Particle-hole Interaction Research Articles

Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States.

The lack of particle-hole attraction and orbital relaxation within time-dependent density functional theory (TDDFT) lead to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n - 1-electron system as the reference, building orbital relaxation and a proper hole into the initial density. Our approach is an exact generalization of the static-exchange approximation that ameliorates the particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems.

Variational and parquet-diagram calculations for neutron matter. IV. Spin-orbit interactions and linear response

We develop the parquet-diagram summation method for neutron matter interacting via potentials that include spin, tensor, and spin-orbit components. For that purpose, we derive an exact expression for the sum of all ring-diagrams in terms effective local particle-hole interactions involving the above four operators. The parquet equations are closed by deriving the spin-orbit contribution to that particle-hole interaction. We show that many-body correlations screen the bare spin-orbit potential considerably, and the corrections of that screened spin-orbit potential to the other three interaction channels are quite small. We apply our method to the calculation of the response of neutron matter to density and both longitudinal and transverse spin-dependent external fields.

BAZI TEK ÇEKİRDEKLİ GERMANYUM İZOTOBU İÇİN DEFORME VE KÜRESEL ÇEKİRDEKLERİN LOG(FT) DEĞERLERİ

The log(ft) values of the allowed 𝛽± decay between odd-A spherical and deformed nuclei are studied for germanium isotopes in this paper. The Pyatov Method (PM) and the Schematic Model (SM)) are used to the GT strength distributions, including the schematic residual spin-isospin interaction between nucleons in the particle-hole and particle-particle channels. Particle-hole and particle-particle interaction parameters are calculated respectively with X_ph^GT= 5.2 A^(0.7 ) MeV and X_pp^GT= 0.58 A^(0.7 ) MeV. Deformed Woods-Saxon potential is used in calculations of single-particle energies and wave functions. The results are also compared with previous experiment values wherever available.

Effective shell-model interaction for nuclei “southeast” of Sn100

We construct an effective shell-model interaction for the valence space spanned by single-particle neutron and single-hole proton states in $^{100}$Sn. Starting from chiral nucleon-nucleon and three-nucleon forces and single-reference coupled-cluster theory for $^{100}$Sn we apply a second similarity transformation that decouples the valence space. The particle-particle components of the resulting effective interaction can be used in shell model calculations for neutron deficient tin isotopes. The hole-hole interaction can be used to calculate the $N = 50$ isotones south of $^{100}$Sn, and the full particle-hole interaction describes nuclei in the region southeast of $^{100}$Sn. We compute low-lying excited states in selected nuclei southeast of $^{100}$Sn, and find reasonable agreement with data. The presented techniques can also be applied to construct effective shell-model interactions for other regions of the nuclear chart.

Large-scale atomic data calculations in Ce V – X ions for application to early kilonova emission from neutron star mergers

ABSTRACT New radiative parameters (wavelengths, transition probabilities, and oscillator strengths) are reported in the present paper for a large number of spectral lines in moderately charged cerium ions, from Ce V to Ce X. These results were obtained through large-scale atomic structure calculations carried out using three different and independent theoretical approaches, namely the relativistic Hartree–Fock method, including core-polarization corrections (HFR + CPOL), the multiconfiguration Dirac–Hartree–Fock method, and the Particle-Hole Configuration Interaction (PH-CI) method implemented in the AMBiT code. The accuracy of the results was assessed through detailed comparisons between the data deduced from these methods and with the few theoretical and experimental data previously published. For the six cerium ions considered, the most complete and reliable sets of transition wavelengths and rates were then used to calculate the expansion opacities characterizing the early phases of kilonovae following neutron star mergers, i.e. for typical conditions corresponding to temperatures T > 20 000 K, a density ρ = 10−10 g cm−3 and a time after the merger t = 0.1 d.

Microscopic Model to Take into Account Complex Configurations for Pygmy and Giant Resonances

A microscopic model for taking into account quasiparticle–phonon interaction in magic nuclei is considered within nuclear quantum many-body theory. This model is of interest for constructing a microscopic theory of pygmy and giant multipole resonances—first of all, a description of their fine structure. This article reports on a continuation and development of our earlier study [1]. Basic physics results of that study are confirmed here, and new results are obtained: (i) exact (not approximate, as in [1]) expressions for the first and second variations of the vertex in the phonon field are found and employed; (ii) a new equation involving, in addition to the known effective interaction, the total amplitude for particle–hole interaction is derived for the vertex, which is the main ingredient in the theory of finite Fermi systems; (iii) the required two-phonon configurations are obtained owing to the last result. The new equation for the vertex now contains complex configurations such as 1p1hotimestextrm{phonon} and two-phonon ones, along with numerous ground-state correlations.

Origin of Low- and High-Energy Monopole Collectivity in 132Sn

Beginning with the Skyrme interaction, we study the properties of the isoscalar giant monopole resonances (ISGMR) of 132Sn. Using the finite-rank separable approximation for the particle-hole interaction, the coupling between one- and two-phonon terms in the wave functions of excited states is taken into account in very large configurational spaces. The inclusion of the phonon–phonon coupling (PPC) results in the formation of a low-energy 0+ state. The PPC inclusion leads to a fragmentation of the ISGMR strength to lower energy states and also to a higher energy tail. Using the same set of parameters, we describe the available experimental data for the ISGMR characteristics of 118,120,122,124Sn and give a prediction for 126,128,130,132Sn.

Identification of strongly interacting organic semimetals

Dirac- and Weyl point- and line-node semimetals are characterized by a zero band gap with simultaneously vanishing density of states. Given a sufficient interaction strength, such materials can undergo an interaction instability, e.g., into an excitonic insulator phase. Due to generically flat bands, organic crystals represent a promising materials class in this regard. We combine machine learning, density functional theory, and effective models to identify specific example materials. Without taking into account the effect of many-body interactions, we found the organic charge transfer salts (EDT-TTF-I$_2$)$_2$(DDQ)$\cdot($CH$_3$CN) and TSeF-TCNQ and a bis-1,2,3-dithiazolyl radical conductor to exhibit a semimetallic phase in our ab initio calculations. Adding the effect of strong particle-hole interactions for (EDT-TTF-I$_2$)$_2$(DDQ)$\cdot($CH$_3$CN) and TSeF-TCNQ opens an excitonic gap in the order of 60 meV and 100 meV, which is in good agreement with previous experiments on these materials.

Generalized Skyrme random-phase approximation for nuclear resonances: Different trends for electric and magnetic modes

We discuss major differences between electric and magnetic excitations in nuclei appearing in self-consistent calculations based on Skyrme energy-density functionals (EDFs). For this we calculate collective low- and high-lying electric and magnetic excitations in $^{208}\mathrm{Pb}$ within a self-consistent Skyrme EDF approach using the random-phase approximation (RPA) and a more sophisticated particle-hole plus phonon-coupling model, coined the time-blocking approximation (TBA). Tools of analysis are Landau-Migdal parameters for bulk properties and the RPA and TBA results for finite nuclei. We show that the interplay between the effective mass and the effective particle-hole interaction, well known in the Landau-Migdal theory, renders the final results rather independent of the effective mass by virtue of the ``backflow effect.'' It explains the success of self-consistent calculations of electric transitions in such approaches. This effect, however, is absent in the magnetic case and leads to higher fluctuations in the results. It calls for further developments of the Skyrme functional in the spin channel.

Neutron-Proton, Neutron-Neutron, Proton-Proton QRPA for the Gamow-Teller and the M1 Spin Transitions of N ≃ Z Nuclei in the s — d Shell

We study the Gamow-Teller (GT) and the M1 spin transitions of the s — d shell nuclei $^{24}$Mg, $^{26}$Mg, $^{28}$Si, $^{32}$S, and $^{36}$Ar by using a quasiparticle random phase approximation (QRPA) scheme that comprises neutron-proton (np), neutron-neutron (nn) and proton-proton (pp) QRPA owing to the inclusion of the np pairing, as well as nn and pp pairing correlations. At present, we work in spherical symmetry under the assumption that the deformations of the nuclei considered in this work are small enough to neglect, as was customary in past applications. For the GT transition, as well as single and double beta decays, the neutron-proton QRPA (np QRPA) is usually employed. For the M1 spin transition, the pp and nn QRPA is needed due to its neutral current property. The np pairing correlations couple the np QRPA to the nn and pp QRPA. Therefore, the coupled np + nn + pp QRPA enables us to investigate simultaneously the GT and the M1 spin transitions. In particular, in this work, detailed analyses of particle-particle and particle-hole interactions at the QRPA stage are performed for the GT and the M1 spin transitions of the well-known s — d shell N ≃ Z nuclei, and the results are compared to available data. The roles of the np pairing correlations are also discussed for those transitions.

Zero-energy quasiparticles in an interacting nanowire containing a topological Josephson junction

We study a Josephson junction in a Kitaev chain with particle-hole symmetric nearest neighbor interactions. When the phase difference across the junction is $\pi$, we show analytically that the full spectrum is fourfold degenerate up to corrections that vanish exponentially in the system size. The Majorana bound states at the ends of the chain are known to survive interactions. Our result proves that the same is true for the zero-energy quasiparticle localized at the junction. We further study finite size corrections numerically, and show how repulsive interactions lead to stronger end-to-end correlations than in a noninteracting system with the same bulk gap.

Self-consistent random-phase approximation based on the relativistic Hartree-Fock theory: Role of ρ -tensor coupling

The framework of the random-phase approximation (RPA) based on the relativistic Hartree-Fock (RHF) theory is extended to achieve a self-consistent calculation with the $\ensuremath{\rho}$-meson tensor coupling. The model self-consistency is verified by the check of the isobaric analog state, and it is found that the $\ensuremath{\rho}$-tensor and $\ensuremath{\rho}$-vector-tensor couplings play significant roles in maintaining the self-consistency. Using the RHF Lagrangian PKA1, the properties of the Gamow-Teller resonances (GTR) are investigated, in which the roles played by the particle-hole residual interaction of various meson-nucleon couplings are clarified in details. Furthermore, the effects of the tensor force, which is introduced naturally via the Fock terms, are analyzed by comparing the calculations with full Lagrangians and the ones artificially dropping the tensor force components. It is found that for the RHF Lagrangians $\mathrm{PKO}i$ $(i=1,2,3)$ and PKA1, the tensor forces play the role mainly via the RHF mean field rather than via the RPA residual interaction in determining the GTR. Moreover, the tensor-force effects are not as strong as those indicated by the Skyrme Hartree-Fock calculations.

Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms. II. Charge exchange

We present the formalism of linear response theory both at zero and finite temperature in the case of asymmetric nuclear matter excited by an isospin flip probe. The particle-hole interaction is derived from a general Skyrme functional that includes spin-orbit and tensor terms. Response functions are obtained by solving a closed algebraic system of equations. Spin strength functions are analyzed for typical values of density, momentum transfer, asymmetry and temperature.

Low-energy M1 excitations in Pb208 and the spin channel of the Skyrme energy-density functional

We investigate the spin dependent part of the Skyrme energy-density functional, in particular its impact on the residual particle-hole interaction in self-consistent calculations of excitations. Test cases are the low-energy M1 excitations in $^{208}$Pb treated within the self-consistent random-phase approximation based on the Skyrme energy-density functional. We investigate different parametrizations of the functionals to find out which parameters of the functional have strongest correlations with M1 properties. We explore a simple method of the modification of the spin-related parameters which delivers a better description of M1 excitations while basically maintaining the good description of ground state properties.

A close look at the competition of isovector and isoscalar pairing in A=18 and 20 even-even N≈Z nuclei * * Supported by the National Natural Science Foundation of China (11675071 and 11375080), the U. S. National Science Foundation (OIA-1738287 and ACI -1713690), U. S. Department of Energy (DE-SC0005248), the Southeastern Universities Research Association, the China-U. S. Theory Institute for Physics

The competition of isovector and isoscalar pairing in A=18 and 20 even-even N≈Z nuclei is analyzed in the framework of the mean-field plus the dynamic quadurpole-quadurpole, pairing and particle-hole interactions, whose Hamiltonian is diagonalized in the basis in the L = 0 configuration subspace. Besides the pairing interaction, it is observed that the quadurpole-quadurpole and particle-hole interactions also play a significant role in determining the relative positions of low-lying excited 0+ and 1+ levels and their energy gaps, which can result in the ground state first-order quantum phase transition from J = 0 to J = 1. The strengths of the isovector and isoscalar pairing interactions in these even-even nuclei are estimated with respect to the energy gap and the total contribution to the binding energy. Most importantly, it is shown that although the mechanism of the particle-hole contribution to the binding energy is different, it is indirectly related to the Wigner term in the binding energy.

Charge fluctuations in lightly hole-doped cuprates: Effect of vertex corrections

Identification of the electronic state that appears upon doping a Mott insulator is important to understand the physics of cuprate high-temperature superconductors. Recent scanning tunneling microscopy of cuprates provides evidence that a charge-ordered state emerges before the superconducting state upon doping the parent compound. We study this phenomenon by computing the charge response function of the Hubbard model including frequency-dependent local vertex corrections that satisfy the compressibility sum-rule. We find that upon approaching the Mott phase from the overdoped side, the charge fluctuations at wave vectors connecting hot spots are suppressed much faster than at the other wave-vectors. It leads to a momentum dependence of the dressed charge susceptibility that is very different from either the bare susceptibility or from the susceptibility obtained from the random phase approximation. We also find that the paramagnetic lightly hole-doped Mott phase at finite-temperature is unstable to charge ordering only at zero wave-vector, confirming the results previously obtained from the compressibility. Charge order is driven by the frequency-dependent scattering processes that induce an attractive particle-hole interaction at large interaction strength and small doping.

Communication: Almost error-free resolution-of-the-identity correlation methods by null space removal of the particle-hole interactions.

We present a method to improve upon the resolution-of-the-identity (RI) for correlation methods. While RI is known to allow for drastic speedups, it relies on a cancellation of errors. Our method eliminates the errors introduced by RI which are known to be problematic for absolute energies. In this way, independence of the error compensation assumption for relative energies is also achieved. The proposed method is based on the idea of starting with an oversized RI basis and projecting out all of its unphysical parts. The approach can be easily implemented into existing RI codes and results in an overhead of about 30%, while effectively removing the RI error. In passing, this process alleviates the problem that for many frequently employed basis sets no optimized RI basis sets have been constructed. In this paper, the theory is presented and results are discussed exemplarily for the random phase approximation and Møller-Plesset perturbation theory.

Calculations of the β-decay half-lives of neutron-deficient nuclei**Supported by National Nature Science Foundation of China (11535004, 11375086, 11120101005, 11175085 and 11235001), 973 Nation Major State Basic Research and Development of China (2013CB834400) and Science and Technology Development Fund of Macau (020/2014/A1 and 039/2013/A2)

In this work, β+/EC decays of some medium-mass nuclei are investigated within the extended quasiparticle random-phase approximation (QRPA), where neutron-neutron, proton-proton and neutron-proton (np) pairing correlations are taken into consideration in the specialized Hartree-Fock-Bogoliubov (HFB) transformation. In addition to the pairing interaction, the Brückner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions. Calculations are performed for even-even proton-rich isotopes ranging from Z=24 to Z=34. It is found that the np pairing interaction plays a significant role in β-decay for some nuclei far from stability. Compared with other theoretical calculations, our calculations show good agreement with the available experimental data. Predictions of β-decay half-lives for some very neutron-deficient nuclei are made for reference.

Landau parameters for energy density functionals generated by local finite-range pseudopotentials

In Landau theory of Fermi liquids, the particle–hole interaction near the Fermi energy in different spin–isospin channels is probed in terms of an expansion over the Legendre polynomials. This provides a useful and efficient way to constrain properties of nuclear energy density functionals in symmetric nuclear matter and finite nuclei. In this study, we present general expressions for Landau parameters corresponding to a two-body central local regularized pseudopotential. We also show results obtained for two recently adjusted NLO and N2LO parametrizations. Such pseudopotentials will be used to determine mean-field and beyond-mean-field properties of paired nuclei across the entire nuclear chart.

GAUGE-INVARIANT RELATIVISTIC PERTURBATION THEORY APPROACH TO DETERMINATION OF ENERGY and SPECTRAL CHARACTERISTICS FOR HEAVY AND SUPERHEAVY ATOMS AND IONS: REVIEW

We reviewed an effective consistent ab initio approach to relativistic calculation of the spectra for multi-electron heavy and superheavy ions with an account of relativistic, correlation, nuclear, radiative effects is presented. The method is based on the relativistic gauge-invariant (approximation to QED) perturbation theory (PT) and generalized effective field nuclear model with using the optimized one-quasiparticle representation firstly in theory of the hyperfine structure for relativistic atom. The wave function zeroth basis is found from the Dirac equation with potential, which includes the core ab initio potential, the electric and polarization potentials of a nucleus. The correlation corrections of the high orders are taken into account within the Green functions method (with the use of the Feynman diagram’s technique). There have taken into account all correlation corrections of the second order and dominated classes of the higher orders diagrams (electrons screening, particle-hole interaction, mass operator iterations). The magnetic inter-electron interaction is accounted in the lowest on α parameter (α is the fine structure constant), approximation, the self-energy part of the Lamb shift is taken effectively into consideration within the Ivanov-Ivanova non-perturbative procedure, the Lamb shift polarization part - in the generalized Uehling-Serber approximation with accounting for the Källen-Sabry α2 (αZ) and Wichmann-Kroll α(αZ)n corrections.