Quantum Electrodynamics

We investigate the influence of the Coulomb interaction on laser-assisted Mott scattering. This is done by using an approximation in which the initial state of the electron is described by a Coulomb function modulated by the laser in the same way as a relativistic Volkov state. Numerical calculations are carried out for medium field intensity, and compared with the corresponding results obtained within the first-order Born approximation (where Coulomb distortion effects are neglected). It is found that the differential cross sections of the present treatment agree well with the Born predictions at small angles. With increasing scattering angles, however, including the Coulomb interaction enhances the cross section, as compared to the first-Born results. Furthermore, we show that the Coulomb distortion of the electron motion leads to a qualitatively different dependence of the cross sections on the laser frequency at high frequencies. The dependences of the differential cross section on the other field parameters, impact energy and the charge state of the residual ion are also studied.

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“…which is obtained by summing equation (16) over the final spin states and averaging over the initial spin polarizations [16], i.e.…”

Section: Theorymentioning

confidence: 99%

Laser-assisted Mott scattering in the Coulomb approximation

Berakdar

Chen

et al. 2004

J. Phys. B: At. Mol. Opt. Phys.

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“…This equation can be considered as a Schrödinger equation with its nonrelativistic kinetic part replaced by a relativistic counterpart. More rigorously, it is obtained from the covariant Bethe-Salpeter equation [22] with the following approximations: Elimination of any dependences on timelike variables and neglect of particle spin degrees of freedom as well as negative energy solutions [23]. The spinless Salpeter Hamiltonian is often used in hadronic physics to study bound states of quarks or gluons [24][25][26][27].…”

Section: Eigenequations In Position and Momentum Spacesmentioning

confidence: 99%

Lagrange-mesh calculations in momentum space

2012

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The Lagrange-mesh method is a powerful method to solve eigenequations written in configuration space. It is very easy to implement and very accurate. Using a Gauss quadrature rule, the method requires only the evaluation of the potential at some mesh points. The eigenfunctions are expanded in terms of regularized Lagrange functions which vanish at all mesh points except one. It is shown that this method can be adapted to solve eigenequations written in momentum space, keeping the convenience and the accuracy of the original technique. In particular, the kinetic operator is a diagonal matrix. Observables in both configuration space and momentum space can also be easily computed with a good accuracy using only eigenfunctions computed in the momentum space. The method is tested with Gaussian and Yukawa potentials, requiring respectively a small or a great mesh to reach convergence.

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“…The upper limit (17) can then be used with either G (1) (m, ∆ ij ) or G (2) (m, ∆ ij ). Of course, using the function G (1) (x, y) yields more stringent results than those obtained by using the function G (2) …”

Section: Upper Limit On the Total Number Of Bound Statesmentioning

confidence: 99%

“…Of course, using the function G (1) (x, y) yields more stringent results than those obtained by using the function G (2) …”

Section: Upper Limit On the Total Number Of Bound Statesmentioning

confidence: 99%