Collective vector method for calculation of E1 moments in atomic transition arrays

Conference · Tue Oct 01 00:00:00 EDT 1985

OSTI ID:6199846

Bloom, S D; Goldberg, A

The CV (collective vector) method for calculating E1 moments for a transition array is described and applied in two cases, herein denoted Z26A and Z26B, pertaining to two different configurations of iron VI. The basic idea of the method is to create a CV from each of the parent (''initial state'') state-vectors of the transition array by application of the E1 operator. The moments of each of these CV's, referred to the parent energy, are then the rigorous moments for that parent, requiring no state decomposition of the manifold of daughter state-vectors. Since, in cases of practical interest, the daughter manifold can be orders of magnitude larger in size than the parent manifold, this makes possible the calculation of many moments higher than the second in situations hitherto unattainable via standard methods. The combination of the moments of all the parents, with proper statistical weighting, then yields the transition array moments from which the transition strength distribution can be derived by various procedures. We describe two of these procedures: (1) The well-known GC (Gram-Charlier) expansion in terms of Hermite polynomials, (2) The Lanczos algorithm or Stieltjes imaging method, also called herein the delta expansion. Application is made in the cases of Z26A (50 lines) and Z26B (5523 lines) and the relative merits and shortcomings of the two procedures are discussed. 10 refs., 15 figs., 2 tabs.

• Research Organization: Lawrence Livermore National Lab., CA (USA)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6199846
• Report Number(s): UCRL-93608; CONF-8510172-2; ON: DE86003471
• Resource Relation: Conference: 3. international conference and workshop on radiative properties of hot dense matter, Williamsburg, VA, USA, 14 Oct 1985
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
E1-TRANSITIONS
CALCULATION METHODS
IRON IONS
ALGORITHMS
ENERGY-LEVEL TRANSITIONS
THEORETICAL DATA
VECTORS
CHARGED PARTICLES
DATA
INFORMATION
IONS
MATHEMATICAL LOGIC
MULTIPOLE TRANSITIONS
NUMERICAL DATA
TENSORS
640302* - Atomic
Molecular & Chemical Physics- Atomic & Molecular Properties & Theory