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.

Invariance Groups in Classical and Quantum Mechanics

1973 ◽  
Vol 28 (3-4) ◽  
pp. 538-540 ◽  
Author(s):  
D. J. Simms
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Energy Levels ◽  
Classical Mechanics ◽  
Symmetry Groups ◽  
Casimir Invariants ◽  
Classical Phase Space ◽  
Invariance Groups ◽  
Classical And Quantum Mechanics

AbstractThis is a report on some new relations and analogies between classical mechanics and quantum mechanics which arise out of the work of Kostant and Souriau. Topics treated are i) the role of symmetry groups; ii) the notion of elementary system and the role of Casimir invariants; iii) energy levels; iv) quantisation in terms of geometric data on the classical phase space. Some applications are described.

NuTeV Structure Function Measurement

2005 ◽  
Vol 20 (16) ◽  
pp. 3759-3761 ◽  
Author(s):  
◽  
M. Tzanov ◽  
T. Adams ◽  
A. Alton ◽  
S. Avvakumov ◽  
...  
Keyword(s):  
Structure Function ◽  
Cross Sections ◽  
Differential Cross ◽  
Charged Current ◽  
Differential Cross Sections ◽  
Neutrino Detector ◽  
Fixed Target ◽  
Function Measurement ◽  
Current Events ◽  
The Difference

The NuTeV experiment obtained high statistics samples of neutrino and antineutrino charged current events during the 1996-1997 Fermilab fixed target run. The experiment combines sign-selected neutrino and antineutrino beams and the upgraded CCFR iron-scintillator neutrino detector. A precision continuous calibration beam was used to determine the muon and hadron energy scales to a precision of 0.7% and 0.43% respectively. The structure functions F2(x, Q2) and xF3(x, Q2) obtained by fitting the y-dependence of the sum and the difference of the ν and [Formula: see text] differential cross sections are presented.

scholarly journals Application of the JISP16 potential to the nucleon induced deuteron breakup process at E=13 MeV and E=65 MeV

2020 ◽  
Author(s):  
Volodymyr Soloviov ◽  
Jacek Golak ◽  
Roman Skibiński ◽  
Kacper Topolnicki ◽  
Henryk Witała
Keyword(s):  
Phase Space ◽  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Nucleon Nucleon ◽  
Breakup Reaction ◽  
Breakup Process ◽  
Deuteron Breakup ◽  
Nucleon Potential ◽  
Incoming Nucleon

The JISP16 nucleon-nucleon potential has been applied to investigations of the nucleon induced deuteron breakup reaction at the incoming nucleon laboratory energies E = 13 MeV and E = 65 MeV. We have found that for the studied process the JISP16 force gives a description of the exclusive cross section, which is generally similar to the ones obtained with the standard realistic nucleon-nucleon AV18 interaction. However, there are some regions of the phase space where the differential cross sections predicted by the JISP16 and AV18 models, differ by more than 100 %. These special kinematical configurations may possibly be useful to refit the JISP16 force parameters.

scholarly journals Doubly and Triply Differential Cross Sections for Single Ionization of He by Fast Au53+ Using a Multi-Body Quasiclassical Model

Atoms ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 19
Author(s):  
François Frémont
Keyword(s):  
Quantum Mechanics ◽  
Cross Sections ◽  
Differential Cross ◽  
Present Model ◽  
Differential Cross Sections ◽  
Free Electrons ◽  
Single Ionization ◽  
Multi Body ◽  
Better Than ◽  
Binary Peak

A multi-body multi-center quasiclassical model was used to determine doubly- and triply-differential cross sections following single ionization in 3.6 MeV/amu Au53+ + He collisions. The present model improved recent calculations, in which free electrons were added in the collision to reproduce, at least qualitatively, the experimental binary peak. In the present calculations, the electrons, that were assumed to originate from the collisions of Au53+ with surfaces before colliding with the He target, were now considered to be in the field of the projectile, with nearly the same velocity. The agreement between the calculations and the experiment was improved, for both the doubly- and the triply-differential cross sections and was better than previous calculations based on quantum mechanics.

Elastic Scattering of 152Eu ? Rays by Tungsten

1981 ◽  
Vol 34 (2) ◽  
pp. 125 ◽  
Author(s):  
RB Taylor ◽  
P Teansomprasong ◽  
IB Whittingham
Keyword(s):  
Form Factor ◽  
Elastic Scattering ◽  
Cross Sections ◽  
Differential Cross ◽  
Dirac Point ◽  
Experimental Results ◽  
Large Momentum ◽  
Small Momentum ◽  
Hartree Fock ◽  
The Difference

Differential cross sections for the elastic scattering of 344, 444, 779, 964, 1086, 1112 and 1408 keY y rays by tungsten have been measured for six scattering angles ranging from 7� to 45� and are compared with theoretical cross sections for Rayleigh plus nuclear-Thomson plus, for the 1408 keY case, Delbriick scattering. For small momentum transfers the experimental results are in best agreement with cross sections computed using the Hartree-Fock form factor Rayleigh amplitudes, but at large momentum transfers the experimental results lie below these theoretical cross sections and also those computed using both the 'exact' Rayleigh amplitudes of Kissel and Pratt and the Dirac point-Coulomb form factor amplitudes. Inclusion of the Papatzacos and Mork Delbruck amplitudes at 1408 keY reduces the difference between experimental and theoretical cross sections for scattering angles less than 25�, but worsens the situation for larger angles.:

Scattering of Ions V. Elastic Scattering of the Symmetric Rare Gas Ion — Rare Gas Atom Systems

1974 ◽  
Vol 29 (3) ◽  
pp. 400-410 ◽  
Author(s):  
H.-U. Mittmann ◽  
H.-P. Weise
Keyword(s):  
Elastic Scattering ◽  
Cross Sections ◽  
Differential Cross ◽  
Energy Difference ◽  
Rare Gas ◽  
Rare Gas Atoms ◽  
Structure Splitting ◽  
The Difference ◽  
Interference Oscillations ◽  
Single Set

Differential cross-sections for the elastic scattering of Ne+ on Ne, Ar+ on Ar, Kr+ on Kr, and Xe+ on Xe have been measured. In the lab.-energy range from 3 eV up to 30 eV a rainbow maximum was observed and attributed to the attractive ground state potentials of these systems. From the angular positions of the primary rainbows the potential depths were derived. In the case of Ne2+ and Ar2+ these values are compared with the results of quantum chemical calculations and of semiempirical estimates. From lowest energies up to Eʟ = 200 eV g-u-interference oscillations were observed for all systems. In the case of Ne+ -Ne two oscillatory structures with different frequencies were detected and attributed to interference between Π-states and Σ-states, respectively. With increasing atomic number of the rare gas atoms the g-u-structure becomes increasingly irregular. The measured angular distances were used to derive the potential energy difference between the interfering molecular states. The evaluation was carried out by varying parameters of analytical model potentials for the lower lying state and the difference potential until the quantum mechanically calculated differential cross-section agreed with the experimental one within the experimental error. In the case of Ne2+ and Ar2+ the results are compared with ab initio calculations and experimental results of other authors. For Kr+ -Kr and Xe+ -Xe a fit at all energies could not be obtained with a single set of parameters. This effect and the high irregularity of the experimental curves are attributed to fine structure splitting of the molecular states via the strong spin-orbit coupling in Kr and Xe

scholarly journals Path Integrals for (Complex) Classical and Quantum Mechanics

10.14311/1414 ◽  
2011 ◽  
Vol 51 (4) ◽  
Author(s):  
R. J. Rivers
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Degrees Of Freedom ◽  
Path Integrals ◽  
Classical Mechanics ◽  
Classical Particle ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Complex Extension ◽  
Classical And Quantum Mechanics

An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolent of quantum mechanics; additional dimensions permit ‘tunnelling’ without recourse to instantons and time/energy uncertainties exist. In practice, ‘classical’ particle trajectories with additional degrees of freedom arise in several different formulations of quantum mechanics. In this talk we compare the extended phase space of the closed time-path formalism with that of complex classical mechanics, to suggest that ℏ has a role in our understanding of the latter. However, differences in the way that trajectories are used make a deeper comparison problematical. We conclude with some thoughts on quantisation as dimensional reduction.

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