Input (INE20)
        The input file INE20 (internally read as unit 10) must
contain the following information.  [Input items (2) through (10)
may be repeated as many times as desired.]
		
        (1)  NOCYPR, NOCYCR, NOCYCE, I216, IW6      (Format 5I5).
 
        The least-squares iteration will proceed for at most NOCYCE
cycles, output being printed every NOCYPR cycles, with input
levels being reordered (into the same numerical order as the
computed eigenvalues) every NOCYCR cycles.  [If NOCYCR