Showing papers on "Random phase approximation published in 2012"

Electron correlation methods based on the random phase approximation

Abstract: In the past decade, the random phase approximation (RPA) has emerged as a promising post-Kohn–Sham method to treat electron correlation in molecules, surfaces, and solids. In this review, we explain how RPA arises naturally as a zero-order approximation from the adiabatic connection and the fluctuation-dissipation theorem in a density functional context. This is contrasted to RPA with exchange (RPAX) in a post-Hartree–Fock context. In both methods, RPA and RPAX, the correlation energy may be expressed as a sum over zero-point energies of harmonic oscillators representing collective electronic excitations, consistent with the physical picture originally proposed by Bohm and Pines. The extra factor 1/2 in the RPAX case is rigorously derived. Approaches beyond RPA are briefly summarized. We also review computational strategies implementing RPA. The combination of auxiliary expansions and imaginary frequency integration methods has lead to recent progress in this field, making RPA calculations affordable for systems with over 100 atoms. Finally, we summarize benchmark applications of RPA to various molecular and solid-state properties, including relative energies of conformers, reaction energies involving weak and covalent interactions, diatomic potential energy curves, ionization potentials and electron affinities, surface adsorption energies, bulk cohesive energies and lattice constants. RPA barrier heights for an extended benchmark set are presented. RPA is an order of magnitude more accurate than semi-local functionals such as B3LYP for non-covalent interactions rivaling the best empirically parametrized methods. Larger but systematic errors are observed for processes that do not conserve the number of electron pairs, such as atomization and ionization.

Assessment of correlation energies based on the random-phase approximation

Abstract: The random-phase approximation to the ground state correlation energy (RPA) in combination with exact exchange (EX) has brought the Kohn-Sham (KS) density functional theory one step closer towards a universal, 'general purpose first-principles method'. In an effort to systematically assess the influence of several correlation energy contributions beyond RPA, this paper presents dissociation energies of small molecules and solids, activation energies for hydrogen transfer and non-hydrogen transfer reactions, as well as reaction energies for a number of common test sets. We benchmark EX+RPA and several flavors of energy functionals going beyond it: second-order screened exchange (SOSEX), single-excitation (SE) corrections, renormalized single- excitation (rSE) corrections and their combinations. Both the SE correction and the SOSEX contribution to the correlation energy significantly improve on the notorious tendency of EX+RPA to underbind. Surprisingly, activation

Ionization energy of atoms obtained from GW self-energy or from random phase approximation total energies.

Abstract: A systematic evaluation of the ionization energy within the GW approximation is carried out for the first row atoms, from H to Ar. We describe a Gaussian basis implementation of the GW approximation, which does not resort to any further technical approximation, besides the choice of the basis set for the electronic wavefunctions. Different approaches to the GW approximation have been implemented and tested, for example, the standard perturbative approach based on a prior mean-field calculation (Hartree-Fock GW@HF or density-functional theory GW@DFT) or the recently developed quasiparticle self-consistent method (QSGW). The highest occupied molecular orbital energies of atoms obtained from both GW@HF and QSGW are in excellent agreement with the experimental ionization energy. The lowest unoccupied molecular orbital energies of the singly charged cation yield a noticeably worse estimate of the ionization energy. The best agreement with respect to experiment is obtained from the total energy differences within the random phase approximation functional, which is the total energy corresponding to the GW self-energy. We conclude with a discussion about the slight concave behavior upon number electron change of the GW approximation and its consequences upon the quality of the orbital energies.

Basis set convergence of molecular correlation energy differences within the random phase approximation

Abstract: The basis set convergence of energy differences obtained from the random phase approximation (RPA) to the correlation energy is investigated for a wide range of molecular interactions. For dispersion bound systems the basis set incompleteness error is most pronounced, as shown for the S22 benchmark [P. Jurecka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)10.1039/b600027d]. The use of very large basis sets (> quintuple-zeta) or extrapolation to the complete basis set (CBS) limit is necessary to obtain a reliable estimate of the binding energy for these systems. Counterpoise corrected results converge to the same CBS limit, but counterpoise correction without extrapolation is insufficient. Core-valence correlations do not play a significant role. For medium- and short-range correlation, quadruple-zeta results are essentially converged, as demonstrated for relative alkane conformer energies, reaction energies dominated by intramolecular dispersion, isomerization energies, and reaction energies of small orga...

Correlation potentials for molecular bond dissociation within the self-consistent random phase approximation

Abstract: Self-consistent correlation potentials for H2 and LiH for various inter-atomic separations are obtained within the random phase approximation (RPA) of density functional theory. The RPA correlation potential shows a peak at the bond midpoint, which is an exact feature of the true correlation potential, but lacks another exact feature: the step important to preserve integer charge on the atomic fragments in the dissociation limit. An analysis of the RPA energy functional in terms of fractional charge is given which confirms these observations. We find that the RPA misses the derivative discontinuity at odd integer particle numbers but explicitly eliminates the fractional spin error in the exact-exchange functional. The latter finding explains the improved total energy in the dissociation limit.

Increasing the applicability of density functional theory. II. Correlation potentials from the random phase approximation and beyond

Abstract: Density functional theory (DFT) results are mistrusted at times due to the presence of an unknown exchange correlation functional, with no practical way to guarantee convergence to the right answer. The use of a known exchange correlation functional based on wave-function theory helps to alleviate such mistrust. The exchange correlation functionals can be written exactly in terms of the density-density response function using the adiabatic-connection and fluctuation-dissipation framework. The random phase approximation (RPA) is the simplest approximation for the density-density response function. Since the correlation functional obtained from RPA is equivalent to the direct ring coupled cluster doubles (ring-CCD) correlation functional, meaning only Coulomb interactions are included, one can bracket RPA between many body perturbation theory (MBPT)-2 and CCD with the latter having all ring, ladder, and exchange contributions. Using an optimized effective potential strategy, we obtain correlation potentials corresponding to MBPT-2, RPA (ring-CCD), linear-CCD, and CCD. Using the suitable choice of the unperturbed Hamiltonian, Kohn-Sham self-consistent calculations are performed. The spatial behavior of the resulting potentials, total energies, and the HOMO eigenvalues are compared with the exact values for spherical atoms. Further, we demonstrate that the self-consistent eigenvalues obtained from these consistent potentials used in ab initio dft approximate all principal ionization potentials as demanded by ionization potential theorem.

Random-phase-approximation correlation method including exchange interactions

Abstract: Two random-phase-approximation correlation methods are introduced that take into account exchange interactions. The first one, termed RPAX, is obtained from a simple modification of the ring coupled-cluster doubles amplitude equation, while the second, termed RPAX2, is based on the first method using a slightly modified update equation for the amplitudes. It is shown that this second RPAX2 method can be implemented with a computational algorithm that scales only with the fifth power of the molecular size with the aid of density fitting or the Cholesky decomposition of two-electron integrals. It is thus not much more costly than standard second-order perturbation theory methods and can be applied to quite large molecular systems. Moreover, numerical tests for chemical reaction energies and intermolecular interaction energies have shown that the RPAX2 method, if based on a Perdew-Burke-Ernzerhof exchange Kohn-Sham reference determinant, yields results which are very close to coupled-cluster with single, double, and perturbative triple excitations reference results.

Low-lying dipole response: Isospin character and collectivity in 68 Ni, 132 Sn, and 208 Pb

Abstract: The isospin character, the collective or single-particle nature, and the sensitivity to the slope of the nuclear symmetry energy of the low-energy isovector dipole response (known as pygmy dipole resonance) are nowadays under debate. In the present work we study, within the fully self-consistent nonrelativistic mean field (MF) approach based on Skyrme Hartree-Fock plus random phase approximation (RPA), the measured even-even nuclei ${}^{68}$Ni, ${}^{132}$Sn, and ${}^{208}$Pb. To analyze the model dependence in the predictions of the pygmy dipole strength, we employ three different Skyrme parameter sets. We find that both the isoscalar and the isovector dipole responses of all three nuclei show a low-energy peak that increases in magnitude, and is shifted to larger excitation energies, with increasing values of the slope of the symmetry energy at saturation. We highlight the fact that the collectivity associated with the RPA state(s) contributing to this peak is different in the isoscalar and isovector case, or in other words it depends on the external probe. While the response of these RPA states to an isovector operator does not show a clear collective nature, the response to an isoscalar operator is recognizably collective, for all analyzed nuclei and all studied interactions.

Extending the random-phase approximation for electronic correlation energies: The renormalized adiabatic local density approximation

Abstract: The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of this approach is the improved description of dispersive forces while chemical bond strengths and absolute correlation energies are systematically underestimated. In this work we extend the RPA by including a parameter-free renormalized version of the adiabatic local-density (ALDA) exchange-correlation kernel. The renormalization consists of a (local) truncation of the ALDA kernel for wave vectors $qg2{k}_{F}$, which is found to yield excellent results for the homogeneous electron gas. In addition, the kernel significantly improves both the absolute correlation energies and atomization energies of small molecules over RPA and ALDA. The renormalization can be straightforwardly applied to other adiabatic local kernels.

Optical properties of bulk semiconductors and graphene/boron nitride: The Bethe-Salpeter equation with derivative discontinuity-corrected density functional energies

Abstract: We present an efficient implementation of the Bethe-Salpeter equation (BSE) for optical properties of materials in the projector augmented wave method. Single-particle energies and wave functions are obtained from the Gritsenko, Leeuwen, Lenthe, and Baerends potential [Phys. Rev. A 51, 1944 (1995)] with the modifications from Kuisma et al. [Phys. Rev. B 82, 115106 (2010)] GLLBSC functional which explicitly includes the derivative discontinuity, is computationally inexpensive, and yields excellent fundamental gaps. Electron-hole interactions are included through the BSE using the statically screened interaction evaluated in the random phase approximation. For a representative set of semiconductors and insulators we find excellent agreement with experiments for the dielectric functions, onset of absorption, and lowest excitonic features. For the two-dimensional systems of graphene and hexagonal boron-nitride (h-BN) we find good agreement with previous many-body calculations. For the graphene/h-BN interface we find that the fundamental and optical gaps of the h-BN layer are reduced by 2.0 and 0.7 eV, respectively, compared to freestanding h-BN. This reduction is due to image charge screening which shows up in the GLLBSC calculation as a reduction (vanishing) of the derivative discontinuity.

Interaction-enhanced coherence between two-dimensional Dirac layers

Abstract: We estimate the strength of interaction-enhanced coherence between two graphene or topological insulator surface-state layers by solving imaginary-axis gap equations in the random phase approximation. Using a self-consistent treatment of dynamic screening of Coulomb interactions in the gapped phase, we show that the excitonic gap can reach values on the order of the Fermi energy at strong interactions. The gap is discontinuous as a function of interlayer separation and effective fine structure constant, revealing a first order phase transition between effectively incoherent and interlayer coherent phases. To achieve the regime of strong coherence the interlayer separation must be smaller than the Fermi wavelength, and the extrinsic screening of the medium embedding the Dirac layers must be negligible. In the case of a graphene double-layer we comment on the supportive role of the remote $\pi$-bands neglected in the two-band Dirac model.

Failure of the random-phase-approximation correlation energy

Abstract: The random phase approximation (RPA) is thought to be a successful method; however, basic errors have been found that have massive implications in the simplest molecular systems. The observed successes and failures are rationalized by examining its performance against exact conditions on the energy for fractional charges and fractional spins. Extremely simple tests reveal that the RPA method satisfies the constancy condition for fractional spins that leads to correct dissociation of closed-shell molecules and no static correlation error (such as in H${}_{2}$ dissociation) but massively fails for dissociation of odd electron systems, with an enormous delocalization error (such as H${{}_{2}}^{+}$ dissociation). Other methods related to the RPA, including the Hartree-Fock response (RPAE) or range-separated RPA, can reduce this delocalization error but only at the cost of increasing the static correlation error. None of the RPA methods have the discontinuous nature required to satisfy both exact conditions and the full unified condition (e.g., dissociation of H${{}_{2}}^{+}$ and H${}_{2}$ at the same time), emphasizing the need to go beyond differentiable energy functionals of the orbitals and eigenvalues.

Dynamical screening effects in correlated materials: Plasmon satellites and spectral weight transfers from a Green's function ansatz to extended dynamical mean field theory

Abstract: Dynamical screening of the Coulomb interactions in correlated electron systems results in a low-energy effective problem with a dynamical Hubbard interaction U(omega). We propose a Green's function ansatz for the Anderson impurity problem with retarded interactions, in which the Green's function factorizes into a contribution stemming from an effective static-U problem and a bosonic high-energy part introducing collective plasmon excitations. Our approach relies on the scale separation of the low-energy properties, related to the instantaneous static U, from the intermediate to high energy features originating from the retarded part of the interaction. We argue that for correlated materials where retarded interactions arise from downfolding higher-energy degrees of freedom, the characteristic frequencies are typically in the antiadiabatic regime. In this case, accurate approximations to the bosonic factor are relatively easy to construct, with the most simple being the boson factor of the dynamical atomic limit problem. We benchmark the quality of our method against numerically exact continuous time quantum Monte Carlo results for the Anderson-Holstein model both, at half- and quarter-filling. Furthermore we study the Mott transition within the Hubbard-Holstein model within extended dynamical mean field theory. Finally, we apply our technique to a realistic three-band Hamiltonian for SrVO3. We show that our approach reproduces both, the effective mass renormalization and the position of the lower Hubbard band by means of a dynamically screened U, previously determined ab initio within the constrained random phase approximation. Our approach could also be used within schemes beyond dynamical mean field theory, opening a quite general way of describing satellites and plasmon excitations in correlated materials.

Plasmons and Coulomb drag in Dirac-Schrödinger hybrid electron systems

Abstract: We show that the plasmon spectrum of an ordinary two-dimensional electron gas (2DEG) hosted in a GaAs heterostructure is significantly modified when a graphene sheet is placed on the surface of the semiconductor in close proximity to the 2DEG. Long-range Coulomb interactions between massive electrons and massless Dirac fermions lead to a set of optical and acoustic intrasubband plasmons. Here we compute the dispersion of these coupled modes within the random phase approximation, providing analytical expressions in the long-wavelength limit that shed light on their dependence on the Dirac velocity and Dirac-fermion density. We also evaluate the resistivity in a Coulomb-drag transport setup. These Dirac-Schr\"odinger hybrid electron systems are experimentally feasible and open research opportunities for fundamental studies of electron-electron interaction effects in two spatial dimensions.

Gamow-Teller response within Skyrme random-phase approximation plus particle-vibration coupling

Abstract: Although many random-phase approximation (RPA) calculations of the Gamow-Teller (GT) response exist, this is not the case for calculations going beyond the mean-field approximation. We apply a consistent model, that includes the coupling of the GT resonance to low-lying vibrations, to nuclei of the $fp$ shell. Among other motivations, our goal is to see if the particle-vibration coupling can redistribute the low-lying GT${}^{+}$ strength that is relevant for electron-capture processes in core-collapse supernova. We conclude that the lowering and fragmentation of that strength are consistent with the experimental findings and validate our model. However, the particle-vibration coupling cannot account for the quenching of the total value of the low-lying strength.

Screened Coulomb interaction of localized electrons in solids from first principles

Abstract: We report the implementation of a first-principles approach for calculating the screened Coulomb and exchange energies for localized electrons in solids. Our method is based on the pseudopotential plane-wave formalism. The localized orbitals are represented by maximally localized Wannier functions, and the screening effects are calculated within the constrained random phase approximation. As first applications of this development, we investigate the onsite Coulomb $U$ and exchange $J$ for the $3d$ electrons in ZnO, NiO, and CuGaS${}_{2}$. Both the bare (unscreened) and the screened $U$ and $J$ matrices are presented. We find that it is very important for these parameters to be calculated self-consistently. Intrachannel (i.e., $d$-$d$) and energy-dependent screening effects are also discussed.

Inelastic scattering of low-energy electrons in liquid water computed from optical-data models of the Bethe surface

Abstract: Purpose: We provide a short overview of optical-data models for the description of inelastic scattering of low-energy electrons (10–10,000 eV) in liquid water. The effect on the inelastic scattering cross section due to different optical data and extension algorithms is examined with emphasis on some recent developments. Materials and methods: The optical-data method whereby experimental optical data and theoretical extension algorithms are used to describe the dependence of the dielectric response function on energy- and momentum-transfer and obtain the Bethe surface of the material, currently represents the most used method for computing the inelastic scattering of lowenergy electrons in condensed media. Two sets of experimental optical data for liquid water obtained from reflectance and inelastic X-ray scattering spectroscopy, respectively, and the extension algorithms of Ritchie, Penn, and Ashley are examined. Recent developments are discussed along with the role of corrections to the random phase approximation (RPA) of electron gas theory. Results: The inelastic scattering cross section in the energy range 200–10,000 eV was found to be rather insensitive (to within 10%) to the choice of optical data or the extension algorithm. In contrast, differences between model calculations increase rapidly below 200 eV with the influence of the extension algorithm being dominant. Conclusion: The choice of the extension algorithm used to extrapolate optical data to finite momentum transfer and obtain the Bethe surface is crucial in modelling the inelastic scattering of electrons with energies below 200 eV. A new set of measurements on the dielectric response function of liquid water beyond the optical limit and the development of extension algorithms that will go beyond RPA by considering the effect of (short-range) electron exchange and correlation should be of some priority.

Density instabilities in a two-dimensional dipolar fermi gas

Abstract: We study the density instabilities of a two-dimensional gas of dipolar fermions with aligned dipole moments. The random phase approximation (RPA) for the density-density response function is never accurate for the dipolar gas, and so we incorporate correlations beyond RPA via an improved version of the Singwi-Tosi-Land-Sjolander scheme. In addition to density-wave instabilities, our formalism captures the collapse instability that is expected from Hartree-Fock calculations but is absent from RPA. Crucially, we find that when the dipoles are perpendicular to the layer, the system spontaneously breaks rotational symmetry and forms a stripe phase, in defiance of conventional wisdom.

Large-scale Continuum random-phase approximation predictions of dipole strength for astrophysical applications

Abstract: Large-scale calculations of the $E1$ strength are performed within the random phase approximation (RPA) based on the relativistic point-coupling mean field approach in order to derive the radiative neutron capture cross sections for all nuclei of astrophysical interest. While the coupling to the single-particle continuum is taken into account in an explicit and self-consistent way, additional corrections like the coupling to complex configurations and the temperature and deformation effects are included in a phenomenological way to account for a complete description of the nuclear dynamical problem. It is shown that the resulting $E1$-strength function based on the PCF1 force is in close agreement with photoabsorption data as well as the available experimental $E1$ strength data at low energies. For neutron-rich nuclei, as well as light neutron-deficient nuclei, a low-lying so-called pygmy resonance is found systematically in the 5--10 MeV region. The corresponding strength can reach 10% of the giant dipole strength in the neutron-rich region and about 5% in the neutron-deficient region, and is found to be reduced in the vicinity of the shell closures. Finally, the neutron capture reaction rates of neutron-rich nuclei is found to be about 2--5 times larger than those predicted on the basis of the nonrelativistic RPA calculation and about a factor 50 larger than obtained with traditional Lorentzian-type approaches.

Plasmon dispersion in semimetallic armchair graphene nanoribbons

Abstract: The dispersion relations for plasmons in intrinsic and extrinsic semimetallic armchair graphene nanoribbons (acGNR) are calculated in the random phase approximation using the orthogonal ${p}_{z}$-orbital tight-binding method. Our model predicts new plasmons for acGNR of odd atomic widths, $N=5,11,17,...$ Our model further predicts plasmons in acGNR of even atomic widths, $N=2,8,14,...$, related to those found using a Dirac continuum model but with different quantitative dispersion characteristics. We find that the dispersion of all plasmons in semimetallic acGNR depends strongly on the localization of the ${p}_{z}$ electronic wavefunctions. We also find that overlap integrals for acGNR behave in a more complex way than predicted by the Dirac continuum model, suggesting that these plasmons will experience a small damping for all $q\ensuremath{ e}0$. Plasmons in extrinsic semimetallic acGNR with the chemical potential in the lowest (highest) conduction (valence) band are found to have dispersion characteristics nearly identical to their intrinsic counterparts, with negligible differences in dispersion arising from the slight differences in overlap integrals for the interband and intraband transitions.

Dielectric function beyond the random-phase approximation: kinetic theory versus linear response theory.

Abstract: Calculating the frequency-dependent dielectric function for strongly coupled plasmas, the relations within kinetic theory and linear response theory are derived and discussed in comparison. In this context, we give a proof that the Kohler variational principle can be extended to arbitrary frequencies. It is shown to be a special case of the Zubarev method for the construction of a nonequilibrium statistical operator from the principle of the extremum of entropy production. Within kinetic theory, the commonly used energy-dependent relaxation time approach is strictly valid only for the Lorentz plasma in the static case. It is compared with the result from linear response theory that includes electron-electron interactions and applies for arbitrary frequencies, including bremsstrahlung emission. It is shown how a general approach to linear response encompasses the different approximations and opens options for systematic improvements.

Phase separation in a lattice model of a superconductor with pair hopping

Abstract: We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have a possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d = 1) in the ground state. Moreover, at T = 0 some results derived within the random phase approximation (and the spin-wave approximation) for d = 2 and 3 lattices and within the low-density expansions for d = 3 lattices are presented. Our investigation of the general case (as a function of the electron concentration n and as a function of the chemical potential μ) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases, superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS–NO). The system considered exhibits interesting multicritical behaviour including tricritical points.

Screened Coulomb interactions of localized electrons in transition metals and transition-metal oxides

Abstract: The screened Coulomb interactions of localized electrons, often treated as adjustable parameters in constructing model Hamiltonians, are important quantities for studying strongly correlated materials. Using a recently implemented constrained random phase approximation approach, we have calculated the screened Coulomb and exchange interactions of $3d$ electrons in transition metals, late transition-metal monoxides, and VO${}_{2}$. For monoxides, we have also calculated the on-site screened Coulomb interaction for oxygen $p$ electrons as well as the intersite $pd$ interaction. Our results compare reasonably well with available experimental and theoretical results. We find that for oxide systems, a self-consistent procedure is very important for an accurate account of the screening effect.

Mean-field theory of the phase diagram of ultrasoft, oppositely charged polyions in solution.

Abstract: We investigate the phase separation of the "ultrasoft restricted primitive model" (URPM), a coarse-grained representation of oppositely charged, interpenetrating polyelectrolytes, within a mean-field description based on the "chemical picture." The latter distinguishes between free ions and dimers of oppositely charged ions (Bjerrum pairs) which are in chemical equilibrium governed by a law of mass action. Interactions between ions, and between ions and dimers are treated within linearized Poisson-Boltzmann theory, at four levels of approximation corresponding to increasingly refined descriptions of the interactions. The URPM is found to phase separate into a dilute phase of dimers, and a concentrated phase of mostly free (unpaired) ions below a critical temperature T(c). The phase diagram differs, however, considerably from the predictions of recent simulations; T(c) is about three times higher, and the critical density is much lower than the corresponding simulation data [D. Coslovich, J. P. Hansen, and G. Kahl, Soft Matter 7, 1690 (2011)]. Possible reasons for this unexpected failure of mean-field theory are discussed. The Kirkwood line, separating the regimes of monotonically decaying and damped oscillatory decay of the charge-charge correlation function at large distances is determined within the random phase approximation.

Giant monopole resonances and nuclear incompressibilities studied for the zero-range and separable pairing interactions

Abstract: Background: Following the 2007 precise measurements of monopole strengths in tin isotopes, there has been a continuous theoretical effort to obtain a precise description of the experimental results. Up to now, there is no satisfactory explanation of why the tin nuclei appear to be significantly softer than Pb-208. Purpose: We determine the influence of finite-range and separable pairing interactions on monopole strength functions in semimagic nuclei. Methods: We employ self-consistently the quasiparticle random phase approximation on top of spherical Hartree-Fock-Bogoliubov solutions. We use the Arnoldi method to solve the linear-response problem with pairing. Results: We found that the difference between centroids of giant monopole resonances measured in lead and tin (about 1 MeV) always turns out to be overestimated by about 100%. We also found that the volume incompressibility, obtained by adjusting the liquid-drop expression to microscopic results, is significantly larger than the infinite-matter incompressibility. Conclusions: The zero-range and separable pairing forces cannot induce modifications of monopole strength functions in tin to match experimental data. (Less)

TDDFT study of time-dependent and static screening in graphene

Abstract: Time-dependent density functional theory (TDDFT) within the random phase approximation (RPA) is used to obtain the time evolution of the induced potential produce by the sudden formation of a C 1s core hole inside a graphene monolayer, and to show how the system reaches the equilibrium potential. The characteristic oscillations in the time-dependent screening potential are related to the excitations of $\ensuremath{\pi}$ and $\ensuremath{\sigma}+\ensuremath{\pi}$ plasmons as well as the low energy 2D plasmons in doped graphene. The equilibrium RPA screened potential is compared with the DFT effective potential, yielding good qualitative agreement. The self energy of a point charge near a graphene monolayer is shown to demonstrate an image potential type behavior, $Ze/(z\ensuremath{-}{z}_{0})$, down to very short distances (4 a.u.) above the graphene layer. Both results are found to agree near quantitatively with the DFT ground state energy shift of a Li${}^{+}$ ion placed near a graphene monolayer.

Collective vibrational states within the fast iterative quasiparticle random-phase approximation method

Abstract: An iterative method we previously proposed to compute nuclear strength functions [Toivanen et al., Phys. Rev. C 81, 034312 (2010)] is developed to allow it to accurately calculate properties of individual nuclear states. The approach is based on the quasiparticle random-phase approximation (QRPA) and uses an iterative non-Hermitian Arnoldi diagonalization method where the QRPA matrix does not have to be explicitly calculated and stored. The method gives substantial advantages over conventional QRPA calculations with regards to the computational cost. The method is used to calculate excitation energies and decay rates of the lowest-lying 2(+) and 3(-) states in Pb, Sn, Ni, and Ca isotopes using three different Skyrme interactions and a separable Gaussian pairing force. (Less)