Periodicity of the Oscillatory J Dependence of Diatomic Molecule Franck–Condon Factors

1975 ◽  
Vol 53 (16) ◽  
pp. 1560-1572 ◽  
Author(s):  
Robert J. Le Roy ◽  
Edward R. Vrscay
Keyword(s):  
Simple Formula ◽  
Radial Wave Function ◽  
Wave Functions ◽  
Final States ◽  
Rotational Constants ◽  
Radial Wave ◽  
Condon Factors ◽  
Oscillating Functions ◽  
Vibration Rotation ◽  
Franck Condon

Numerical calculations have shown that vibration–rotation interaction often contributes significantly to the J dependence of transition intensities of diatomic molecules. This occurs because centrifugal displacements of the vibrational wave functions cause the Franck–Condon amplitudes (radial overlap integrals) to behave as oscillating functions of J(J + 1). The present paper discusses the origin of this behavior and derives and tests a simple formula for predicting the periodicity of such oscillations. This procedure requires only a knowledge of the rotational constants and vibrational spacings of the initial and final states. It utilizes the result that the average centrifugal displacement rate of a diatomic molecule's radial wave function is approximately [Formula: see text], where Bν and Dν are the usual diatomic rotational constants.

Direct Photodisintegration of 9Be in the Low and Sub-Giant Resonance Energy Region

1969 ◽  
Vol 24 (8) ◽  
pp. 1188-1195
Author(s):  
Terje Aurdal
Keyword(s):  
Cross Sections ◽  
Giant Resonance ◽  
Resonance Energy ◽  
Wave Functions ◽  
Nuclear Model ◽  
Final States ◽  
Core State ◽  
Radial Wave ◽  
Total Cross Sections ◽  
Reaction Channels

Abstract Photodisintegration cross sections for the reaction 9Be(γ,n) 8Be with photonenergies varied from threshold to about 17 MeV are calculated. As nuclear model is assumed a single particle shell model where the valence neutron outside the 8Be core is feeling a spherical field. The core state is assumed to be a mixture of the ground (0+) and the first excited (2+) state of the 8Be nucleus. The total cross sections are splitted up according to the different contributing reaction channels. The radial wave functions in initial as well as final states are of the Saxon-Woods type.

scholarly journals Franck-Condon factors based on anharmonic vibrational wave functions of polyatomic molecules

2006 ◽  
Vol 125 (1) ◽  
pp. 014109 ◽  
Author(s):  
Valerie Rodriguez-Garcia ◽  
Kiyoshi Yagi ◽  
Kimihiko Hirao ◽  
Suehiro Iwata ◽  
So Hirata
Keyword(s):  
Polyatomic Molecules ◽  
Wave Functions ◽  
Condon Factors ◽  
Franck Condon

Atomic wave functions for gold and thallium

1955 ◽  
Vol 51 (3) ◽  
pp. 486-503 ◽  
Author(s):  
A. S. Douglas ◽  
D. R. Hartree ◽  
W. A. Runciman
Keyword(s):  
Wave Function ◽  
Absorption Edge ◽  
Radial Wave Function ◽  
Wave Functions ◽  
Radial Wave ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Independent Variable ◽  
Independent Calculation

Before the war, self-consistent field calculations for the Au+ ion had been carried out by W. Hartree but were left still unpublished at his death (see prefatory note in (5)). These results have been used by Brenner and Brown (1) in a relativistic calculation of the K-absorption edge for gold, and they were also used in obtaining initial estimates for the partial self-consistent field calculations for thallium of which results are given in §§3–5 of the present paper. In the meantime an independent calculation for Au+ has been carried out by Henry (6), and his results agree closely with those of W. Hartree. However, it still seems desirable to publish the latter, since they give directly the radial wave function P(nl; r) at exact values of r, whereas Henry used log r as independent variable, as had been done for similar calculations for Hg(4), and has tabulated r½P(nl; r) which is the natural dependent variable to use with log r as independent variable (2); in some applications it is more convenient to have the radial wave functions themselves.

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