scholarly journals Schalenmodell-Approximation für drei Körper im Ausgangskanal / Shell-Model Approach for Three Body Final States

1973 ◽  
Vol 28 (2) ◽  
pp. 185-205
Author(s):  
A. Grauel
Keyword(s):  
Energy Distribution ◽  
Shell Model ◽  
Cross Section ◽  
Scattering Theory ◽  
Wave Functions ◽  
Final States ◽  
S Matrix ◽  
Coulomb Effects ◽  
Three Body ◽  
Model Approach

A scattering theory for reactions with three-particle channels above the two-particle threshold is developed. The S-matrix-technique is used for the calculation of the extended S-matrix. Correlated two-particle wave functions in the exit channels are employed to describe the exact two-particle continuum. For the usual shell model only a few partial waves dominate. The cross section depends on the energy-distribution between the two outgoing nucleons. Numerical results are presented for the model (d, 2n)-reaction exciting 0+ -states in O16 without Coulomb-effects. The treatment is restricted to three (2p2h)-states with the particles in the (sd)-shell and holes in the p-shell.

POLARIZATION EFFECTS IN THE 3He(d,p)4He FUSION REACTION

2003 ◽  
Vol 18 (02n06) ◽  
pp. 302-305
Author(s):  
S. GOJUKI ◽  
S. ORYU
Keyword(s):  
Cross Section ◽  
Fusion Reaction ◽  
Resonance State ◽  
Resonance Region ◽  
Group Method ◽  
Polarization Effects ◽  
Effective Potentials ◽  
Low Energies ◽  
Coulomb Effects ◽  
Three Body

We calculate the cross section of the reaction 3 He(d,p) 4 He at very low energies using the three-body Faddeev formalism in which the target nucleus 3 He is considered as a cluster with spin 1/2 and the projectile deuteron as a proton and a neutron. For the n-p interaction we adopted the AV14 potential while for the p -3 He and n -3 He channel we constructed effective potentials based on the well known Resonating Group Method (RGM). Since the n-3He and p -3 He effective potentials are essentially different, the three-body system is treated as a three-channel problem. A resonance state is found using the 1 S 0 and 3 S 1-3 D 1 input states for the n-p and the 1 S 0 and 3 S 1 input states for both nucleon-cluster interactions. Coulomb effects were taken into account for the initial and the final states only. The polarization effects on the total cross section around the resonance region are discussed.

Scattering on Magnetic Monopoles

1980 ◽  
Vol 35 (12) ◽  
pp. 1276-1284
Author(s):  
Herbert-Rainer Petry
Keyword(s):  
Line Bundle ◽  
Cross Section ◽  
Scattering Theory ◽  
Charged Particles ◽  
Scattering Matrix ◽  
Magnetic Monopoles ◽  
Wave Functions ◽  
Complex Line ◽  
Complex Line Bundle ◽  
Frame Work

Abstract The time-dependent scattering theory of charged particles on magnetic monopoles is investigated within a mathematical frame-work, which duely pays attention to the fact that the wave-functions of the scattered particles are sections in a non-trivial complex line-bundle. It is found that Möller operators have to be defined in a way which takes into account the peculiar long-range behaviour of the monopole field. Formulas for the scattering matrix and the differential cross-section are derived, and, as a by-product, a momentum space picture for particles, which are described by sections in the underlying complex line-bundle, is presented.

Resonance charge transfer between H(1s) and H + calculated by means of an approximation based on an expansion in atomic eigenfunctions

1961 ◽  
Vol 264 (1319) ◽  
pp. 547-557 ◽  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Atomic Hydrogen ◽  
High Energy ◽  
Wave Functions ◽  
Final States ◽  
Energy Limit ◽  
Full Account ◽  
The Cross ◽  
Resonance Charge

An expression for the cross-section describing electron capture by protons in atomic hydrogen is derived from an expansion based on atomic wave functions. Full account is taken of momentum transfer and of the non-orthogonality of the wave functions of the initial and final states by the method due to Bates. The cross-sections have been computed for proton energies from 100 to 1 MeV. In the low energy limit, the results agree with the p.s.s. calculations of Dalgarno & Yadav and in the high energy limit with the calculations of Brinkm an & Kramers.

Three-body annihilations of and the quark rearrangement model

1977 ◽  
Vol 55 (23) ◽  
pp. 2059-2065 ◽  
Author(s):  
Robert K. Logan ◽  
Stephan Kogitz ◽  
Seiichi Tanaka
Keyword(s):  
Experimental Data ◽  
Cross Section ◽  
Final States ◽  
Three Body ◽  
Annihilation Reactions

Aphenomenological study of the quark rearrangement model is made using the results of cross section measurements of a number of [Formula: see text] annihilation reactions. The experimental data is shown to be consistent with the quark rearrangement model and Zweig's rule, if we restricted ourselves in the three-meson final states.

Electron capture by fast protons and α-particles in hydrogen

1963 ◽  
Vol 272 (1351) ◽  
pp. 542-556 ◽  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Wave Functions ◽  
Final States ◽  
Resonance Case ◽  
Ion Energies ◽  
The Cross ◽  
Proper Allowance ◽  
Fast Protons ◽  
Α Particles

Cross-sections are calculated for the accidental resonance reaction, He 2+ + H(ls) -> He + (2s or 2p) + H + , and the non-resonance reaction, H + + H (ls)-> H(2s or 2p) + H + by means of the method due to Bates in which account is taken of the non-orthogonality of the wave functions describing the initial and final states. Proper allowance is made for the effects of distortion and of momentum transfer. The calculations are carried out for incident ion energies in the range 25 to 800 keV. In the accidental resonance case, the cross-section is small at low velocities of relative motion, and tends rapidly towards zero as the velocity is decreased in accordance with the prediction of Bates & Lynn. In all processes investigated the effect of distortion is considerable. Using the results of McCarroll & McElroy and of McCarroll for capture into the ground states of He + and H, the cross-sections for capture into all states are estimated. Comparisons are made with the experimental data of Fite, Smith & Stebbings for the incident alpha particle case and with that of Fite, Stebbings, Hummer & Brackman for the incident proton case. The highest energy for which cross-sections are measured in either case is however only 40 keV.

scholarly journals Laser-Assisted (e, 2e) Collisions in the Symmetric/Asymmetric Coplanar Geometry

Atoms ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 40
Author(s):  
Abdelkader Makhoute ◽  
Driss Khalil ◽  
Imane Ajana
Keyword(s):  
Cross Section ◽  
Born Approximation ◽  
Laser Field ◽  
Target Atom ◽  
Wave Functions ◽  
Final States ◽  
Triple Differential Cross Section ◽  
Comprehensive Survey ◽  
Direction Of Polarization ◽  
Target Wave

In this review, we present a comprehensive survey of laser-assisted (e, 2e) reactions. The influence of a laser field on the dynamics of (e, 2e) collisions in atomic hydrogen is analyzed in the symmetric and asymmetric coplanar geometries. Particular attention is devoted to the construction of the dressed (laser-modified) target wave functions, in both the initial and final states. The calculation is performed in the framework of Coulomb-Volkov-Born approximation, where the initial and final electrons are described by Volkov wave functions, while the interaction of the incident electron with the target atom is treated in the first and the second Born approximation. The state of the ejected electron is described by a Volkov/Coulomb-Volkov wave function. A detailed account is also given of the techniques we have used to evaluate the scattering amplitudes. The influence of the laser parameters (frequency, intensity, and direction of polarization) on the angular distribution of the ejected electron is discussed, and a number of illustrative examples are given. The structure of the triple differential cross section in the vicinity of resonances is also analyzed.

COULOMB AND NUCLEAR FIELD EFFECTS ON TWO-BODY RESONANCES

1987 ◽  
Vol 02 (02) ◽  
pp. 81-87 ◽  
Author(s):  
V.V. KOMAROV ◽  
A.M. GREEN ◽  
A.M. POPOVA ◽  
V.L. SHABLOV
Keyword(s):  
Differential Cross Section ◽  
Cross Section ◽  
Differential Cross ◽  
Scattering Theory ◽  
Charged Particles ◽  
The Other ◽  
Final States ◽  
Nuclear Field ◽  
Field Effects

The influence of the fields of charged particles on two-particle resonances is discussed. One of the resonating particles can be charged. From few-body scattering theory there follows differential cross section formulae for the shapes and positions of the resonances. The resonances in the final states of the reactions 11 B (p, α)α, α, d(α, n) p, α and 7 Li (p, n)3 He , α are considered as examples. The possible changes in the forms and positions of mesonic resonances due to the influence of the other particles in the final states are also mentioned.

Energy Distribution in Electron Beams

1972 ◽  
Vol 30 ◽  
pp. 568-569
Author(s):  
Tamotsu Ohno
Keyword(s):  
Electron Beam ◽  
Energy Distribution ◽  
Cross Section ◽  
Integral Curve ◽  
Electron Beams ◽  
Electron Gun ◽  
Angular Divergence ◽  
Apparent Increase ◽  
Integral Width ◽  
The Cross

The energy distribution in an electron; beam from an electron gun provided with a biased Wehnelt cylinder was measured by a retarding potential analyser. All the measurements were carried out with a beam of small angular divergence (<3xl0-4 rad) to eliminate the apparent increase of energy width as pointed out by Ichinokawa.The cross section of the beam from a gun with a tungsten hairpin cathode varies as shown in Fig.1a with the bias voltage Vg. The central part of the beam was analysed. An example of the integral curve as well as the energy spectrum is shown in Fig.2. The integral width of the spectrum ΔEi varies with Vg as shown in Fig.1b The width ΔEi is smaller than the Maxwellian width near the cut-off. As |Vg| is decreased, ΔEi increases beyond the Maxwellian width, reaches a maximum and then decreases. Note that the cross section of the beam enlarges with decreasing |Vg|.

scholarly journals Classical black hole scattering from a worldline quantum field theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gustav Mogull ◽  
Jan Plefka ◽  
Jan Steinhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Quantum Field ◽  
Expectation Values ◽  
Path Integral Representation ◽  
S Matrix ◽  
Feynman Rules ◽  
Definition Of ◽  
Three Body

Abstract A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field hμν(x) and position $$ {x}_i^{\mu}\left({\tau}_i\right) $$ x i μ τ i of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection $$ \Delta {p}_i^{\mu } $$ Δ p i μ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.

Energy distribution over the cross section of the track of charged particles having the same linear energy transfer

1973 ◽  
Vol 34 (4) ◽  
pp. 372-373
Author(s):  
I. K. Kalugina ◽  
I. B. Keirim-Markus ◽  
A. K. Savinskii ◽  
I. V. Filyushkin
Keyword(s):  
Energy Transfer ◽  
Energy Distribution ◽  
Cross Section ◽  
Linear Energy Transfer ◽  
Charged Particles ◽  
The Cross
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