Collision between two ortho-positronium (Ps) atoms: A four-body Coulomb problem

The elastic collision between two ortho-positronium (e.g. S = 1) atoms is studied using an ab-initio static exchange model (SEM) in the centre of mass (CM) frame by considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly. A coupled channel methodology in momentum space is used to solve Lippman–Schwinger equation following the integral approach. A new SEM code is developed in which the Born–Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude adapting the partial wave analysis. The s-, p- and d-wave elastic phase shifts and the corresponding partial cross-sections for the spin alignment S = 0, i.e., singlet (+) and S = 2, i.e., triplet (?) states are studied. An augmented Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross-section (σ), the quenching cross-section (σ_q) and ortho-to-para conversion ratio (σ/σ_q). The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The theory includes the non-adiabatic short-range effects due to exchange.     

Collective states in highly symmetric atomic configurations and single-photon traps

We study correlated states in circular and linear-chain configurations of identical two-level atoms containing the energy of a single quasi-resonant photon in the form of a collective excitation, where the collective behavior is mediated by exchange of transverse photons between the atoms. For a circular atomic configuration containing N atoms, the collective energy eigenstates can be determined by group-theoretical means making use of the fact that the configuration possesses a cyclic symmetry group Z _N . For these circular configurations, the carrier spaces of the various irreducible representations of the symmetry group are at most two-dimensional, so that the effective Hamiltonian on the radiationless subspace of the system can be diagonalized analytically. As a consequence, the radiationless energy eigenstates carry a Z _N quantum number p = 0, 1, …, N, which is analogous to the angular momentum quantum number l = 0, 1, … carried by particles propagating in a central potential, such as a hydrogen-like system. Just as the hydrogen s states are the only electronic wave functions that can occupy the central region of the Coulomb potential, the quasi-particle corresponding to a collective excitation of the circular atomic sample can occupy the central atom only for vanishing Z _N quantum number p. When a central atom is present, the p = 0 state splits into two, showing level crossing at certain radii; in the regions between these radii, damped oscillations between two “ extreme” p = 0 states occur, where the excitation occupies either the outer atoms or the central atom only. For large numbers of atoms in a maximally subradiant state, a critical interatomic distance of λ/2 emerges both in the linear-chain and in the circular configuration of atoms. The spontaneous decay rate of the linear configuration exhibits a jumplike “critical” behavior for next-neighbor distances close to a half-wavelength. Furthermore, both the linear-chain and the circular configurations exhibit exponential photon trapping once the next-neighbor distance becomes less than a half-wavelength, with the suppression of spontaneous decay being particularly pronounced in the circular system. In this way, circular configurations containing sufficiently many atoms may be natural candidates for single-photon traps.     

Glauber Monte Carlo program for NICA/MPD and CBM experiments

A program code widely applied at RHIC and LHC for calculations of geometrical properties of nucleus-nucleus interactions is adapted for NICA/MPD and CBM energies. A parameterization of pp elastic scattering amplitude earlier proposed by the authors and valid at √s ≥ 3 GeV is used for a setting of the nucleon-nucleon collision profile. An approach well known in physics of low and intermediate energies is used for a determination of nuclear parameters. The code is enlarged by a possibility to account for the Gribov inelastic screening.     

Coulomb deexcitation of muonic hydrogen within the quantum close-coupling method

The Coulomb deexcitation of muonic hydrogen in collisions with the hydrogen atom has been studied in the framework of the fully quantum-mechanical close-coupling method for the first time. The calculations of the l-averaged cross sections of the Coulomb deexcitation are performed for (μp)_n and (μd)_n atoms in the initial states with the principal quantum number n = 3–9 and at relative energies E = 0.1–100 eV. The obtained results for the n and E dependences of the Coulomb deexcitation cross sections drastically differ from the semiclassical results. An important contribution of the transitions with Δn > 1 to the total Coulomb deexcitation cross sections (up to ～37%) is predicted.     

Phase diagram of the Kohn-Luttinger superconducting state for bilayer graphene

The effect of Coulomb interaction between Dirac fermions on the formation of the Kohn-Luttinger superconducting state in bilayer doped graphene is studied disregarding of the effect of the van der Waals potential of the substrate and impurities. The phase diagram determining the boundaries of superconductive domains with different types of symmetry of the order parameter is built using the extended Hubbard model in the Born weak-coupling approximation with allowance for the intratomic, interatomic, and interlayer Coulomb interactions between electrons. It is shown that the Kohn-Luttinger polarization contributions up to the second order of perturbation theory in the Coulomb interaction inclusively and an account for the long-range intraplane Coulomb interactions significantly affect the competition between the superconducting phases with the f-, p + ip-, and d + id-wave symmetries of the order parameter. It is demonstrated that the account for the interlayer Coulomb interaction enhances the critical temperature of the transition to the superconducting phase.     

Collision frequency shift of hyperfine transitions in atomic hydrogen at a low temperature

The experimental results on the collision frequency shift of ESR in diluted two-and three-dimensional atomic hydrogen at ultralow temperature have been analyzed. The apparent contradiction between experiment and theory is resolved by taking into account the relation between the symmetry of the state of two atoms and their total electron spin S. For example, transitions between symmetric and antisymmetric states of a pair of atoms induced by a symmetric perturbation are forbidden. If symmetric and antisymmetric states are, respectively, pure electronic triplets (S= 1) and singlets (S = 0), this results in the cancellation of the singlet-triplet transitions. Thus, the collision frequency shift of b → c and b → a transitions vanishes in a completely electron and nuclear spin-polarized gas (hyperfine state b). The comparison is performed with experiments in ultracold alkali vapors.     

Dependence of the differential cross sections for radiative-collisional excitation of metastable atomic states on the polarization of radiation

We calculate the total and differential cross sections for radiative-collisional excitation of the metastable 2¹S state of He atoms at collisions with Ne atoms in external radiation fields of various frequencies and polarizations. The calculations are performed for a thermal collision energy of E = 10^?3 atomic units and light intensity of I = 1 MW cm^?2, which corresponds to a single photon absorption by a quasi-molecule during the collision. Both the differential and total cross sections are shown to depend strongly on the relative orientation of the radiation polarization vector and the initial relative velocity vector of the colliding atoms. We analyze the azimuthal scattering asymmetry related to the orientation of the angular momentum of the absorbed photon.     

Magnetism of Fe clusters embedded in Cu,Ag, and Au fcc matrices: density functional calculations

We present extensive first principles density functional theory (DFT) calculations dedicated to analyze the magnetic properties of small Fe _n clusters (n = 2,3) embedded in Cu fcc, Ag fcc and Au fcc matrices. We consider several dimers and trimers having different interatomic distances. In all cases the Fe atoms are embedded as substitutional impurities in the metallic network. For the case of the Fe dimers we have considered two magnetic configurations: ferromagnetic (antiferromagnetic), when the atomic magnetic moment of the Fe atoms are parallel (antiparallel) each other. For the case of dimers immersed in Cu and Ag matrices, the ground state corresponds to the ferromagnetic Fe dimer whose interatomic distance is a/√2. For Fe dimer immersed in the Au matrix the ground state corresponds to a ferromagnetic coupling when the interatomic distance is a√(3/2). In the case of the Fe trimers we have considered three or four magnetic configurations, depending on the Fe cluster geometry. For the case of Fe trimer immersed in Cu and Ag matrices we have found that the ground state corresponds to the ferromagnetic trimer forming an equilateral triangle with an interatomic distance equal to a/√2. The ground state for the Fe trimer immersed in the Au matrix corresponds to the ferromagnetic Fe trimer forming a right angle triangle.     

Influence of an external electric field on the probabilities of two-photon transitions between 2<Emphasis Type="Italic">s</Emphasis>, 2<Emphasis Type="Italic">p</Emphasis> and 1<Emphasis Type="Italic">s</Emphasis> levels for hydrogen and antihydrogen atoms

The probabilities of two-photon decay for hydrogen (H) and antihydrogen (\(\bar H\)) atoms in the presence and absence of an external electric field are analytically calculated. In particular, the probabilities of the E1E2 and E1M1 transitions between the 2p and 1s levels are calculated for the case when emitted photons are characterized by polarization vectors and wavevectors. It is shown that, in an external electric field, the decay probabilities for 2s and 2p levels differ for H and \(\bar H\) atoms because of interference terms linear in field. Coulomb Green’s function method is used for summing over intermediate states.     

Microscopic theory of second-order and third-order elastic constants for an NaCl crystal

Relations between the second-order and third-order symmetry-independent elastic constants and the energy of interatomic interactions dependent on the mutual arrangement of pairs and triplets of atoms are obtained for crystals belonging to the crystal class O _h. The derived relations and experimental data on the elastic constants are used to calculate four third-order elastic constants and the temperature dependence of the elastic anisotropy factor a(T) for an NaCl crystal. The calculated dependence a(T) is in qualitative agreement with the experimental dependence a _exp(T).     

Messungen des van der Waals-Potentials zwischen Alkaliatomen

Total collision cross sections for the interaction between alkali atoms have been measured using a modulated atomic beam technique. Since the determination of the density in the scattering chamber is the main source of error in absolute scattering measurements, particular attention is given to this problem: The cross section for partnersA andB is measured first withA as beam particles anB as target particles, and then withB as beam particles andA as target particles. The data are used to deduce the long rangevan der Waals (inverse sixth power) potential constants, which can be compared with theoretically calculated values of different authors. The interaction constants resulting from the present measurements are in good agreement with those calculated byFontana, while other calculations give much larger values.     

Inelastische Positronenstreuung am Atomkern

The ratio of the total and differential cross section for the inelastic positron-nucleus scattering (ē, N)-process to the total (γ, N) -cross section is derived in Born approximation for electric and magnetic dipole transitions. The result agrees with that obtained for the (e, N)-processes. Using the relativistic Coulomb Eigenfunctions for the continuous spectrum of the positrons, the Coulomb correction, the effect of screening and that of finite nuclear size agree with the (e, N)-process, when the annihilation of positrons with atomic electrons is neglected, and for positron energiesE _1,2 ⁺ >10 MeV. The effect of finite nuclear size is only calculated in Born approximation. ForE _1,2 ⁺ ≦2 MeV only the Coulomb correction differs from that obtained for the (e, N)-process. In the angular distribution for the (ē, N)-process there should be no interference of positron waves scattered by different multipoles, where the inelastic scattered positrons are detected. Numerical calculations have been carried out for nuclei withZ=6.29 and 82 and scattering angles ?=1°, 132°, 160° and 180° of the positron. This theory can be compared with the experiments in progress by W.C.Barber et al. using positrons for the inelastic scattering process at nuclei. The two-and three-virtual quanta-exchange effect in the (ē, N)-cross section is below 1.3% for positron energies between 10≦E ₁ ⁺ ≦300 MeV, and decreases rapidly for higher energies. This theory is also valied for inelastic scattering processes with positiveμ-mesons at nuclei; one has only to change the mass in the following equations.     

Dimension of an optimum impurity cluster and multiple-occupancy corrections in the theory of scattering of vibrational excitations in a solid solution

A relationship is derived for the correlation length L determining the size of the region in a solid solution in which excitations are scattered coherently. The correlation length depends on the fraction of impurity atoms x in the solid solution and the lattice dimension d. In the physical analysis of single-particle scattering processes in the solid solution and calculations, it is sufficient to take into account clusters with the number of cells n corresponding to the correlation volume L ^d . A theoretical analysis is illustrated by calculations of the spectral functions of the solid solution at different values of x and n. The multiple-occupancy corrections (polynomials in powers of x) to scattering diagrams are calculated using the method of sequential breaking apart of the interaction lines in the diagrams for the self-energy part. The method used was previously applied to the case of scattering by a single impurity. In this paper, the efficiency of the method is checked for scattering by multi-impurity clusters. It is demonstrated that the method can be useful in analyzing and estimating the contributions of scattering diagrams.     

The resonance pole and the residue of the scattering amplitude while the Coulomb forces gradually decrease

Trajectories for the S-wave pole of the scattering amplitude are constructed in the complex planes of the resonance momentum and of the renormalized vertex constant squared. They correspond to transitions from the resonance states to the virtual states of the singlet deuteron and the doublet triton while the Coulomb interaction gradually decreases to zero. The effective-range theory and a Yukawa-potential model are used. Physical reasons for the differences between the corresponding trajectories for Np and Nd systems are found. The results obtained explain why the resonances in the doublet Nd scattering are more difficult to detect in experiments in comparison with the well-studied singlet NN resonances.     

Excitation and ionization cross sections of hydrogen-like atoms in collisions with relativistic highly charged ions

The relativistic eikonal approximation and a matching procedure are used to describe excitation and ionization of hydrogen-like atoms from an arbitrary discrete energy state by the impact of a highly charged relativistic bare ion. Bethe-type formulas are derived that are asymptotically valid in the limits of v → c and Z ? 1, where v is the relative collision velocity, c is the speed of light, and Z is the ion charge.     

Die charakteristische Thermokraft der Grenzflächenatome

For a single-band conductor where two or more scattering mechanisms are present, each giving rise to a characteristic thermoelectric powerS _n and a electrical resistivity? _n the resultant thermoelectric powerS is given, as a first approximation, by\(S = \sum\limits_n {\varrho _n S_n /\varrho } \). Denoting withS ₀ the characteristic thermoelectric power due to the scattering of the conduction electrons by the boundary atoms, and withS _i and? _i the resultant thermoelectric power and electrical resistivity arising from all other scattering mechanisms, one may writeS=S ₀+? _i(S _i?S ₀)/?. The thermoelectric powerS and the electrical resistivity? of thin layers of potassium, evaporated in a vacuum ～5·10^?9 Torr on a glass substrate at 90° K temperature, were measured at different thicknesses. The variation ofS as a function of 1/? verifies the above mentioned relation. Thus, the thermoelectric power, characteristic for the scattering by potassium boundary atoms can be determined.     

Folding model analysis of the nucleus–nucleus scattering based on Jacobi coordinates

This paper presents the results of scattering of ¹⁶O+²⁰⁹Bi interaction near the Coulomb barrier. The interaction potential between two nuclei is calculated using the double folding model with the effective nucleon–nucleon (NN) interaction. The calculations of the exchange part of the interaction were assumed to be of finite-range and the density dependence of the NN interaction is accounted for. Also the results are compared with the zero-range approximation. All these calculations are done using the wave functions of the two colliding nuclei in place of their density distributions. The wave functions are obtained by the D-dimensional wave equation using the hyperspherical calculations on the basis of Jacobi coordinates. The numerical results for the interaction potential and the differential scattering are in good agreement with the previous works.     

On the diffraction scattering of particles with spin 1/2

The differential cross-section and polarization of spin 1/2 particles are calculated using the method of complex angular momenta on the assumption that both the scattering functionη(l) and nuclear phase shiftδ(l) have poles in the complexl-plane. The Coulomb effects are considered. Qualitative agreement with experiment was obtained.