Effective nucleus-nucleus potentials derived from the generator coordinate method

The equivalence of the generator coordinate method (GCM) and the resonating group method (RGM) and the formal equivalence of the RGM and the orthogonality condition model (OCM) lead to a relation connecting the effective nucleus-nucleus potentials of the OCM with matrix elements of the GCM. This relation may be used to derive effective nucleus-nucleus potentials directly from GCM matrix elements without explicit reference to the potentials of the RGM. In a first application local and l-independent effective potentials are derived from diagonal GCM matrix elements which represent the energy surfaces of a two-centre shell model. Using these potentials the OCM can reproduce the results of a full RGM calculation very well for the elastic scattering of two α-particles and fairly well for elastic ¹⁶O-¹⁶O scattering.     

Effective potentials for heavy-ion scattering derived from channel coupling

Starting from coupled-channels equations, we use suitable approximations to derive effective interaction potentials for elastic heavy-ion scattering. These potentials are local, complex and l-dependent, and determined solely by the transition form factors and the zero-order elastic S-matrix elements. Although here we treat the couplings in first order only, our method can easily be extended to higher-order coupling by iteration. As examples we give explicit expressions for coupling to inelastic collective channels, by both Coulomb and nuclear excitation, and to transfer reaction channels. Aside from identifying the dynamical origin of various components of the total elastic interaction, we suggest that our potentials (or appropriate generalizations thereof) may be used in conventional optical model and DWBA codes as a simple substitute for coupled-channels calculations.     

Extraction of tight binding parameters from in-situ ARPES on the continuously doped surface of cuprates

Recently we developed a technique of ozone/vacuum annealing to continuously change the doping level of the surface of Bi_2Sr_2CaCu_2O_(8+x)and measured a nearly whole superconducting dome on one surface by in-situ angle-resolved photoemission spectroscopy [arXiv: 1805.06450]. Here we study the evolution of the electronic structures of Bi_2Sr_2CaCu_2O_(8+)xusing this technique together with tight binding fits. The tight binding parameters are extracted to study their evolution with doping.     

On the tight binding theory of the heats of formation

The accuracy of a recently proposed simple analytic theory of the heats of formation ΔH of transition metal alloys is demonstrated by comparison with the tight binding coherent potential approximation calculations of Van der Rest et al. The d charge transfer is evaluated within a model that includes explicitly the deformation of the pure metal bands on alloying.     

Constructive proof of localization in the Anderson tight binding model

We prove that, for large disorder or near the band tails, the spectrum of the Anderson tight binding Hamiltonian with diagonal disorder consists exclusively of discrete eigenvalues. The corresponding eigenfunctions are exponentially well localized. These results hold in arbitrary dimension and with probability one. In one dimension, we recover the result that all states are localized for arbitrary energies and arbitrarily small disorder. Our techniques extend to other physical systems which exhibit localization phenomena, such as infinite systems of coupled harmonic oscillators, or random Schrödinger operators in the continuum.Work supported in part by National Science Foundations grant MCS-8108814 (A03).Work supported in part by National Science Foundation grant DMR 81-00417.     

Magnetoconductivity of disordered two dimensional tight binding electrons in CPA

The magnetotransport properties of a tight binding model of electrons on a two dimensional square lattice with diagonal disorder and in a perpendicular magnetic field is investigated. The disorder is treated in the coherent potential approximation (CPA) and a quasiclassical solution of the Harper equation is used to calculate the one particle Green's function. Analytical expressions for the CPA vertex corrections to the magnetoconductivity are derived. Numerical results for the density of states and the diagonal magnetoconductivity are discussed. The vertex correction vanishes if the Harper band width is neglected.     

Folded diagrams and 1s-Od effective interactions derived from Reid and Paris nucleon-nucleon potentials

The sd-shell effective-interaction matrix elements are derived from the Paris and Reid potentials using a microscopic folded-diagram effective-interaction theory. A comparison of these matrix elements is carried out by calculating spectra and energy centroids for nuclei of mass 18 to 24. The folded diagrams were included by both solving for the energy-dependent effective interaction self-consistently and by including the folded diagrams explicitly. In the latter case the folded diagrams were grouped either according to the number of folds or as prescribed by the Lee and Suzuki iteration technique; the Lee-Suzuki method was found to converge better and yield the more reliable results. Special attention was given to the proper treatment of one-body connected diagrams in the calculation of the two-body effective interaction.We first calculate the (energy-dependent) G-matrix appropriate for the sd-shell for both potentials using a momentum-space matrix-inversion method which treats the Pauli exclusion operator essentially exactly. This G-matrix interaction is then used to calculate the irreducible and non- folded diagrams contained in the $\text{Q}\text{?}\text{-}\text{box}$. The effective-interaction matrix elements are obtained by evaluating a $\text{Q}\text{?}\text{-}\text{box}$ folded diagram series. We considered four approximations for the basic $\text{Q}\text{?}\text{-}\text{box}$. These were (C1) the inclusion of diagrams up to 2nd order in G, (C2) 2nd order plus hole-hole phonons, (C3) 2nd order plus (bare TDA) particle-hole phonons, and (C4) 2nd order plus both hole-hole and particle-hole phonons.The contribution of the folded diagrams was found to be quite large, typically about 30%, and to weaken the interaction. Also, due to the greater energy dependence of higher-order diagrams, the effect of folded diagrams was much greater in higher orders. That is, the contribution from higher-order diagrams for most cases was greatly reduced by the folded diagrams. The convergence of the folded-diagram series deteriorates with the inclusion of higher-order $\text{Q}\text{?}\text{-}\text{box}$ processes in the method which groups diagrams by the number of folds, but remains excellent in the Lee-Suzuki method.Whereas the inclusion of the particle-hole phonon was essential to obtain agreement with experiment in earlier work, when the folded diagrams are included the effect of the particle-hole phonon is to reduce the amount of binding. All four approximations to both potentials produce interactions which badly underbind nuclei. The excitation spectra given by these interactions are, however, all rather similar to each other. The Paris interaction produces more binding than does the Reid, but differences between results obtained with the two interactions were often less than differences obtained in the four approximations. Essentially no difference was found between the effective non-central interactions from the Reid and Paris potentials after including the folded diagrams, although these two potentials themselves are quite different, especially in the strength of the tensor force.Comparisons between.calculated spectra and experiment were done for ¹⁸O, ¹⁸F, ¹⁹F, ²⁰O, ²⁰Ne, ²²Ne, ²²Na and ²⁴Mg.     

A new proof of localization in the Anderson tight binding model

We give a new proof of exponential localization in the Anderson tight binding model which uses many ideas of the Frohlich, Martinelli, Scoppola and Spencer proof, but is technically simpler-particularly the probabilistic estimates.Partially supported by NSF Grant DMS 8702301     

Spectral properties of a tight binding Hamiltonian with period doubling potential

We study a one dimensional tight binding hamiltonian with a potential given by the period doubling sequence. We prove that its spectrum is purely singular continuous and supported on a Cantor set of zero Lebesgue measure, for all nonzero values of the potential strength. Moreover, we obtain the exact labelling of all spectral gaps and compute their widths asymptotically for small potential strength.     

Local fluctuation of the spectrum of a multidimensional Anderson tight binding model

We consider the Anderson tight binding modelH=–+V acting inl ²(Z ^d ) and its restrictionH to finite hypercubes Z ^d . HereV={V _x ;xZ ^d } is a random potential consisting of independent identically distributed random variables. Let {E _j ()} _j be the eigenvalues ofH , and let _j (,E)=||(E _j ()–E),j1, be its rescaled eigenvalues. Then assuming that the exponential decay of the fractional moment of the Green function holds for complex energies nearE and that the density of statesn(E) exists atE, we shall prove that the random sequence { _j (,E)} _j , considered as a point process onR ¹, converges weakly to the stationary Poisson point process with intensity measuren(E)dx as gets large, thus extending the result of Molchanov proved for a one-dimensional continuum random Schrödinger operator. On the other hand, the exponential decay of the fractional moment of the Green function was established recently by Aizenman, Molchanov and Graf as a technical lemma for proving Anderson localization at large disorder or at extreme energy. Thus our result in this paper can be summarized as follows: near the energyE where Anderson localization is expected, there is no correlation between eigenvalues ofH if is large.     

Comparison of nearly free electron and tight binding limits in one-dimensional solids

We introduce a new one-dimensional crystal model that interpolates smoothly between the (nearly) free electron and δ-well models used before. In those two limits the energy band structure can be determined analytically. In the general case an efficient numerical scheme is established. We investigate the effects of truncating the infinite determinant arising in this context and compare our results with previous work. For a sufficiently strong potential the lowest lying energy levels are very narrow. The transition to this tight binding limit is discussed.     

Device characteristics and tight binding based modeling of bilayer graphene field-effect transistor

In this work the device characteristic of bilayer graphene MOSFET is investigated by calculation of transmission coefficient using tight-binding method. The real shape of applied potential on the bilayer graphene was included in the tight binding calculation. As obtained transmission coefficient is used to explore the current–voltage characteristics of the device in both on and off regimes. Electrical behavior of the device was obtained for different gate and drains voltages and channel length.     

Comparative study of recent phenomenological potentials for the NaCl-type alkali halides derived from elastic and dielectric data

A comparative study is presented of various phenomenological potentials for the NaCl-type alkali halides-based on elastic and dielectric data and on a “combination” of the Born model with a deformable ion mode-reported in recent years by Catlow, Diller and Norgett, by Corish, Parker and Jacobs, by Sangster et al. and by Hardy and Karo. First a critical analysis is made of the models adopted by the various AA and of the procedures to determine the pertinent parameters, emphasizing the different, often crude approximations used and the thermodynamic inconsistencies present in them. The quality of the fits achieved, and of the predictions made with the different models is then discussed. Finally, one compares directly the resulting effective pair potentials for the short-range interactions cation-anion, anion-anion and cation-cation, as well as the various types of parameters (specifically the potential parameters (Born repulsive parameters and van der Waals coefficients) and the shell-model parameters). One finds that the effective short-range potentials for each pair interaction in a given salt reported by the various AA-taken as a whole-have a sizeable indeterminacy, due both to the Born repulsive and vdW contributions.     

Estimation of bond energies from mulliken overlap populations

Estimations of the bond energies from Mulliken overlap populations are taken. The strength of a bond is undoubtedly connected with the density of electrons constituting this bond. In the present paper the electron densities _i ^bond belonging to the particular bonds are represented by the total overlap populations defined byMulliken. The heat of atomization of the molecule is subdivide in the ratio of these electron densities _i ^bond belonging to the individual bond.My thanks are due to Drs. S.erný, Z.Knor, J.Pancí and R.Zahradník for their interest and stimulating discussions.     

Notes on the semiempirical LUC approach of solids

A mistake in the original derivation of the semiempirical large unit cell approach is corrected and the role of the CNDO parameters is discussed. The calculations presented applying the CNDO/S-CI method, show that the simulation of both the valence and the conduction band of diamond are satisfactory with a C₁₆ cluster.     

Heavy-ion optical potentials at finite temperature calculated using a complex effective interaction derived from a realistic force

Hot density distributions of heavy ions generated by a modified Thomas-Fermi calculation at finite temperature are used to calculate the optical potential using the double-folding method and a complex effective energy and density-dependent interaction deduced from a realistic NN (Reid soft-core) force in nuclear matter. The real and the imaginary part of the optical potential become more attractive when the temperature increases.