Superoperator methods for calculating cross sections. IV: Decoupled motions approximation

1984 ◽  
Vol 62 (5) ◽  
pp. 505-511
Author(s):  
Ralph Eric Turner ◽  
R. F. Snider ◽  
John S. Dahler
Keyword(s):  
Quantum Mechanics ◽  
Time Evolution ◽  
Impact Parameter ◽  
Cross Sections ◽  
First Principles ◽  
Translational Motion ◽  
Inelastic Collisions ◽  
The Impact ◽  
Parameter Approximation ◽  
Classical And Quantum Mechanics

A decoupled motions approximation to the time evolution of binary inelastic collisions is presented. The translational motion of the particles is described by a reference Hamiltonian while the internal motion is parameterized by the average trajectory associated with the translational motion. This description is applicable to both classical and quantum mechanics and any combination thereof. Thus it includes the standard impact parameter approximation. Cross sections for this decoupled evolution are derived from first principles. Explicit results for the impact parameter approximation are given.

scholarly journals A note on the relations between elastic and inelastic interactions and increasing ratio σel(s)/σtot(s) at the LHC

2019 ◽  
Vol 34 (32) ◽  
pp. 1950259 ◽  
Author(s):  
S. M. Troshin ◽  
N. E. Tyurin
Keyword(s):  
Elastic Scattering ◽  
Energy Dependence ◽  
Impact Parameter ◽  
Cross Sections ◽  
Parameter Dependence ◽  
Slope Parameter ◽  
Short Notice ◽  
Inelastic Interactions ◽  
The Impact ◽  
Mode A

We comment briefly on relations between the elastic and inelastic cross-sections valid for the shadow and reflective modes of the elastic scattering. Those are based on the unitarity arguments. It is shown that the redistribution of the probabilities of the elastic and inelastic interactions (the form of the inelastic overlap function becomes peripheral) under the reflective scattering mode can lead to increasing ratio of [Formula: see text] at the LHC energies. In the shadow scattering mode, the mechanism of this increase is a different one, since the impact parameter dependence of the inelastic interactions probability is central in this mode. A short notice is also given on the slope parameter and the leading contributions to its energy dependence in both modes.

Superoperator methods of calculating cross sections: III. Unified description of classical and quantal scattering

1980 ◽  
Vol 58 (8) ◽  
pp. 1171-1182 ◽  
Author(s):  
R. E. Turner ◽  
R. F. Snider
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Time Dependence ◽  
Stationary State ◽  
Cross Sections ◽  
Differential Cross ◽  
Density Operator ◽  
The Difference ◽  
Unified Description ◽  
Classical And Quantum Mechanics

It is shown how differential cross sections can be obtained from the time dependence of phase space packets. This procedure is valid both for classical and quantum mechanics. Two methods are described. In one the trajectory of the packet is emphasized, while in the second the packet is appropriately spread to infinite size. Both methods are applicable to either mechanics. It is shown how the quantal results agree with those of the stationary state approach as formulated in terms of the density operator. The description is also used to elucidate the difference between the scattered flux and the generalized flux that arises naturally in the superoperator formulation.

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