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一套应用很广的光谱程序

                           Robert D. Cowan
                            December 1999
 
     This suite of four programs calculates atomic structures and
spectra via the superposition-of-configuration method:
     (1)  RCN calculates one-electron radial wavefunctions (bound or
free) for each of any number of specified electron configurations,
using the Hartree-Fock or any of several more approximate methods.
The principal output, for each configuration, consists of the center-
of-gravity energy (Eav) of the configuration, and those radial Coulomb
(Fk and Gk) and spin-orbit (zeta) integrals required to calculate the
energy levels for that configuration.
     (2)  RCN2 is an interface program that uses the output wave-
functions from RCN (on a file called tape2n) to calculate the
configuration-interaction Coulomb integrals (Rk) between each pair
of interacting configurations, and the electric-dipole (E1) and/or
electric quadrupole (E2) radial integrals between each pair of
configurations.  RCN2 prepares an output file called out2ing that
(after being renamed ing11) serves as input to RCG.
     (3)  RCG sets up energy matrices for each possible value of the
total angular momentum J, diagonalizes each matrix to get eigenvalues
(energy levels) and eigenvectors (multi-configuration, intermediate-
coupling wavefunctions in various possible angular-momentum-coupling
representations), and then computes M1 (magnetic dipole), E2, and/or
E1 radiation spectra, with wavelengths, oscillator strengths, radiative
transition probabilities, and radiative lifetimes.  Other options, when
a continuum (free) electron is present, are photoionization cross-
sections, autoionization transition probabilities, total lifetimes,
branching ratios for autoionization, and plane-wave Born collision
strengths.
     (4)  When higher accuracy results are desired, RCE can be used
to vary the various radial energy parameters Eav, Fk, Gk, zeta, and Rk
to make a least-squares fit of experimental energy levels by an
iterative procedure.  The resulting least-squares-fit parameters can
then be used to repeat the RCG calculation with the improved energy
levels and (presumeably) wavefunctions.
     Reference:  Robert D. Cowan, "The Theory of Atomic Structure and
Spectra," (University of California Press, Berkeley, 1981), esp.
Chapters 8 and 16.
 
RCN input
     A sample input file (to be named in36) for the HF program RCN is:
 
2  -9    2   10  0.2    5.e-08    1.e-11-2   090    1.0 0.65  0.0  0.0
-6
    1    1H I   1s      1s
   -1
   19    6K VI  3s2 3p2     3s2 3p2
   19    6K VI  3p4         3p4
   19    6K VI  3p 3d       3s2 3p 3d
   -1
   29    1Cu I 1s2 4s        1s2 3d10 4s
   29    1Cu I 1s 4s .1p     1s  3d10 4s 99p  0.1
   29    1Cu I 1s 4s 1.p     1s  3d10 4s 99p  1.0
   -1
 
     The first line is an almost universal control card, except that
the "090" should be changed to "190" if relativistic corrections in the
wavefunctions are desired (used mainly for elements with Z greater than
about 30), and that the "-6" in columns 74-75 (which sends abbreviated
output on the course of the calculation to the monitor screen) should
be deleted for batch running on a mainframe computer.
     Each remaining line specifies an electron configuration, except
that a negative atomic number (in columns 3-5) specifies a normal exit
from RCN; thus the input file as given above will result in a calcula-
tion for only the ground configuration 1s of hydrogen.  If the hydrogen
card and associated exit card are removed (or moved to the end of the
file), then the next four cards will cause a calculation to be made for
the two even-parity configurations 3s2 3p2 and 3p4 and the odd-parity
configuration 3s2 3p 3d of K VI (5-fold ionized potassium, Z=19).
(With output passed on through RCN2 to RCG, one would then obtain a
calculation of a 3s2 3p2 + 3p4 to 3s2 3p 3d electric-dipole spectrum.)
The remaining four cards, if placed directly after the control card,
would result in calculations for the ground configuration 3d10 4s of
neutral copper together with two continuum configurations (a principal
"quantum number" of 99 signifying a free electron) with free-electron
kinetic energies of 0.1 and 1.0 rydbergs, for purposes in RCG of
calculating photoionization cross-sections for 1s to ep transitions
at e=0.1 and 1.0 Ry.
     The value of atomic number must lie in columns 2-5, the spectrum
number (one more than the ionization stage) in columns 9-10, and the
ion and configuration description (for printed information only) in
columns 11-28.  For maximum legibility in output from programs RCG and
RCE, it is desirable that the element and spectrum identification be
limited to columns 11-16 (e.g., "C I   ", "O III ", "Fe23+ " or
"Fe+23 ", etc.), and that the configuration label be limited to columns
17-22 or maybe 17-24.
     The actual specification of electron orbitals for calculational
purposes can follow a semi free-form format, beginning at least three
blank spaces after the configuration label, with at least one blank
space separating orbitals (and kinetic energy, if present).  The
complete electron configuration is set up by RCN as follows: The number
of electrons is calculated to be Z+1-spectrum number, and a configur-
ation is set up for the ground configuration of the neutral noble gas
(He, Ne, Ar, Kr, Xe, or Rn) containing no more than this number of
electrons.  This configuration is then modified and/or added to
according to the given orbital information.  As an example, for neutral
copper, the number of electrons is 29+1-1=29, and so the code starts
from the ground configuration 1s2 2s2 2p6 3s2 3p6 of neutral argon
(18 electrons).  For the first copper configuration above, ten 3d
electrons and one 4s electron are added to give the ground configur-
ation of neutral copper.  For the other two Cu cases, 1s2 is modified
to 1s (the occupation number is obtained by table lookup, and either
a blank or a one will give unit occupation--similarly, d occupation
numbers must be typed ...d7, d8, d9, d10, with no blank space for
occupation less than 10), and then ten 3d electrons, a 4s electron,
and a continuum p electron added.
    Units internally to RCN are Bohr units of length and Rydberg units
(units of 13.6058 eV) for energy.  The final line of the output (in
file out36) for each configuration gives the quantities needed for
energy-level calculations in RCG, with Eav in Ry and all other energy
radial integrals in units of kK (1000 cm-1); these same quanties are
given in the last line of the monitor-screen output for each cofigur-
ation.
 
RCN2 input
     The two-card input for RCN2 is more-or-less universally of the form
 
g5inp     000 0.0000          00                339099909090 0.00
07229
        -1
 
The items on the control card will not be described except to say that
if either digit in the "00" is made non-zero, then eigenvectors in the
LS or jj-coupling representation, respectively, will not be printed in
RCG; the "33" calls for M1 and E2 spectra, respectively, to be
calculated in RCG for both parities (zeros will delete these), and the
"7" calls for print in RCG of the spectrum line list sorted by first-
parity energy levels, by second-parity energies, and by wavenumber
(inverse wavelength); a 1, 2, or 4 instead of 7, prints only one of
these sorts, and a 3, 5, or 6 will print two of them.  The "9099909090"
represent 2-digit scale factors (in percent, 99 representing 100%) for
respectively Fk between equivalent electrons, spin-orbit parameters,
Fk and Gk for non-equivalent electrons, and configuration-interaction
Rk radial integrals: It is known empirically that scaling down of the
HF Coulomb radial integral values by 5 to 30 percent will give RCG
eigenvalues in better agreement with experimental energy levels, the
smaller factors being for neutral or weakly ionized systems, with
factors approaching unity being appropriate for highly ionized systems.
 
RCG input
     Output from RCN2 consists of print output in file out2 and a file
out2ing that, renamed ing11, forms an input file for RCG.  With the
three K VI configurations used as input for RCN, this file (with "33"
on the rcn2 control card replaced by "00" or "30") will be
 
    3     10e-350e05    000005   10.        0 5.0  2.0  1.0  0.5  0.2
    0                         0000000000          1000.0000
    1    03 2 23 1 10         00                 0 1000.0000 0.00   1 07-6 0 0
s 2  p 2  s 0  s 0  s 0  s 0  s 0  s 0  K VI  3s2 3p2       -130337.379   0.0000
s 0  p 4  s 0  s 0  s 0  s 0  s 0  s 0  K VI  3p4           -129993.306   0.0000
s 2  p 1  d 1  s 0  s 0  s 0  s 0  s 0  K VI  3p 3d         -130106.201   0.0000
K VI  3s2 3p2      3        00   7609731    178682        00        00hf90999090
K VI  3p4          3  34407320   7574361    178422        00        00hf90999090
3s2 3p2  -3p4      1 101.64285   0.00005   0.00005   0.00005   0.00005hf90999090
K VI  3p 3d        6  23117760    180352      8932   7177693   8834344hf90999090
   5512094
K VI  3s2 3p2       K VI  3p 3d            1.70752( 3p//r1// 3d)-0.990hf -92 -96
K VI  3p4           K VI  3p 3d            0.00000(   //r1//   )0.0000hf   0   0