Random Phase Approximation Calculations Research Articles

E1 and M1 strength functions from average resonance capture data

The average resonance capture (ARC) data measured at different filter beam facilities are re-analyzed. They include all measurements made between 1970 and 1990, but only partially exploited. Updated spectroscopic information on the states of interest as well as on $s$-wave resonance spacing are used to extract the $E1$ and $M1$ photon strength function. This re-evaluation aims at providing experimental information on the $E1$ and $M1$ strength function around the neutron binding energy and in doing so provides also constraints for existing models used in statistical reaction codes. The revised data are compared to the photon strength function extracted from other experimental methods, such as photoneutron data and Oslo-method data. We also compare the ARC data with recent quasiparticle random phase approximation calculations based on the D1M Gogny force. The ratio of the $E1$ to $M1$ strength functions is also analyzed and proposed as a new stringent test for the future elaboration of theoretical models for the dipole strength function.

Hybrid configuration mixing model for odd nuclei

In this work, we introduce a new approach which is meant to be a first step towards complete self-consistent low-lying spectroscopy of odd nuclei. So far, we essentially limit ourselves to the description of a double-magic core plus an extra nucleon. The model does not contain any free adjustable parameter and is instead based on a Hartree-Fock (HF) description of the particle states in the core, together with self-consistent random-phase approximation (RPA) calculations for the core excitations. We include both collective and noncollective excitations, with proper care of the corrections due to the overlap between them (i.e., due to the nonorthonormality of the basis). As a consequence, with respect to traditional particle-vibration coupling calculations in which one can only address single-nucleon states and particle-vibration multiplets, we can also describe states of shell-model types like 2 particle--1 hole. We will report results for $^{49}\mathrm{Ca}$ and $^{133}\mathrm{Sb}$ and discuss future perspectives.

Coincident excitation and radiative decay in electron-nucleus collisions

The distorted-wave Born approximation formalism for the description of the $(e,{e}^{\ensuremath{'}}\ensuremath{\gamma})$ reaction, in which emitted photons and scattered electrons are simultaneously detected, is outlined. Both the Coulomb and the magnetic scattering are fully taken into account. The influence of electron bremsstrahlung is estimated within the plane-wave Born approximation. Recoil effects are also discussed. The formalism is applied for the low-energy $(e,{e}^{\ensuremath{'}}\ensuremath{\gamma})^{92}\mathrm{Zr}$ reaction with excitation of the first collective (${2}_{1}^{+}$) and mixed-symmetry (${2}_{2}^{+}$) states. The corresponding transition charge and current densities are taken from a random-phase approximation (RPA) calculation within the quasiparticle phonon model. It is shown, by this example, in which way the magnetic subshell population of the excited state influences the angular distribution of the decay photon. For these quadrupole excitations the influence of magnetic scattering is only prominent at the backmost scattering angles, where a clear distinction of the photon pattern pertaining to the two states is predicted.

Low-energy modification of the γ strength function of the odd-even nucleus In115

Photoactivation yield measurements on $^{115}\mathrm{In}$ have been performed at the ELSA facility with Bremsstrahlung photon beams over a range of endpoint energies between 4.5 and 18 MeV. The measured photoexcitation yields of the $^{115m}\mathrm{In}$ metastable state are compared with calculated yields using cross sections obtained with different models of the photon strength function. It is shown that additional photon strength with respect to the general Lorentzian model is needed at 8.1 MeV for the calculated yields to reproduce the data. The origin of this extra strength is unclear, because it is compatible with additional strength predicted in both $E1$ and $M1$ photon strength distributions by quasiparticle random-phase approximation calculations using the Gogny D1S force.

Robust upward dispersion of the neutron spin resonance in the heavy fermion superconductor Ce1-xYbxCoIn5.

The neutron spin resonance is a collective magnetic excitation that appears in the unconventional copper oxide, iron pnictide and heavy fermion superconductors. Although the resonance is commonly associated with a spin-exciton due to the d(s±)-wave symmetry of the superconducting order parameter, it has also been proposed to be a magnon-like excitation appearing in the superconducting state. Here we use inelastic neutron scattering to demonstrate that the resonance in the heavy fermion superconductor Ce1−xYbxCoIn5 with x=0, 0.05 and 0.3 has a ring-like upward dispersion that is robust against Yb-doping. By comparing our experimental data with a random phase approximation calculation using the electronic structure and the momentum dependence of the -wave superconducting gap determined from scanning tunnelling microscopy (STM) for CeCoIn5, we conclude that the robust upward-dispersing resonance mode in Ce1−xYbxCoIn5 is inconsistent with the downward dispersion predicted within the spin-exciton scenario.

Nuclear response functions with finite-range Gogny force: Tensor terms and instabilities

A fully-antisymmetrized random phase approximation calculation employing the continued fraction technique is performed to study nuclear matter response functions with the finite range Gogny force. The most commonly used parameter sets of this force, as well as some recent generalizations that include the tensor terms are considered and the corresponding response functions are shown. The calculations are performed at the first and second order in the continued fraction expansion and the explicit expressions for the second order tensor contributions are given. Comparison between first and second order continued fraction expansion results are provided. The differences between the responses obtained at the two orders turn to be more pronounced for the forces including tensor terms than for the standard Gogny ones. In the vector channels the responses calculated with Gogny forces including tensor terms are characterized by a large heterogeneity, reflecting the different choices for the tensor part of the interaction. For sake of comparison the response functions obtained considering a G-matrix based nuclear interaction are also shown. As first application of the present calculation, the possible existence of spurious finite-size instabilities of the Gogny forces with or without tensor terms has been investigated. The positive conclusion is that all the Gogny forces, but the GT2 one, are free of spurious finite-size instabilities. In perspective, the tool developed in the present paper can be inserted in the fitting procedure to construct new Gogny-type forces.

Nature of ground and electronic excited states of higher acenes

Higher acenes have drawn much attention as promising organic semiconductors with versatile electronic properties. However, the nature of their ground state and electronic excited states is still not fully clear. Their unusual chemical reactivity and instability are the main obstacles for experimental studies, and the potentially prominent diradical character, which might require a multireference description in such large systems, hinders theoretical investigations. Here, we provide a detailed answer with the particle-particle random-phase approximation calculation. The (1)Ag ground states of acenes up to decacene are on the closed-shell side of the diradical continuum, whereas the ground state of undecacene and dodecacene tilts more to the open-shell side with a growing polyradical character. The ground state of all acenes has covalent nature with respect to both short and long axes. The lowest triplet state (3)B2u is always above the singlet ground state even though the energy gap could be vanishingly small in the polyacene limit. The bright singlet excited state (1)B2u is a zwitterionic state to the short axis. The excited (1)Ag state gradually switches from a double-excitation state to another zwitterionic state to the short axis, but always keeps its covalent nature to the long axis. An energy crossing between the (1)B2u and excited (1)Ag states happens between hexacene and heptacene. Further energetic consideration suggests that higher acenes are likely to undergo singlet fission with a low photovoltaic efficiency; however, the efficiency might be improved if a singlet fission into multiple triplets could be achieved.

N-block separable random phase approximation: dipole oscillations in sodium clusters and fullerene

We generalize the schematic model based on the Random Phase Approximation (RPA) with separable interaction, to a collection of subspaces of ph excitations which interact with different coupling constants. This ansatz notably lowers the numerical effort involved, by reducing the RPA eigenvalue problem to a finite small dimensional system of equation. We derive the associated dispersion relation and the normalization condition for the newly defined unknowns of the system. In contrast with the standard separable approach, the present formalism is able to describe more than one collective excitation even in the degenerate limit, giving also access to the nature of the resonance. The theoretical framework is tested investigating the dipolar oscillations in various neutral and singly charged sodium clusters and C60 fullerene with results in good agreement with full RPA calculations and experimental data. It is proven that the 40 eV resonance present in photoabsorption spectra of C60 is a localized surface plasmon.

Gogny interactions with tensor terms

We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations.

Hexagonal boron nitride and water interaction parameters.

The study of hexagonal boron nitride (hBN) in microfluidic and nanofluidic applications at the atomic level requires accurate force field parameters to describe the water-hBN interaction. In this work, we begin with benchmark quality first principles quantum Monte Carlo calculations on the interaction energy between water and hBN, which are used to validate random phase approximation (RPA) calculations. We then proceed with RPA to derive force field parameters, which are used to simulate water contact angle on bulk hBN, attaining a value within the experimental uncertainties. This paper demonstrates that end-to-end multiscale modeling, starting at detailed many-body quantum mechanics and ending with macroscopic properties, with the approximations controlled along the way, is feasible for these systems.

Effect of the Pauli principle on the deformed quasiparticle random-phase approximation calculations and its consequence forβ-decay calculations of deformed even-even nuclei

In this work, I take into consideration the Pauli exclusion principle (PEP) in the quasiparticle random-phase approximation (QRPA) calculations for the deformed systems by replacing the traditional quasiboson approximation (QBA) with the renormalized one. With this new formalism, the parametrization of QRPA calculations has been changed and the collapse of QRPA solutions could be avoid for realistic ${g}_{pp}$ values. I further find that the necessity of the renormalization parameter of particle-particle residual interaction ${g}_{pp}$ in QRPA calculations is due to the exclusion of PEP. So with the inclusion of PEP, I could easily extend the deformed QRPA calculations to the less-explored region where lack of experimental data prevent effective parametrization of ${g}_{pp}$ for QRPA methods. With this theoretical improvement, I give predictions of weak decay rates for even-even isotopes in the rare-earth region and compare the results with existing calculations.

Hubbard-Ucorrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS,TiO2, and NiO

In non-self-consistent calculations of the total energy within the random-phase approximation (RPA) for electronic correlation, it is necessary to choose a single-particle Hamiltonian whose solutions are used to construct the electronic density and non-interacting response function. Here we investigate the effect of including a Hubbard-$U$ term in this single-particle Hamiltonian, to better describe the on-site correlation of 3$d$ electrons in the transition metal compounds ZnS, TiO$_2$ and NiO. We find that the RPA lattice constants are essentially independent of $U$, despite large changes in the underlying electronic structure. We further demonstrate that the non-self-consistent RPA total energies of these materials have minima at nonzero $U$. Our RPA calculations find the rutile phase of TiO$_2$ to be more stable than anatase independent of $U$, a result which is consistent with experiments and qualitatively different to that found from calculations employing $U$-corrected (semi)local functionals. However we also find that the +$U$ term cannot be used to correct the RPA's poor description of the heat of formation of NiO.

Effects of symmetry energy and momentum dependent interaction on low-energy reaction mechanisms

We study the dipole response associated with the Pygmy Dipole Resonance (PDR) and the Isovector Giant Dipole Resonance (IVGDR), in connection with specific properties of the nuclear effective interaction (symmetry energy and momentum dependence), in the neutron-rich systems $^{68}$Ni, $^{132}$Sn and $^{208}$Pb. We perform our investigation within a microscopic transport model based on the Landau-Vlasov kinetic equation. We observe that the peak energies of PDR and IVGDR are shifted to higher values when employing momentum dependent interactions, with respect to the results obtained neglecting momentum dependence. The calculated energies are close to the experimental values and similar to the results obtained in Hartree-Fock (HF) with Random Phase Approximation (RPA) calculations.

Gamow-Teller strength and beta-decay rate within the self-consistent deformed pnQRPA

In recent years fully consistent quasiparticle random-phase approximation (QRPA) calculations using finite range Gogny force have been performed to study electromagnetic excitations of several axially-symmetric deformed nuclei up to the 238U. Here we present the extension of this approach to the charge-exchange nuclear excitations (pnQRPA). In particular we focus on the Gamow-Teller (GT) excitations which are known to play a crucial role in several fields of physics, in particular in nuclear astrophysics (stellar evolution and nucleosynthesis). A comparison of the predicted GT strength distribution with existing experimental data is presented. The role of nuclear deformation is shown. Special attention is paid to β-decay halflives calculations for which experimental data exist and for specific isotonic chains of relevance for the r-process nucleosynthesis.

Effects of 2p-2h configurations on low-energy dipole states in neutron-rich N=80, 82 and 84 isotones

Starting from the Skyrme interaction SLy4 we study the effects of phonon-phonon coupling on the low-energy electric dipole response in 130−134 Sn, 132−136 Te and 134−138 Xe. Our calculations are performed within the finite-rank separable approximation, which enables one to perform quasiparticle random phase approximation calculations in very large two-quasiparticle configuration spaces. A dependence of the pygmy dipole resonance strengths on the neutron skin thickness is found. The inclusion of the two-phonon configurations gives a considerable contribution to the low-lying strength.

Collective Excitations in the $^{14}$C Nucleus Populated by the $^{12}$C($^{18}$O,$^{16}$O) Reaction at 84 MeV

The 12C(18O,16O)14C reaction at 84 MeV incident energy has been explored up to high excitation energy of the residual nucleus thanks to the use of the MAGNEX spectrometer to detect the ejectiles. In the region above the two-neutron separation energy, a resonance at 16.9 MeV has been observed. Continuum quasi-particle random phase approximation calculations of the response function, corresponding to the transfer of a neutron pair to the 12C nucleus, have been performed to investigate the possible presence of the Giant Pairing Vibration in that energy region.

Shape study of theN=ZnucleusKr72viaβdecay

The $\ensuremath{\beta}$ decay of the $N=Z$ nucleus $^{72}\text{Kr}$ has been studied with the total absorption spectroscopy technique at ISOLDE (CERN). A total $B(\text{GT})=0.79(4){g}_{A}^{2}/4\ensuremath{\pi}$ has been found up to an excitation energy of 2.7 MeV. The $B(\text{GT})$ distribution obtained is compared with predictions from state-of-the-art theoretical calculations to learn about the ground state deformation of $^{72}\text{Kr}$. Although a dominant oblate deformation is suggested by direct comparison with quasiparticle random phase approximation (QRPA) calculations, beyond-mean-field and shell-model calculations favor a large oblate-prolate mixing in the ground state.

Low-energy spin-wave excitations in amplitude-modulated magnetic structure of PrNi2Si2

Inelastic neutron scattering (INS) experiments and random phase approximation calculations have been used to investigate the low-energy spin-wave excitations in PrNi2Si2. The modulated magnitude of the ordered magnetic moments of Pr3+ ions implies that the associate, longitudinally polarized magnetic excitations are more intense and dispersive than the usual transverse spin waves. Within the random phase approximation the results are in good overall agreement with the predictions made by the model determined previously from the paramagnetic excitations. The most unusual observation is the well-defined amplitude mode detected close to the magnetic Bragg point existing simultaneously with the phason mode. At low energies, an extra mode is observed to hybridize with the magnetic phasons in the neighborhood of the magnetic Brillouin zone center. A magnetoelastic interaction between the magnetic excitations and the longitudinal phonons is able to explain part of the disturbances, but it is concluded that the extra mode must be of some other, unknown origin.

Isoscalar giant resonances inZr90,92,94

Isoscalar giant resonances in $^{90,92,94}\text{Zr}$ have been studied with inelastic scattering of 240 MeV $\ensuremath{\alpha}$ particles at small angles including ${0}^{\ensuremath{\circ}}$. A significant fraction of the energy-weighted sum rule (EWSR) was found for isoscalar $E0$ (106%,103%,106%), $E1$ (64%,53%,96%), $E2$ (92%,93%,67%) and high energy octupole $E3$ (59%,69%,58%) resonances in $^{90,92,94}\text{Zr}$ respectively. Hartree-Fock random phase approximation (RPA) calculations were made for each multipole using the KDE0v1 Skyrme-type effective nucleon-nucleon interaction and the results are compared to the experimental distributions.

Comparative study of van der Waals corrections to the bulk properties of graphite

Graphite is a stack of honeycomb (graphene) layers bound together by nonlocal, long-range van der Waals (vdW) forces, which are poorly described by density functional theory (DFT) within local or semilocal exchange-correlation functionals. Several approximations have been proposed to add a vdW correction to the DFT total energies (Stefan Grimme (D2 and D3) with different damping functions (D3-BJ), Tkatchenko–Scheffler (TS) without and with self-consistent screening (TS + SCS) effects). Those corrections have remarkly improved the agreement between our results and experiment for the interlayer distance (from 3.8 to 0.1%) and high-level random-phase approximation (RPA) calculations for interlayer binding energy (from 56.2 to 0.6%). We report a systematic investigation of various structural, energetic and electron properties with the aforementioned vdW corrections followed by comparison with experimental and theoretical RPA data. Comparison between the resulting relative errors shows that the TS + SCS correction provides the best results; the other corrections yield significantly larger errors for at least one of the studied properties. If considerations of computational costs or convergence problems rule out the TS + SCS approach, we recommend the D3-BJ correction. Comparison between the computed -splitting and experimental results shows disagreements of 10% or more with all vdW corrections. Even the computationally more expensive hybrid PBE0 has proved unable to improve the agreement with the measured splitting. Our results indicate that improvements of the exchange-correlation functionals beyond the vdW corrections are necessary to accurately describe the band structure of graphite.