Isospin dynamics in heavy ion collisions: From Coulomb barrier to quark gluon plasma

Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this report, we present a selection of new reaction observables in dissipative collisions particularly sensitive to the symmetry term of the nuclear Equation of State (Iso-EoS). We will first discuss the Isospin Equilibration Dynamics. At low energies, this manifests via the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation, with the symmetry term acting as a restoring force. At higher beam energies, Iso-EoS effects will be seen in Imbalance Ratio Measurements, in particular from the correlations with the total kinetic energy loss. For fragmentation reactions in central events, we suggest to look at the coupling between isospin distillation and radial flow. In Neck Fragmentation reactions, important Iso-EoS information can be obtained from the correlation between isospin content and alignment. The high density symmetry term can be probed from isospin effects on heavy ion reactions at relativistic energies (few AGeV range). Rather, isospin sensitive observables are proposed from nucleon/cluster emissions, collective flows and meson production. The possibility to shed light on the controversial neutron/proton effective mass splitting in asymmetric matter is also suggested. A large symmetry repulsion at high baryon density will also lead to an “earlier” hadron-deconfinement transition in n-rich matter. A suitable treatment of the isovector interaction in the partonic EoS appears very relevant.     

Gravitational radiation from Coulomb collisions

The problem is considered of gravitational bremsstrahlung radiation from collisions between nonrelativistic charged particles at arbitrary values of the Born parameter ¦e₁e₂¦/hv (with exact Coulomb wave functions). It is shown that the existing estimates of this type of radiation from the solar plasma are far too high as they are based on equations for the cross section which are not applicable at the given temperature. A new estimate is derived.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 12, pp. 94–99, December, 1974.     

Coulomb collisions in strong magnetic fields

Summary Scattering cross-sections, reflection and transmission coefficients are derived for charged-particle potential scattering in the presence of a quantizing constant magnetic field within the Green's function approach. The optical theorem and the limit of the cross-section for vanishing values of the magnetic field have also been obtained. A numerical analysis of the total cross-section for different magnetic-field intensities and values of the screening constant has been performed. The total cross-sections are found to differ significantly from the field-free ones only for magnetic-field intensities and incident particle energies such that only few Landau channels are open. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Coulomb effects in relativistic nuclear collisions

We derive simple analytical formulas for Coulomb final-state interactions and apply them to the analysis of recent data on nuclear collisions. The π^?/π⁺ ratio, the π⁺ inclusive cross section, and the n/p ratio are studied. A relativistic field theoretic model is used to derive the formulas to first order in Zα. Using well-known non-perturbative results, we recast those formulas into an approximate non-perturbative form valid when finite-size effects are negligible. This allows us to calculate the important k → 0 limit. The final formulas are covariant and take into account multiple independently moving charged fragments of finite size and finite thermal expansion velocities. Our studies demonstrate analytically the complexity and importance of Coulomb distortions in nuclear collisions.     

Close-coupling approach to Coulomb three-body problems

The convergent close-coupling method is shown to overcome the remaining discrepancies with experiment of electron-hydrogen ionization. Consequently, this method is able to calculate accurately the Coulomb three-body problems which include electron collisions with hydrogen and helium (within the frozen core model), and helium double photoionization at all incident energies and kinematical or geometrical arrangements of the outgoing electrons.     

Positronium formation in positron-helium collisions with a screened Coulomb interaction

A study is conducted on positronium (Ps) formation in positron-helium collisions under the effect of a Coulomb screening, e⁺ + He(1s ²) ?? Ps(100) + He⁺(100), using the second-order distorted-wave approximation (DWA) and taking into consideration the screened dipole polarisation potential at low and intermediate incident positron energies in the range, 6 ? 500 eV. The theoretical model for the scattering calculation is fairly accurate and predicts a number of interesting features in the total and differential cross sections for the screening parameter, ?? = 0.0?0.4. The existence of resonances in the S-, P-, D- and F-partial waves has been reported in this work. Surface plots of the total and differential cross sections have also been presented to illustrate the interesting nature of the Ps formation in this scattering process.     

Coulomb collisions and the bound-electron recombination distribution function

A detailed analysis is made of how the distribution function of bound electrons is formed in the presence of three-bodyi—e—e recombination. The kinetic K matrix is obtained, characterizing the number of transitions from one energy range to another due to Coulomb collisions. It is found to have a pole of the third order in the magnitude of the transferred energy. This makes it possible to transform from the balance equation described by the K matrix to the Fokker — Planck equation describing diffusion and drift along the energy axis. Numerical solution of the time-dependent Fokker — Planck equation demonstrates that the characteristic relaxation time of the bound-electron distribution function is the time interval between Coulomb collisions. A comparison with previous computer modeling of the distribution function from first principles demonstrates that these results cannot be in agreement without rejecting the principle of detailed balance in its present formulation for a Coulomb plasma. This agrees with the conclusions previously reached in a computer modeling of the properties of a classical Coulomb plasma.General Physics Institute, Russian Academy of Sciences, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 3–19, September, 1994.     

Langevin representation of Coulomb collisions for bi-Maxwellian plasmas

Langevin model corresponding to the Fokker–Planck equation for bi-Maxwellian particle distribution functions is developed. Rosenbluth potentials and their derivatives are derived in the form of triple hypergeometric functions. The Langevin model is tested in the case of relaxation of the proton temperature anisotropy and implemented into the hybrid expanding box model. First results of this code are presented and discussed.     

QCD Coulomb gauge approach to exotic hadrons

The Coulomb gauge Hamiltonian model is used to calculate masses for selected J^PC states consisting of exotic combinations of quarks and gluons: ggg glueballs (oddballs), qˉg hybrid mesons and qˉqˉ tetraquark systems. An odderon Regge trajectory is computed for the J^- glueballs with intercept much smaller than the pomeron, explaining its nonobservation. The lowest 1^-+ hybrid-meson mass is found to be just above 2.2GeV while the lightest tetraquark state mass with these exotic quantum numbers is predicted around 1.4GeV consistent with the observed π(1400).     

Coulomb law and hypercomplex approach to electrodynamics

For a Coulomb-type field of a single point charge, generalized expressions are considered which are obtained on the basis of a hypercomplex generalization of electrodynamics with magnetic charges [1]. Along with the usual electrostatic field, in this approach a single charge can create a magnetic field, provided that the space points around the charge are oriented in a different way than the field source (charge) itself. Aside from vector fields, such a charge can create scalar and pseudoscalar fields, if time flows differently at the field points around the charge than at the location of the charge, or if the charge itself moves with respect to a fixed reference frame. The sources of the dual symmetry of the Maxwell equations are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 101–104, September, 1990.     

Feynman diagram approach to atomic collisions

A quantum field theoretic formulation of atomic collision phenomena involving non-relativistic free and bound systems is developed and a calculational procedure in terms of Feynman diagrams is prescribed. Matrix elements of several atomic collision processes have been calculated. In most cases standard quantum mechanical results are reproduced. But in some cases new terms appear in the scattering matrix whose contribution though negligibly small in the low energy region, become important at higher energies. A large portion of this work formed material for an invited talk delivered by one of us (T.P.) at the Second National Workshop on Atomic and Molecular Physics at Visva-Bharati, Santiniketan (India) held from 18–23 November 1979.     

Dusty photoresonant plasma with coulomb collisions

We have studied the charging of dust particles in a dense photoresonant sodium plasma with electron and ion densities as high as 10¹⁶ cm^?3 produced by laser pumping of the resonance level of Na, which was a small admixture (up to 1%) in an argon buffer gas. We show that the charge of dust particles with a radius of 10 mm at maximum reaches 3 × 10⁵ electron charges and that the potential of the dust particles at a low electron bulk loss rate agrees well with the orbital motion limited (OML) model data. The behavior of the electric field near a dust particle was found to be nonmonotonic. We established that the distribution of the potential near a solitary charged dust particle agrees well with the Debye one, but the screening length proves to be much larger than even the electron Debye length; the discrepancies are largest at the afterglow stage of the photoresonant plasma, when the sodium ion with a low recombination coefficient is the main plasma ion. We determined the domain of parameters for a dense plasma where an ensemble of dust particles can crystallize.     

Coulomb quantum kinetics in pulse-excited semiconductors

The quantum kinetic equations of the electron and hole densities and the interband polarization are derived for a laser-pulse-excited semiconductor with Coulomb interaction including renormalization effects, excitonic effects and scattering with memory kernels. Numerical solutions of this set of non-Markovian, nonlinear integro-differential equations are obtained for a statically screened Coulomb potential.     

Group theoretic approach to the screened Coulomb problem

Perturbation method based on the group theory is developed for the radial solution of the Schrödinger equation with screened Coulomb potential. It may be treated as an alternative to the analytic perturbation theory proposed recently by McEnnan, Kissel, and Pratt (Phys. Rev. A, 2 (1976), 532) and is based on the expansion of the potential of the following form $\text{V(r) = ?(}\text{a}\text{r}\text{) × (1 + λV}{}_1\text{r + λ}{}^2\text{V}{}_2\text{r}{}^2\text{+ …)}$. Corrections to the point-Coulomb energy levels are given as series in λ and also the screened Coulomb eigenstates are given in the form of expansions in powers of λ. The method is applied also to the continuous spectrum and similar expansions are found. The problem of the normalization of both discrete and continuous spectrum eigenstates is discussed and we find some differences in the case of the scattering states. Origin of this discrepancy is explained.     

Quantum mechanical stability approach to the Coulomb quasipotential

The critical coupling constant characterizing the stability behaviour of the Coulomb quasipotential has been evaluated as α ? α_c = 2. The present stability approach is based on the quantum-mechanical controllability requirement of the dispersion shifts due to the interactions. The dispersions characterizing the Coulomb quasipotential have been established suitably within the high-energy euclidian region.