We survey the results of a long-term study of the process of radiative recombination. A rigorous theory of nonrelativistic electron radiative recombination with a hydrogen-like ion is used to calculate the total cross section of the process, the effective radiation, the recombination rate coefficient, and the emission coefficient in a plasma with a Maxwellian electron distribution. The exact results are compared with the numerous known asymptotic and interpolation formulas. We propose interpolation formulas which ensure a uniform approximation of all mentioned quantities in a wide range of plasma temperatures.
It is shown in the framework of the fully relativistic Dirac-Fock treatment of photoionization and radiative recombination processes that taking into account all significant multipoles of the radiative field is of considerable importance at electron energy higher than several keV. For the first time, we show that the relativistic Maxwell-Bolzmann distribution of continuum electrons should be used in hot thermal plasmas. This decreases the radiative recombination rate coefficient up to several multipoles compared to the non-relativistic distribution commonly used.
We present a detailed study about ion-atom-atom three-body recombination in hydrogen and deuterium plasmas based on classical trajectory calculations in hyperspherical coordinates. Our results, due to the predominant role of the long-range charged-induced dipole interaction, indicate that H$_2^+$ and D$_2^+$ are the main reaction products in the case of hydrogen and deuterium plasmas, respectively. Besides, we find a more steep energy-dependent reaction rate when the collision energy surpasses the dissociation energy of the molecular ion, thus entering a new dynamical regime dominated by short…
The cross section of dipole-magnetic photodisintegration of the negative hydrogen ion has been calculated within the framework of an effective-range theory. The dipole-magnetic cross section of photodetachment within the very narrow range of energy near the process threshold dominates over the dipole-electric one. It has been shown that in ultracold hydrogen plasma at temperatures below kT=3.29.10-4 K the dipole-magnetic photo-recombination becomes a main mechanism of electron capture by hydrogen atoms.
The process of recombination for the hydrogen atom in the heat bath creating the blackbody radiation is descibed within the frameworks of quantum electrodynamics. For this purpose the self-energy for unbound electron in the field of the nucleus is considered. The imaginary part of this self-energy is directly connected with the recombination cross-section. The same procedure is applied to the hydrogen atom in the field of blackbody radiation. This leads to the new thermal correction to the process of recombination for the hydrogen atom in the heat bath. This correction takes into account the f…
In the framework of a quasi-molecular approach, the formation of hydrogen atom in the pre-recombination period of evolution of the universe is analysed quantitatively. Calculations in an adiabatic multi-level representation enable estimates of probabilities of radiative transitions. The quasi-molecular mechanism of recombination allows the formation of hydrogen molecular ion, $H_2^+$, in its ground state. The probability of this process is comparable with the probability of the creation of atomic hydrogen. The participation of a second proton in the recombination increases the binding energy o…
A rigorous QED theory of the multiphoton decay of excited states in hydrogen atom is presented. The "two-photon" approximation is formulated which is limited by the one-photon and two-photon transitions including cascades transitions with two-photon links. This may be helpful for the strict description of the recombination process in hydrogen atom and, in principle, for the history of the hydrogen recombination in the early Universe.
The recombination of an electron with an (initially) hydrogen-like ion is investigated. The effect of the electron-electron interaction is treated rigorously to the first order in the parameter 1/Z and within the screening-potential approximation to higher orders in 1/Z, with Z being the nuclear charge number. The two-electron correction contains the dielectronic-recombination part, which contributes to the process not only under the resonance condition for the projectile energy but also in the regions far from resonances. The mechanism of the off-resonant dielectronic recombination is studied…
A general expression for the double differential cross section of fluorescence radiation following photorecombination (PRF) of polarized electrons and polarized ions is derived by using usual atomic theory methods and is represented in the form of multiple expansions over spherical tensors. The ways of the application of the general expression suitable for the specific experimental conditions are outlined by deriving the asymmetry parameter of angular distribution of PRF radiation in the case of nonpolarized ions and electrons. This parameter is calculated for neon-like ions and bare nuclei. A…
An effect of atomic line broadening induced by the blackbody radiation is discussed. The level mixing effect and anti-Stokes Raman scattering are compared. It is shown that the mixing effect gives the most significant contribution to the line broadening and it is indicated how to distinguish these two effects in laboratory experiments. The influence of the level mixing on the recombination history of primordial plasma is also discussed.
The radiative recombination of a free electron into an excited state of a bare, high-Z ion is studied, together with its subsequent decay, within the framework of the density matrix theory and Dirac's relativistic equation. Special attention is paid to the polarization and angular correlations between the recombination and the decay photons. In order to perform a systematic analysis of these correlations the general expression for the double-differential recombination cross section is obtained by making use of the resonance approximation. Based on this expression, detailed computations for the…
The parity nonconservation effect on the radiative recombination of electrons with heavy hydrogenlike ions is studied. Calculations are performed for the recombination into the $2^1S_0$ state of helium-like thorium and gadolinium, where, due to the near-degeneracy of the opposite-parity $2^1S_0$ and $2^3P_0$ states, the effect is strongly enhanced. Two scenarios for possible experiments are studied. In the first scenario, the electron beam is assumed to be fully polarized while the H-like ions are unpolarized and the polarization of the emitted photons is not detected. In the second scenario, …
We introduce a new method that allows one to obtain an analytical cross section for the laser-assisted electron-ion collision in a closed form. As an example we perform a calculation for the hydrogen laser-assisted recombination. The $S$-matrix element for the process is constructed from an exact electron Coulomb-Volkov wave function and an approximate laser modified hydrogen state. An explicit expression for the field-enhancement coefficient of the process is expressed in terms of the dimensionless parameter $κ= |{eε_{0}}/{qω_{0}}|^{2}$, where $e$ and $q$ are the electron charge and momentum …
The results for the total multi-photon decay rates of the 3p and 4s levels of hydrogen, presented by D. Solovyev and L. Labzowsky within the cascade approximation, are revisited. The corrected results for certain decay channels differ from original ones of those authors sometimes by order of magnitude. Some aspects with respect to the cosmological recombination process are clarified.
A free electron can form a bound state with an atomic center $A$ upon photo emission (radiative recombination). In the presence of a neighboring atom $B$, such a bound state can, under certain conditions, be also formed via resonant transfer of energy to $B$, with its subsequent relaxation through radiative decay (two-center dielectronic recombination). This two-center process is very efficient in the 'static' case where $A$ and $B$ form a weakly bound system, dominating over single-center radiative recombination up to internuclear distances as large as several nanometers. Here we study its dy…
We present a theoretical investigation of the radiative recombination of twisted Bessel electrons with initially hydrogen-like (finally helium-like) heavy ions. In our study, we focus especially on the linear polarization of x-ray photons emitted in the electron capture into the ground $1s^2_{1/2}$ ionic state. Particular emphasis is placed on the question of how this polarization is affected if incident hydrogen-like ions are themselves spin-polarized. To explore such a "polarization transfer" we apply the density matrix theory and derive the Stokes parameters of recombination x-rays for the …
An interest for the low-energy range of the nonextensive distribution function arises from the study of radiative recombination in electron cooling devices in particle accelerators, whose experimentally measured reaction rates are much above the theoretical prediction. The use of generalized distributions, that differ from the Maxwellian in the low energy part (due to subdiffusion between electron and ion bunches), may account for the observed rate enhancement. In this work, we consider the isotropic distribution function and we propose a possible experiment for verifying the existence of a cu…
We investigate the quantum interference between the resonant process of nuclear excitation by electron capture (NEEC) followed by the radiative decay of the excited nucleus, and radiative recombination (RR). In order to derive the interference cross section, a Feshbach projection operator formalism is used. The electromagnetic field is considered by means of multipole fields. The nucleus is described by a phenomenological collective model and by making use of experimental data. The Fano profile parameters as well as the interference cross section for electric and magnetic multipole transitions…
We present a theoretical study on the recombination of a free electron into the ground state of a hydrogen-like ion in the presence of an external laser field. Emphasis is placed on the effects caused by the laser dressing of the residual ionic bound state. To investigate how this dressing affects the total and angle-differential cross section of laser assisted radiative recombination (LARR) we apply first-order perturbation theory and the separable Coulomb-Volkov-continuum ansatz. Using this approach detailed calculations were performed for low-$Z$ hydrogen like ions and laser intensities in …
We present a fully relativistic investigation of the radiative recombination of a twisted electron with a bare heavy nucleus. The twisted electron is described by the wave function which accounts for the interaction with the nucleus in all orders in $αZ$. We use this wave function to derive the probability of the radiative recombination with a single ion being shifted from the twisted electron propagation direction. We also consider more realistic experimental scenarios where the target is either localized (mesoscopic) or infinitely wide (macroscopic). The situation when the incident electron …
In the presence of an intensive laser field the radiative recombination of the continuum electron into an atomic bound state generally is accompanied by absorption or emission of several laser quanta. The spectrum of emitted photons represents an equidistant pattern with the spacing equal to the laser frequency. The distribution of intensities in this spectrum is studied employing the Keldysh-type approximation, i.e. neglecting interaction of the impact electron with the atomic core in the initial continuum state. Within the adiabatic approximation the scale of emitted photon frequencies is su…
Parity nonconservation (PNC) effect in recombination of a polarized electron with a heavy H-like ion in case of resonance with a doubly excited state of the corresponding He-like ion is studied. It is assumed that photons of the energy corresponding to the one-photon decay of the doubly excited state into the $2^1S_0$ or the $2^3P_0$ state are detected at a given angle with respect to the incident electron momentum. Calculations are performed for heliumlike thorium ($Z = 90$) and gadolinium ($Z = 64$), where the $2^1S_0$ and $2^3P_0$ levels are near to cross and, therefore, the PNC effect is s…
Investigation of the cosmic microwave background formation processes is one of the most actual problem at present time. In this paper we analyze the response of the hydrogen atom to the external photon fields. Field characteristics are defined via conditions corresponding to the recombination era of universe. Approximation of three-level atom is used to describe the "atom - fields" interaction. It is found that the phenomena of the electromagnetically induced transparancy takes place in this case. Consideration of EIT phenomena makes it necessary to update astrophysical description of the proc…
In the presence of a neighboring atom, electron-ion recombination can proceed resonantly via excitation of an electron in the atom, with subsequent relaxation through radiative decay. It is shown that this two-center dielectronic process can largely dominate over single-center radiative recombination at internuclear distances as large as several nanometers. The relevance of the predicted process is demonstrated by using examples of water-dissolved alkali cations and warm dense matter.
We provide a data set of emission and recombination coefficients of hydrogen using a kappa-distribution of electron energies rather than the more traditional Maxwell-Boltzmann (MB) distribution. The data are mainly relevant to thin and relatively cold plasma found in planetary nebulae and H II regions. The data set extends the previous data sets provided by Storey and Hummer which were computed using a MB distribution. The data set, which is placed in the public domain, is structured as a function of electron number density, temperature and kappa. Interactive fortran 77 and C++ data servers ar…
Tungsten is an important metal in nuclear fusion reactors. It will be used in the divertor component of ITER (Latin for 'the way'). The Tungsten Project aims to calculate partial and total DR rate coefficients for the isonuclear sequence of Tungsten. The calculated data will be made available as and when they are produced via the open access database OPEN- ADAS in the standard adf09 and adf48 file formats. We present our progress thus far, detailing calculational methods, and showing comparisons with other available data. We conclude with plans for the future.
We show that the spectrum and eigenstates of open-shell multicharged atomic ions near the ionization threshold are chaotic, as a result of extremely high level densities of multiply excited electron states ($10^3 eV^{-1}$ in Au^{24+}) and strong configuration mixing. This complexity enables one to use statistical methods to analyse the system. We examine the dependence of the orbital occupation numbers and single-particle energies on the excitation energy of the system, and show that the occupation numbers are described by the Fermi-Dirac distribution, and temperature and chemical potential ca…
The electromagnetically induced transparency (EIT) phenomenon in earlier universe is considered. We evaluated the elementary processes of the single scattering of photon on the hydrogen atom with the purpose of their use in the tasks of the radiation transfer theory. The additional function $f$, which depends on external conditions, is found. This function can be considered as an adjustment of the optical depth that leads to the necessity of modernization of the escape probability $p_{ij}(τ_S)\rightarrow p_{ij}(τ_S(1+f))$. The numerical values of $f$ for the different schemes of atom in three-…
We aim to present a comprehensive theoretical investigation of dielectronic recombination (DR) of the silicon-like isoelectronic sequence and provide DR and radiative recombination (RR) data that can be used within a generalized collisional-radiative modelling framework. Total and final-state level-resolved DR and RR rate coefficients for the ground and metastable initial levels of 16 ions between $\rm{P^{+}}$ and $\rm{Zn^{16+}}$ are determined. We carried out multi-configurational Breit-Pauli (MCBP) DR calculations for silicon-like ions in the independent processes, isolated resonance, distor…
Electron-ion recombination of completely stripped Bi83+ was investigated at the Experimental Storage Ring (ESR) of the GSI in Darmstadt. It was the first experiment of this kind with a bare ion heavier than argon. Absolute recombination rate coefficients have been measured for relative energies between ions and electrons from 0 up to about 125 eV. In the energy range from 15 meV to 125 eV a very good agreement is found between the experimental result and theory for radiative recombination (RR). However, below 15 meV the experimental rate increasingly exceeds the RR calculation and at Erel = 0 …
A statistical theory of resonant multielectron recombination based on properties of chaotic eigenstates is developed. The level density of many-body states increases exponentially with the number of excited electrons. When the residual electron-electron interaction exceeds the interval between these levels, the eigenstates (called compound states or compound resonances if these states are in the continuum) become "chaotic" superpositions of large numbers of Hartree-Fock configurational basis states. This situation takes place in some rare-earth atoms and many open-shell multiply charged ions e…
Radiative corrections to the 2E1 decay width of the 2s-state in the low-Z hydrogen-like system are examined within logarithmic approximation. The correction is found to be 2.025(1) alpha (Z alpha)^2 / pi log(Z alpha)^2 in units of the non-relativistic rate.
Highly excited eigenstates of atoms and ions with open f shell are chaotic superpositions of thousands, or even millions of Hartree-Fock determinant states. The interaction between dielectronic and multielectronic configurations leads to the broadening of dielectronic recombination resonances and relative enhancement of photon emission due to opening of thousands of radiative decay channels. The radiative yield is close to 100% for electron energy . 1 eV and rapidly decreases for higher energies due to opening of many autoionization channels. The same mechanism predicts suppression of photoion…
Within the framework of QED theory at finite temperature the thermal radiative corrections to spontaneous one-photon transition rates in hydrogen atom are investigated. The radiative one-loop self-energy corrections are described in the thermal case. Closed analytical expressions are derived and their numerical calculations for the spontaneous decay rate of the $ 2p $ state are carried out. Dominance of thermal radiative corrections to spontaneous Ly$_α $ decay rate over ordinary induced transition rate up to temperatures $ T < 6000 $ K is demonstrated.
In our recent papers (Kereslidze et all 2019a, 2021) a non-standard quasi-molecular mechanism was suggested and applied to treat the cosmological recombination. It was assumed that in the pre-recombination stage of evolution of the Universe an electron combined with two neighbouring protons and created the hydrogen molecular ion, $H_2^+$ in highly excited states, which then descended into the lower-lying states or dissociated. In this work, we elaborate the scheme of calculation for free-bound radiative transitions into attractive states of $H_2^+$ as functions of redshift $z$. Together with t…
Hydrogen and helium emission lines in nebulae form by radiative recombination. This is a simple process which, in principle, can be described to very high precision. Ratios of He I and H I emission lines can be used to measure the He$^+$/H$^+$ abundance ratio to the same precision as the recombination rate coefficients. This paper investigates the controversy over the correct theory to describe dipole $l$-changing collisions ($nl\rightarrow nl'=l\pm 1$) between energy-degenerate states within an $n$-shell. The work of Pengelly & Seaton (1964) has, for half-a-century, been considered the defini…
The radiative correction to the nuclear charge radius contribution to the Lamb shift of order $α(Zα)^5m_r^3<r^2>$ is calculated. In view of the recent high precision experimental data, this theoretical correction produces a significant contribution to the hydrogen-deuterium isotopic shift.
The current paper presents atomic data generated to investigate the recombination lines of C II in the spectra of planetary nebulae. These data include energies of bound and autoionizing states, oscillator strengths and radiative transition probabilities, autoionization probabilities, and recombination coefficients. The R-matrix method of electron scattering theory was used to describe the C2+ plus electron system.
