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Accurate Hartree-Fock energy of extended systems using large Gaussian basis sets
Calculating highly accurate thermochemical properties of condensed matter via
wave function-based approaches (such as e.g. Hartree-Fock or hybrid
functionals) has recently attracted much interest. We here present two
strategies providing accurate Hartree-Fock energies for solid LiH in a large
Gaussian basis set and applying periodic boundary conditions. The total
energies were obtained using two different approaches, namely a supercell
evaluation of Hartree-Fock exchange using a truncated Coulomb operator and an
extrapolation toward the full-range Hartree-Fock limit of a Pad\'e fit to a
series of short-range screened Hartree-Fock calculations. These two techniques
agreed to significant precision. We also present the Hartree-Fock cohesive
energy of LiH (converged to within sub-meV) at the experimental equilibrium
volume as well as the Hartree-Fock equilibrium lattice constant and bulk
modulus.Comment: 7.5 pages, 2 figures, submitted to Phys. Rev. B; v2: typos removed,
References adde
Phenomenological construction of a relativistic nucleon-nucleon interaction for the superfluid gap equation in finite density systems
We construct phenomenologically a relativistic particle-particle channel
interaction which suits the gap equation for nuclear matter. This is done by
introducing a density-independent momentum-cutoff parameter to the relativistic
mean field (Hartree and Hartree-Fock) models so as to reproduce the pairing
properties obtained by the Bonn-B potential and not to change the saturation
property. The interaction so obtained can be used for the Relativistic
Hartree-Bogoliubov calculation, but some reservation is necessary for the
Relativistic Hartree-Fock-Bogoliubov calculation.Comment: 30 pages, 18 eps figures, uses elsart. Major revision ---
Hartree-Fock calculations are added. To appear in Nuclear Physics
On Blowup for time-dependent generalized Hartree-Fock equations
We prove finite-time blowup for spherically symmetric and negative energy
solutions of Hartree-Fock and Hartree-Fock-Bogoliubov type equations, which
describe the evolution of attractive fermionic systems (e. g. white dwarfs).
Our main results are twofold: First, we extend the recent blowup result of
[Hainzl and Schlein, Comm. Math. Phys. \textbf{287} (2009), 705--714] to
Hartree-Fock equations with infinite rank solutions and a general class of
Newtonian type interactions. Second, we show the existence of finite-time
blowup for spherically symmetric solutions of a Hartree-Fock-Bogoliubov model,
where an angular momentum cutoff is introduced. We also explain the key
difficulties encountered in the full Hartree-Fock-Bogoliubov theory.Comment: 24 page
On the Isovector Channels in Relativistic Point Coupling Models within the Hartree and Hartree-Fock Approximations
We investigate the consequences of Fierz transformations acting upon the
contact interactions for nucleon fields occurring in relativistic point
coupling models in Hartree approximation, which yield the same models but in
Hartree-Fock approximation instead. We find for four-fermion interactions
occurring in two existing relativistic point coupling phenomenologies that
whereas in Hartree the isovector-scalar strength, corresponding to delta-meson
exchange, is unnaturally small, indicating a possible new symmetry, in
Hartree-Fock it is instead comparable to the isovector-vector strength
corresponding to rho-meson exchange, but the sum of the two isovector coupling
constants appears to be preserved in both approaches. Furthermore, in
Hartree-Fock approximation, both QCD-scaled isovector coupling constants are
natural (dimensionless and of order 1) whereas in Hartree approximation only
that of the isovector-vector channel is natural. This indicates that it is not
necessary to search for a new symmetry and, moreover, that the role of the
delta-meson should be reexamined.Comment: 10 pages; accepted for publication in Nuclear Physics
Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms
In this paper we study the problem of uniqueness of solutions to the Hartree
and Hartree-Fock equations of atoms. We show, for example, that the
Hartree-Fock ground state of a closed shell atom is unique provided the atomic
number is sufficiently large compared to the number of electrons. More
specifically, a two-electron atom with atomic number has a unique
Hartree-Fock ground state given by two orbitals with opposite spins and
identical spatial wave functions. This statement is wrong for some , which
exhibits a phase segregation.Comment: 18 page
Symmetric and asymmetric nuclear matter in the relativistic approach at finite temperatures
The properties of hot matter are studied in the frame of the relativistic
Brueckner-Hartree-Fock theory. The equations are solved self-consistently in
the full Dirac space. For the interaction we used the potentials given by
Brockmann and Machleidt. The obtained critical temperatures are smaller than in
most of the nonrelativistic investigations. We also calculated the
thermodynamic properties of hot matter in the relativistic Hartree--Fock
approximation, where the force parameters were adjusted to the outcome of the
relativistic Brueckner--Hartree--Fock calculations at zero temperature. Here,
one obtains higher critical temperatures, which are comparable with other
relativistic calculations in the Hartree scheme.Comment: 8 pages, 9 figures, submitted in a shorter version to Phys. Rev.
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