scholarly journals THE ASYMPTOTIC BEHAVIOUR OF THE S-MATRIX ELEMENT IN HIGHLY SINGULAR POTENTIAL SCATTERING FOR LARGE IMAGINARY VALUES OF ANGULAR MOMENTUM

1966 ◽  
Vol 22 (9) ◽  
pp. 1046
Author(s):  
CHQU LON-SHIANG
Keyword(s):  
Angular Momentum ◽  
Matrix Element ◽  
Asymptotic Behaviour ◽  
Singular Potential ◽  
Potential Scattering ◽  
S Matrix

scholarly journals A REPRESENTATION OF THE S MATRIX ELEMENT FOR A HIGHLY SINGULAR POTENTIAL

1966 ◽  
Vol 22 (9) ◽  
pp. 1038
Author(s):  
CHQU LON-SHIANG
Keyword(s):  
Matrix Element ◽  
Singular Potential ◽  
S Matrix

scholarly journals A REPRESENTATION OF THE S MATRIX ELEMENT FOR A HIGHLY SINGULAR POTENTIAL

1965 ◽  
Vol 21 (5) ◽  
pp. 983
Author(s):  
DAI YUAN-BEN
Keyword(s):  
Matrix Element ◽  
Singular Potential ◽  
S Matrix

A Multichannel “Potential Curves Hopping” Model for Inelastic Collisions

1986 ◽  
Vol 41 (5) ◽  
pp. 704-714
Author(s):  
D. Campos ◽  
J. M. Tejeiro ◽  
F. Cristancho
Keyword(s):  
Matrix Element ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Inelastic Collisions ◽  
Interaction Matrix ◽  
Quantum Mechanical ◽  
Interaction Matrix Element ◽  
S Matrix ◽  
Hopping Model ◽  
Potential Curves

We introduce a multichannel “potential curves hopping” model and obtain the exact quantum mechanical S-matrix by solving the associated set of coupled second-order ordinary differential equations that describes the inelastic collisions between atomic particles. The only assumption is that the interaction matrix element between each pair of channels (say, γ and β) is of the form Uγβ(r) = Uβγ(r) =: Uγβ δ( r - rγβ), where δ (c) is the Dirac deltafunction, and rγβ and Uγβ are parameters which can be chosen freely.Semiclassical techniques can be incorporated directly in the theory if the Schrödinger equations for the uncoupled channels allow this treatment. The formulation is particularized to the two-channel problem and illustrated with a semiclassical example the He+ + Ne problem at 70.9 eV.

scholarly journals Partial conservation law in a schematic single j shell model

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740021 ◽  
Author(s):  
Wesley Pereira ◽  
Ricardo Garcia ◽  
Larry Zamick ◽  
Alberto Escuderos ◽  
Kai Neergård
Keyword(s):  
Angular Momentum ◽  
Matrix Element ◽  
Shell Model ◽  
Linear Function ◽  
Conservation Law ◽  
Interaction Matrix ◽  
Stationary States ◽  
Interaction Matrix Element ◽  
Angular Momenta ◽  
Partial Conservation

We report the discovery of a partial conservation law obeyed by a schematic Hamiltonian of two protons and two neutrons in a [Formula: see text] shell. In our Hamiltonian, the interaction matrix element of two nucleons with combined angular momentum [Formula: see text] is linear in [Formula: see text] for even [Formula: see text] and constant for odd [Formula: see text]. It turns out that in some stationary states, the sum of the angular momenta [Formula: see text] and [Formula: see text] of the proton and neutron pairs is conserved. The energies of these states are given by a linear function of [Formula: see text]. The systematics of their occurrence is described and explained.

Fredholm method in potential scattering and applications to complex angular momentum

1963 ◽  
Vol 23 (2) ◽  
pp. 187-220 ◽  
Author(s):  
Lowell Brown ◽  
Daniel I Fivel ◽  
Benjamin W Lee ◽  
Raymond F Sawyer
Keyword(s):  
Angular Momentum ◽  
Potential Scattering ◽  
Complex Angular Momentum

Angular momentum in general relativity I. Definition and asymptotic behaviour

1977 ◽  
Vol 354 (1679) ◽  
pp. 379-405 ◽  
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Angular Momentum ◽  
Asymptotic Behaviour ◽  
Event Horizon ◽  
Conservation Law ◽  
General Definition ◽  
Field Equations ◽  
Spin Coefficient ◽  
Coefficient Formalism

Angular momentum in axisymmetric space-times is investigated. The conclusions lead to a general definition suitable for all asymptoticallyflat spaces which is valid both at infinity and on the event horizon of a black hole. This first paper restricts attention to considerations at infinity. Working in terms of the spin coefficient formalism, the field equations are solved asymptotically at large distances and the definition is evaluated. A conservation law is derived and finally the effect on the angular momentum of a supertranslation of the coordinates is discussed.

On angular momentum analyticity in hard core potential scattering

1963 ◽  
Vol 4 (4) ◽  
pp. 218-219 ◽  
Author(s):  
O. Brander
Keyword(s):  
Angular Momentum ◽  
Hard Core ◽  
Potential Scattering ◽  
Core Potential

Shadow pole contribution to the S-matrix in potential scattering

1974 ◽  
Vol 7 (18) ◽  
pp. 2267-2272
Author(s):  
G Sethia ◽  
M C Gupta ◽  
C S Shastry
Keyword(s):  
Potential Scattering ◽  
Pole Contribution ◽  
S Matrix
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