Some Properties of the Racah and Associated Coefficients

The modeling of complex atomic spectra is a difficult task, due to the huge number of levels and lines involved. In the presence of a magnetic field, the computation becomes even more difficult. The anomalous Zeeman pattern is a superposition of many absorption or emission profiles with different Zeeman relative strengths, shifts, widths, asymmetries and sharpnesses. We propose a statistical approach to study the effect of a magnetic field on the broadening of spectral lines and transition arrays in atomic spectra. In this model, the σ and π profiles are described using the moments of the Zeeman components, which depend on quantum numbers and Landé factors. A graphical calculation of these moments, together with a statistical modeling of Zeeman profiles as expansions in terms of Hermite polynomials are presented. It is shown that the procedure is more efficient, in terms of convergence and validity range, than the Taylor-series expansion in powers of the magnetic field which was suggested in the past. Finally, a simple approximate method to estimate the contribution of a magnetic field to the width of transition arrays is proposed. It relies on our recently published recursive technique for the numbering of LS-terms of an arbitrary configuration.

show abstract

“…with the convention of Biedenharn et al [22],x = x(x + 1). The quantity g s represents the anomalous gyromagnetic ratio defined in section 1.…”

Section: Approximation Of the Coefficient G Ementioning

confidence: 99%

Characterization of anomalous Zeeman patterns in complex atomic spectra

Pain

Gilleron

2012

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…where e is the effective charge (e = Ne/A for proton and e = −Ze/A for neutron), S (k) l j is the spectroscopic factor and Z(LJl j; 1 2 1) is the Z-coefficient [12]. As for the semidirectcapture amplitude, it is calculated as…”

Section: Direct-semidirect Cross Sectionmentioning

confidence: 99%

Direct and semidirect radiative capture of nucleons with Hartree-Fock-BCS bound states

Bonneau

Kawano

Watanabe

et al. 2007

Nd2007

View full text Add to dashboard Cite

Abstract. Nucleon radiative capture is one of the most important process for nucleo-synthesis calculations in astrophysics. The nucleon capture can occur in two different mechanisms: the compound reaction and the directsemidirect (DSD) process. The compound capture cross sections become very small when many neutron channels open because the neutron width becomes much larger than the γ width. For incident nucleon energies above about 5 MeV, the capture process can be described by the DSD theory only. In the DSD process, the incident particle is captured directly by an unoccupied bound state (direct) or it excites a collective state and is then scattered into a bound state (semidirect). In this picture, the calculation is sensitive to the radial wave functions of the bound state, which are often calculated with a single-particle model using a Wood-Saxon potential. For astrophysical calculations, since experimental information on nuclear structure is uncertain or inaccessible, we apply a Hartree-Fock-BCS (HFBCS) structure model to generate the radial wave functions. The DSD cross sections are obtained by calculating a transition amplitude to the HFBCS states and using the calculated spectroscopic factors. We calculate the neutron capture cross sections for even-even spherical and deformed targets, namely 208 Pb, 122,132 Sn and 238 U. The agreement with the experimental cross sections, only available for 208 Pb and 238 U, is very good.

show abstract

“…Triple directional correlations and directional correlations of two radiations emitted from oriented nuclear states have been considered previously. 3 ' 4 This paper presents a more practical formulation of these phenomena, and the explicit definition of the reduced gamma matrix If 2P(m)= l,thenB 0 (I,)= 1. m In nuclear-reaction experiments or for low-temperature orientation, the P(m) must be computed on the basis of the reaction mechanism or from the orientation mechanism. Krane 6 has prepared tables of B^ (Ij) for the latter case.…”

Section: Observotion Of Preceding Rcdiotion In Directionmentioning

confidence: 99%

Angular Distributions and Correlations of Radiations Emitted From Oriented Nuclei. Iii. Directional Correlations of Two Radiations Emitted From Oriented Nuclei and Triple Directional Correlations.

Krane¹,

Steffen²

1972

View full text Add to dashboard Cite

A convenient and generally applicable formulation of the directional correlation of two successive nuclear radiations emitted from an initial oriented nuclear state and of triple directional correlations is presented. The pertinent generalized directional-distribution coefficients are expressed in terms of generalized F-coefficients. Extensive numerical tables of these coefficients are given. For normal and parallel geometries, the directional correlation of radiations from oriented states or the triple directional correlation can be expressed in terms of the ordinary Legendre polynomials; i.e., W(0) = 2 T^P^ (cos 0). Graphs of the distribution parameters F^ as a func-A tion of the explicitly defined gamma muldpole mixing ratios 5 are presented, and some special cases are discussed in detail.

show abstract

Some Properties of the Racah and Associated Coefficients

Cited by 256 publications

References 11 publications

Characterization of anomalous Zeeman patterns in complex atomic spectra

Characterization of anomalous Zeeman patterns in complex atomic spectra

Direct and semidirect radiative capture of nucleons with Hartree-Fock-BCS bound states

Angular Distributions and Correlations of Radiations Emitted From Oriented Nuclei. Iii. Directional Correlations of Two Radiations Emitted From Oriented Nuclei and Triple Directional Correlations.

Contact Info

Product

Resources

About