The Los Alamos LEDCOP Opacity Code
         N.H. Magee, A.L. Merts, J.J. Keady and D.P. Kilcrease
The Los Alamos Light Element Detailed Configuration OPacity code (LEDCOP)
uses a basis set of detailed LS terms (plus average configuration terms
for complex ion stages) to calculate opacities for elements with Z < 31.
Each ion stage is considered in detail and interactions with the plasma
are treated as pertubations.  Calculations are done in local thermodynamic
equilibrium (LTE) and only radiative processes are included.
A  self-consistent Hartree-Fock code[1,2] with relativistic corrections is
used to generate both single configuration LS term energies, radial dipole
matrix elements and angular factors for all ion stages and unresolved
transition array (UTA) energies and variances[3] in intermediate coupling
for selected ion stages.  This large quantity of atomic physics "data" is
then reduced by fitting the term energies and dipole matrix elements with
a quantum defect method[4] and using the fits in the opacity code.  Every
energetically relevant configuration is included in the equation of state
(EOS) and every allowed valence and inner shell transition from these
configurations is used in the opacity calculations.  Either the LS, UTA or
statistical transition array[5] model is chosen, depending on the
complexity of the transition array and/or the plasma density.
Nonhydrogenic photoionization cross sections are calculated[6] for each
configuration subshell with l < 5, using distorted wave continuum functions
and the same Hartree-Fock structure calculations as for the bound-bound
transtions in order to conserve oscillator strength across the photo-
electric edges. Cross sections for n > 5, l > 4 are hydrogenic[7].
The EOS model is based on the Saha equation[8], including degeneracy, where
the bound Rydberg sequences are cut off by plasma corrections[9], including
exchange[10] and correlation[11].  It does not consider liquid or solid
phases, but uses an explicit ion model[12] to treat, in detail, all of the
bound electron states of every ionization stage.  The modified Saha
equation is solved iteratively to obtain a consistent set of ion
abundances, bound state occupancies and free electrons.
LEDCOP uses three different line profiles for bound-bound transitions.  The
general line shape is the Voigt convolution of a thermal Doppler (Gaussian)
profile and a Lorentz profile with both natural and collision[13] broadened
halfwidths.  Lyman and Balmer transitions from hydrogen-like ions and
ground state transitions from helium-like ions use Stark profiles[14,15]
based on APEX microfield calculations.  A coherent scattering profile[8]
is used to modify resonance lines in the far line wings.
The inverse bremsstrahlung is calculated from the Kramers cross section
formula and relativistic free-free Gaunt factors[16].  H- free-free[17]
and H- bound-free[18] absorption are included for hydrogen.  Free electron
scattering is obtained from the Thomson cross section, modified by
relativistic corrections and thermal motions[19], and collective
Opacities are calculated for pure elements on a standard temperature T,
electron degeneracy "eta", and reduced photon energy (u=hv/kT) grid.  The
T-"eta" grid characterizes the plasma conditions at the ion sphere boundary
for all elements.  This allows the opacity of pure elements to be combined
for mixtures without recalculating the basic data[20,21].
[1]  R.D. Cowan, The Theory of Atomic Structure and Spectra, University of
     California Press, Berkeley, (1981).
[2]  J. Abdallah, Jr., R.E.H. Clark, and R.D. Cowan, "CATS:  Cowan Atomic
     Structure Code", LA-11436-M, Vol. 1, Los Alamos National Laboratory,
[3]  D.P. Kilcrease, J. Abdallah, Jr., J.J. Keady and R.E.H. Clark, J.
     Phys. B, vol. 26, L717 (1993).
[4]  R.E.H. Clark and A.L. Merts, JQSRT, vol. 38, 287 (1987).
[5]  P. Duffy, M. Klapisch, J. Bauche and C. Bauche-Arnoult, Phys. Rev. A,
     vol. 44, 5715 (1991).
[6]  R.E.H. Clark, GIPPER Photoionization Code, private communication.
[7]  W.J. Karzas and R. Latter, Ap. J. Suppl., vol. 6, 167 (1961).
[8]  A.N. Cox, "Stellar Absorption Coefficients and Opacities" eds. L.H.
     Allen and D.B. McLaughlin (Stars and Stellar Systems, Vol. 8,
     University of Chicago, Chicago, 1965), pg. 195.
[9]  J.C. Stewart and K.D. Pyatt, Ap. J., vol. 144, 1203 (1966).
[10] F. Seitz, "The Modern Theory of Solids", (McGraw-Hill Book Company,
     New York, 1940), Mg. 365.
[11] S.H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys., vol. 58, 1200
[12] W.F. Huebner, "Atomic and Radiative Processes in the Solar Interior",
     ed. P.A. Sturrock (The Physics of the Sun, Vol. 1, D. Reidel
     Publishing Company, Dordrecht-Holland, 1986), pg. 33.
[13] B.H. Armstrong, R.R. Johnson, H.E. DeWitt, and S.G. Brush, "Opacity
     of High Temperature Air" ed. C.A. Rouse (Progress in High of High
     Temperature Physics and Chemistry, Vol 1., Pergamon Press, Oxford,
     New York, 1966).
[14] R.W. Lee, JQSRT, vol. 40, 561 (1988).
[15] G.L. Olson, J.C. Comly, J.K. LaGattuta, and D.P. Kilcrease, JQSRT,
     vol. 51, 255 (1994).
[16] M. Nakagawa, Y. Kohyama, and N. Itoh, Ap. J. Suppl., vol. 63, 661
[17] S. Geltman, Ap. J., vol. 141, 376 (1964).
[18] S. Geltman, Ap. J., vol. 136, 935 (1962).
[19] D.H. Sampson, Ap. J., vol. 129, 734 (1959).
[20] W.F. Huebner, A.L. Merts, N.H. Magee, and M.F. Argo, "Astrophysical
     Opacity Library", LA-6760-M, Los Alamos National Laboratory, (1977).
[21] J. Abdallah, Jr. and R.E.H. Clark, "TOPS:  A Multigroup Opacity
     Code", LA-10454-M, Los Alamos National Laboratory, (1985).