Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method is applied to a test set of about 67 molecules, representing various types of chemical binding. A close correlation is observed between the atomic charges and the Hirshfeld-I atomic charges.Comment: 10 pages, 3 figures, preprint, communicatio

Projected seniority-two orbital optimization of the Antisymmetric Product of one-reference orbital Geminal

We present a new, non-variational orbital-optimization scheme for the Antisymmetric Product of one-reference orbital Geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [J. Chem. Phys., 135, 044119 (2011)]. A numerical analysis is performed for the C$_2$, LiF and CH$_2$ molecules as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases.Comment: 7 pages, 2 figure

Nonlocal extension of the dispersive-optical-model to describe data below the Fermi energy

Present applications of the dispersive-optical-model analysis are restricted by the use of a local but energy-dependent version of the generalized Hartree-Fock potential. This restriction is lifted by the introduction of a corresponding nonlocal potential without explicit energy dependence. Such a strategy allows for a complete determination of the nucleon propagator below the Fermi energy with access to the expectation value of one-body operators (like the charge density), the one-body density matrix with associated natural orbits, and complete spectral functions for removal strength. The present formulation of the dispersive optical model (DOM) therefore allows the use of elastic electron-scattering data in determining its parameters. Application to ${}^{40}$Ca demonstrates that a fit to the charge radius leads to too much charge near the origin using the conventional assumptions of the functional form of the DOM. A corresponding incomplete description of high-momentum components is identified, suggesting that the DOM formulation must be extended in the future to accommodate such correlations properly. Unlike the local version, the present nonlocal DOM limits the location of the deeply-bound hole states to energies that are consistent with (\textit{e,e}$^{\prime}$\textit{p}) and (\textit{p,2p}) data.Comment: 14 pages, 10 figures, submitted to Physical Review

Saturation of nuclear matter and short-range correlations

A fully self-consistent treatment of short-range correlations in nuclear matter is presented. Different implementations of the determination of the nucleon spectral functions for different interactions are shown to be consistent with each other. The resulting saturation densities are closer to the empirical result when compared with (continuous-choice) Brueckner-Hartree-Fock values. Arguments for the dominance of short-range correlations in determining the nuclear-matter saturation density are presented. A further survey of the role of long-range correlations suggests that the inclusion of pionic contributions to ring diagrams in nuclear matter leads to higher saturation densities than empirically observed. A possible resolution of the nuclear-matter saturation problem is suggested.Comment: 5 pages, 1 figure, to be published in Phys.Rev.Let

Chemical verification of variational second-order density matrix based potential energy surfaces for the N-2 isoelectronic series

A variational optimization of the second-order density matrix under the P-, Q-, and G-conditions was carried out for a set of diatomic 14-electron molecules, including N-2, O-2(2+), NO+, CO, and CN-. The dissociation of these molecules is studied by analyzing several chemical properties (dipole moments, population analysis, and bond indices) up to the dissociation limit (10 and 20 A degrees). Serious chemical flaws are observed for the heteronuclear diatomics in the dissociation limit. A careful examination of the chemical properties reveals that the origin of the dissociation problem lies in the flawed description of fractionally occupied species under the P-, Q-, and G-conditions. A novel constraint is introduced that imposes the correct dissociation and enforces size consistency. The effect of this constraint is illustrated with calculations on NO+, CO, CN-, N-2, and O-2(2+)

Nuclear structure studies with the 7Li(e,e'p) reaction

Experimental momentum distributions for the transitions to the ground state and first excited state of 6He have been measured via the reaction 7Li(e,e'p)6He, in the missing momentum range from -70 to 260 MeV/c. They are compared to theoretical distributions calculated with mean-field wave functions and with variational Monte Carlo (VMC) wave functions which include strong state-dependent correlations in both 7Li and 6He. These VMC calculations provide a parameter-free prediction of the momentum distribution that reproduces the measured data, including its normalization. The deduced summed spectroscopic factor for the two transitions is 0.58 +/- 0.05, in perfect agreement with the VMC value of 0.60. This is the first successful comparison of experiment and ab initio theory for spectroscopic factors in p-shell nuclei.Comment: 4 pages, 3 figure

The Nucleon Spectral Function at Finite Temperature and the Onset of Superfluidity in Nuclear Matter

Nucleon selfenergies and spectral functions are calculated at the saturation density of symmetric nuclear matter at finite temperatures. In particular, the behaviour of these quantities at temperatures above and close to the critical temperature for the superfluid phase transition in nuclear matter is discussed. It is shown how the singularity in the thermodynamic T-matrix at the critical temperature for superfluidity (Thouless criterion) reflects in the selfenergy and correspondingly in the spectral function. The real part of the on-shell selfenergy (optical potential) shows an anomalous behaviour for momenta near the Fermi momentum and temperatures close to the critical temperature related to the pairing singularity in the imaginary part. For comparison the selfenergy derived from the K-matrix of Brueckner theory is also calculated. It is found, that there is no pairing singularity in the imaginary part of the selfenergy in this case, which is due to the neglect of hole-hole scattering in the K-matrix. From the selfenergy the spectral function and the occupation numbers for finite temperatures are calculated.Comment: LaTex, 23 pages, 21 PostScript figures included (uuencoded), uses prc.sty, aps.sty, revtex.sty, psfig.sty (last included

Relativistic mean field approximation to the analysis of 16O(e,e'p)15N data at |Q^2|\leq 0.4 (GeV/c)^2

We use the relativistic distorted wave impulse approximation to analyze data on 16O(e,e'p)15N at |Q^2|\leq 0.4 (GeV/c)^2 that were obtained by different groups and seemed controversial. Results for differential cross-sections, response functions and A_TL asymmetry are discussed and compared to different sets of experimental data for proton knockout from p_{1/2} and p_{3/2} shells in 16O. We compare with a nonrelativistic approach to better identify relativistic effects. The present relativistic approach is found to accommodate most of the discrepancy between data from different groups, smoothing a long standing controversy.Comment: 28 pages, 7 figures (eps). Major revision made. New figures added. To be published in Phys. Rev.

Restoration of Overlap Functions and Spectroscopic Factors in Nuclei

An asymptotic restoration procedure is applied for analyzing bound--state overlap functions, separation energies and single--nucleon spectroscopic factors by means of a model one--body density matrix emerging from the Jastrow correlation method in its lowest order approximation for $^{16}O$ and $^{40}Ca$ nuclei . Comparison is made with available experimental data and mean--field and natural orbital representation results.Comment: 5 pages, RevTeX style, to be published in Physical Review