Random Phase Approximation Research Articles

Validity of Brink-Axel Hypothesis for calculations of allowed stellar weak rates of heavy nuclei

The knowledge of beta-decay transitional probabilities and Gamow-Teller (GT) strength functions from highly excited states of nuclides is of particular importance for applications to astrophysical network calculations of nucleosynthesis in explosive stellar events. These quantities are challenging to achieve from measurements or computations using various nuclear models. Due to unavailability of feasible alternatives, many theoretical studies often rely on the Brink-Axel (BA) hypothesis, that is, the response of strength functions depends merely on the transition energy of the parent nuclear ground state and is independent of the underlying details of the parent state, for the calculation of stellar rates. BA hypothesis has been used in many applications from nuclear structure determination to nucleosynthesis yield in the astrophysical matter. We explore here the the validity of BA hypothesis in the calculation of stellar beta-decay (BD) and electron capture (EC) weak rates of fp- and fpg-shell nuclides for GT transitions. Strength functions have been computed employing the fully microscopic proton-neutron QRPA (quasi-particle random-phase approximation) within a broad density, ρY e = (10-1011) [g cm−3], and temperature, T = (1−30) [GK], grid relevant to the pre-collapse astrophysical environment. Our work provides evidence that the use of the approximation based on the BA hypothesis does not lead to reliable calculations of excited states strength functions under extreme temperature-density conditions characteristic of presupernova and supernova evolution of massive stars. Weak rates obtained by incorporating the BA hypothesis in the calculation of strength functions substantially deviate from the rates based on the state-by-state microscopically calculated strength functions. Deviation in the two calculations becomes significant as early as neon burning phases of massive stars. The deviation in the calculation of BD rates is even more pronounced, reaching up to three orders of magnitude.

Unveiling protein-protein interaction potential through Monte Carlo simulation combined with small-angle X-ray scattering

Protein interactions are investigated under different conditions of lysozyme concentration, temperature and ionic strength by means of in-solution small angle X-Ray scattering (SAXS) experiments and Monte Carlo (MC) simulations. Initially, experimental data were analysed through a Hard-Sphere Double Yukawa (HSDY) model combined with Random Phase Approximation (RPA), a closure relationship commonly used in the literature for monodisperse systems. We realized by means of MC that the HSDY/RPA modelling fails to describe the protein-protein pair potential for moderated and dense systems at low ionic strength, mainly due to inherent distortions of the RPA approximation. Our SAXS/MC results thus show that lysozyme concentrations between 2 (diluted) and 20 mg/mL (not crowded) present similar protein-protein pair potential preserving the values of surface net charge around 7 e, protein diameter of 28 Å, decay range of attractive well potential of 3 Å and a depth of the well potential varying from 1 to 5 kBT depending on temperature and salt addition. Noteworthy, we here propose a novel method to analyse the SAXS data from interacting proteins through MC simulations, which overcomes the deficiencies presented by the use of a closure relationship. Furthermore, this new methodology of combining SAXS with MC simulations gives a step forward to investigate more complex systems as those composed of a mixture of proteins of distinct species presenting different molecular weights (and hence sizes) and surface net charges at low, moderate and very dense systems.

Enhanced DFT predictions of the structural and optoelectronic properties of MoTe2 for high performance photodetection: Application to GW-based functionals and Hubbard U and V corrections

Molybdenum ditelluride (MoTe2) is a promising two-dimensional material with ultimate prospective usage in high performance photodetection devices. In this study, we elucidate how this may be revealed and discuss how structural and optoelectronic properties of MoTe2 can be numerically accurately simulated since earlier experimental and theoretical studies on the bandgap of MoTe2 produced contradictory findings. In doing so, GW-based functionals using Hubbard U and V corrections are included in density functional theory (DFT) calculations to improve bandgap estimations. Interestingly, we reliably demonstrated that the estimated values of the bandgaps of 0.83 eV and 0.73 eV obtained, respectively, within this framework of DFT+U+V and GW, perfectly match the reported experimental results. Specifically, the quantum espresso simulation package is used for accurate DFT calculations allowing thereby a comprehensive investigation of the impact of the Hubbard U correction on the bandgap of MoTe2. Additionally, the optical absorption spectrum is examined for both GW and RPA levels of theory using the Yambo simulation tool, allowing for a readily distinctly identification of the material’s light absorption spectrum. Contrasted by previous theoretical results, the random phase approximation (RPA) approach, which performs quite well in showing increased optical efficiency, reveals its effectiveness for obtaining appreciable gains in the values of the real, imaginary, refractive index, and extinction coefficient. The expected trends obtained with GW-based functionals using Hubbard U and V corrections approximate methods are encouraging, and altogether support ongoing attempts to optimize the physical properties of MoTe2 for high-performance photodetection systems by offering more precise bandgap predictions and valuable insights related particularly to the optical properties.

Theoretical study of interactions and structural and thermodynamical properties of nanopores within bilayer-membranes: Experimental inspiration

In this work, we consider a bilayer-membrane which is crossed by an assembly of (parallel) nanopores formed generally by peptide molecules. The deformations and thermal fluctuations of this bilayer-membrane give rise to repulsive effective pair-interactions between the parallel nanopores. Some recent experiment has revealed that the repulsive effective pair-potentials, as function of distance between adjacent nanopores, are of Born-Mayer type (soft-potential). Beside the repulsive forces, the nanopores mutually attract through the van der Waals forces. Our main goal is an extensive theoretical study of the structural and thermodynamical properties of the nanopores we consider as a dense gas system. When the bath temperature is fixed to some value (room temperature), the only remaining pertinent parameter of discussion is the nanopore-density, denoted as n, or equivalently, the peptide-molar-fraction, P/L. First, we propose a closer expression of the effective pair-potentials taking into account recent experimental measurements dealt with many lipid-bilayers (Gramicidin/DLPC, Gramicidin/C12EO5...). Second, we classify these effective pair-potentials in terms of the nanopore-density, and in particular, we show the existence of a typical nanopore-density, nc, below which the total pair-potential exhibits an energy-barrier which prevents the coagulation of the nanopores. When the nanopore-density reaches threshold, nc, the energy-barrier ceases to exist, and beyond this threshold, one assists to a complete coagulation of the nanopores. Third, we determine an exact theoretical expression of the structure factor of the nanopores, as a function of the wave-vector, within the framework of Random Phase Approximation, using a hard-disk model as a reference system. Finally, from the obtained structure factor, we extract the thermodynamical properties of the integrated nanopores, such as the virial pressure (state of equation), the isothermal compressibility and the chemical potential which are nanopore-density dependent.

Thermodynamics of Highly Interacting Blend PCHMA/dPS by TOF-SANS.

We investigate the thermodynamics of a highly interacting blend of poly(cyclohexyl methacrylate)/deuterated poly(styrene) (PCHMA/dPS) with small-angle neutron scattering (SANS). This system is experimentally challenging due to the proximity of the blend phase boundary (>200 °C) and degradation temperatures. To achieve the large wavenumber q-range and flux required for kinetic experiments, we employ a SANS diffractometer in time-of-flight (TOF) mode at a reactor source and ancillary microscopy, calorimetry, and thermal gravimetric analysis. Isothermal SANS data are well described by random-phase approximation (RPA), yielding the second derivative of the free energy of mixing (G″), the effective interaction (χ̅) parameter, and extrapolated spinodal temperatures. Instead of the Cahn-Hilliard-Cook (CHC) framework, temperature (T)-jump experiments within the one-phase region are found to be well described by the RPA at all temperatures away from the glass transition temperature, providing effectively near-equilibrium results. We employ CHC theory to estimate the blend mobility and G″(T) conditions where such an approximation holds. TOF-SANS is then used to precisely resolve G″(T) and χ̅(T) during T-jumps in intervals of a few seconds and overall timescales of a few minutes. PCHMA/dPS emerges as a highly interacting partially miscible blend, with a steep dependence of G″(T) [mol/cm3] = -0.00228 + 1.1821/T [K], which we benchmark against previously reported highly interacting lower critical solution temperature (LCST) polymer blends.

Quantifying the Impact of Halogenation on Intermolecular Interactions and Binding Modes of Aromatic Molecules.

Halogenation of aromatic molecules is frequently used to modulate intermolecular interactions with ramifications for optoelectronic and mechanical properties. In this work, we accurately quantify and understand the nature of intermolecular interactions in perhalogenated benzene (PHB) clusters. Using benchmark binding energies from the fixed-node diffusion Monte Carlo (FN-DMC) method, we show that generalized Kohn-Sham semicanonical projected random phase approximation (GKS-spRPA) plus approximate exchange kernel (AKX) provides reliable interaction energies with mean absolute error (MAE) of 0.23 kcal/mol. Using the GKS-spRPA+AXK method, we quantify the interaction energies of several binding modes of PHB clusters ((C6X6)n; X = F, Cl, Br, I; n = 2, 3). For a given binding mode, the interaction energies increase 3-4 times from X = F to X = I; the X-X binding modes have energies in the range of 2-4 kcal/mol, while the π-π binding mode has interaction energies in the range of 4-12 kcal/mol. SAPT-DFT-based energy decomposition analysis is then used to show that the equilibrium geometries are dictated primarily by the dispersion and exchange interactions. Finally, we test the accuracy of several dispersion-corrected density functional approximations and show that only the r2SCAN-D4 method has a low MAE and correct long-range behavior, which makes it suitable for large-scale simulations and for developing structure-function relationships of halogenated aromatic systems.

Drift phase resolved diffusive radiation belt model: 1. Theoretical framework

Most physics-based models provide a coarse three-dimensional representation of radiation belt dynamics at low time resolution, of the order of a few drift periods. The description of the effect of trapped particle transport on radiation belt intensity is based on the random phase approximation, and it is in one dimension only: the third adiabatic invariant coordinate, akin to a phase-averaged radial distance. This means that these radiation belt models do not resolve the drift phase or, equivalently, the magnetic local time. Yet, in situ measurements suggest that radiation belt intensity frequently depends on magnetic local time, at least transiently, such as during active times. To include processes generating azimuthal variations in trapped particle fluxes and to quantify their relative importance in radiation belt energization, an improvement in the spatiotemporal resolution of the radiation belt models is required. The objective of this study is to pave the way for a new generation of diffusive radiation belt models capable of retaining drift phase information. Specifically, we highlight a two-dimensional equation for the effects of trapped particle transport on radiation belt intensity. With a theoretical framework that goes beyond the radial diffusion paradigm, the effects of trapped particle bulk motion, as well as diffusion, are quantified in terms of Euler potentials, α,β, quantities akin to the radial and azimuthal directions. This work provides the theoretical foundations underlying the drift phase resolved transport equation for radiation belt dynamics. It also brings forward the concept of azimuthal diffusion as a phase-mixing agent.

ISOSCALAR DIPOLE RESPONSE IN 92Mo AND 100Mo ISOTOPES

In this work, the Isoscalar (IS) Giant Dipole Resonance (GDR) and Pygmy Dipole Resonance (PDR) of 92Mo and 100Mo Isotopes were calculated in the farmwork of the self-consistent quasi-particle random phase approximation (QRPA) based on the results of Hartree-Fock-Bardeen, Cooper and Schrieffer (HF-BCS) using 10 Skyrme-type interactions: KDE0v1, eMSL08, SKX, SGOI, v080, SKP, SIV, SIII, SKIII, and SGI. The strength distributions of isoscalar dipole response were compared with the available experimental data. Also, we discussed the statistical relation between the centroid energy and the nuclear matter incompressibility KNM.

Higgs response and pair condensation energy in superfluid nuclei

Abstract The pairing correlation in nuclei causes a characteristic excitation, known as the pair vibration, which is populated by the pair transfer reactions. Here we introduce a new method of characterizing the pair vibration by employing an analogy to the Higgs mode, which emerges in infinite superconducting/superfluid systems as a collective vibrational mode associated with the amplitude oscillation of the Cooper pair condensate. The idea is formulated by defining a pair-transfer probe, the Higgs operator, and then describing the linear response and the strength function to this probe. We will show that the pair condensation energy in nuclei can be extracted with use of the strength sum and the static polarizability of the Higgs response. In order to demonstrate and validate the method, we perform numerical analysis for Sn isotopes based on the quasi-particle random phase approximation to the Skyrme–Hartree–Fock–Bogoliubov model. We discuss the possibility of applying this new scheme to pair-transfer experiments.

Many-Body Calculations of Excitons in Two-Dimensional GaN

We present an ab initio study on quasiparticle (QP) excitations and excitonic effects in two-dimensional (2D) GaN based on density-functional theory and many-body perturbation theory. We calculate the QP band structure using GW approximation, which generates an indirect band gap of 4.83 eV (K→Γ) for 2D GaN, opening up 1.24 eV with respect to its bulk counterpart. It is shown that the success of plasmon-pole approximation in treating the 2D material benefits considerably from error cancellation. On the other hand, much better gaps, comparable to GW ones, could be obtained by correcting the Kohn–Sham gap with a derivative discontinuity of the exchange–correlation functional at much lower computational cost. To evaluate excitonic effects, we solve the Bethe–Salpeter equation (BSE) starting from Kohn–Sham eigenvalues with a scissors operator to open the single-particle gap. This approach yields an exciton binding energy of 1.23 eV in 2D GaN, which is in good agreement with the highly demanding GW-BSE results. The enhanced excitonic effects due to reduced dimensionality are discussed by comparing the optical spectra from BSE calculations with that by random-phase approximation (RPA) for both the monolayer and bulk GaN in wurtzite phase. Additionally, we find that the spin–orbit splitting of excitonic peaks is noticeable in 2D GaN but buried in the bulk crystal.

Bandgap narrowing in zincblende III–V semiconductors: Finite-temperature full random-phase approximation and general analytical model

The bandgap narrowing (BGN) in zincblende III–V semiconductors is calculated in a finite-temperature full Random-Phase Approximation (RPA) formalism based on an isotropic dispersion model. The cases of n-type and p-type quasi-neutral regions and the case of a neutral electron–hole plasma are elaborated for the technologically important materials GaAs, AlAs, InAs, GaP, InP, GaSb, InSb, zb-GaN, zb-InN, Al0.3Ga0.7As GaAs0.5Sb0.5, InP0.69Sb0.31, InAs0.4P0.6, InAs0.4Sb0.6, In0.52Al0.48As In0.49Ga0.51P, In0.53Ga0.47As In0.5Ga0.5Sb, and zb-Ga0.5In0.5N (60 cases). In quasi-neutral regions, the correlation energy of the interaction between carriers and ionized dopants adds two terms to the total BGN. At low temperatures, inefficient screening makes the hole term dominant in n-type materials with a large ratio of the valence band to the conduction band (CB) density-of-states. The inclusion of the CB nonparabolicity is decisive here, as it prevents a diverging BGN at high concentrations. For all 60 cases, the BGN is evaluated in the temperature range from 0 to 500 K. A strong temperature dependence over the whole density range is observed in all direct n-type materials. Otherwise, the temperature dependence quickly ceases with increasing density. An analytical model of BGN without material-dependent free fit parameters is derived and compared with the full-RPA results.

Nuclear Spin-Isospin Response within the Fayans Functional

An effective approximation to a fully self-consistent global description of the total force function of b decay within the framework of the theory of finite Fermi systems is presented, based on the calculation of ground states within the framework of the modified energy density functional of Fayans et al. (DF3-f) and the continuum quasiparticle random phase approximation (CQRPA). The isovector parameter ℎ2− of the volume part of the functional has been refined, the permissible range of which was determined earlier by us from restrictions on the parameters of the equation of state for nuclear matter—the symmetry energy and its derivative at equilibrium density, obtained from a joint analysis of the value of the ‘‘neutron skin’’ ΔRnp of the nuclei 208Pb and 48Ca, found in the PREX-II and CREX experiments, results of ab initio calculations of the properties of the ground states of nuclei with the interaction of N3LO and systematics of data on the masses of neutron stars from astrophysical observations. New calculations of the Gamow–Teller strength functions for the reference doubly magic nuclei 208Pb and 132Sn, as well as for the nucleus 130Sn with developed neutron pairing have been carried out. In the proposed model, the global DF3-a + CQRPA calculations of beta-decay half-lives of heavy (quasi)spherical nuclei with Z = 81–83 and T1/2 240 s are conducted. Experimental lifetimes are described with accuracy up to factor 5.

Effective Interaction between Homo- and Heteropolymer Block of Poly(n-butyl acrylate)-b-poly(methyl methacrylate-r-styrene) Diblock Copolymers.

We investigated the segregation behavior of a molten diblock copolymer, poly(n-butyl acrylate)-b-poly(methyl methacrylate-r-styrene) (PBA-b-P(MMA-r-S)), wherein styrene (S) is incorporated as a comonomer in the second block to modulate the effective interaction between homopolymer and a random copolymer block. The temperature dependence of the effective interaction parameter χeff between n-butyl acrylate (BA) and the average monomer of the MMA-r-S random block was evaluated from small-angle X-ray scattering (SAXS) analysis using the random phase approximation (RPA) approach. The calculated χeff, as a function of the styrene fraction in the random copolymer block, shows a good agreement with the mean-field binary interaction model. This consistency indicates that the effective interaction between component BA and the average monomer of the random copolymer block is smaller than the interactions between pure components (χBA,MMA,χBA,S). The present study suggests that the introduction of a random copolymer block to a block copolymer can effectively reduce the degree of incompatibility of the block copolymer system without altering the constituent species, which may serve as a viable methodology in designing novel thermoplastic elastomers based on triblock or multiblock copolymers.

Predicting disordered regions driving phase separation of proteins under variable salt concentration

We investigate intrinsically disordered regions (IDRs) of phase separating proteins regarding their impact on liquid-liquid phase separation (LLPS) of the full protein. Our theoretical approach uses a mean-field theory that accounts for sequence-dependent electrostatic interactions via a Random Phase Approximation (RPA) and in addition allows for variable salt concentration for the condensed and dilute protein phases. The numerical solution of the complete phase diagrams together with the tie lines that we derive for this model system leaves two parameters to be determined by fitting experimental data on concentrations of all species involved in the system. For our comparisons, we focus on two proteins, PGL-3 and FUS, known to undergo LLPS. For PGL-3 we predict that its long IDR near the C-terminus promotes LLPS, which we validate through direct comparison with in vitro experimental results under the same physiological conditions. For the structurally more complex protein FUS the role of the low complexity (LC) domain in LLPS has been intensively studied. Apart from the LC domain we here investigate theoretically two IDRs, one near the N-terminus and another near the C-terminus. Our theoretical analysis of these domains predict that the IDR at the N-terminus (aa 1-285) is the main driver of LLPS of FUS by comparison to in vitro experiments of the full length protein under the same physiological temperature and salt conditions.

Magnetic ground state and perturbations of the distorted kagome Ising metal TmAgGe

Magnetic order and excitations of the distorted kagome intermetallic magnet TmAgGe are explored using a variety of methods, including single-crystal neutron diffraction, inelastic neutron scattering, Monte Carlo simulations, and the random phase approximation. The magnetic properties are governed by strong, local single-ion anisotropy and geometrically frustrated magnetic exchanges. The authors establish multi-k structures at several different magnetic field configurations and model effective exchange parameters using field-dependencies of the magnetic neutron diffraction reflections and the weakly dispersive crystal electric field mode.

Excitation spectrum and momentum distribution of the ionic Bose–Hubbard model

We investigate the excitation spectrum and momentum distribution of the ionic Bose–Hubbard model by the standard basis operator method. We derive Green’s functions in the random phase approximation in Mott insulator, superfluid, charge density wave, and supersolid phases. The excitation spectrum has gapped modes and gapless Goldstone modes in the superfluid and supersolid phases. We show that the momentum distribution has a peak at the zone corner in the supersolid phase and the charge density wave phase close to the phase boundary. In addition, we demonstrate that the momentum distribution can be explained by the excitation spectrum and spectral weights of hole excitation modes.

Nuclear ground state correlations

The paper discusses ground state correlations (GSC) in nuclei, which are especially clearly manifested when using the formalism of quantum Green’s functions (FG) and Feynman diagrams. In addition to one-particleone-hole GSC, which appear in the well known random phase approximation method (RPA), there exist and give a noticeable quantitative contribution THE GSCs resulting from the use of configurations that are more complex than in RPA. Namely, configurations containing phonons and configurations containing only three quasiparticles, respectively, the GSC-phon and GSC3. This last case of GSC3 is considered in detail in the present paper. It is shown that GSC3 make a significant quantitative contribution IN THE problems related to the explanation of some characteristics of low-lying excited states (phonons) and transitions between them in even-even nuclei.

Continuum random-phase approximation for (n,γ) reactions on neutron-rich nuclei: Collective effects and resonances

We formulate a microscopic theory to calculate cross section of the radiative neutron capture reaction on neutron-rich nuclei using the continuum random-phase approximation (cRPA) to the time-dependent density functional theory (TDDFT). With an intention of applying to the $r$ process, for which the statistical reaction model may not be appropriate, we describe the transition between a initial state of incident neutron and a final state of the $\ensuremath{\gamma}$ decay by means of a single many-body framework of the cRPA-TDDFT. With the cRPA approach, it is possible to describe various excitation modes present in the $(n,\ensuremath{\gamma})$ reaction, including soft dipole excitation, the giant resonances, as well as noncollective excitations and the single-particle resonances. Furthermore, it enables us to describe the $(n,\ensuremath{\gamma})$ reaction where the the final states of the $\ensuremath{\gamma}$ transition are low-lying surface vibrational states. We demonstrate the theory by performing numerical calculation for the reaction $^{139}\mathrm{Sn}(n,\ensuremath{\gamma})^{140}\mathrm{Sn}$. We discuss various new features which are beyond the single-particle model: the presence of narrow and wide resonances originating from noncollective and collective excitations and roles of low-lying quadrupole and octupole vibrational states.

Drag resistivity in double-layer gapped graphene structures

We study the frictional drag phenomenon in a double-layer system made of two parallel gapped graphene layers by calculating the Coulomb drag resistivity. The random-phase approximation is employed to determine the polarizability functions of layers and the frequency-dependent dielectric function of the structure. Our computations illustrate that the Coulomb drag resistivity in double-layer gapped graphene systems show some interesting different features, compared to that in other double-layer ones. Coulomb drag resistivity in the system steadily increases as temperature increases but quickly decreases with the increase in interlayer distance. With small interlayer separations, the drag resistivity behaves as a smoothly increasing function of the bandgap. Nevertheless, with sufficiently large separations, the Coulomb drag resistivity increases with small bandgaps but decreases with larger ones. We observe that a finite bandgap has remarkable contributions to the frictional drag phenomenon, therefore it is necessary to take into account this factor in calculations to make better agreements with experimental works.

Electric dipole response in 156–170Er nuclei

For the first time, this study investigated an energy region that covers both the Pygmy Dipole Resonance (PDR) and the Giant Dipole Resonance (GDR) for a broad set of even-even erbium isotopes. More specifically, translational and Galilean invariant (TGI-) quasiparticle random phase approximation (QRPA) was applied to investigate eight even-even 156–170Er isotopes. Through cross-section calculations, we obtained information about the structure of the GDR and PDR modes, as well as the splitting between the K = 0 and K = 1 branches. The PDR region was explored in more detail by investigating the region up to both 8 MeV and 10 MeV to determine the main distribution area of the PDR. It was found that only the E1 strengths below 8 MeV matched well with the well-known systematics of the PDR.