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

Extension of the HF program to partially filled f-subshells

A new version of a Hartree-Fock program is presented that includes extensions for partially filled f-subshells. The program allows the calculation of term dependent Hartree-Fock orbitals and energies in LS coupling for configurations with no more than two open subshells, including f-subshells

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 $r^{-2}$, for macroscopic systems $\cos{(k_f r)} r^{-\nu}$, where $k_f$ is the Fermi momentum and $\nu=3$ for 1D, $\nu=$3.5 for 2D and $\nu=$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-$Z$, 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

Multiconfiguration electron density function for the ATSP2K-package

A new ATSP2K module is presented for evaluating the electron density function of any multiconfiguration Hartree-Fock or configuration interaction wave function in the non relativistic or relativistic Breit-Pauli approximation. It is first stressed that the density function is not a priori spherically symmetric in the general open shell case. Ways of building it as a spherical symmetric function are discussed, from which the radial electron density function emerges. This function is written in second quantized coupled tensorial form for exploring the atomic spherical symmetry. The calculation of its expectation value is performed using the angular momentum theory in orbital, spin, and quasispin spaces, adopting a generalized graphical technique. The natural orbitals are evaluated from the diagonalization of the density matrix

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

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