Superoperator methods for calculating cross sections: I. Correlation functions and the Born approximation

1976 ◽  
Vol 54 (13) ◽  
pp. 1313-1327 ◽  
Author(s):  
R. E. Turner ◽  
R. F. Snider
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Correlation Functions ◽  
Born Approximation ◽  
Time Correlation ◽  
Space Representation ◽  
Collision Dynamics ◽  
Quantum Mechanical Scattering ◽  
Line Trajectory ◽  
Semiclassical Approximations

Quantum mechanical scattering theory has recently been formulated exclusively in terms of density operators. The present work interprets the resulting generalized collision cross sections as integrals overtime correlation functions of relative coordinate, two body operators. It is shown that a straight line trajectory approximation to these time correlation functions is identical to the Born approximation. A phase space representation of the quantum collision dynamics is formulated. In these terms, the quantum cross section can be reduced in a natural way to the corresponding classical cross section provided there is no 'singular' behaviour. It would appear that this formulation would be very appropriate for making semiclassical approximations for the differential cross sections.

Superoperator methods of calculating cross sections: II. Distorted wave Born approximation

1976 ◽  
Vol 54 (13) ◽  
pp. 1328-1342 ◽  
Author(s):  
R. F. Snider ◽  
R. E. Turner
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Correlation Functions ◽  
Born Approximation ◽  
Collision Cross Section ◽  
Internal State ◽  
Time Correlation ◽  
State Transitions ◽  
Distorted Wave ◽  
Distorted Wave Born Approximation

The superoperator form of the collision cross section is evaluated within the distorted wave Born approximation. It is first verified that the obvious expansion methods give a result identical to that obtained by standard methods. Formalistically, the algebraic expansions of the transition operator and superoperator are shown to have parallel structures. The distorted wave Born approximation for the cross section also has a structure parallel to the structure of the Born approximation cross section. This is especially brought out by formulating the results in terms of time correlation functions. Certain simplifying features are found for cross sections averaged over initial and final velocity directions. These cross sections for internal state transitions are further simplified by averaging over a Maxwellian distribution of initial velocities in such a way as to obtain 'kinetic cross sections' appropriate for gas kinetic phenomena. Connection is also made with the 'constant acceleration approximation' used to estimate correlation functions in gas phase NMR.

The Scattering of Positrons by Helium: Total Cross Sections up to 270 eV

1975 ◽  
Vol 53 (10) ◽  
pp. 962-967 ◽  
Author(s):  
B. Jaduszliwer ◽  
A. Nakashima ◽  
D. A. L. Paul
Keyword(s):  
Energy Range ◽  
Cross Section ◽  
Cross Sections ◽  
Born Approximation ◽  
Reasonable Agreement ◽  
Experimental Results ◽  
Formation Cross Section ◽  
Sum Rule ◽  
Total Cross Sections ◽  
High Energies

The total cross sections for the scattering of positrons by helium have been measured by the method of transmission in the 16 to 270 eV energy range. The experimental results are higher than those of Canter et al. but are in reasonable agreement with recent results of Griffith et al., and at high energies tend towards Born approximation calculations. The integral of the cross section over positron momentum is smaller than the sum rule estimate made by Bransden et al. A tentative value of (0.034 ± 0.017)πa02 is assigned to the positronium formation cross section at threshold.

Bremsstrahlung linear polarization

1989 ◽  
Vol 67 (6) ◽  
pp. 545-561
Author(s):  
W. Del Bianco ◽  
M. Carignan
Keyword(s):  
Differential Cross Section ◽  
Cross Section ◽  
Cross Sections ◽  
Linear Polarization ◽  
Differential Cross ◽  
Born Approximation ◽  
Gamma Ray ◽  
High Energy ◽  
Scattered Electron ◽  
Triple Differential Cross Section

The dependence of the bremsstrahlung perpendicular and parallel triple differential cross sections and the linear polarization on the angles and energies of the incident and scattered electron and of the emitted gamma-ray has been studied in the high-energy small-angle hypothesis. The expression used for the bremsstrahlung triple differential cross section is valid in the Born approximation and for an unscreened Coulomb potential of the nucleus.

Charge transfer in the presence of a radiation field

1998 ◽  
Vol 76 (3) ◽  
pp. 245-250 ◽  
Author(s):  
S -M Li ◽  
J -G Khou ◽  
Z -F Zhou ◽  
J Chen ◽  
Y -Y Liu
Keyword(s):  
Charge Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Born Approximation ◽  
Atomic Hydrogen ◽  
Capture Cross ◽  
Exchange Collision ◽  
Increasing Functions ◽  
Theoretical Results ◽  
Capture Cross Sections

In the first Born approximation, the dressing modification in laser-assisted charge exchange collision is investigated. The crosssections for electron capture by a proton from dressed atomic hydrogen and dressed helium targets are calculated within awide energy range. Theoretical results show that with impact energy increasing, the dressing effect leads to increasingly significant cross-section modifications. The modified capture cross sections are increasing functions of the ratio of laser strength to frequency. PACS Nos.: 34.50.Rk; 34.70.+e; 32.80.Wr; and 34.90.+q

The 1 s -2 s excitation of hydrogen atoms by electron impact

1960 ◽  
Vol 258 (1293) ◽  
pp. 245-250 ◽  
Keyword(s):  
Electron Impact ◽  
Cross Section ◽  
Cross Sections ◽  
Born Approximation ◽  
Impact Excitation ◽  
Electron Impact Excitation ◽  
Hydrogen Atoms ◽  
Third Order ◽  
The Third ◽  
Intermediate States

The expression for the cross-section obtained from the second Born approximation by including only terms to the third order in the interaction energy is employed to calculate cross-sections for the electron impact excitation of the 2 s level of atomic hydrogen, allow­ance being made for distortion and polarization due to the 1 s , 2 s and 2 p 0.± 1 intermediate states. These cross-sections are compared with the available experimental data.

The absorption of high-energy photons in matter

1958 ◽  
Vol 244 (1237) ◽  
pp. 245-258 ◽  
Keyword(s):  
Pair Production ◽  
Cross Section ◽  
Cross Sections ◽  
Born Approximation ◽  
Liquid Scintillation ◽  
Scintillation Counter ◽  
High Energy ◽  
A Value ◽  
Peak Energy ◽  
Better Than

Total absorption cross-sections of hydrogen, carbon, copper, silver, lead and uranium have been measured for photons of mean energy 94 MeV. The method was to measure the transmission through an absorber of photons from the Oxford synchrotron, using a biased liquid scintillation counter to select photons of energy near the peak energy of the machine. The experimental data for hydrogen have been used to deduce a value for the cross-section for pair production in the field of the electron of 4.7 ± 0.4 millibarn. The relative cross-sections for the heavier elements have been determined to better than ± 0.2 %, and confirm the most recent calculations of the correction to the Born approximation in the theory of pair production.

scholarly journals Positron Impact Excitation of the nS States of Atomic Hydrogen

Atoms ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 9 ◽  
Author(s):  
Anand K. Bhatia
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Born Approximation ◽  
Atomic Hydrogen ◽  
Impact Excitation ◽  
Orbital Method ◽  
Positron Impact ◽  
Excitation Cross Sections ◽  
Theoretical Results ◽  
Incident Positron

The excitation cross sections of the nS states, n = 2 to 6, of atomic hydrogen at various incident positron energies (10.23 to 300 eV) were calculated using the variational polarized-orbital method. Nine partial waves were used to obtain converged cross sections. The present results should be useful for comparison with results obtained from other theories and approximations. The positron-impact cross section was found to be higher than the electron-impact cross sections. Experimental and other theoretical results are discussed. The threshold law of excitation is discussed and the cross sections in this region were seen to obey the threshold law proportional to ( ln k f ) − 2 . Cross sections were calculated in the Born approximation also and compared to those obtained using the variational polarized orbital method.

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