Particle hole state densities

The influence of correlations on the critical temperature and density for the onset of superfluidity in nuclear matter is investigated within the scheme of Nozières and Schmitt-Rink [1]. For symmetric nuclear matter a smooth transition from Bose-Einstein condensation (BEC) of deuteronlike bound states at low densities and low temperatures to Bardeen-Cooper-Schrieffer (BCS) pairing at higher densities is described. Compared with the mean field approach a lowering of the critical temperature is obtained for symmetric nuclear matter as well as for pure neutron matter. The Mott transition in symmetric nuclear matter is discussed. Regions in the temperature-density plane are identified where correlated pairs give the main contribution to the composition of the system, so that approximations beyond the quasi-particle picture are requested.     

Pauli blocking in degenerate plasmas and the separable potential approach

The Mott effect describes the dissolution of bound states in a dense partially ionized plasma. It occurs when the ionization potential depression, owing to effects of correlation and degeneracy, compensates the binding energy of the bound state. At high densities and moderate temperatures, the Pauli blocking becomes important and influences significantly the degree of ionization in the region of degenerate plasmas. A quantum statistical approach is used where the total density is decomposed in an uncorrelated, “free” part and correlations, as a consequence of the cluster decomposition of the self‐energy. The contribution of correlations to the total density is given by bound states and continuum correlations. Exact solutions for a separable potential are compared to perturbation theory and numerical solutions of the in‐medium Schrödinger equation. The in‐medium scattering phase shifts are evaluated, and the role of continuum correlations is discussed. The Pauli blocking of bound states and the density of states are considered for warm dense matter conditions.     

Thermodynamic Functions,Ionization Equilibrium and Phase Transitions in Coulomb Systems

Macroscopic matter is considered as a quantum statistical system of electrons and nuclei. After the discussion of several exact bounds and stability theorems, the low and high density structures of the thermodynamic functions (corresponding to ideal gases) are given. The intermediate regions in the density temperature plane are treated by means of thermodynamic Green functions. This requires partial summations corresponding to the effects of screening (chains), bound states (ladders), and chemical equilibria (quasi particle summations). The thermodynamic instabilities corresponding to the first order plasma phase transitions are studied for several examples.     

Experimental determination of in-medium cluster binding energies and Mott points in nuclear matter

In-medium binding energies and Mott points for d, t, 3He and α clusters in low-density nuclear matter have been determined at specific combinations of temperature and density in low-density nuclear matter produced in collisions of 47A MeV 40Ar and 64Zn projectiles with 112Sn and 124Sn target nuclei. The experimentally derived values of the in-medium modified binding energies are in good agreement with recent theoretical predictions based upon the implementation of Pauli blocking effects in a quantum statistical approach.     

Physical properties of hot,dense matter: The general case

The thermodynamic properties of hot, dense matter are examined in the density range 10^?5 fm^?3 ? n ? 0.35 fm^?3 and the temperature range 0 ? T ? 21 MeV, for fixed lepton fractions Y_? = 0.4, 0.3 and 0.2 and for matter in β-equilibrium with no neutrinos. Three phases of the matter are considered: the nuclei phase is assumed to consist of Wigner-Seitz cells with central nuclei surrounded by a nucleon vapor containing also α-particles; in the bubbles phase the cell contains a central spherical bubble of nucleon vapor surrounded by dense nuclear matter; the third phase is that of uniform nuclear matter. All are immersed in a sea of leptons (electrons and neutrinos) and photons. The nuclei and bubbles are described by a compressible liquid drop model which is self-consistent in the sense that all of the constituent properties — bulk, surface, Coulomb energies and other minor contributions — are calculated from the same nuclear effective hamiltonian, in this case the Skyrme 1' interaction. The temperature dependence of all of these energies is included, for bulk and surface energies by direct calculation, for the Coulomb energy by combining in a plausible way the usual electrostatic energy and the numerical results pertaining to a hot Coulomb plasma. Lattice contributions to the Coulomb energy are an essential ingredient, and lattice modifications to the nuclear translational energy are included. A term is constructed to allow also for the reduced density of excited states of light nuclei. All of these modifications incorporate necessary physical effects which modify significantly the matter properties in some regions.     

Particle clustering and Mott transition in nuclear matter at finite temperature (II): Self-consistent ladder Hartree-Fock approximation and model calculations for cluster abundances and the phase diagram

Hot nuclear matter is described in terms of a quantum statistical approach. A self-consistent ladder Hartree-Fock approximation is derived in order to achieve a simultaneous treatment of free nucleons, douterons and higher clusters. In this approximation the effect of the correlated medium on the cluster abundances is studied. The Mott mechanism is pointed out in which clusters are destructed for densities beyond the Mott density. Cluster abundances and a phase diagram are calculated by means of a model calculation based on a simplified Skyrme interaction. The role of the higher clusters in calculating the phase diagram is investigated. The possible existence of a first-order phase transition in hot nuclear matter is discussed.     

Hadronic spectral function and charm meson production

At the chiral restoration/deconfinement transition, most hadrons undergo a Mott transition from being bound states in the confined phase to resonances in the deconfined phase. We investigate the consequences of this qualitative change in the hadron spectrum on final state interactions of charmonium in hot and dense matter, and show that the Mott effect for D-mesons leads to a critical enhancement of the J/ψ dissociation rate. Anomalous J/ψ suppression in the NA50 experiment is discussed as well as the role of the Mott effect for the heavy-flavor kinetics in future experiments at the LHC. The status of our calculations of hadron–hadron cross sections using the quark interchange and chiral Lagrangian approaches is reviewed, and an ansatz for a unification of these schemes is given.     

Quantum condensates in nuclear matter

Nonrelativistic nuclear matter is considered as a special example of a many-particle system. Quantum statistical methods are applied to treat the formation and dissolution of bound states in dense matter. The formation of quantum condensates is investigated. Special aspects are the transition from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) pairing as well as the occurrence of quartetting. Consequences for the structure of nuclei are compared with experimental data. Exercises to illustrate the main features of in-medium effects in nuclear matter are given. The text was submitted by the author in English.     

Finite-temperature density-dependent HF calculation of nuclear matter with gogny interaction

A finite-temperature density-dependent Hartree-Fock method is formulated starting from a variational principle for the thermodynamic potential. Based on this method, we have carried out a nuclear-matter calculation using the Gogny D1 finite-range effective interaction. The equation of state and several other thermal properties of nuclear matter so obtained are found to be rather similar to those given by the Skyrme SkM¹ interaction. The critical temperature and density for the liquid-gas phase transition of nuclear matter are found to be 15.1 MeV and 0.05 fm⁻³, respectively. The effect of the finite-temperature rearrangement potential is discussed     

Parametrization of light nuclei quasiparticle energy shifts and composition of warm and dense nuclear matter

Correlations and the formation of bound states (nuclei) are essential for the properties of nuclear matter in equilibrium as well as in nonequilibrium. In a quantum statistical approach, quasiparticle energies are obtained for the light elements that reflect the influence of the medium. We present analytical fits for the quasiparticle energy shifts of light nuclei that can be used in various applications. This is a prerequisite for the investigation of warm and dense matter that reproduces the nuclear statistical equilibrium and virial expansions in the low-density limit as well as relativistic mean field and Brueckner Hartree-Fock approaches near saturation density.     

Beta processes in a high-temperature field and nuclear multibeta decays

Sources of the temperature dependence of rates of nuclear beta processes in matter of massive stars are systematized. Electron and positron beta decays and electron capture (K capture and the capture of unbound electrons) fromexcited nuclear states (thermal decays) are considered along with the photobeta decays from ground and excited nuclear states. The possible quantum degeneracy of an electron gas in matter and the degree of ionization of an atomic K shell in a high-temperature field are taken into account. For a number of multidecay odd-nuclei, the temperature dependences of the ratios of the total rates of their β ^? decays to the sum of the total rates over all of decay modes for the same nuclei are calculated in the range of nuclear temperature from 2 to 3 × 10⁹ K. It is shown that the deviation of this ratio from the experimental value obtained at “normal” temperature may be quite sizable. This circumstance should be taken into account in models that consider the problem of synthesis of nuclei in matter of massive stars.     

Gebundene Paare in Fermi-Flüssigkeiten

The effect of a hard core on the energy of bound pair states in fermi-liquids is considered. It turns out that such bound pairs can exist in nuclear matter for the real nuclear forces, but not in the (non superfluid) He³. The importance of this fact for a possible understanding of the superfluidity is discussed briefly.     

Field-theoretical treatment of the liquid-vapor phase transition in nuclear systems

The liquid-vapor phase transition in hot nuclear matter is investigated in a field-theoretical approach employing euclidean-space (imaginary time) path-integral techniques. This approach allows us to study the nucleation due to both quantum and thermodynamic fluctuations. The bubbles of the new phase appear as instanton solutions of the euclidean-space field equations. The critical bubble sizes and associated transition probabilities are calculated. We examine the temperature and density values for which a phase transition may develop in hot nuclear matter produced in the course of a heavy-ion reaction.     

Functional Integral Approach to a Many Fermion System with Bound States

The equation of state for a dense system of interacting Fermions is derived using functional integral technique. To investigate the formation of bound states, a Hubbard-Stratonovich transformation is applied which expresses the action as functional of pair fields. The evaluation of the partition function in lowest orders with respect to the pair fields leads to a result which can be interpreted as the contribution of two-particle states, accounting for density corrections as Pauli blocking and self-energy shift. Comparison is performed with results for the equation of state of hot dense matter (plasmas, nuclear matter) obtained within a Green's function approach.     

In-medium two-nucleon properties in high electric fields

The quantum mechanical two — particle problem is considered in hot dense nuclear matter under the influence of a strong electric field such as the field of the residual nucleus in heavy — ion reactions. A generalized Galitskii-Bethe-Salpeter equation is derived and solved which includes retardation and field effects. Compared with the in-medium properties in the zero-field case, bound states are turned into resonances and the scattering phase shifts are modified. Four effects are observed due to the applied field: (i) A suppression of the Pauli-blocking below nuclear matter densities, (ii) the onset of pairing occurs already at higher temperatures due to the field, (iii) a field dependent finite lifetime of deuterons and (iv) the imaginary part of the quasiparticle self-energy changes its sign for special values of density and temperatures indicating a phase instability. The latter effect may influence the fragmentation processes. The lifetime of deuterons in a strong Coulomb field is given explicitly.     

In-medium two-nucleon properties in high electric fields

The quantum mechanical two — particle problem is considered in hot dense nuclear matter under the influence of a strong electric field such as the field of the residual nucleus in heavy — ion reactions. A generalized Galitskii-Bethe-Salpeter equation is derived and solved which includes retardation and field effects. Compared with the in-medium properties in the zero-field case, bound states are turned into resonances and the scattering phase shifts are modified. Four effects are observed due to the applied field: (i) A suppression of the Pauli-blocking below nuclear matter densities, (ii) the onset of pairing occurs already at higher temperatures due to the field, (iii) a field dependent finite lifetime of deuterons and (iv) the imaginary part of the quasiparticle self-energy changes its sign for special values of density and temperatures indicating a phase instability. The latter effect may influence the fragmentation processes. The lifetime of deuterons in a strong Coulomb field is given explicitly.     

Expansion and hadronization of a chirally symmetric quark-meson plasma

Using a chirally symmetric Lagrangian, which contains quarks as elementary degrees of freedom and mesons as bound states, we investigate the expansion and hadronization of a fireball, which initially contains only quarks and produces mesons by collisions. For this model, we study the time scales of expansion and thermal and chemical equilibration. We find that the expansion progresses relatively fast, leaving not necessarily enough time to establish thermal and chemical equilibrium. Mesons are produced in the bulk of the fireball rather than at a surface, at a temperature below the Mott temperature. Initial density fluctuations become amplified during the expansion. These observations challenge the applicability of hydrodynamical approaches to the expansion of a quark-gluon plasma.     

Effect of magnetic field on Mott's variable-range hopping parameters in multiwall carbon nanotube mat

We report the temperature and magnetic field dependence of the conductivity of multiwall carbon nanotube mat in the temperature range 1.4-150 K and in magnetic fields up to 10 T. It is observed that charge transport in this system is governed by Mott’s variable-range hopping of three-dimensional type in the higher temperature range and two-dimensional type in the lower temperature range. Mott’s various parameters, such as localization length, hopping length, hopping energy and density of states at the Fermi level are deduced from the variable-range hopping fit. The resistance of the sample decreases with the magnetic field applied in the direction of tube axis of the nanotubes. The magnetic field gives rise to delocalization of states with the well-known consequence of a decrease in Mott’s T0 parameter in variable-range hopping. The application of magnetic field lowers the crossover temperature at which three-dimensional variable-range hopping turns to two-dimensional variable-range hopping. The conductivity on the lower temperature side is governed by the weak localization giving rise to positive magnetoconductance. Finally, a magnetic field-temperature diagram is proposed showing different regions for different kinds of transport mechanism.