Shell Model Potential Research Articles

The melting of CaF2 and its (110) surface structure investigated by molecular dynamics simulation

Abstract Classical molecular dynamics using rigid-ion and shell-model potentials has been used to investigate the high-temperature properties of the (110) surface of CaF2. The rigid-ion model generates missing-row defects well below the melting point, giving alternate (111), (111) and (110) microfacets along the [001] direction. Simulations of about 1 ns duration are necessary to establish these surface structures. It is suggested that ultimately this process would result in the formation of extended (111) facets in a larger system than those studied here. Shell-model simulations, which were necessarily shorter than their rigid-ion counterparts, did not produce these structures. However, the inclusion of polarizability markedly increases the rate of F− superionic diffusion at a given temperature, and of cation and anion diffusion in the melt. It also results in a reduction of about 15% in the melting point compared with the rigid-ion model.

Structure-stability relationships for all-silica structures.

We will discuss predictions for the stability and structures of all-silica zeolitic structures. We will show that we have derived a shell-model potential, based on ab initio calculations, which gives good predictions for the structure and stability of all-silica structures. We will compare three shell-model predictions with two rigid-ion model predictions for the structure and stability of silicates. We will show that shell-model predictions for the relative stability of zeolites are much closer to experiment than rigid-ion model predictions, due to the canceling of covalent and electrostatic terms in the shell models which does not occur in the rigid-ion models. Using the potentials with the highest predictive power on both stabilities and structures of silicates we will discuss structure-stability relationships that have been proposed in the literature.

Study of catastrophic dechannelling resonance in strained layer superlattices using a shell structure potential

Catastrophic dechannelling resonance (CDR) occurs when the half wavelength ( lambda /2) of a planar channelled ion beam matches the path length per layer, s, of a strained layer superlattice (SLS). CDR has been used for probing important properties of SLS. The dependence of CDR on various parameters, like incident angle, minimum impact parameter for channelling and superlattice strain in strained layer superlattices, are studied using a shell structure potential, which is based on the atomic shell structure of the target (SLS) atom. We have taken a GaAs0.09P0.91/GaP (s=48.2 nm) superlattice as our target and a 4He ion beam as the incident probe beam. Comparison with other frequently used Thomas-Fermi-type potentials and good agreement with experimental results shows the usefulness and accuracy of this shell model potential.

Dynamics with the Shell Model

Abstract Potentials for ionic materials are among the best classical models currently available, giving very realistic descriptions of many physical properties. The key feature in providing this realism has been found to be the inclusion of ion polarisability, most often via the shell model. Until recently though, the dynamical properties of such models, and their comparison with experiment, have received little attention due to the computational workload involved in dealing with the extra degrees of freedom. We discuss here recent progress in the dynamical simulation of ionic materials using shell-model potentials. This includes the approaches which have successfully been developed to deal with the central problem, which is the requirement that the system obeys the Born-Oppenheimer principle with respect to the polarisation. The results of extensive simulations of UO2, using the best potentials available, and comparison with neutron-scattering and other experimental data reveal the feasibility of shell-model MD, and also shed new light on the capabilities of the potentials.

Evolution of pre-collective nuclei: Structural signatures near the drip lines

Recent studies have shown that the phenomenology of single-magic and near-magic nuclei has universal characteristics analogous to those of collective nuclei and that, moreover, this phenomenology attaches smoothly to that describing collective nuclei. This has led to a number of new signatures of structure as well as to a new, tripartite, classification of nuclear structure that embraces the gamut of structures from magic, through pre-collective, to fully collective and rotational nuclei. Aside from the natural appeal of simple global correlations of collective observables, these results have particular significance for soon-to-be accessible exotic nuclei near the drip lines since they rely on only the simplest-to-obtain data, in particular, the energies of just the first two excited states, E(41+) and E(21+), of even-even nuclei, and the B(E2: 21+ → 01+) value. Indeed, without the need for more extensive level schemes, these basic data alone can reveal information about the goodness of seniority, about the validity of pair-addition mode relationships of adjacent even-even nuclei, about underlying shell structure (validity of magic numbers) and even about the shell model potential itself (e.g., the strengths of the l · s and l2 terms).

Ab initio approach to the development of interatomic potentials for the shell model of silica polymorphs

We have developed a new method for deriving parameters for the shell model of silica polymorphs. All parameters for the shell model are derived in a self-consistent way from ab initio energy surfaces, polarizabilities and dipole moments of small clusters. This yields an ab initio partial charge shell model potential. The predictive power of our potential is demonstrated by presenting predictions for the structure of α-quartz, α-cristobalite, coesite, stishovite and the IR spectrum of α-quartz which are compared with experiment and predictions of the widely used potentials of Jackson and Catlow, and Kramer, Farragher, van Beest and van Santen.

On the relativistic description of the nucleus

We present a formalism able to generalise to a relativistically covariant scheme the standard nuclear shell model. We show that, using some generalised nuclear Green’s functions and their Lehmann representation we can define the relativistic equivalent of the non-relativistic single-particle wave function (not losing, however, the physical contribution of other degrees of freedom, like mesons and antinucleons). It is shown that the mass operator associated to the nuclear Green’s function can be approximated with the equivalent of a shell model potential and that the corresponding “single-particle wave functions” can be easily derived in a specified frame of reference and then boosted to any other system, thus fully restoring the Lorentz covariance.

Proton-90Zr mean field between -60 and +185 MeV from a dispersive optical model analysis.

Elastic scattering of protons from $^{90}\mathrm{Zr}$ in the energy range ${\mathit{E}}_{\mathit{p}}$=9.8 to 135 MeV is analyzed using a dispersive optical model potential (OMP). In this analysis, a dispersion relation connects the volume integrals of the imaginary and the real parts of the OMP. Best-fit dispersive OMP parameters are obtained from fits to experimental cross section and analyzing power data at each energy, while the volume integrals of the imaginary potential and dispersive correction terms are fixed at the empirical values obtained in the individual proton elastic scattering analyses from 9.8 to 135 MeV. Predictions of the cross section and analyzing power angular distributions from the best-fit dispersive OMP and conventional OMP are obtained, and give similar quality fits to data. A dispersive OMP with parameters that show a smooth energy dependence are determined from fits to the entire data set. Comparison of cross sections and analyzing powers calculated by the dispersive OMP with experimental data at 160 and 185 MeV is also presented. The dispersive OMP with a smooth energy dependence is extended to the negative energy region with the guidance of the known first single-particle and single-hole state energies near the Fermi energy, ${\mathit{E}}_{\mathit{F}}$=-6.8 MeV, to provide parameters for the shell model potential. This analysis also provides estimates for single-particle and hole energies ${\mathit{E}}_{\mathit{n}\mathit{l}\mathit{j}}$, root-mean-square radii ${\mathit{R}}_{\mathit{n}\mathit{l}\mathit{j}}$, expectat ion values of the effective mass 〈${\mathit{m}}^{\mathrm{*}}$/m${\mathrm{〉}}_{\mathit{n}\mathit{l}\mathit{j}}$, occupation probabilities ${\mathit{N}}_{\mathit{n}\mathit{l}\mathit{j}}$, absolute spectroscopic factors ${\mathit{S}}_{\mathit{n}\mathit{l}\mathit{j}}$, and spectral functions ${\mathrm{\ensuremath{\zeta}}}_{\mathit{n}\mathit{l}\mathit{j}}$(${\mathit{E}}_{\mathit{x}}$) for proton single-particle and single-hole orbits in $^{90}\mathrm{Zr}$. These estimates are compared with available experimental information.

Effects of nuclear structure in the spin-dependent scattering of weakly interacting massive particles

We present calculations of the nuclear from factors for spin-dependent elastic scattering of dark matter WIMPs from123Te and131Xe isotopes, proposed to be used for dark matter detection. A method based on the theory of finite Fermi systems was used to describe the reduction of the single-particle spin-dependent matrix elements in the nuclear medium. Nucleon single-particle states were calculated in a realistic shell model potential; pairing effects were treated within the BCS model. The coupling of the lowest single-particle levels in123Te to collective 2+ excitations of the core was taken into account phenomenologically. The calculated nuclear form factors are considerably less then the single-particle ones for low momentum transfer. At high momentum transfer some dynamical amplification takes place due to the pion exchange term in the effective nuclear interaction. But as the momentum transfer increases, the difference disappears, the momentum transfer increases and the quenching effect disappears. The shape of the nuclear form factor for the131Xe isotope differs from the one obtained using an oscillator basis.

The dispersive optical model for n + 208Pb and n + 209Bi

The dispersive optical model (DOM) provides a natural connection between the shell model potential for bound states and the optical model for nucleon scattering at positive energies. At TUNL we have developed DOMs for neutron scattering for ten nuclei between 27Al and 209Bi. In these studies we rely on TUNL measurements of differential cross-section (σ(θ)) and analyzing power, as well as a wealth of σ(θ) and total cross section measurements from numerous other laboratories. In this paper we briefly outline the DOM method and the achievements in describing scattering data for n + 208Pb and n + 209Bi and single-particle bound-state data for neutrons in 208Pb.

Defect energy calculations of alkali chlorides using ab initio potentials

We report the results of a simulation study using shell-model pair-wise potentials describing polarization effects and interactions in alkali halides. The simulation technique used is the HADES procedure, and the potentials applied are based on ab initio quantum mechanical calculations of atoms in crystals. The study of point defects, including formation energy and diffusion process is in good agreement with experimental data, as well with other calculations indicating the accuracy and reliability of ab initio potentials.

Microscopic approach to pion-nucleus dynamics.

Elastic scattering of pions from finite nuclei is investigated utilizing a contemporary, momentum-space first-order optical potential combined with microscopic estimates of second-order corrections. The calculation of the first-order potential includes (1) full Fermi-averaging integration including the \ensuremath{\Delta} propagation and the intrinsic nonlocalities in the \ensuremath{\pi}-N amplitude, (2) covariant kinematics, (3) invariant amplitudes, and (4) a finite-range off-shell pion-nucleon model which contains the nucleon-pole term. The \ensuremath{\Delta} nucleus interaction is included via the mean spectral-energy approximation. This approach produces a convergent perturbation theory in which the Pauli corrections (treated as a second-order term) cancel remarkably against the pion true-absorption terms. Parameter-free results, including the \ensuremath{\Delta}-nucleus shell-model potential, Pauli corrections, pion true absorption, and short-range correlations, are presented.

Lattice parameter changes in the mixed-oxide system Ce1–xLaxO2–x/2: a combined experimental and theoretical study

X-Ray diffraction measurements are reported of ceramic samples of the mixed-oxide system Ce1–xLaxO2–x/2 for 0<x<0.9, where x has been determined by EDXA. The solid-state reaction forms a highly crystalline product at an ageing temperature of 1200 °C. The solubility limit of La in the bulk CeO2 at this temperature has been determined as ca. 52% by monitoring the lattice parameter increase and the subsequent appearance of a second La2O3 phase. To model the experimental measurements, atomistic lattice calculations based on electron-gas shell-model potentials have been carried out to estimate the variation of the lattice parameter with La content.

Derivation of pair potentials from first principles and simulation of NaF clusters

Pair potentials of Buckingham from are derived for NaF, based on Hartree-Fock calculations with correlation correction. These potentials are compared with empirical shell-model potentials derived from (bulk) crystalline NaF physical properties. Both derived and empirical potentials are used to study two classes of small clusters: cubic clusters consisting of nxnxn arrays (n = 2,4,6,8,10), and clusters of arbitrary geometry consisting of m (Na+-F-) neutral pairs (m=1,2,…15). Equilibrium configurations and energies in all cases are determined by a Monte Carlo method. For cubic (nxnxn) clusters, the approach to bulk nearest-neighbor spacing is clearly illustrated. For clusters consisting of m pairs, cubic arrays predominate, except for m=3 and m=9, where the derived potentials predict a hexagonal configuration.

Computer Modelling of Elastic Properties of LaF3Using Free Energy Minimisation Techniques

Abstract An effective use of computer simultion methods in the study of solids depends on the derivation of reliable potential models. Hence, the empirically derived interionic potentials of LaF3 were tested by free energy minimisation techniques, within the quasi-harmonic approximation. This was achieved by calculating the temperature variation of elastic constants derived directly from the shell model potentials. These changes agree reasonably well with those calculated from an experimental lattice expansion, below 800 K. However, the departure from linearity and experimental results occur in the range 800–1100 K, which is below the transition temperature to the state of high ionic conductivity. This shows how far the fitted shell model potentials can reliably predict the elastic behaviour of LaF3.

Light scattering by alkali halides melts: a comparison of shell-model and rigid-ion computer simulation results

Molecular dynamics computer simulations with shell-model potentials have been used to calculate the light scattering (Raman) spectra of molten LiCl. A significant improvement in the level of agreement with experiment is found over previous simulations with rigid-ion potentials. The improvement is attributed to the better description of the relaxation of the charge-density fluctuations in the shell-model simulations.

Off-axis configuration of FA(II) centres in alkali halides

Abstract The experimental values of the off-axis angle of FA(II) dipoles in KCl:Li+, RbCl:Li+ and KF:Li+ are in good agreement with those obtained from theoretical estimates of the off-centre displacements of the Li+ ion calculated with the shell model potentials. On this basis, one can quantitatively predict the off-axis behaviour of FA(II) centres from the calculated off-centre positions of small impurity ions in alkali halides.

Why Are Most Nuclei Axially Symmetric?

AbstractA previous publication was concerned with the average prolateness of nuclei [1]. With the same methods as there it is shown here that axial symmetry should be predominant in nuclei, which it is indeed. The tools for the proof are special collective and single particle coordinates. The nucleon‐nucleus interaction is approximated by a shell model potential plus Nilsson coupling; strong coupling is used. The minimum of the total energy is found for axial symmetry.

Neutron scattering from elemental indium: Optical model and bound-state potential.

Neutron elastic-scattering cross sections of indium are measured from 4.5 to 10 MeV at intervals of \ensuremath{\approxeq}500 keV. Seventy or more differential values are obtained at each incident energy, distributed between \ensuremath{\approxeq}18\ifmmode^\circ\else\textdegree\fi{} and 160\ifmmode^\circ\else\textdegree\fi{}. These are combined with lower-energy data previously obtained at this laboratory, and with 11- and 14-MeV results from the literature, to form a comprehensive elastic-scattering database extending from \ensuremath{\approxeq}1.5 to 14 MeV. These data are interpreted in terms of a conventional spherical optical model. The resulting potential is extrapolated to the bound-state regime. It is shown that in the middle of the 50--82 neutron shell, the potential derived from the scattering results adequately describes the binding energies of particle states, but does not do well for hole states. The latter shortcoming is attributed to hole states having occupational probabilities sufficiently different from unity so that the exclusion principle becomes a factor, to rearrangement of the neutron core, and to the fact that the shell-model potential was assumed to have an energy-independent geometry. The systematic behavior of the real optical potential is discussed, and it is shown that the isovector strength deduced from neutron scattering is consistent with the nucleon-nucleon scattering data when a mass dependence of the radius is used.

Coulomb energy of a proton in the relativistic nuclear shell model.

We examine the Dirac equation for a proton in a nucleus, with a shell-model potential consisting of nuclear and Coulomb parts. When the Dirac equation is reduced to a Schr\"odinger-like equation, the effective potential W in it exhibits two Coulomb-related effects that are absent in the usual nonrelativistic treatment: (I) W contains a Coulomb-nuclear interference term; (II) W depends strongly on the proton energy, which in turn depends on the Coulomb energy. If the shell-model potential consists of a strongly attractive Lorentz scalar and a strongly repulsive Lorentz vector, effect I by itself is very large. However, effect II counteracts effect I, leaving a small yet significant decrease in the Coulomb energy as compared with its nonrelativistic counterpart.