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G. L. Kotkin

Publications and source records attributed to G. L. Kotkin.

18 recordsLinked to original sources
arXiv2016

Scattering of twisted electron wave-packets by atoms in the Born approximation

The potential scattering of electrons carrying non--zero quanta of the orbital angular momentum (OAM) is studied in a framework of the generalized Born approximation, developed in our recent paper by Karlovets \textit{et al.}, Phys. Rev. A. {\textbf 92}, 052703 (2015). We treat these so--called \textit{twisted} electrons as spatially localized wave--packets. The simple and convenient expressions are derived for a number of scattering events in collision of such a vortex electron with a single potential, located at a given impact parameter with respect to the wave-packet's axis. The more realistic scenarios are also considered with either localized (mesoscopic) targets or infinitely wide (macroscopic) ones that consist of the randomly distributed atoms. Dependence of the electron scattering pattern on a size and on a relative position of the target is studied in detail for all three scenarios of the single--potential--, mesoscopic-- and the macroscopic targets made of hydrogen in the ground $1s$ state. The results demonstrate that the angular distribution of the outgoing electrons can be very sensitive to the OAM and to kinematic parameters of the focused twisted beams, as well as to composition of the target. Scattering of vortex electrons by atoms can, therefore, serve as a valuable tool for diagnostic of such beams.

quant-ph↗
arXiv2015

Born approximation for scattering of wave packets on atoms. I. Theoretical background for scattering of a wave packet on a potential field

Laser photons carrying non-zero orbital angular momentum are known and exploited during the last twenty years. Recently it has been demonstrated experimentally that such (twisted) electrons can be produced and even focused to a subnanometer scale. Thus, twisted electrons emerge as a new tool in atomic physics. The state of a twisted electron can be considered as a specific wave packet of plane waves. In the present paper-I we consider elastic scattering of the wave packets of fast non-relativistic particles on a potential field. We obtain simple and convenient formulae for a number of events in such a scattering. The equations derived represent, in fact, generalization of the well-known Born approximation for the case when finite sizes and inhomogeneity of the initial packet should be taken into account. To illustrate the obtained results, we consider two simple models corresponding to scattering of a Gaussian wave packet on the Gaussian potential and on the hydrogen atom. The scattering of twisted electrons on atoms will be considered in the next paper-II.

quant-ph↗
arXiv2009

Beam-size effect and particle losses at Super$B$ factory (Italy)

In the colliders, the macroscopically large impact parameters give a substantial contribution to the standard cross section of the $e^+ e^- \to e^+ e^- γ$ process. These impact parameters may be much larger than the transverse sizes of the colliding bunches. It means that the standard cross section of this process has to be substantially modified. In the present paper such a beam-size effect is calculated for bremsstrahlung at Super$B$ factory developed in Italy. We find out that this effect reduces beam losses due to bremsstrahlung by about 40%.

hep-ph↗
arXiv2009

Emission of Low-Energy Photons by Electrons at Electron-Positron and Electron-Ion Colliders with Dense Bunches

Usually, the emission of low-energy photons in electron-positron (or electron-ion) bunch collisions is calculated with the same approach as for synchrotron radiation (beamstrahlung). However, for soft photons (E_gamma < E_c where E_c is a critical photon energy), when the coherence length of the radiation becomes comparable to the bunch length, the beamstrahlung approximation becomes invalid. In this paper, we present results of our calculation for this region based on approximation of classical currents. We consider several colliders with dense bunches. The number of low-energy photons dN_gamma emitted by N_e electrons per bunch crossing in the energy interval dE_gamma is dN_gamma = alpha g N_e dE_gamma/E_gamma, where alpha is the fine-structure constant, and the function g, which depends on the bunch parameters, typically is of order unity for modern colliders. In particular, for the ILC, we find that E_c = 83 keV and g=5.5 at a vanishing beam axis displacement, and g=0.88, E_c=0.24 keV for KEKB. We also calculate the specific dependence of dN_gamma on the impact parameter between the two beam axes. In principle, the latter aspect allows for online monitoring of the beam axis displacement.

physics.acc-ph↗
arXiv2005

Polarization effects in the non-linear Compton scattering

We consider emission of a photon by an electron in the field of a strong laser wave. A probability of this process for circularly or linearly polarized laser photons and for arbitrary polarization of all other particles is calculated. We obtain the complete set of functions which describe such a probability in a compact invariant form. Besides, we discuss in some detail the polarization effects in the kinematics relevant to the problem of electron to photon conversion at photon-photon and electron-photon colliders.

hep-ph↗
arXiv2004

Complete description of polarization effects in e^+e^- pair production by a photon in the field of a strong laser wave

We consider production of a e^+e^- pair by a high-energy photon in the field of a strong laser wave. A probability of this process for circularly or linearly polarized laser photons and for arbitrary polarization of all other particles is calculated. We obtain the complete set of functions which describe such a probability in a compact invariant form. Besides, we discuss in some detail the polarization effects in the kinematics relevant to the problem of electron-photon conversion at photon-photon and electron-photon colliders.

hep-ph↗
arXiv2003

Complete description of polarization effects in the nonlinear Compton scattering. II. Linearly polarized laser photons

We consider emission of a photon by an electron in the field of a strong laser wave. Polarization effects in this process are important for a number of physical problems. We discuss a probability of this process for linearly polarized laser photons and for arbitrary polarization of all other particles. We obtain the complete set of functions which describe such a probability in a compact form.

hep-ph↗
arXiv2003

Muon Colliders, Monte Carlo and Gauge Invariance

If calculated in the standard way, the cross section for the collision of two unstable particles turns out to diverge. This is because this cross section is actually proportional to the size of the colliding beams. The effect is called the "linear beam size effect". We present a way of including this linear beam size effect in the usual Monte Carlo integration procedure. Furthermore we discuss the gauge breaking that this may cause.

hep-ph↗
arXiv2003

Complete description of polarization effects in the nonlinear Compton scattering. I. Circularly polarized laser photons

We consider emission of a photon by an electron in the field of a strong laser wave. Polarization effects in this process are important for a number of physical problems. We discuss a probability of this process for circularly polarized laser photons and for arbitrary polarization of all other particles. We obtain the complete set of functions which describe such a probability in a compact covariant form. Besides, we discuss an application of the obtained formulas to the problem of electron -> photon conversion at photon-photon and photon-electron colliders.

hep-ph↗
arXiv2003

Beam-size or MD-effect at colliders and correlations of particles in a beam

For several processes at colliding beams, macroscopically large impact parameters give an essential contribution to the standard cross section. These impact parameters may be much larger than the transverse sizes of the colliding bunches. In that case, the standard calculations have to be essentially modify. The corresponding formulae for such a beam-size effect were given twenty years ago without taking into account correlations of particle coordinates in the beams. In the present paper we derive formulae which necessary to take into account quantitatively the effect of particle correlations in the spectrum of bremsstrahlung as well as in pair production. Besides, we consider critically recent papers of Baier and Katkov [Phys. Rev. D {\bf 66}, 053009 (2002) and hep-ph/0305304] in which it was calculated a new additional ``subtraction term'' related to the coherent contribution into beam-size effect. We show that this result is groundless and point out the origin of the mistake.

hep-ph↗
arXiv2002

Influence of the beam-size or MD-effect on particle losses at B-factories PEP-II and KEKB

For the $e^+ e^- \to e^+ e^- γ$ process at colliding beams, macroscopically large impact parameters give an essential contribution to the standard cross section. These impact parameters may be much larger than the transverse sizes of the colliding bunches. It means that the standard calculations have to be essentially modify. In the present paper such a beam-size or MD-effect is calculated for bremsstrahlung at B-factories PEP-II and KEKB using the list of nominal parameters from Review of Particle Physics (2002). We find out that this effect reduces beam losses due to bremsstrahlung by about 20%.

hep-ph↗
arXiv2002

Once Again about Beam-Size or MD-Effect at Colliding Beams

For several processes at colliding beams, macroscopically large impact parameters give an essential contribution to the standard cross section. These impact parameters may be much larger than the transverse sizes of the colliding bunches. In that case, the standard calculations have to be essentially modify. The corresponding formulae were given twenty years ago. In recent paper of Baier and Katkov [17] it was claimed that the previous results about bremsstrahlung spectrum have to be revised and an additional subtraction related to the coherent contribution has to be done. This additional term has been calculated with the result that it may be essential for the performed and future experiments. In the present paper we analyze in detail the coherent and incoherent contributions in the conditions, considered in paper [17]. In contract to above claims, we found out that under these conditions the coherent contribution is completely negligible and, therefore, there is no need to revise the previous results.

hep-ph↗
arXiv1999

Effective photon spectra for Photon Colliders

The luminosity distribution in the effective $γγ$ mass at photon collider has usually two peaks which are well separated: high energy peak with mean energy spread 5-7% and wide low energy peak.The low energy peak depends strongly on details of design it is unsuitablefor the study of New Physics phenomena. We find simple approximte form of spectra of collided photons for $γγ$ and $eγ$ colliders wich convolution describes high energy luminosity peak with good accuracy in the most essential preferable region of parameters.

hep-ph↗
arXiv1998

Production of para-- and orthopositronium at relativistic heavy ion colliders

We consider the ortho-- and parapositronium production in the process $AA \to AA+$ Ps where A is a nucleus with the charge number Z. The inclusive cross section and the energy distribution of the relativistic Ps are calculated which are of primary interest from the experimental point of view. The accuracy of the corresponding cross sections is given by omitting terms $\sim (Zα)^2/L^2$ for the para--Ps and $\sim (Zα)^2/L$ for the ortho--Ps production where $L=\ln{γ^2} \approx 9$ and 16 for the RHIC and the LHC. Within this accuracy the multiphoton (Coulomb) corrections are taken into account. We show that the RHIC and the LHC will be Ps factories with a productions rate of about $10^5 ÷10^8$ relativistic Ps per day. The fraction of the ortho--Ps is expected to be of the same order as that of the para--Ps for Au--Au and Pb--Pb collisions.

hep-ph↗
arXiv1997

Polarization of high-energy electrons traversing a laser beam

When polarized electrons traverse a region where the laser light is focused their polarization varies even if their energy and direction of motion are not changed. This effect is due to interference of the incoming electron wave and an electron wave scattered at zero angle. Equations are obtained which determine the variation of the electron density matrix, and their solutions are given. The change in the electron polarization depends not only on the Compton cross section but on the real part of the forward Compton amplitude as well. It should be taken into account, for example, in simulations of the $e \to γ$ conversion for future $γγ$ colliders.

hep-ph↗
arXiv1996

Variation in polarization of high-energy $γ$-quanta traversing a bunch of polarized laser photons

The elastic light-light scattering below the threshold of the $e^+e^-$ pair production leads to a variation in polarization of hard $γ$-quanta traversing without loss a region where the laser light is focused. Equations are obtained which determine the variation of Stokes parameters of $γ$-quanta in this case, and their solutions are given. It is pointed out that this effect can be observed in the experiment E-144 at SLAC. It should be taken into account (and, perhaps, it can be used) in experiments at future $γγ$ colliders.

hep-ph↗
arXiv1996

Physical mechanism of the linear beam-size effect at colliders

We present qualitative but precise description of the linear beam-size effect predicted for the processes in which unstable but long--living particles collide with each other. We derive physically pronounced equation for the events rate which proves that the linear beam-size effect corresponds to the scattering of one beam of particles on the decay products of the other. We compare this linear beam-size effect with the known logarithmic beam-size effect measured in the experiments on a single bremsstrahlung at VEPP-4 and HERA.

hep-ph↗