Publisher Summary This chapter discusses how to examine atomic collisions in a dense plasma environment. Knowing how plasma responds to an electromagnetic disturbance is basic to developing a model of atomic collisions in high-density plasma environments. The calculation of microfields in electron–ion plasmas is complicated by the disparity of response frequencies. The “low-frequency” microfields arising from the ions have distributions with weaker average fields, because the more mobile electrons tend to localize about, and shield, individual ions. Because the correlation time among ions greatly exceeds that among electrons, the quasi-static ionic microfield causes the basis states of an ion in plasma to be admixtures of (shifted) states of the isolated ion. In the special case of a central potential, the mixing is described exactly by coefficients of the transformation from spherical to parabolic coordinate eigenstates.

Atomic Excitation in Dense Plasmas

We present a time-dependent formulation of coupled cluster theory. This theory allows for direct computation of the free energy of quantum systems at finite temperature by imaginary time integration and is closely related to the thermal cluster cumulant theory of Mukherjee and co-workers [ Chem. Phys. Lett. 1992, 192, 55−61; Phys. Rev. E 1993, 48, 3373−3389; Chem. Phys. Lett. 2001, 335, 281−288; Chem. Phys. Lett. 2002, 352, 63−69; Int. J. Mod. Phys. B 2003, 17, 5367−5377]. Our derivation of the finite-temperature theory highlights connections to perturbation theory and to zero-temperature coupled cluster theory. We show explicitly how the finite-temperature coupled cluster singles and doubles amplitude equations can be derived in analogy with the zero-temperature theory and how response properties can be efficiently computed using a variational Lagrangian. We discuss the implementation for realistic systems and showcase the potential utility of the method with calculations of the exchange correlation ener...

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A Time-Dependent Formulation of Coupled-Cluster Theory for Many-Fermion Systems at Finite Temperature

Within the Debye-Huckel model, and within the first Born approximation, the authors consider non-spherical screening of the electron-ion interaction and screened bound-electron wavefunctions to obtain collision strengths for the inelastic scattering of electrons by one-electron ions in dense plasmas. It is found that whether or not one uses unscreened bound-electron wavefunctions is less influential than the fact of having spherical screening or not, with the non-sphericity leading to an important increase of the collision strengths with respect to earlier calculations which considered spherical screening.

Effects of non-spherical screening for inelastic electron-ion scattering

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. We extract various exact free-energy correlation components and the exact adiabatic connection formula.

Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

Finite-temperature density functional theory (DFT) has become of topical interest, partly due to the increasing ability to create novel states of warm-correlated matter (WCM).Warm-dense matter (WDM), ultra-fast matter (UFM), and high-energy density matter (HEDM) may all be regarded as subclasses of WCM. Strong electron-electron, ion-ion and electron-ion correlation effects and partial degeneracies are found in these systems where the electron temperature Te is comparable to the electron Fermi energy EF. Thus, many electrons are in continuum states which are partially occupied. The ion subsystem may be solid, liquid or plasma, with many states of ionization with ionic charge Zj. Quasi-equilibria with the ion temperature Ti ≠ Te are common. The ion subsystem in WCM can no longer be treated as a passive “external potential”, as is customary in T = 0 DFT dominated by solid-state theory or quantum chemistry. Many basic questions arise in trying to implement DFT for WCM. Hohenberg-Kohn-Mermin theory can be adapted for treating these systems if suitable finite-T exchange-correlation (XC) functionals can be constructed. They are functionals of both the one-body electron density ne and the one-body ion densities ρj. Here, j counts many species of nuclei or charge states. A method of approximately but accurately mapping the quantum electrons to a classical Coulomb gas enables one to treat electron-ion systems entirely classically at any temperature and arbitrary spin polarization, using exchange-correlation effects calculated in situ, directly from the pair-distribution functions. This eliminates the need for any XC-functionals. This classical map has been used to calculate the equation of state of WDM systems, and construct a finite-T XC functional that is found to be in close agreement with recent quantum path-integral simulation data. In this review, current developments and concerns in finite-T DFT, especially in the context of non-relativistic warm-dense matter and ultra-fast matter will be presented.

https://www.mdpi.com/2079-3197/4/2/16/pdf

Current Issues in Finite-T Density-Functional Theory and Warm-Correlated Matter †

The exchange and correlation potentials which are needed in the study of electron systems (atoms, plasmas) at finite temperatures and finite degeneracies have been calculated and presented in a parametrised form convenient for use in Thomas-Fermi, Hartree-Fock, density-functional type effective single-particle models. The exchange corrected single-particle energies and chemical potential are calculated self-consistently and in the linear approximation. The natural generalisation of the Debye-Huckel screening length is used to extract a static model valid at intermediate degeneracies. The higher-order corrections (i.e., beyond Hartree-Fock) are evaluated from the ring sum and the second-order screened contributions to the thermodynamic grand potential. The ring sum is calculated via an approximation to the polarisation function which is known to be satisfactory at 0K and exact in the Debye-Huckel limit. The numerical results show that the correlation potential at finite temperatures consists of a static contribution and a dynamic part which goes to zero at high temperatures.

M W C Dharma-wardana

Papers

Exchange and correlation potentials for finite temperature quantum calculations at intermediate degeneracies