Free and Exact Radial Wave Functions

1986 ◽  
pp. 425-451
Author(s):  
Arno Bohm
Keyword(s):  
Wave Functions ◽  
Radial Wave

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

Elastic form factor of the 6Li nucleus using improved radial wave functions

1969 ◽  
Vol 123 (3) ◽  
pp. 673-680 ◽  
Author(s):  
S. Radhakant ◽  
Nazakat Ullah
Keyword(s):  
Form Factor ◽  
Wave Functions ◽  
Elastic Form Factor ◽  
Radial Wave ◽  
Elastic Form

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.

scholarly journals The bound state solutions of the D-dimensional Schrödinger equation for the Woods–Saxon potential

2016 ◽  
Vol 25 (01) ◽  
pp. 1650002 ◽  
Author(s):  
V. H. Badalov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Wave Functions ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Pekeris Approximation

In this work, the analytical solutions of the [Formula: see text]-dimensional radial Schrödinger equation are studied in great detail for the Wood–Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the Nikiforov–Uvarov (NU) and Supersymmetric quantum mechanics (SUSYQM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformed each other is demonstrated. In addition, a finite number energy spectrum depending on the depth of the potential [Formula: see text], the radial [Formula: see text] and orbital [Formula: see text] quantum numbers and parameters [Formula: see text] are defined as well.

Quantum scar and breakdown of universality in graphene: A theoretical insight

2017 ◽  
Vol 31 (32) ◽  
pp. 1750257
Author(s):  
Kombiah Iyakutti ◽  
Ratnavelu Rajeswarapalanichamy ◽  
Velappa Jayaraman Surya ◽  
Yoshiyuki Kawazoe
Keyword(s):  
Theoretical Study ◽  
New Physics ◽  
Wave Functions ◽  
Dirac Fermions ◽  
Mass Ratio ◽  
Radial Part ◽  
Radial Wave ◽  
Graphene Quantum Dot ◽  
Dirac Equations ◽  
Theoretical Insight

Graphene has brought forward a lot of new physics. One of them is the emergence of massless Dirac fermions in addition to the electrons and these features are new to physics. In this theoretical study, the signatures for quantum scar and the breakdown of universality in graphene are investigated with reference to the presence of these two types of fermions. Taking the graphene quantum dot (QD) potential as the confining potential, the radial part of Dirac equations are solved numerically. Concentrations of the two component eigen-wavefunctions about classical periodic orbits emerge as the signatures for the quantum scar. The sudden variations, in the ratio of the radial wave-functions (large and small components), R(g/f), with mass ratio [Formula: see text] are the signatures for breakdown of universality in graphene. The breakdown of universality occurs for the states k = −1 and k = 1, and the state k = −1 is more susceptible to the breakdown of universality.

Asymptotics of three-body bound state radial wave functions of halo nuclei

2002 ◽  
Vol 705 (3-4) ◽  
pp. 335-351 ◽  
Author(s):  
R. Yarmukhamedov ◽  
D. Baye ◽  
C. Leclercq-Willain
Keyword(s):  
Bound State ◽  
Wave Functions ◽  
Halo Nuclei ◽  
Radial Wave ◽  
Three Body
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