Virial coefficients of the uniform electron gas from path-integral Monte Carlo simulations

The properties of plasmas in the low-density limit are described by virial expansions. Analytical expressions are known from Green's function approaches only for the first three virial coefficients. Accurate path-integral Monte Carlo (PIMC) simulations have recently been performed for the uniform electron gas, allowing the virial expansions to be analyzed and interpolation formulas to be derived. The exact expression for the second virial coefficient is used to test the accuracy of the PIMC simulations and the range of validity of the interpolation formula of Groth et al. [Phys. Rev. Lett. 119, 135001 (2017)0031-900710.1103/PhysRevLett.119.135001], and we discuss the fourth virial coefficient, which is not exactly known yet. Combining PIMC simulations with benchmarks from exact virial expansion results would allow us to obtain more accurate representations of the equation of state for parameter ranges of conditions which are of interest, e.g., for helioseismology.

Virial expansion of the electrical conductivity of hydrogen plasmas

The low-density limit of the electrical conductivity σ(n,T) of hydrogen as the simplest ionic plasma is presented as a function of the temperature T and mass density n in the form of a virial expansion of the resistivity. Quantum statistical methods yield exact values for the lowest virial coefficients which serve as a benchmark for analytical approaches to the electrical conductivity as well as for numerical results obtained from density functional theory-based molecular dynamics simulations (DFT-MD) or path-integral Monte Carlo simulations. While these simulations are well suited to calculate σ(n,T) in a wide range of density and temperature, in particular, for the warm dense matter region, they become computationally expensive in the low-density limit, and virial expansions can be utilized to balance this drawback. We present new results of DFT-MD simulations in that regime and discuss the account of electron-electron collisions by comparison with the virial expansion.

Polarized angular-dependent reflectivity and density-dependent profiles of shock-compressed xenon plasmas

New data for the reflectivity of shock-compressed xenon plasmas at pressures of 10-12 GPa at large incident angles are presented. In addition, measurements have been performed at different densities. These data allow to analyze the free-electron density profile across the shock wave front. Assuming a Fermi-like density profile, the width of the front layer is inferred. The reflectivity coefficients for the s- and p-polarized waves are calculated. The influence of atoms, which was taken into account on the level of the collision frequency, proves to be essential for the understanding of the reflection process. Subsequently, a unique density profile is sufficient to obtain good agreement with the experimental data at different incident angles and at all investigated optical laser frequencies. Reflectivity measurements for different densities allow to determine the dependence of shock-front density profiles on the plasma parameters. As a result, it was found that the width of the front layer increases with decreasing density.

Comment on "Isochoric, isobaric, and ultrafast conductivities of aluminum, lithium, and carbon in the warm dense matter regime"

Dharma-wardana et al. [M. W. C. Dharma-wardana et al., Phys. Rev. E 96, 053206 (2017)2470-004510.1103/PhysRevE.96.053206] recently calculated dynamic electrical conductivities for warm dense matter as well as for nonequilibrium two-temperature states termed "ultrafast matter" (UFM) [M. W. C. Dharma-wardana, Phys. Rev. E 93, 063205 (2016)2470-004510.1103/PhysRevE.93.063205]. In this Comment we present two evident reasons why these UFM calculations are neither suited to calculate dynamic conductivities nor x-ray Thomson scattering spectra in isochorically heated warm dense aluminum. First, the ion-ion structure factor, a major input into the conductivity and scattering spectra calculations, deviates strongly from that of isochorically heated aluminum. Second, the dynamic conductivity does not show a non-Drude behavior which is an essential prerequisite for a correct description of the absorption behavior in aluminum. Additionally, we clarify misinterpretations by Dharma-wardana et al. concerning the conductivity measurements of Gathers [G. R. Gathers, Int. J. Thermophys. 4, 209 (1983)IJTHDY0195-928X10.1007/BF00502353].

Contribution of electron-atom collisions to the plasma conductivity of noble gases

We present an approach which allows the consistent treatment of bound states in the context of dc conductivity in dense partially ionized noble gas plasmas. Besides electron-ion and electron-electron collisions, further collision mechanisms owing to neutral constituents are taken into account. Especially at low temperatures of 10^{4}to10^{5} K, electron-atom collisions give a substantial contribution to the relevant correlation functions. We suggest an optical potential for the description of the electron-atom scattering which is applicable for all noble gases. The electron-atom momentum-transfer cross section is in agreement with experimental scattering data. In addition, the influence of the medium is analyzed, the optical potential is advanced including screening effects. The position of the Ramsauer minimum is influenced by the plasma. Alternative approaches for the electron-atom potential are discussed. Good agreement of calculated conductivity with experimental data for noble gas plasmas is obtained.

Optical conductivity of warm dense matter within a wide frequency range using quantum statistical and kinetic approaches

Fundamental properties of warm dense matter are described by the dielectric function, which gives access to the frequency-dependent electrical conductivity; absorption, emission, and scattering of radiation; charged particles stopping; and further macroscopic properties. Different approaches to the dielectric function and the related dynamical collision frequency are compared in a wide frequency range. The high-frequency limit describing inverse bremsstrahlung and the low-frequency limit of the dc conductivity are considered. Sum rules and Kramers-Kronig relation are checked for the generalized linear response theory and the standard approach following kinetic theory. The results are discussed in application to aluminum, xenon, and argon plasmas.

Reply to "Comment on 'Direct linear term in the equation of state of plasmas' "

The long-standing discrepancy in the equation of state of charge neutral plasmas, the occurrence of an e(2) direct term in the second virial coefficient, is dealt with. We state that such a contribution should not appear for a pure Coulomb interaction.

Free-electron X-ray laser measurements of collisional-damped plasmons in isochorically heated warm dense matter

We present the first highly resolved measurements of the plasmon spectrum in an ultrafast heated solid. Multi-keV x-ray photons from the Linac Coherent Light Source have been focused to one micrometer diameter focal spots producing solid density aluminum plasmas with a known electron density of n_{e}=1.8×10^{23}  cm^{-3}. Detailed balance is observed through the intensity ratio of up- and down-shifted plasmons in x-ray forward scattering spectra measuring the electron temperature. The plasmon damping is treated by electron-ion collision models beyond the Born approximation to determine the electrical conductivity of warm dense aluminum.

Conductivity of warm dense matter including electron-electron collisions

We present an approach that can resolve the controversy with respect to the role of electron-electron collisions in calculating the dynamic conductivity of dense plasmas. In particular, the dc conductivity is analyzed in the low-density, nondegenerate limit where the Spitzer theory is valid and electron-electron collisions lead to the well-known reduction in comparison to the result considering only electron-ion collisions (Lorentz model). With increasing degeneracy, the contribution of electron-electron collisions to the dc conductivity is decreasing and can be neglected for the liquid metal domain where the Ziman theory is applicable. We give expressions for the effect of electron-electron collisions in calculating the conductivity in the warm dense matter region, i.e., for strongly coupled Coulomb systems at arbitrary degeneracy.

Cluster virial expansion of the equation of state for hydrogen plasma with e-H(2) contributions

The equation of state of partially ionized hydrogen plasma is considered with special focus on the contribution of the e-H(2) interaction. Traditional semiempirical concepts such as the excluded volume are improved using microscopic approaches to treat the e-H(2) problem. Within a cluster virial expansion, the Beth-Uhlenbeck formula is applied to infer the contribution of bound and scattering states to the temperature-dependent second virial coefficient. The scattering states are calculated using the phase expansion method for the polarization interaction that incorporates experimental data for the e-H(2) scattering cross section. We present results for the scattering phase shifts, differential scattering cross sections, and the second virial coefficient due to the e-H(2) interaction. The influence of this interaction on the composition of the partially ionized hydrogen plasma is confined to the parameter range where both the H(2) and the free-electron components are abundant.

Direct linear term in the equation of state of plasmas

We discuss a long-standing discrepancy in the equation of state of charge-neutral plasmas, the occurrence of an e(2) direct term. This e(2) term may appear in dependence of the way to determine the mean value of the potential energy. We show that such a contribution should not appear for pure Coulomb interaction.

Nonlocalized clustering: a new concept in nuclear cluster structure physics

We investigate the α+^{16}O cluster structure in the inversion-doublet band (Kπ=0(1)±}) states of 20Ne with an angular-momentum-projected version of the Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function, which was successful "in its original form" for the description of, e.g., the famous Hoyle state. In contrast with the traditional view on clusters as localized objects, especially in inversion doublets, we find that these single THSR wave functions, which are based on the concept of nonlocalized clustering, can well describe the Kπ=0(1)- band and the Kπ=0(1)+ band. For instance, they have 99.98% and 99.87% squared overlaps for 1- and 3- states (99.29%, 98.79%, and 97.75% for 0+, 2+, and 4+ states), respectively, with the corresponding exact solution of the α+16O resonating group method. These astounding results shed a completely new light on the physics of low energy nuclear cluster states in nuclei: The clusters are nonlocalized and move around in the whole nuclear volume, only avoiding mutual overlap due to the Pauli blocking effect.

Laboratory tests of low density astrophysical nuclear equations of state

Clustering in low density nuclear matter has been investigated using the NIMROD multidetector at Texas A&M University. Thermal coalescence modes were employed to extract densities, ρ, and temperatures, T, for evolving systems formed in collisions of 47A MeV (40)Ar+(112)Sn, (124)Sn and (64)Zn+(112)Sn, (124)Sn. The yields of d, t, (3)He, and (4)He have been determined at ρ=0.002 to 0.03 nucleons/fm(3) and T=5 to 11 MeV. The experimentally derived equilibrium constants for α particle production are compared with those predicted by a number of astrophysical equations of state. The data provide important new constraints on the model calculations.

Dielectric function beyond the random-phase approximation: kinetic theory versus linear response theory

Calculating the frequency-dependent dielectric function for strongly coupled plasmas, the relations within kinetic theory and linear response theory are derived and discussed in comparison. In this context, we give a proof that the Kohler variational principle can be extended to arbitrary frequencies. It is shown to be a special case of the Zubarev method for the construction of a nonequilibrium statistical operator from the principle of the extremum of entropy production. Within kinetic theory, the commonly used energy-dependent relaxation time approach is strictly valid only for the Lorentz plasma in the static case. It is compared with the result from linear response theory that includes electron-electron interactions and applies for arbitrary frequencies, including bremsstrahlung emission. It is shown how a general approach to linear response encompasses the different approximations and opens options for systematic improvements.

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.

Cluster virial expansion for the equation of state of partially ionized hydrogen plasma

We study the contribution of electron-atom interaction to the equation of state for partially ionized hydrogen plasma using the cluster-virial expansion. We use the Beth-Uhlenbeck approach to calculate the second virial coefficient for the electron-atom (bound cluster) pair from the corresponding scattering phase shifts and binding energies. Experimental scattering cross-sections as well as phase shifts calculated on the basis of different pseudopotential models are used as an input for the Beth-Uhlenbeck formula. By including Pauli blocking and screening in the phase shift calculation, we generalize the cluster-virial expansion in order to cover also near solid density plasmas. We present results for the electron-atom contribution to the virial expansion and the corresponding equation of state, i.e. pressure, composition, and chemical potential as a function of density and temperature. These results are compared with semiempirical approaches to the thermodynamics of partially ionized plasmas. Avoiding any ill-founded input quantities, the Beth-Uhlenbeck second virial coefficient for the electron-atom interaction represents a benchmark for other, semiempirical approaches.

Symmetry energy of dilute warm nuclear matter

The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions, and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular, by the appearance of bound states. A recently developed quantum-statistical approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.

Observation of ultrafast nonequilibrium collective dynamics in warm dense hydrogen

We investigate ultrafast (fs) electron dynamics in a liquid hydrogen sample, isochorically and volumetrically heated to a moderately coupled plasma state. Thomson scattering measurements using 91.8 eV photons from the free-electron laser in Hamburg (FLASH at DESY) show that the hydrogen plasma has been driven to a nonthermal state with an electron temperature of 13 eV and an ion temperature below 0.1 eV, while the free-electron density is 2.8x10{20} cm{-3}. For dense plasmas, our experimental data strongly support a nonequilibrium kinetics model that uses impact ionization cross sections based on classical free-electron collisions.

Temperature and Kalpha-yield radial distributions in laser-produced solid-density plasmas imaged with ultrahigh-resolution x-ray spectroscopy

We study warm dense matter formed by subpicosecond laser irradiation at several 10(19) W/cm(2) of thin Ti foils using x-ray spectroscopy with high spectral (E/DeltaE approximately 15,000) and one-dimensional spatial (Deltax=13.5 microm) resolutions. Ti Kalpha doublets modeled by line-shape calculations are compared with Abel-inverted single-pulse experimental spectra and provide radial distributions of the bulk-electron temperature and the absolute-photon number Kalpha yield in the target interiors. A core with approximately 40 eV extends homogeneously up to ten times the laser-focus size. The spatial distributions of the bulk-electron temperature and Kalpha yield are strongly correlated.

Bremsstrahlung and line spectroscopy of warm dense aluminum plasma heated by xuv free-electron-laser radiation

We report the creation of solid-density aluminum plasma using free-electron laser (FEL) radiation at 13.5nm wavelength. Ultrashort pulses were focused on a bulk Al target, yielding an intensity of 2x10;{14}Wcm;{2} . The radiation emitted from the plasma was measured using an xuv spectrometer. Bremsstrahlung and line intensity ratios yield consistent electron temperatures of about 38eV , supported by radiation hydrodynamics simulations. This shows that xuv FELs heat up plasmas volumetrically and homogeneously at warm-dense-matter conditions, which are accurately characterized by xuv spectroscopy.

alpha-particle condensation in 16O studied with a full four-body orthogonality condition model calculation

To explore the four-alpha-particle condensate state in 16O, we solve a full four-body equation of motion based on the four-alpha-particle orthogonality condition model in a large four-alpha-particle model space spanned by Gaussian basis functions. A full spectrum up to the 0_{6};{+} state is reproduced consistently with the lowest six 0;{+} states of the experimental spectrum. The 0_{6};{+} state is obtained at about 2 MeV above the four-alpha-particle breakup threshold and has a dilute density structure, with a radius of about 5 fm. The state has an appreciably large alpha condensate fraction of 61%, and a large component of alpha+12C(0_{2};{+}) configuration, both features being reliable evidence for this state to be of four-alpha-particle condensate nature.

Plasmon resonance in warm dense matter

Collective Thomson scattering with extreme ultraviolet light or x rays is shown to allow for a robust measurement of the free electron density in dense plasmas. Collective excitations like plasmons appear as maxima in the scattering signal. Their frequency position can directly be related to the free electron density. The range of applicability of the standard Gross-Bohm dispersion relation and of an improved dispersion relation in comparison to calculations based on the dielectric function in random phase approximation is investigated. More important, this well-established treatment of Thomson scattering on free electrons is generalized in the Born-Mermin approximation by including collisions. We show that, in the transition region from collective to noncollective scattering, the consideration of collisions is important.

Molecular dynamics simulations of optical conductivity of dense plasmas

The optical conductivity sigma (omega) for dense Coulomb systems is investigated using molecular dynamics simulations on the basis of pseudopotentials to mimic quantum effects. Starting from linear response theory, the response in the long-wavelength limit k=0 can be expressed by different types of autocorrelation functions (ACF's) such as the current ACF, the force ACF, or the charge density ACF. Consistent simulation data for transverse as well as longitudinal ACF's are shown which are based on calculations with high numerical accuracy. Results are compared with perturbation expansions which are restricted to small values of the plasma parameter. The relevance with respect to a quantum Coulomb plasma is discussed. Finally, results are presented showing a consistent description of these model plasmas in comparison to quantum statistical approaches and to experimental data.

Internal versus external conductivity of a dense plasma: many-particle theory and simulations

In the long-wavelength limit k=0, the response function has been investigated with respect to the external and internal fields which is expressed by the external and internal conductivity, respectively. Molecular dynamics simulations are performed to obtain the current-current correlation function and the dynamical collision frequency which are compared with analytical expressions. Special attention is given to the dynamical collision frequency and the description of plasma oscillations in the case of k=0. The relation between the external and internal conductivity and the current-current correlation function is analyzed.

Frequency-dependent reflectivity of shock-compressed xenon plasmas

Results for the reflection coefficient of shock-compressed dense xenon plasmas at pressures of 1.6-20 GPa and temperatures around 30 000 K using laser beams of wavelengths 1.06 micro m and 0.694 micro m are presented, which indicate metallic behavior at high densities. For the theoretical description of the experiments, a quantum statistical approach to the dielectric function is used. The comparison with molecular dynamics simulations is discussed. We conclude that reflectivity measurements at different wavelengths can provide information about the density profile of the shock wave front.

Alpha cluster condensation in 12C and 16O

A new alpha-cluster wave function is proposed which is of the alpha-particle condensate type. Applications to 12C and 16O show that states of low density close to the 3 and 4 alpha-particle thresholds in both nuclei are possibly of this kind. It is conjectured that all self-conjugate 4n nuclei may show similar features.

Dynamic structure factor for a two-component model plasma

Analytical results for the structure factor of a two-component model plasma that describe an electron-ion plasma with modified interaction are derived from a Green function approach in different approximations. The random-phase approximation is improved by including the dynamic collision frequency, and results for the long-wavelength limit are extended to arbitrary wave numbers using the Mermin ansatz. After taking the classical limit of the resulting expressions, they are compared with molecular dynamics simulation results for the classical two-component model plasma.

Isentropes and Hugoniot curves for dense hydrogen and deuterium

Multiple-shock experiments with fluid hydrogen have shown that a transition from semiconducting behavior to metal-like conductivity occurs at pressures (p) of about 140 GPa and temperatures (T) near 3000 K. We model the p-T pathway by Hugoniot curves (initial shock) and isentropes (subsequent shocks). For the calculation of these curves we apply an expression for the free energy developed recently for dense hydrogen and deuterium plasma in the regions of partial dissociation and partial ionization. Furthermore, we discuss the relations between Hugoniot curves, isentropes and the coexistence line of the plasma phase transition.

Short-time dynamics with initial correlations

The short-time dynamics of correlated systems is strongly influenced by initial correlations, giving rise to an additional collision integral in the non-Markovian kinetic equation. Exact cancellation of the two integrals is found if the initial state is thermal equilibrium, which is an important consistency criterion. Analytical results are given for the time evolution of the correlation energy, which are confirmed by comparisons with molecular dynamics simulations.

Increase in proliferation rate and normalization of TNF-alpha secretion by blockage of gene transfer-induced apoptosis in lymphocytes using low-dose cyclosporine A

Efficient gene transfer of lymphocytes is extremely difficult. We have shown previously that induction of apoptosis may play a role in the gene transfer resistance of lymphocytes. Anti-CD3 antibody can be used as a surrogate for receptor-mediated gene transfer in T lymphocytes. However, anti-CD3 antibody has been shown to be the causative agent of apoptosis in receptor-mediated gene transfer. In this study, we show that blockage of apoptosis by addition of low-dose cyclosporine A can lead to normalization of elevated TNF-alpha secretion and to a significant increase in the proliferation rate of transfected lymphocytes. In contrast, this had no negative effect on cytotoxic activity of immunologic effector cells called cytokine-induced killer cells. Therefore, blockage of apoptosis should have an impact on the use of lymphocytes transfected with cytokine genes as immunologic effector cells in cancer gene therapy protocols.

Efficient gene transfer into lymphoma cells using adenoviral vectors combined with lipofection

Tumor cells, such as lymphoma cells, are possible targets for gene therapy. In general, gene therapeutic approaches require efficient gene transfer to host cells and sufficient transgene expression. However, lymphoma cells previously have been demonstrated to be resistant to most of the currently available gene transfer methods. The aim of this study was to analyze various methods for transfection of lymphoma cells and to improve the efficiency of gene delivery. In accordance with previously published reports, lymphoma cells were demonstrated to be resistant to lipofection and electroporation. In contrast, we present an improved adenoviral protocol leading to highly efficient gene transfer to lymphoma cell lines derived from B cells as well as primary lymphoma cells being achieved with an adenoviral vector system encoding the beta-galactosidase protein. At a multiplicity of infection of 200, up to 100% of Daudi cells and Raji cells and 70% of OCI-Ly8-LAM53 cells could be transfected. Even at high adenoviral concentrations, no marked toxicity was observed, and the growth characteristics of the lymphoma cell lines were not impaired. The transfection rates in primary cells derived from six patients with non-Hodgkin's lymphoma were 30-65%, respectively. Transfection efficiency could be further increased by addition of cationic liposomes to adenoviral gene transfer. Furthermore, we examined the expression of the Coxsackie-adenoviral receptor (CAR) and the integrin receptors on the lymphoma cell surface. Flow cytometric analysis showed that 88% of Daudi cells, 69% of Raji cells, and 6% of OCI-Ly8-LAM53 cells expressed CAR on the cell surface. According to our data, adenoviral infection of lymphoma cells seems to be mediated by CAR. In contrast, integrin receptors are unlikely to play a major role, because lymphoma cells were negative for alphavbeta3-integrins and negative for alphavbeta5-integrins. In conclusion, this study demonstrates that B-lymphoma cell lines and primary lymphoma cells can be efficiently transfected using an adenoviral vector system. By adding cationic liposomes, the efficiency of adenoviral gene transfer to primary tumor cells could be further improved. This protocol may have an impact on the use of lymphoma cells in cancer gene therapy.

TNF-alpha secretion and apoptosis of lymphocytes mediated by gene transfer

Efficient gene transfer of lymphocytes is extremely difficult. Apoptosis may play a role in this gene transfer resistance of lymphocytes. Here we show that transfection of lymphocytes via non-viral vectors leads to induction of apoptosis in a significant proportion of cells. Since apoptosis may be mediated via tumor necrosis factor d (TNF-alpha) and the TNF-alpha receptor pathway, we studied the amount of TNF-alpha secreted by lymphocytes transfected without gene insert. TNF-alpha secretion was dependent on the gene transfer method used. High amounts were detected using receptor-mediated gene transfer and lipofection. In contrast, only low amounts of TNF-alpha were detected after electroporation and retroviral gene transfer. In receptor-mediated gene transfer, TNF-alpha secretion was due to the use of anti-CD3 antibody. Transfection of lymphocytes led to selective decrease in CD120b/TNF-alpha receptor II (TNFR-2)-positive cells. Induction of apoptosis and necrosis mediated by TNF-alpha via TNFR-2 (p80) was partially blocked using a neutralizing anti-TNF-alpha antibody. Blockage of apoptosis and necrosis could be further increased by adding anti-Fas-ligand (FasL) antibody, suggesting that induction of apoptosis via FasL and Fas receptor (Apo-1/CD95) may also play a role. This blockage led to a significant increase in the proliferation rate of lymphocytes transfected with cytokine genes. In conclusion, various gene transfer techniques led to TNF-alpha secretion, apoptosis and necrosis of lymphocytes. Apoptosis and necrosis could be partially blocked using a neutralizing anti-TNF-alpha antibody.

Response function including collisions for an interacting fermion gas

The response function of an interacting fermion gas is considered in the entire (k-->,omega) space. Applying a generalized linear response theory, it is expressed in terms of determinants of equilibrium correlation functions, which allow for a systematic perturbative treatment. The relation to dynamical local-field factors is given. As a special case, the dielectric function is evaluated for two-component (hydrogen) plasmas at arbitrary degeneracies. Collisions are treated in Born approximation leading to a (k-->,omega)-dependent collision integral. The link to the dynamical conductivity is given in the long-wavelength limit. Sum rules are discussed.