Configuration mixing within the energy density functional formalism: pathologies and cures

Configuration mixing calculations performed in terms of the Skyrme/Gogny Energy Density Functional (EDF) rely on extending the Single-Reference energy functional into non-diagonal EDF kernels. The standard way to do so, based on an analogy with the pure Hamiltonian case and the use of the generalized Wick theorem, is responsible for the recently observed divergences and steps in Multi-Reference calculations. We summarize here the minimal solution to this problem recently proposed [Lacroix et al, arXiv:0809.2041] and applied with success to particle number restoration[Bender et al, arXiv:0809.2045]. Such a regularization method provides suitable corrections of pathologies for EDF depending on integer powers of the density. The specific case of fractional powers of the density[Duguet et al, arXiv:0809.2049] is also discussed.Comment: 5 pages, Proceedings of the French-Japanese Symposium, September 2008. To be published in Int. J. of Mod. Phys.

Ab initio Bogoliubov coupled cluster theory for open-shell nuclei

Ab initio many-body methods address closed-shell nuclei up to mass A ~ 130 on the basis of realistic two- and three-nucleon interactions. Several routes to address open-shell nuclei are currently under investigation, including ideas which exploit spontaneous symmetry breaking. Singly open-shell nuclei can be efficiently described via the sole breaking of $U(1)$ gauge symmetry associated with particle number conservation, to account for their superfluid character. The present work formulates and applies Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wavefunction of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code is implemented in $m$-scheme, which will eventually permit the treatment of doubly open-shell nuclei. Proof-of-principle calculations in an $N_{\text{max}}=6$ spherical harmonic oscillator basis are performed for $^{16,18,20}$O, $^{18}$Ne, $^{20}$Mg in the BCCD approximation with a chiral two-nucleon interaction, comparing to results obtained in standard coupled cluster theory when applicable. The breaking of $U(1)$ symmetry is monitored by computing the variance associated with the particle-number operator. The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e. potentially to reach several hundred additional mid-mass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei.Comment: 22 pages, 13 figure

Quasiparticle Coupled Cluster Theory for Pairing Interactions

We present an extension of the pair coupled cluster doubles (p-CCD) method to quasiparticles and apply it to the attractive pairing Hamiltonian. Near the transition point where number symmetry gets spontaneously broken, the proposed BCS-based p-CCD method yields significantly better energies than existing methods when compared to exact results obtained via solution of the Richardson equations. The quasiparticle p-CCD method has a low computational cost of $\mathcal{O}(N^3)$ as a function of system size. This together with the high quality of results here demonstrated, points to considerable promise for the accurate description of strongly correlated systems with more realistic pairing interactions

On the off-diagonal Wick's theorem and Onishi formula

The projected generator coordinate method based on the configuration mixing of non-orthogonal Bogoliubov product states, along with more advanced methods based on it, require the computation of off-diagonal Hamiltonian and norm kernels. While the Hamiltonian kernel is efficiently computed via the off-diagonal Wick theorem of Balian and Brezin, the norm kernel relies on the Onishi formula (or equivalently the Pfaffian formula by Robledo or the integral formula by Bally and Duguet). Traditionally, the derivation of these two categories of formulae rely on different formal schemes. In the present work, the formulae for the operator and norm kernels are computed consistently from the same diagrammatic method. The approach further offers the possibility to address kernels involving more general states in the future

Quantum calculation of Coulomb reorientation and near-barrier fusion

We investigate the role of deformation on the fusion probability around the barrier using the Time-Dependent Hartree-Fock theory with a full Skyrme force. We obtain a distribution of fusion probabilities around the nominal barrier due to the different contributions of the various orientations of the deformed nucleus at the touching point. It is also shown that the long range Coulomb reorientation reduces the fusion probability around the barrier.Comment: 6pages, 2 figures. Proceeding of FUSION0

Gorkov algebraic diagrammatic construction formalism at third order

Background. The Gorkov approach to self-consistent Green's function theory has been formulated in [V. Som\`a, T. Duguet, C. Barbieri, Phys. Rev. C 84, 064317 (2011)]. Over the past decade, it has become a method of reference for first-principle computations of semi-magic nuclear isotopes. The currently available implementation is limited to a second-order self-energy and neglects particle-number non-conserving terms arising from contracting three-particle forces with anomalous propagators. For nuclear physics applications, this is sufficient to address first-order energy differences, ground-state radii and moments on an accurate enough basis. However, addressing absolute binding energies, fine spectroscopic details of $N\pm1$ particle systems or delicate quantities such as second-order energy differences associated to pairing gaps, requires to go to higher truncation orders. Purpose. The formalism is extended to third order in the algebraic diagrammatic construction (ADC) expansion with two-body Hamiltonians. Methods. The expansion of Gorkov propagators in Feynman diagrams is combined with the algebraic diagrammatic construction up to the third order as an organization scheme to generate the Gorkov self-energy. Results. Algebraic expressions for the static and dynamic contributions to the self-energy, along with equations for the matrix elements of the Gorkov eigenvalue problem, are derived. It is first done for a general basis before specifying the set of equations to the case of spherical systems displaying rotational symmetry. Workable approximations to the full self-consistency problem are also elaborated on. The formalism at third order it thus complete for a general two-body Hamiltonian. Conclusion. Working equations for the full Gorkov-ADC(3) are now available for numerical implementation.Comment: 30 pages, 8 figures; published versio

Al–Cu intermetallic coatings processed by sequential metalorganic chemical vapour deposition and post-deposition annealing

Sequential processing of aluminum and copper followed by reactive diffusion annealing is used as a paradigm for the metalorganic chemical vapour deposition (MOCVD) of coatings containing intermetallic alloys. Dimethylethylamine alane and copper N,N'-di-isopropylacetamidinate are used as aluminum and copper precursors, respectively. Deposition is performed on steel and silica substrates at 1.33 kPa and 493–513 K. Different overall compositions in the entire range of the Al–Cu phase diagram are obtained by varying the relative thickness of the two elemental layers while maintaining the overall thickness of the coating close to 1 µm. As-deposited films present a rough morphology attributed to the difficulty of copper to nucleate on aluminum. Post-deposition annealing is monitored by in situ X-ray diffraction, and allows smoothening the microstructure and identifying conditions leading to several Al–Cu phases. Our results establish a proof of principle following which MOCVD of metallic alloys is feasible, and are expected to extend the materials pool for numerous applications, with innovative thin film processing on, and surface properties of complex in shape parts

Metallization of polymer composites by metalorganic chemical vapor deposition of Cu: Surface functionalization driven films characteristics

The present work is an evaluation of the most efficient pretreatments that are used in the field ofmetallization of poly-epoxies. In particular, we treat the case of MOCVD metallization with the constraints of limiting preparation steps and non-null, though limited thermal budget, and obtaining smooth, adherent, and highly conductive Cu coatings. Several results are presented after applying ex or in situ mechanical and chemical treatments. For the first time, transmission electron microscopy investigations illustrate the effect on the coating of H2O vapor addition during the first steps of the deposition process. In an originalmanner, we showthat the enhancement of surface reactivity displaces the center of mass of the deposit towards the gas entry in the hot-wall reactor. Additionally,with the particularity of the hot-wall configuration,we show that differences in the deposition conditions along the reactor locally place the deposition in different regimes, i.e. diffusional or kinetic, with a strong effect on the coating microstructure and properties. Therefore, for both controlling the film properties and tuning the MOCVD reactor and the processing conditions,surface reactivity must be considered, in addition to the classical macroscopic processing parameters

Surface-driven, one-step chemical vapor deposition of γ-Al4Cu9 complex metallic alloy film

The present paper is a paradigm for the one-step formation of complex intermetallic coatings by chemical vapor deposition. It genuinely addresses the challenge of depositing an intermetallic coating with comparable contents of Cu and Al. Depending on processing conditions, a pure γ-Al4Cu9 and multi-phase Al-Cu films are grown with wetting properties of the former being similar to its bulk counterpart. The deposition process and its parametric investigation are detailed. Two metalorganic precursors are used taking into account their transport and chemical properties, and deposition temperature ranges. On line and ex situ characterizations enlighten the competition which occurs at the growing surface between molecular fragments, and which limits growth rates. Notably, introducing a partial pressure of hydrogen gas during deposition reduces Al growth rate from dimethylethylamine alane (DMEAA), by displacing the hydrogen desorption equilibrium. This Al partial growth rate decrease is not sufficient to achieve a Cu/Al atomic ratio that is high enough for the formation of intermetallics with close Al and Cu compositions. A fivefold increase of the flux of the gaseous copper(I) cyclopentadienyl triethylphosphine CpCuPEt3, whereas the DMEAA flux remains constant, results in the targeted Al/Cu atomic ratio equal to 44/56. Nevertheless, the global growth rate is rendered extremely low by the deposition inhibition caused by a massive phosphine adsorption (-PEt3). Despite these limitations, the results pave the way towards the conformal coating of complex surface geometries by such intermetallic compounds

Combined Macro/Nanoscale Investigation of the Chemical Vapor Deposition of Fe from Fe(CO)5

Experiments and computations are performed to model the chemical vapor deposition of iron (Fe) from iron pentacarbonyl (Fe(CO)5). The behavior of the deposition rate is investigated as a function of temperature, in the range 130–250 °C, and pressure in the range 10–40 Torr. Furthermore, the evolution of the surface roughness is correlated with the deposition temperature. By combining previously published mechanisms for the decomposition of Fe(CO)5, a predictive 3D macroscale model of the process is built. Additionally, a nanoscale and a multiscale framework are developed for linking the evolution of the surface of the film with the operating conditions at the reactor scale. The theoretical predictions from the coupled macro/nanoscale models are in very good agreement with experimental measurements indicating poisoning of the surface from carbon monoxide and decrease of the film roughness when temperature increases