389 research outputs found
Multiconfiguration Dirac-Hartree-Fock energy levels and transition probabilities for 3d^5 in Fe IV
Multiconfiguration Dirac-Hartree-Fock electric quadrupole (E2) and magnetic
dipole (M1) transition probabilities are reported for transitions between
levels of 3d^5 in [Fe IV]. The accuracy of the ab initio energy levels and the
agreement in the length and velocity forms of the line strength for the E2
transitions are used as indicators of accuracy. The present E2 and M1
transition probabilities are compared with earlier Breit-Pauli results and
other theories. An extensive set of transition probabilites with indicators of
accuracy are reported in Appendices A and B. Recommended values of A(E2) +
A(M1) are listed in Appendix C.Comment: 16 pages, three appendices containing accuracy indicators and
recommended values for E2 and M1 transition rate
Ultra-low Q values for neutrino mass measurements
We investigate weak nuclear decays with extremely small kinetic energy
release (Q value) and thus extremely good sensitivity to the absolute neutrino
mass scale. In particular, we consider decays into excited daughter states, and
we show that partial ionization of the parent atom can help to tune Q values to
<< 1 keV. We discuss several candidate isotopes undergoing beta+, beta-, bound
state beta, or electron capture decay, and come to the conclusion that a
neutrino mass measurement using low-Q decays might only be feasible if no
ionization is required, and if future improvements in isotope production
technology, nuclear mass spectroscopy, and atomic structure calculations are
possible. Experiments using ions, however, are extremely challenging due to the
large number of ions that must be stored. New precision data on nuclear
excitation levels could help to identify further isotopes with low-Q decay
modes and possibly less challenging requirements.Comment: 7 pages, 2 figures; v2: Typos corrected, references adde
Exchange interaction and correlations radically change behaviour of a quantum particle in a classically forbidden region
Exchange interaction strongly influences the long-range behaviour of
localised electron orbitals and quantum tunneling amplitudes. It violates the
oscillation theorem (creates extra nodes) and produces a power-law decay
instead of the usual exponential decrease at large distances. For inner
orbitals inside molecules decay is , for macroscopic systems , where is the Fermi momentum and for 1D, 3.5
for 2D and 4 for 3D crystal. Correlation corrections do not change these
conclusions. Slow decay increases the exchange interaction between localized
spins and the under-barrier tunneling amplitude. The under-barrier transmission
coefficients in solids (e.g. for point contacts) become temperature-dependent
Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg
We report smooth relativistic Hartree-Fock pseudopotentials (also known as
averaged relativistic effective potentials or AREPs) and spin-orbit operators
for the atoms H to Ba and Lu to Hg. We remove the unphysical extremely
non-local behaviour resulting from the exchange interaction in a controlled
manner, and represent the resulting pseudopotentials in an analytic form
suitable for use within standard quantum chemistry codes. These
pseudopotentials are suitable for use within Hartree-Fock and correlated wave
function methods, including diffusion quantum Monte Carlo calculations.Comment: 13 pages, 3 figure
The nonrelativistic limit of Dirac-Fock codes: the role of Brillouin configurations
We solve a long standing problem with relativistic calculations done with the
widely used Multi-Configuration Dirac-Fock Method (MCDF). We show, using
Relativistic Many-Body Perturbation Theory (RMBPT), how even for relatively
high-, relaxation or correlation causes the non-relativistic limit of states
of different total angular momentum but identical orbital angular momentum to
have different energies. We show that only large scale calculations that
include all single excitations, even those obeying the Brillouin's theorem have
the correct limit. We reproduce very accurately recent high-precision
measurements in F-like Ar, and turn then into precise test of QED. We obtain
the correct non-relativistic limit not only for fine structure but also for
level energies and show that RMBPT calculations are not immune to this problem.Comment: AUgust 9th, 2004 Second version Nov. 18th, 200
Exploring Biorthonormal Transformations of Pair-Correlation Functions in Atomic Structure Variational Calculations
Multiconfiguration expansions frequently target valence correlation and
correlation between valence electrons and the outermost core electrons.
Correlation within the core is often neglected. A large orbital basis is needed
to saturate both the valence and core-valence correlation effects. This in turn
leads to huge numbers of CSFs, many of which are unimportant. To avoid the
problems inherent to the use of a single common orthonormal orbital basis for
all correlation effects in the MCHF method, we propose to optimize independent
MCHF pair-correlation functions (PCFs), bringing their own orthonormal
one-electron basis. Each PCF is generated by allowing single- and double-
excitations from a multireference (MR) function. This computational scheme has
the advantage of using targeted and optimally localized orbital sets for each
PCF. These pair-correlation functions are coupled together and with each
component of the MR space through a low dimension generalized eigenvalue
problem. Nonorthogonal orbital sets being involved, the interaction and overlap
matrices are built using biorthonormal transformation of the coupled basis sets
followed by a counter-transformation of the PCF expansions.
Applied to the ground state of beryllium, the new method gives total energies
that are lower than the ones from traditional CAS-MCHF calculations using large
orbital active sets. It is fair to say that we now have the possibility to
account for, in a balanced way, correlation deep down in the atomic core in
variational calculations
The correlation energy functional within the GW-RPA approximation: exact forms, approximate forms and challenges
In principle, the Luttinger-Ward Green's function formalism allows one to
compute simultaneously the total energy and the quasiparticle band structure of
a many-body electronic system from first principles. We present approximate and
exact expressions for the correlation energy within the GW-RPA approximation
that are more amenable to computation and allow for developing efficient
approximations to the self-energy operator and correlation energy. The exact
form is a sum over differences between plasmon and interband energies. The
approximate forms are based on summing over screened interband transitions. We
also demonstrate that blind extremization of such functionals leads to
unphysical results: imposing physical constraints on the allowed solutions
(Green's functions) is necessary. Finally, we present some relevant numerical
results for atomic systems.Comment: 3 figures and 3 tables, under review at Physical Review
Beyond density functional theory: the domestication of nonlocal potentials
Due to efficient scaling with electron number N, density functional theory
(DFT) is widely used for studies of large molecules and solids. Restriction of
an exact mean-field theory to local potential functions has recently been
questioned. This review summarizes motivation for extending current DFT to
include nonlocal one-electron potentials, and proposes methodology for
implementation of the theory. The theoretical model, orbital functional theory
(OFT), is shown to be exact in principle for the general N-electron problem. In
practice it must depend on a parametrized correlation energy functional.
Functionals are proposed suitable for short-range Coulomb-cusp correlation and
for long-range polarization response correlation. A linearized variational
cellular method (LVCM) is proposed as a common formalism for molecules and
solids. Implementation of nonlocal potentials is reduced to independent
calculations for each inequivalent atomic cell.Comment: Accepted for publication in Modern Physics Letters B (2004
Symmetry Breaking of Relativistic Multiconfiguration Methods in the Nonrelativistic Limit
The multiconfiguration Dirac-Fock method allows to calculate the state of
relativistic electrons in atoms or molecules. This method has been known for a
long time to provide certain wrong predictions in the nonrelativistic limit. We
study in full mathematical details the nonlinear model obtained in the
nonrelativistic limit for Be-like atoms. We show that the method with sp+pd
configurations in the J=1 sector leads to a symmetry breaking phenomenon in the
sense that the ground state is never an eigenvector of L^2 or S^2. We thereby
complement and clarify some previous studies.Comment: Final version, to appear in Nonlinearity. Nonlinearity (2010) in
pres
- …