J. Phys. Colloques
Volume 49, Number C1, Mars 1988IAU Colloquium N° 102 on UV and X-ray Spectroscopy of Astrophysical and Laboratory Plasmas
|Page(s)||C1-79 - C1-81|
J. Phys. Colloques 49 (1988) C1-79-C1-81
MONTE CARLO ALGORITHMS FOR MOMENTS OF TRANSITION ARRAYSA. GOLDBERG et S.D. BLOOM
Lawrence Livermore National Laboratory, Livermore, CA 94550, U.S.A.
Closed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a "collective" state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe a statistical (or Monte Carlo) approach which requires only one representative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with ≈ 250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.