Semiclassical model of the structure of matter

Shpatakovskaya, G. V.

doi:10.3367/ufne.0182.201205a.0457

Cited by 45 publications

(7 citation statements)

References 93 publications

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“…In a spherically symmetric potential the density of the electron distribution often shows an oscillating behavior along the radius. This can be seen in the solutions by Hartree-Fock, Hartree-Fock-Dirac methods, in Thomas-Fermi approximation [1,2], and in DFT [3]. Such oscillating behavior is observed, not only for the electrons, but also for the other particles, and for Coulomb as well as for other interaction potentials between particles (Yukawa potential, hard core, etc.)…”

Section: Introductionmentioning

confidence: 85%

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Quantum shell effects in compressed mesoscopic system

Kuratov,

Shidlovski,

Blinnikov

2018

Preprint

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The article demonstrates the nontrivial manifestation of quantum shell effects in a compressed mesoscopic system. It is shown that there are two spatial scales in the distribution of degenerate electrons in a spherical well. The first scale is the Fermi length ∼ h/pF. By quantum shell effect, the authors mean the existence of the new spatial scale, which is order of the system size and much larger than the first scale. The theoretical analysis for the large amount of free electrons (N 10 9 ) in an infinite spherical well demonstrates what causes the appearance of the spatial nonuniformity and gives analytical expression for the electron distribution function. These results are confirmed by a numerical summation of exact solutions for the electron wave functions in an infinite potential well. It is shown that an analogous effect for the spatial distribution of electrons exists in a compressed hydrogen gas bubble of submicron size (< 0.1µm). The numerical simulation of the electron distribution was carried out by the DFT (Density Functional Theory) method. The consequence of this effect is the nontrivial dynamics of the compressible cold gas bubble. This system can be realized in the thermonuclear experiments. The limiting factors of the analyzed effect are considered: symmetry of system, electron temperature, and curvature of system boundary.

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Section: Introductionmentioning

confidence: 85%

“…The semiclassical approach was widely used for the analysis of metal clusters [2], for the calculation of the nuclei energy spectrum [5], for the calculation of the electron concentration oscillations in the atom.…”

Section: A the Theoretical Analysismentioning

confidence: 99%

Quantum shell effects in compressed mesoscopic system

Kuratov,

Shidlovski,

Blinnikov

2018

Preprint

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“…Taking into account Eq. (5) in the quasi-classical approximation [27][28][29] for the energy density of states of the holes in the v-band, we find 24,25…”

Section: Statistics Of Holes and Charge States Of Hydrogen-like Acceptors In P-type Diamond Crystalsmentioning

confidence: 99%

Ionization equilibrium at the transition from valence-band to acceptor-band migration of holes in boron-doped diamond

Poklonski

Вырко

Poklonskaya

et al. 2016

Journal of Applied Physics

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A quasi-classical model of ionization equilibrium in the p-type diamond between hydrogen-like acceptors (boron atoms which substitute carbon atoms in the crystal lattice) and holes in the valence band (v-band) is proposed. The model is applicable on the insulator side of the insulatormetal concentration phase transition (Mott transition) in p-Dia:B crystals. The densities of the spatial distributions of impurity atoms (acceptors and donors) and of holes in the crystal are considered to be Poissonian, and the fluctuations of their electrostatic potential energy are considered to be Gaussian. The model accounts for the decrease in thermal ionization energy of boron atoms with increasing concentration, as well as for electrostatic fluctuations due to the Coulomb interaction limited to two nearest point charges (impurity ions and holes). The mobility edge of holes in the v-band is assumed to be equal to the sum of the threshold energy for diffusion percolation and the exchange energy of the holes. On the basis of the virial theorem, the temperature T j is determined, in the vicinity of which the dc band-like conductivity of holes in the v-band is approximately equal to the hopping conductivity of holes via the boron atoms. For compensation ratio (hydrogen-like donor to acceptor concentration ratio) K % 0.15 and temperature T j , the concentration of "free" holes in the v-band and their jumping (turbulent) drift mobility are calculated. Dependence of the differential energy of thermal ionization of boron atoms (at the temperature 3T j /2) as a function of their concentration N is calculated. The estimates of the extrapolated into the temperature region close to T j hopping drift mobility of holes hopping from the boron atoms in the charge states (0) to the boron atoms in the charge states (À1) are given. Calculations based on the model show good agreement with electrical conductivity and Hall effect measurements for p-type diamond with boron atom concentrations in the range from 3 Â 10 17 to 3 Â 10 20 cm À3 , i.e., up to the Mott transition. The model uses no fitting parameters. Published by AIP Publishing.

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“…To describe shell effects one should take into account discrete energy levels. Analytically shell corrections to the TF model have been studied in [12,13] using the Poisson formula in the transition from summation to integration (see also the review [14]). Average atom models [15][16][17][18][19] are based on a radial solution of the single-particle Schrödinger (Dirac) equation so that the discrete spectrum and shell effects are taken into account implicitly.…”

Section: Introductionmentioning

confidence: 99%

Influence of shell effects on thermodynamic properties of matter at high pressures

Levashov

Minakov

2018

J. Phys.: Conf. Ser.

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Abstract. We analyze the influence of shell effects on thermodynamic properties of matter at high pressures. Spherically symmetric average atom models show significant contribution of electronic transitions to cold pressure which is not confirmed by more accurate density functional theory models. In particular, the s-d transition in aluminum and potassium does not reveal itself on the shock Hugoniots. Oscillations on shock Hugoniots at very high pressures predicted earlier by many authors should be confirmed by precise first-principle calculations. IntroductionThermodynamic properties of matter at high pressure are of importance in many problems of high energy density physics, in particular, in astrophysics [1], in wide-range equations of state [2,3], in the problems of interaction of intense energy fluxes with matter [4-6], in perspective power generation facilities [7] and in some others. The finite-temperature Thomas-Fermi (TF) model [8] based upon semiclassical approximation is widely used to describe thermodynamic properties of matter, but there are many phenomena beyond this approach. In particular, shell effects reflect non-regularities of physical parameters because of the discrete energy spectrum. For example, in low-density plasma step-wise dependencies of thermodynamic functions on isochors or isobars are quite typical [9]. The other well-known effect is connected with the non-regular behavior of density of elements vs. atomic mass [10,11]. To describe shell effects one should take into account discrete energy levels. Analytically shell corrections to the TF model have been studied in [12,13] using the Poisson formula in the transition from summation to integration (see also the review [14]). Average atom models [15][16][17][18][19] are based on a radial solution of the single-particle Schrödinger (Dirac) equation so that the discrete spectrum and shell effects are taken into account implicitly. During the last 30 years it became possible to obtain approximate three-dimensional (3D) solutions of a quantum many-particle problem using density functional theory (DFT) [20,21]. In this case one gets a 3D band structure of a system of particles that provides for the appearance of shell effects through non-regularities of the electronic density and some thermodynamic functions. There were several attempts to register shell effects at high pressures and temperatures experimentally [22][23][24] using underground nuclear explosions. It is claimed [24] that the influence of the discrete energy spectrum is

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Semiclassical model of the structure of matter

Cited by 45 publications

References 93 publications

Quantum shell effects in compressed mesoscopic system

Quantum shell effects in compressed mesoscopic system

Ionization equilibrium at the transition from valence-band to acceptor-band migration of holes in boron-doped diamond

Influence of shell effects on thermodynamic properties of matter at high pressures

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