On the calculation of radial wave functions corresponding to energies in the continuum part of the helium spectrum

1961 ◽  
Vol 19 (4) ◽  
pp. 696-722 ◽  
Author(s):  
C. C. Grosjean ◽  
R. T. Walle
Keyword(s):  
Wave Functions ◽  
Radial Wave ◽  
The Continuum

Angular Distribution of Products from Photodissociation of Diatomic Molecules

1971 ◽  
Vol 49 (19) ◽  
pp. 2425-2431 ◽  
Author(s):  
S. H. Lin ◽  
C. J. Koizumi
Keyword(s):  
Angular Distribution ◽  
Electronic Transition ◽  
Function Approximation ◽  
Adiabatic Approximation ◽  
Diatomic Molecules ◽  
Delta Function ◽  
Wave Functions ◽  
Transition Moment ◽  
Radial Wave ◽  
The Continuum

The angular distribution of dissociation products in the photodissociation of diatomic molecules has been calculated quantum-mechanically. It is shown that in the adiabatic approximation the angular distribution of the electronic transition with the transition moment along the molecular axis can be expressed as σ(θ0) = (σ0/4π) [1 + βP2 (cos θ0)], and the angular distribution for the case of perpendicular transitions is very complicated and can be approximately expressed in the same form as that for the case of parallel transitions only in the limiting conditions. Approximate calculations of the angular distribution of photodissociation are also carried out by using the delta function approximation to the continuum radial wave functions, and it is found that in this approximation β = 2 for the parallel transition; that is, the angular distribution of dissociation products is of the form cos2 θ0.

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.

Stueckelberg-Landau-Zener-(SLZ)-Modell für atomare Stoßprozesse / Stueckelberg-Landau-Zener-(SLZ) Model for Atomic Scattering Processes

1973 ◽  
Vol 28 (10) ◽  
pp. 1642-1653
Author(s):  
G.-P. Raabe
Keyword(s):  
Cross Sections ◽  
Differential Cross ◽  
Wave Functions ◽  
Differential Cross Sections ◽  
Rare Gases ◽  
Radial Wave ◽  
Atomic Scattering ◽  
The Cross

Scattering processes of atoms, molecules and ions with two crossing electronic potentials may be treated in the Stueckelberg-Landau-Zener-(SLZ) model. In this paper the WKB-solutions for the radial wave functions, given by Stueckelberg are used to calculate differential cross sections. The effects on the cross sections are explained in a semiclassical picture, following the procedures of Ford and Wheeler, and Berry. In the scattering of H+ by rare gases, some effects in the elastic cross sections are observed which can be explained by the influence of the potential of the chargeexchanged particles, using the SLZ-model. The structure in the elastic cross sections for H2+-Kr can be explained as a rainbow structure with superimposed Stueckelberg oscillations.

KANTBP: A program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

2007 ◽  
Vol 177 (8) ◽  
pp. 649-675 ◽  
Author(s):  
O. Chuluunbaatar ◽  
A.A. Gusev ◽  
A.G. Abrashkevich ◽  
A. Amaya-Tapia ◽  
M.S. Kaschiev ◽  
...  
Keyword(s):  
Energy Levels ◽  
Wave Functions ◽  
Radial Wave ◽  
Reaction Matrix ◽  
Adiabatic Approach ◽  
Hyperspherical Adiabatic ◽  
Coupled Channel

Double zeta d radial wave functions for transition elements

1986 ◽  
Vol 111 (2) ◽  
pp. 139-140 ◽  
Author(s):  
Noel J. Fitzpatrick ◽  
George H. Murphy
Keyword(s):  
Wave Functions ◽  
Transition Elements ◽  
Radial Wave ◽  
Double Zeta

Theory of spin-orbit coupling in atoms, II. Comparison of theory with experiment

1963 ◽  
Vol 271 (1347) ◽  
pp. 565-578 ◽  
Keyword(s):  
Wave Functions ◽  
Coupling Constants ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Outer Electron ◽  
Coupling Constant ◽  
Radial Wave ◽  
Order Of Magnitude ◽  
Experimental Values

Results of calculations of the spin-orbit coupling constant for 2 p , 3 p , 4 p , and 3 d shell ions and atoms are presented. The calculations are based on a theory developed in a previous paper. Excellent agreement of this theory with experiment is obtained for the 2 p and 3 d shell ions, while calculations using the familiar < ∂ V / r ∂ r > expression for the coupling constant lie 10 to 20 % too high. The exchange terms discussed in the earlier paper make a contribution to the coupling constant of the same sign and order of magnitude as the ordinary shielding terms. For the 3 p and 4 p shell atoms, the calculated coupling constants based on the exact theory and on the < ∂ V / r ∂ r > expression both tend to lie below the experimental values. An explanation for this disagreement is suggested, based on the noded nature of the outer-electron radial wave functions for these atoms. The importance of the residual-spin-other-orbit interaction is discussed, and it is shown that ignoring the form of this interaction may lead to a large variation in the coupling constant within a configuration.

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