Random Phase Approximation Model Research Articles

Investigation of nuclear structure and [formula omitted]-decay properties of As isotopes

The nuclear ground state properties of 67−80As nuclei have been investigated within the framework of relativistic mean field (RMF) approach. The RMF model with density-dependent (DD-ME2) interaction is utilized for the calculation of potential energy curves and the nuclear ground-state deformation parameters (β2) of selected As isotopes. Later, the β-decay properties of As isotopes were studied using the proton–neutron quasi particle random phase approximation (pn-QRPA) model. These include Gamow Tellar (GT) strength distributions, log ft values, β-decay half-lives, stellar β± decays and stellar electron/positron capture rates. The β2 values computed from RMF model were employed in the pn-QRPA model as an input parameter for the calculations of β-decay properties for 67−80As. The calculated log ft values were in decent agreement with the measured data. The predicted β-decay half-lives matched the experimental values within a factor of 10. The stellar rates were compared with the shell model results. Only at high temperature and density values, the sum of β+ and electron capture rates had a finite contribution. On the other hand, the sum of β− and positron capture rates were sizeable only at low density and high temperature values. For all such cases, the pn-QRPA rates were found to be bigger than the shell model rates up to a factor of 33 or more. The findings reported in the current investigation could prove valuable for simulating the late-stage stellar evolution of massive stars.

Re-examination of nuclear structure properties and shape co-existence of nuclei around A ∼ 70

We re-examine the nuclear structure properties of waiting point nuclei around A ∼ 70 using the interacting boson model-1 (IBM-1) and the relativistic mean field (RMF) model. Effective density-dependent meson-exchange functional (DD-ME2) and density-dependent point-coupling functional (DD-PC1) were used for the RMF calculations. We calculated the energy levels, the geometric shapes, binding and separation energies of nucleons and quadrupole deformation parameters (β2). The shape co-existence phenomena in A ∼ 70 nuclei (68Se, 70Se, 70Br, 70Kr, 72Kr, 74Kr, 74Rb and 74Sr) was later investigated. Spherical and deformed shapes of the selected waiting point nuclei were computed using the IBM-1 and RMF models, respectively. The proton-neutron quasiparticle random phase approximation (pn-QRPA) model was used to calculate β-decay properties (Gamow-Teller strength distributions, β-decay half-lives and branching ratios) of selected nuclei as a function of β2. The results revealed a significant variation in calculated half-lives and Gamow-Teller strength distributions as the shape parameter was changed. The β2 computed via DD-ME2 functional resulted in half-lives in best agreement with the measured data.

Role of surface roughness potential on temperature dependent scattering rate of double layer graphene structure

In this work we have reported the role of surface roughness potential (SRP) on scattering rate of double layer graphene structure (DLGS) in presence of different dielectric environment, interlayer distance and temperature. We have also compared it with the scattering contribution from charged impurity (CI). In our scattering rate calculation, temperature dependent screening effect is incorporated using the random phase approximation (RPA) model. The scattering due to SRP depends on height of ripples and therefore eventually, the impurity concentration and temperature. The temperature also plays an important role in screening of the SRP. The SRP has proved to be an important factor in the low Coulomb impurity regime, while in high impurity samples SRP can be neglected. We found that above room temperature, the scattering due to SRP decreases gradually. Dielectric constant and thickness of spacer material contribute decisively to total scattering rate of DLGS.

Re-analysis of temperature dependent neutron capture rates and stellar β-decay rates of 95-98Mo

The neutron capture rates and temperature dependent stellar beta decay rates of Mo isotopes are investigated within the framework of the statistical code TALYS v1.96 and the proton neutron quasi particle random phase approximation (pn-QRPA) model. The Maxwellian average cross-section (MACS) and neutron capture rates for the Mo(n,γ) Mo radiative capture process are analyzed within the framework of the statistical code TALYS v1.96 based on the phenomenological nuclear level density model and gamma strength functions. The present model-based computations for the MACS are comparable to the existing measured data. The sensitivity of stellar weak interaction rates to various densities and temperatures is investigated within the framework of the pn-QRPA model. Particular attention is paid to the impact of thermally filled excited states in the decaying nuclei ( Mo) on electron emission and positron capture rates. Furthermore, we compare the neutron capture rates and stellar beta decay rates. It is found that neutron capture rates are higher than stellar beta decay rates at both lower and higher temperatures.

Re-examination of effects of pairing gaps on charge-changing transitions

We re-examine the effects of pairing gaps on charge-changing transitions and the associated β-decay half-lives. Calculations are performed using the proton-neutron quasiparticle random phase approximation (pn-QRPA) model for 250 nuclei possessing astrophysical significance. Pairing gaps between like nucleons are key model parameters in the pn-QRPA approach. Three different values of empirically computed pairing gaps were used as input parameters in our nuclear model. Changing the pairing gap values significantly altered the Gamow-Teller distributions including the total strength and centroid values. The β-decay half-lives also changed substantially. The half-lives computed via the three-term pairing formula, based on separation energies of nucleons, were in best agreement with the measured data.

Nuclear structure properties and weak interaction rates of even–even Fe isotopes

Nuclear structure properties and weak interaction rates of neutron-rich even–even iron (Fe) isotopes (A = 50 – 70) are investigated using the Interacting Boson Model-1 (IBM-1) and the proton–neutron Quasiparticle Random Phase Approximation (pn-QRPA) model. The IBM-1 is used for the calculation of energy levels and the B(E2) values of neutron-rich Fe isotopes. Later their geometry was predicted within the potential energy formalism of the IBM-1 model. Weak interaction rates on neutron-rich nuclei are needed for the modeling and simulation of presupernova evolution of massive stars. In the current study, we investigate the possible effect of nuclear deformation on stellar rates of even–even Fe isotopes. The pn-QRPA model is applied to calculate the weak interaction rates of selected Fe isotopes using three different values of deformation parameter. It is noted that, in general, bigger deformation values led to smaller total strength and larger centroid values of the resulting Gamow–Teller distributions. This later translated to smaller computed weak interaction rates. The current finding warrants further investigation before it may be generalized. The reported stellar rates are up to 4 orders of magnitude smaller than previous calculations and may bear astrophysical significance.

Electric dipole polarizability of magic nuclei

The correlations between the electric dipole polarizability and neutron skin thickness are studied by the magic nuclei 40,48Ca, 68,78Ni, 132Sn, and 208Pb. The strength distribution of the E1 transitions is calculated within the random phase approximation model based on the Skyrme nuclear energy density functional. A comparison with the experimental data has allowed us to constrain the value of the nuclear symmetry energy J = 30–37 MeV.

Re-Examination of the Effect of Pairing Gaps on Gamow–Teller Strength Distributions and β-Decay Rates

β-decay is one of the key factors for understanding the r-process and evolution of massive stars. The Gamow–Teller (GT) transitions drive the β-decay process. We employ the proton–neutron quasiparticle random phase approximation (pn-QRPA) model to calculate terrestrial and stellar β-decay rates for 50 top-ranked nuclei possessing astrophysical significance according to a recent survey. The model parameters of the pn-QRPA model affect the predicted results of β-decay. The current study investigates the effect of nucleon–nucleon pairing gaps on charge-changing transitions and the associated β decay rates. Three different values of pairing gaps, namely TF, 3TF, and 5TF, were used in our investigation. It was concluded that both GT strength distributions and half-lives are sensitive to pairing gap values. The 3TF pairing gap scheme, in our chosen nuclear model, resulted in the best prediction with around 80% of the calculated half-lives within a factor 10 of the measured ones. The 3TF pairing scheme also led to the calculation of the biggest β-decay rates in stellar matter.

Structure of Single-Chain Nanoparticles under Crowding Conditions: A Random Phase Approximation Approach.

The conformation of poly(methyl methacrylate) (PMMA)-based single-chain nanoparticles (SCNPs) and their corresponding linear precursors in the presence of deuterated linear PMMA in deuterated dimethylformamide (DMF) solutions has been studied by small-angle neutron scattering (SANS). The SANS profiles were analyzed in terms of a three-component random phase approximation (RPA) model. The RPA approach described well the scattering profiles in dilute and crowded solutions. Considering all the contributions of the RPA leads to an accurate estimation of the single chain form factor parameters and the Flory-Huggins interaction parameter between PMMA and DMF. The value of the latter in the dilute regime indicates that the precursors and the SCNPs are in good solvent conditions, while in crowding conditions, the polymer becomes less soluble.

Machine Learning Density Functionals from the Random-Phase Approximation.

Kohn-Sham density functional theory (DFT) is the standard method for first-principles calculations in computational chemistry and materials science. More accurate theories such as the random-phase approximation (RPA) are limited in application due to their large computational cost. Here, we use machine learning to map the RPA to a pure Kohn-Sham density functional. The machine learned RPA model (ML-RPA) is a nonlocal extension of the standard gradient approximation. The density descriptors used as ingredients for the enhancement factor are nonlocal counterparts of the local density and its gradient. Rather than fitting only RPA exchange-correlation energies, we also include derivative information in the form of RPA optimized effective potentials. We train a single ML-RPA functional for diamond, its surfaces, and liquid water. The accuracy of ML-RPA for the formation energies of 28 diamond surfaces reaches that of state-of-the-art van der Waals functionals. For liquid water, however, ML-RPA cannot yet improve upon the standard gradient approximation. Overall, our work demonstrates how machine learning can extend the applicability of the RPA to larger system sizes, time scales, and chemical spaces.

Isoscalar Giant Octupole Resonance ISGOR of 116Cd using Self-Consistent Skyrme QRPA

Collective models based on the random phase approximation (RPA) are widely used to accurately depict collective modes of response. They can quickly calculate the strength function for the entire nuclear mass range. The quasi-particle random phase approximation (QRPA), which considers the pairing effect, is an enhanced RPA model. It is anticipated that this effect will be significant for open-shell nuclei. In this work, the self-consistent Skyrme Hartree-Fock-Bardeen, Cooper, and Schrieffer (HF-BCS) and QRPA models have been used to study the isoscalar giant octupole resonance (ISGOR) in the 116Cd isotope. Ten Skyrme-type parameters are utilized in the computations since they may be identified by different values of the incompressibility modulus KMN in nuclear matter. The calculated strength distributions and centroid energy are compared with available experimental data. We saw that the strength distributions varied depending on the type of Skyrme-interaction, and we also observed a definite impact of the KNM values on the centroid energy.

Thermodynamic Interactions in Polydiene/Polyolefin Blends Containing Diverse Polydiene and Polyolefin Units

Thermodynamic interactions were investigated in blends of melts containing 1,4-polyisoprene (1,4-PI) and copolymers of 1,2-polybutadiene (1,2-PBD), poly(ethyl ethylene) (PEE), and/or polyethylene (PE) units. Specifically, two classes of blends were examined: one contained the polydiene 1,4-PI and a diene-olefin copolymer of 1,2-PBD and PEE units (1,2-PBD-co-PEE, with the PEE volume fraction varying from 0 to 1), and the other contained 1,4-PI and a fully olefinic copolymer of PE and PEE units (PE-co-PEE, with the PEE volume fraction varying from 0.05 to 1). The Flory–Huggins interaction parameter, χ, was measured using small-angle neutron scattering (SANS) for homogeneous blends at or close to their critical compositions. SANS data were analyzed through the Zimm method and fitting of the random phase approximation model to extract χ(T). Random copolymer theory (RCT) was applied to understand the resulting χ(T) behavior. In 1,2-PBD-co-PEE/1,4-PI blends, predictions using the RCT model showed excellent agreement with the measured χ(T), indicating the presence of random mixing and dominance of dispersive forces in these blends. By contrast, RCT failed to describe the χ(T) behavior in PE-co-PEE/1,4-PI blends. The PE-co-PEE/1,4-PI blends were further examined using lattice cluster theory and solubility parameter formalism, yet neither approach could explain the χ(T) behavior. The locally correlated lattice model, which correlates the equation of state properties with the polymer blend miscibility, was found to reasonably describe the phase behavior of PE-co-PEE/1,4-PI blends.

Entropic Mixing of Ring/Linear Polymer Blends.

The topological constraints of nonconcatenated ring polymers force them to form compact loopy globular conformations with much lower entropy than unconstrained ideal rings. The closed-loop structure of ring polymers also enables them to be threaded by linear polymers in ring/linear blends, resulting in less compact ring conformations with higher entropy. This conformational entropy increase promotes mixing rings with linear polymers. Here, using molecular dynamics simulations for bead-spring chains, ring/linear blends are shown to be significantly more miscible than linear/linear blends and that there is an entropic mixing, negative χ, for ring/linear blends compared to linear/linear and ring/ring blends. In analogy with small angle neutron scattering, the static structure function S(q) is measured, and the resulting data are fit to the random phase approximation model to determine χ. In the limit that the two components are the same, χ = 0 for the linear/linear and ring/ring blends as expected, while χ < 0 for the ring/linear blends. With increasing chain stiffness, χ for the ring/linear blends becomes more negative, varying reciprocally with the number of monomers between entanglements. Ring/linear blends are also shown to be more miscible than either ring/ring or linear/linear blends and stay in single phase for a wider range of increasing repulsion between the two components.

Implementation of the continuum random phase approximation model in the GENIE generator and an analysis of nuclear effects in low-energy transfer neutrino interactions

We present the implementation and validation of the Hartree-Fock continuum random phase approximation (HF-CRPA) model in the GENIE neutrino-nucleus interaction event generator and a comparison of the subsequent predictions to experimental measurements of lepton kinematics from interactions with no mesons in the final state. These predictions are also compared to those of other models available in GENIE. It is shown that, with respect to these models, HF-CRPA predicts a significantly different evolution of the cross section when moving between different interaction targets, when considering incoming anti-neutrinos compared to neutrinos and when changing neutrino energies. These differences are most apparent for interactions with low energy and momentum transfer. It is also clear that the impact of nucleon correlations within the HF-CRPA framework is very different than in GENIE's standard implementation of RPA corrections. Since many neutrino oscillation experiments rely on their input model to extrapolate between targets, flavours, and neutrino energies, the newly implemented HF-CRPA model provides a useful means to verify that such differences between models are appropriately covered in oscillation analysis systematic error budgets.

Half-life prediction of some neutron-rich exotic nuclei prior to peak A = 130

β-decay is amongst the key properties of nuclei required for the modeling of r-process nucleosynthesis. It also governs the flow of abundances among neighboring isotopic chains of high-mass elements. In the present work, a simple proton-neutron quasi particle random phase approximation (p–n-QRPA) model has been used for the calculation of β-decay half-lives of Rb, Sr, Y and Zr neutron-rich isotopes. For 97−103Rb, 98−107Sr, 101−109Y and 104−112Zr, where the experimental data were available, the half-life values are reproduced with reasonable accuracy. The same set of model parameters are later used to predict half-lives for few neutron-rich nuclei (104−112Rb, 108−113Sr, 110−114Y and 113−115Zr) where measured data is not available. The p–n-QRPA results (including only allowed transitions) are compared with previous calculations (allowed plus forbidden) and exhibit agreement within a factor of 2.0 when compared with the recent available experimental data.

Comprehensive Analysis of the Neutrino Process in Core-collapsing Supernovae

We investigate the neutrino flavor change effects due to neutrino self-interaction and shock wave propagation, as well as the matter effects on the neutrino process in core-collapsing supernovae (CCSNe). For the hydrodynamics, we use two models: a simple thermal bomb model and a specified hydrodynamics model for SN1987A. For the presupernova model, we take an updated model, adjusted to explain SN1987A, which employs recent developments in the (n, γ) reaction rates for nuclei near the stability line (A ∼ 100). As for the neutrino luminosity, we adopt two different models: equivalent neutrino luminosity and nonequivalent luminosity models. The latter is taken from a synthetic analysis of CCSN simulation data, which quantitatively presented the results obtained by various neutrino transport models. Relevant neutrino-induced reaction rates are calculated using a shell model for light nuclei and a quasiparticle random phase approximation model for heavy nuclei. For each model, we present abundances of the light nuclei (7Li, 7Be, 11B, and 11C) and the heavy nuclei (92Nb, 98Tc, 138La, and 180Ta) produced by the neutrino process. The light nuclei abundances turn out to be sensitive to the Mikheyev–Smirnov–Wolfenstein (MSW) region around O-Ne-Mg layer while the heavy nuclei are mainly produced prior to the MSW region. Through detailed analyses, we find that neutrino self-interaction becomes a key ingredient, in addition to the MSW effect, for understanding the neutrino process and the relevant nuclear abundances. The normal mass hierarchy is shown to be more compatible with the meteorite data. The main nuclear reactions for each nucleus are also investigated in detail.

Electron capture and β-decay rates for nuclei with A = 65–80

Recently a list of top 50 most important electron capture (ec) and β-decay (bd) nuclei, averaged throughout the stellar trajectory for 0.500 > Y e > 0.400, was published. The current study presents the calculation of ec and bd rates, from the published list with A = 65–80, on a detailed temperature-density grid. The ec and bd rates were calculated using the proton-neutron quasiparticle random phase approximation model (pn-QRPA). Our calculation did not employ the Brink-Axel hypothesis. A systematic comparison of the current calculation with the previous pn-QRPA and independent particle model (IPM) results is presented for the first time. The reported ec rates are almost the same when compared with the previous pn-QRPA calculation. On the other hand, the reported bd rates are generally smaller up to an order of magnitude. Comparison with IPM results show that our calculated rates are bigger, by two orders of magnitude. The current calculation may contribute to a more realistic simulation of late phases of stellar evolution and modeling of x-ray bursts.

Model dielectric functions for fluctuation potential calculations in electron gas: A critical assessment

In this article, we report a critical assessment of dielectric function calculations in electron gas through the comparison of different modelling methods. This work is motivated by the fact that the dielectric function is a key quantity in the multiple scattering description of plasmon features in various electron-based spectroscopies. Starting from the standard random phase approximation (RPA) expression, we move on to correlation-augmented RPA, then damped RPA models. Finally, we study the reconstruction of the dielectric function from its moments, using the Nevanlinna and memory function approaches. We find the memory function method to be the most effective, being highly flexible and customizable.

Evaluation of exchange-correlation effects on the heat-shielding performance of carrier electrons in LaB6 using momentum-transfer resolved electron energy-loss spectroscopy

Exchange-correlation (XC) effects in carrier electrons have a significant influence on the dielectric properties and electric characteristics of a material. In this study, momentum-transfer (q) resolved electron energy-loss spectroscopy was conducted to experimentally evaluate the XC effects of carrier electrons in LaB6 bulk crystals, whose nanoparticles have been used for near-infrared-light shielding filters. By measuring q dependence of plasmon energy due to carrier electrons and evaluating the deviation from the free electron gas model in random phase approximation, the dielectric correction factor due to the XC effects, i.e., the local field correction G(q), for the carrier electrons in LaB6 were experimentally derived. This experimental result confirmed that the XC effects are non-negligible for the carrier electrons in LaB6. Because the XC effects influence dipole surface plasmon energy of LaB6 nanoparticles, the evaluation of the XC effects is important for a precise understanding of the optical properties of LaB6 nanoparticles.

Effect of screening on energy-dependent electron–phonon relaxation rate via intrinsic and extrinsic scattering channels in graphene on GaAs substrate

We obtain analytical results on the effect of screening on electron–phonon (e-p) relaxation rate in single-layer graphene (SLG) placed on any substrate using the Boltzmann transport formalism (BTF). The screening has been taken into account through the Thomas-Fermi (TF) and Random Phase Approximation (RPA) model. The four intrinsic and extrinsic phononic modes considered for electron-phonon scattering are the acoustic, optic, surface polar acoustic (piezoelectric), and surface polar optic (SO) phonons. All the four considered phononic modes coupling with free carriers provide significant pathways for e-p relaxation. We further investigate the significance of screening in the four phononic modes in electron energy-dependent e-p relaxation rate in SLG on GaAs substrate in particular. The obtained screened analytical solutions are novel and are not reported elsewhere.