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Autor: Grafiati
Data publikacji: 4 czerwca 2021
Data aktualizacji: 20 lutego 2023

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1

Jorge, F. E., i A. B. F. Da Silva. "The generator coordinate Dirac–Fock method applied to beryllium-like atomic species". Canadian Journal of Chemistry 74, nr 9 (1.09.1996): 1748–52. http://dx.doi.org/10.1139/v96-193.

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The recently formulated generator coordinate Dirac–Fock method for relativistic closed-shell atoms is applied to the Be atom and Be-like ions Ne6+, Ar14+, and Sn46+ in order to assess its efficacy for light atomic systems. The Dirac–Fock equations are integrated numerically in the generator coordinate Dirac–Fock method so as to generate Gaussian basis sets for the atomic species under study. The results obtained with the application of the generator coordinate Dirac–Fock method in this work for Dirac–Fock–Coulomb and Dirac–Fock–Breit energies for Be-like ions are in excellent agreement with Declaux's benchmark numerical calculations, and are better than the Dirac–Fock–Coulomb and Dirac–Fock–Breit energies obtained with even-tempered Gaussian-type function calculations. For the Be atom, the Dirac–Fock–Coulomb energy result obtained with the generator coordinate Dirac–Fock method is lower than the corresponding value obtained with the Declaux's numerical finite-difference program. Key words: Dirac–Fock–Coulomb energy, Dirac–Fock–Breit energy, Gaussian basis sets, generator coordinate Dirac–Fock method.
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2

Levitt, Antoine. "Solutions of the multiconfiguration Dirac–Fock equations". Reviews in Mathematical Physics 26, nr 07 (sierpień 2014): 1450014. http://dx.doi.org/10.1142/s0129055x14500147.

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The multiconfiguration Dirac–Fock (MCDF) model uses a linear combination of Slater determinants to approximate the electronic N-body wave function of a relativistic molecular system, resulting in a coupled system of nonlinear eigenvalue equations, the MCDF equations. In this paper, we prove the existence of solutions of these equations in the weakly relativistic regime. First, using a new variational principle as well as the results of Lewin on the multiconfiguration non-relativistic model, and Esteban and Séré on the single-configuration relativistic model, we prove the existence of critical points for the associated energy functional, under the constraint that the occupation numbers are not too small. Then, this constraint can be removed in the weakly relativistic regime, and we obtain non-constrained critical points, i.e. solutions of the multiconfiguration Dirac–Fock equations.
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3

Esteban, M. J., i E. Séré. "Nonrelativistic Limit of the Dirac-Fock Equations". Annales Henri Poincaré 2, nr 5 (październik 2001): 941–61. http://dx.doi.org/10.1007/s00023-001-8600-7.

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4

Paturel, Eric. "Solutions of the Dirac-Fock Equations without Projector". Annales Henri Poincaré 1, nr 6 (grudzień 2000): 1123–57. http://dx.doi.org/10.1007/pl00001024.

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5

Ladik, Janos J. "Four-component Dirac-Hartree-Fock equations for solids; generalization of the relativistic Hartree-Fock equations". Journal of Molecular Structure: THEOCHEM 391, nr 1-2 (luty 1997): 1–14. http://dx.doi.org/10.1016/s0166-1280(96)04791-4.

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6

Al-Badawi, A., i I. sakalli. "Dirac and Klein–Gordon–Fock equations in Grumiller’s spacetime". International Journal of Geometric Methods in Modern Physics 15, nr 04 (13.03.2018): 1850051. http://dx.doi.org/10.1142/s0219887818500512.

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We study the Dirac and the chargeless Klein–Gordon–Fock equations in the geometry of Grumiller’s spacetime that describes a model for gravity of a central object at large distances. The Dirac equation is separated into radial and angular equations by adopting the Newman–Penrose formalism. The angular part of the both wave equations are analytically solved. For the radial equations, we managed to reduce them to one dimensional Schrödinger-type wave equations with their corresponding effective potentials. Fermions’s potentials are numerically analyzed by serving their some characteristic plots. We also compute the quasinormal frequencies of the chargeless and massive scalar waves. With the aid of those quasinormal frequencies, Bekenstein’s area conjecture is tested for the Grumiller black hole. Thus, the effects of the Rindler acceleration on the waves of fermions and scalars are thoroughly analyzed.
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7

Goldman, S. P., i A. Dalgarno. "Finite-Basis-Set Approach to the Dirac-Hartree-Fock Equations". Physical Review Letters 57, nr 4 (28.07.1986): 408–11. http://dx.doi.org/10.1103/physrevlett.57.408.

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8

Esteban, Maria J., i Eric Séré. "Solutions of the Dirac-Fock Equations for Atoms¶and Molecules". Communications in Mathematical Physics 203, nr 3 (1.06.1999): 499–530. http://dx.doi.org/10.1007/s002200050032.

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9

Ring, Peter, Sibo Wang, Qiang Zhao i Jie Meng. "Relativistic Brueckner-Hartree-Fock Theory in Infinite Nuclear Matter". EPJ Web of Conferences 252 (2021): 02001. http://dx.doi.org/10.1051/epjconf/202125202001.

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On the way of a microscopic derivation of covariant density functionals, the first complete solution of the relativistic Brueckner-Hartree-Fock (RBHF) equations is presented for symmetric nuclear matter. In most of the earlier investigations, the G-matrix is calculated only in the space of positive energy solutions. On the other side, for the solution of the relativistic Hartree-Fock (RHF) equations, also the elements of this matrix connecting positive and negative energy solutions are required. So far, in the literature, these matrix elements are derived in various approximations. We discuss solutions of the Thompson equation for the full Dirac space and compare the resulting equation of state with those of earlier attempts in this direction.
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10

Jorge, F. E., i A. B. F. da Silva. "A generator coordinate version of the closed‐shell Dirac–Fock equations". Journal of Chemical Physics 104, nr 16 (22.04.1996): 6278–85. http://dx.doi.org/10.1063/1.471288.

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11

BELAVKIN, V. P., i V. N. KOLOKOL'TSOV. "STOCHASTIC EVOLUTION AS A QUASICLASSICAL LIMIT OF A BOUNDARY VALUE PROBLEM FOR SCHRÖDINGER EQUATIONS". Infinite Dimensional Analysis, Quantum Probability and Related Topics 05, nr 01 (marzec 2002): 61–91. http://dx.doi.org/10.1142/s0219025702000717.

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We develop systematically a new unifying approach to the analysis of linear stochastic, quantum stochastic and even deterministic equations in Banach spaces. Solutions to a wide class of these equations (in particular those describing the processes of continuous quantum measurements) are proved to coincide with the interaction representations of the solutions to certain Dirac type equations with boundary conditions in pseudo-Fock spaces. The latter are presented as the semiclassical limit of an appropriately dressed unitary evolutions corresponding to a boundary-value problem for rather general Schrödinger equations with bounded below Hamiltonians.
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12

Hacyan, Shahen. "The Riemann-Silberstein vector in the Dirac algebra". Revista Mexicana de Física 65, nr 1 (31.12.2018): 65. http://dx.doi.org/10.31349/revmexfis.65.65.

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It is shown that the Riemann-Silberstein vector, defined as ${\bf E} + i{\bf B}$, appears naturally in the $SL(2,C)$ algebraic representation of the electromagnetic field. Accordingly, a compact form of the Maxwell equations is obtained in terms of Dirac matrices, in combination with the null-tetrad formulation of general relativity. The formalism is fully covariant; an explicit form of the covariant derivatives is presented in terms of the Fock coefficients.
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13

Takka, N., A. Bouda i T. Foughali. "Maxwell’s equations in the context of the Fock transformation and the magnetic monopole". Canadian Journal of Physics 95, nr 10 (październik 2017): 987–92. http://dx.doi.org/10.1139/cjp-2016-0717.

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In the R-Minkowski space–time, which we recently defined from an appropriate deformed Poisson brackets that reproduce the Fock coordinate transformation, we derive an extended form for Maxwell’s equations by using a generalized version of Feynman’s approach. Also, we establish in this context the Lorentz force. As in deformed special relativity, modifying the angular momentum in such a way as to restore the R-Lorentz algebra generates the magnetic Dirac monopole.
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14

Fischer, Charlotte Froese, i Andrew Senchuk. "Numerical Procedures for Relativistic Atomic Structure Calculations". Atoms 8, nr 4 (26.11.2020): 85. http://dx.doi.org/10.3390/atoms8040085.

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Variational methods are used extensively in the calculation of transition rates for numerous lines in a spectrum. In the GRASP code, solutions of the multiconfiguration Dirac–Hartree–Fock (MCDHF) equations that optimize the orbitals are represented by numerical values on a grid using finite differences for integration and differentiation. The numerical accuracy and efficiency of existing procedures are evaluated and some modifications proposed with heavy elements in mind.
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15

ARMINJON, MAYEUL, i FRANK REIFLER. "FOUR-VECTOR VERSUS FOUR-SCALAR REPRESENTATION OF THE DIRAC WAVE FUNCTION". International Journal of Geometric Methods in Modern Physics 09, nr 04 (6.05.2012): 1250026. http://dx.doi.org/10.1142/s0219887812500260.

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In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincaré group. This is not an option in a curved spacetime. Therefore, in the equation proposed independently by Fock and Weyl, the four complex components of the Dirac wave function transform as scalars under a general coordinate transformation. Recent work has shown that a covariant complex four-vector representation is also possible. Using notions of vector bundle theory, we describe these two representations in a unified framework. We prove theorems that relate together the different representations and the different choices of connections within each representation. As a result, either of the two representations can account for a variety of inequivalent, linear, covariant Dirac equations in a curved spacetime that reduce to the original Dirac equation in a Minkowski spacetime. In particular, we show that the standard Dirac equation in a curved spacetime, with any choice of the tetrad field, is equivalent to a particular realization of the covariant Dirac equation for a complex four-vector wave function.
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16

Dvoeglazov, Valeriy V. "Generalized equations and their solutions in the (S, 0) + (0, S) representations of the Lorentz group". Journal of Physics: Conference Series 2197, nr 1 (1.03.2022): 012008. http://dx.doi.org/10.1088/1742-6596/2197/1/012008.

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Abstract I present explicit examples of generalizations in relativistic quantum mechanics. First of all, I discuss the generalized spin-1/2 equations for neutrinos. They have been obtained by means of the Gersten-Sakurai method for derivations of arbitrary-spin relativistic equations. Possible physical consequences are discussed. Next, it is easy to check that both Dirac algebraic equation Det( p ^ – m) = 0 and Det( p ^ + m) = 0 for u – and υ – 4-spinors have solutions with p 0 = ± E p = ± p 2 + m 2 . The same is true for higher-spin equations. Meanwhile, every book considers the equality p0 = Ep for both u – and υ – spinors of the (1/2, 0) ⊕ (0, 1/2) representation, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination of the negative-energy solutions. The recent Ziino works (and, independently, the articles of several others) show that the Fock space can be doubled. We re-consider this possibility on the quantum field level for both S = 1/2 and higher spin particles. The third example is: we postulate the non-commutativity of 4-momenta, and we derive the mass splitting in the Dirac equation. The applications are discussed.
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17

DANILOV, YU A., A. V. ROZHKOV i V. L. SAFONOV. "POSSIBILITY OF GEOMETRIC DESCRIPTION OF QUASIPARTICLES IN SOLIDS". International Journal of Modern Physics B 10, nr 07 (30.03.1996): 777–91. http://dx.doi.org/10.1142/s0217979296000325.

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New phenomenological approach for the description of elementary collective excitations is proposed. The crystal is considered to be an anisotropic space-time vacuum with a prescribed metric tensor in which the information on electromagnetic crystalline fields is included. The quasiparticles in this space are supposed to be described by the equations structurally similar to the relativistic wave equations for particles in empty space. The generalized Klein–Gordon–Fock equation and the generalized Dirac equation in external electromagnetic field are considered. The applicability of the proposed approach to the case of conduction electron in a crystal is discussed.
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18

Klishevich, Vladimir V. "Exact solution of Dirac and Klein-Gordon-Fock equations in a curved space admitting a second Dirac operator". Classical and Quantum Gravity 18, nr 17 (17.08.2001): 3735–52. http://dx.doi.org/10.1088/0264-9381/18/17/322.

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19

Inoue, Nobuki, i Takahito Nakajima. "Douglas–Kroll and infinite order two-component transformations of Dirac–Fock operator". Journal of Chemical Physics 158, nr 4 (28.01.2023): 044103. http://dx.doi.org/10.1063/5.0131926.

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We extended the conventional Douglas–Kroll (DK) and infinite order two-component (IOTC) methods to a technique applicable to Fock matrices, called extended DK (EDK) and extended IOTC (EIOTC), respectively. First, we defined a strategy to divide the Dirac–Fock operator into zero- and first-order terms. We then demonstrated that the first-order extended DK transformation, which is the Foldy–Wouthuysen transformation for the zero-order term, as well as the second- and third-order EDK and EIOTC, could be well defined. The EDK- and EIOTC-transformed Fock matrix, kinetic energy operator, nuclear attraction operator, and density matrix were derived. These equations were numerically evaluated, and it was found that these methods were accurate. In particular, EIOTC was consistent with the four-component approach. Four-component and extended two-component calculations are more expensive than non-relativistic calculations due to small-component-type two-electron integrals. We developed a new approximation formula, RIS-V, for small-component-type two-electron integrals, including the spin–orbit interaction between electrons. These results suggest that the RIS-V formula effectively accelerates the four-component and extended two-component methods.
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20

Cortez, Jerónimo, Beatriz Elizaga Navascués, Guillermo A. Mena Marugán, Santiago Prado i José M. Velhinho. "Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology". Universe 6, nr 12 (13.12.2020): 241. http://dx.doi.org/10.3390/universe6120241.

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In generic curved spacetimes, the unavailability of a natural choice of vacuum state introduces a serious ambiguity in the Fock quantization of fields. In this review, we study the case of fermions described by a Dirac field in non-stationary spacetimes, and present recent results obtained by us and our collaborators about well-motivated criteria capable to ensure the uniqueness in the selection of a vacuum up to unitary transformations, at least in certain situations of interest in cosmology. These criteria are based on two reasonable requirements. First, the invariance of the vacuum under the symmetries of the Dirac equations in the considered spacetime. These symmetries include the spatial isometries. Second, the unitary implementability of the Heisenberg dynamics of the annihilation and creation operators when the curved spacetime is treated as a fixed background. This last requirement not only permits the uniqueness of the Fock quantization but, remarkably, it also allows us to determine an essentially unique splitting between the phase space variables assigned to the background and the fermionic annihilation and creation variables. We first consider Dirac fields in 2 + 1 dimensions and then discuss the more relevant case of 3 + 1 dimensions, particularizing the analysis to cosmological spacetimes with spatial sections of spherical or toroidal topology. We use this analysis to investigate the combined, hybrid quantization of the Dirac field and a flat homogeneous and isotropic background cosmology when the latter is treated as a quantum entity, and the former as a perturbation. Specifically, we focus our study on a background quantization along the lines of loop quantum cosmology. Among the Fock quantizations for the fermionic perturbations admissible according to our criteria, we discuss the possibility of further restricting the choice of a vacuum by the requisite of a finite fermionic backreaction and, moreover, by the diagonalization of the fermionic contribution to the total Hamiltonian in the asymptotic limit of large wave numbers of the Dirac modes. Finally, we argue in support of the uniqueness of the vacuum state selected by the extension of this diagonalization condition beyond the commented asymptotic region, in particular proving that it picks out the standard Poincaré and Bunch–Davies vacua for fixed flat and de Sitter background spacetimes, respectively.
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21

Dvoeglazov, Valeriy V. "Negative Energies in the Dirac Equation". Zeitschrift für Naturforschung A 71, nr 4 (1.04.2016): 345–49. http://dx.doi.org/10.1515/zna-2015-0494.

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AbstractIt is easy to check that both algebraic equation $Det(\hat p\, - \,m)\, = \,0$ and $Det(\hat p\, + \,m)\, = \,0$ for u– and v– 4-spinors have solutions with ${p_0}\, = \, \pm {E_p}\, = \, \pm \,\sqrt {{{\bf{p}}^2}\, + \,{m^2}} .$ The same is true for higher-spin equations. Meanwhile, every book considers the equality p0=Ep for both u– and v– spinors of the (1/2, 0)⊕(0, 1/2) representation only, thus applying the Dirac–Feynman–Stueckelberg procedure for elimination of the negative-energy solutions. The recent Ziino works (and, independently, the articles of several others) show that the Fock space can be doubled. We reconsider this possibility on the quantum field level for both s=1/2 and higher-spin particles.
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22

FITZGERALD, P. L. "THE SUPERFIELD QUANTISATION OF A SUPERPARTICLE ACTION WITH AN EXTENDED LINE ELEMENT". International Journal of Modern Physics A 20, nr 12 (10.05.2005): 2639–55. http://dx.doi.org/10.1142/s0217751x05022263.

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A massive superparticle action based on the generalised line element in N = 1 global superspace is quantised canonically. A previous method of quantising this action, based on a Fock space analysis, showed that states existed in three supersymmetric multiplets, each of a different mass. The quantisation procedure presented uses the single first class constraint as an operator condition on a general N = 1 superwavefunction. The constraint produces coupled equations of motion for the component wavefunctions. Transformations of the component wavefunctions are derived that decouple the equations of motion and partition the resulting wavefunctions into three separate supermultiplets. Unlike previous quantisations of superparticle actions in N = 1 global superspace, the spinor wavefunctions satisfy the Dirac equation and the vector wavefunctions satisfy the Proca equation. The off-shell closure of the commutators of the supersymmetry transformations, that include mass parameters, are derived by the introduction of auxiliary wavefunctions. To avoid the ghosts arising in a previous Fock space quantisation an alternative conjugation is used in the definition of the current, based on a Krein space approach.
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23

Huber, Matthias, i Heinz Siedentop. "Solutions of the Dirac–Fock Equations and the Energy of the Electron-Positron Field". Archive for Rational Mechanics and Analysis 184, nr 1 (7.06.2006): 1–22. http://dx.doi.org/10.1007/s00205-006-0016-6.

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24

PUDDU, G. "A TIME-DEPENDENT MULTI-DETERMINANT APPROACH TO NUCLEAR DYNAMICS". International Journal of Modern Physics E 22, nr 06 (czerwiec 2013): 1350040. http://dx.doi.org/10.1142/s0218301313500407.

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We propose a Time-Dependent Multi-Determinant (TDMD) approach to the description of the time evolution of the nuclear wave functions. We use the Dirac variational principle to derive the equations of motion using as ansatz for the nuclear wave function a linear combination of Slater determinants. We prove explicitly that the norm and the energy of the wave function are conserved during the time evolution. This approach is a generalization of the time-dependent Hartree–Fock method to many Slater determinants. We apply this approach to a case study of 6 Li using the N3LO interaction renormalized to four major harmonic oscillator shells. We solve the TDMD equations of motion using Krylov subspace methods of Lanczos type. As an application, we discuss the isoscalar monopole strength function.
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25

Ovsiyuk, E. M., A. D. Koral’kov, A. V. Chichurin i V. M. Red’kov. "Dirac Particle in the Coulomb Field on the Background of Hyperbolic Lobachevsky Model". Nonlinear Phenomena in Complex Systems 24, nr 3 (12.10.2021): 260–71. http://dx.doi.org/10.33581/1561-4085-2021-24-3-260-271.

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The known systems of radial equations describing the relativistic hydrogen atom on the base of the Dirac equation in Lobachevsky hyperbolic space is solved. The relevant 2-nd order differential equation has six regular singular points, its solutions of Frobenius type are constructed explicitly. To produce the quantization rule for energy values we have used the known condition for determination of the transcendental Frobenius solutions. This defines the energy spectrum which is physically interpretable and similar to the spectrum arising for the scalar Klein-Fock-Gordon equation in Lobachevsky space. In the present paper, exact analytical solutions referring to this spectrum are constructed. Convergence of the series involved is proved analytically and numerically. Squared integrability of the solutions is demonstrated numerically. It is shown that the spectrum coincides precisely with that previously found within the semi-classical approximation.
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26

KRUGLOV, S. I. ""SQUARE ROOT" OF THE PROCA EQUATION: SPIN-3/2 FIELD EQUATION". International Journal of Modern Physics A 21, nr 05 (20.02.2006): 1143–55. http://dx.doi.org/10.1142/s0217751x06024980.

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New equations describing particles with spin-3/2 are derived. The nonlocal equation with the unique mass can be considered as "square root" of the Proca equation in the same sense as the Dirac equation is related to the Klein–Gordon–Fock equation. The local equation describes spin-3/2 particles with three mass states. The equations considered involve fields with spin-3/2 and spin-1/2, i.e. multispin 1/2, 3/2. The projection operators extracting states with definite energy, spin, and spin projections are obtained. All independent solutions of the local equation are expressed through projection matrices. The first order relativistic wave equation in the 20-dimensional matrix form, the relativistically invariant bilinear form and the corresponding Lagrangian are given. Two parameters characterizing nonminimal electromagnetic interactions of fermions are introduced, and the quantum-mechanical Hamiltonian is found. It is proved that there is only causal propagation of waves in the approach considered.
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27

Nishiyama, Seiya. "Resonating Relativistic Mean Field Theory of Finite Nuclei". International Journal of Modern Physics E 07, nr 05 (październik 1998): 601–24. http://dx.doi.org/10.1142/s0218301398000348.

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We develop a general theory based on relativistic fields to describe finite nuclei with large quantum fluctuations. The theory is a direct extension of the resonating Hartree-Fock (HF) and resonating Hartree-Bogoliubov (HB) theories to the relativistic mean field case including an effective nucleon mass and an effective potential mediated by mesons. We start from the Walecka model and construct coherent state representations of a system of nucleons described by Dirac spinors and of mesons described in terms of bosons. A state with large quantum fluctuations is approximated by superpositions of non-orthogonal nucleon and meson wave functions with different correlation structures. We derive the variational equations to determine the two kinds of coefficients of fermionic and bosonic configuration mixings and the two kinds of fermionic and bosonic orbitals in the resonating nucleon and meson wave functions.
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28

Lokot, Lyubov E. "Particle-hole pair and beelectron states in ZnO/(Zn,Mg)O quantum wells and Dirac materials." JOURNAL OF ADVANCES IN PHYSICS 10, nr 1 (5.08.2015): 2583–604. http://dx.doi.org/10.24297/jap.v10i1.1344.

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In this paper a theoretical studies of the space separation of electron and hole wave functions in the quantum well ZnO/Mg(0.27)Zn(0.73)O are presented. For this aim the self-consistent solution of the Schrödinger equations for electrons and holes and the Poisson equations at the presence of spatially varying quantum well potential due to the piezoelectric effect and local exchange-correlation potential is found. The one-dimensional Poisson equation contains the Hartree potential which includes the one-dimensional charge density for electrons and holes along the polarization field distribution. The three-dimensional Poisson equation contains besides the one-dimensional charge density for electrons and holes the exchange-correlation potential which is built on convolutions of a plane-wave part of wave functions in addition. The shifts of the Hartree valence band spectrums and the conduction band spectrum with respect to the flat band spectrums as well as the Hartree-Fock band spectrums with respect to the Hartree ones are found. An overlap integrals of the wave functions of holes and electron with taking into account besides the piezoelectric effects the exchange-correlation effects in addition is greater than an overlap integral of Hartree ones. The Hartree particles distribute greater on edges of quantum well than Hartree-Fock particles. It is found that an effective mass of heavy hole of Mg(0.27)Zn(0.73)O under biaxial strain is greater than an effective-mass of heavy hole of ZnO. It is calculated that an electron mass is less than a hole mass. It is found that the Bohr radius is grater than the localization range particle-hole pair, and the excitons may be spontaneously created.Schrödinger equation for pair of two massless Dirac particles when magnetic field is applied in Landau gauge is solved exactly. In this case the separation of center of mass and relative motion is obtained. Landau quantization $\epsilon=\pm\,B\sqrt{l}$ for pair of two Majorana fermions coupled via a Coulomb potential from massless chiral Dirac equation in cylindric coordinate is found. The root ambiguity in energy spectrum leads into Landau quantization for beelectron, when the states in which the one simultaneously exists are allowed. The tachyon solution with imaginary energy in Cooper problem ($\epsilon^{2}<0$) is found.
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29

Wei, Liqiang, i Chiachung Sun. "Orbital approximation for the reduced Bloch equations: Fermi–Dirac distribution for interacting fermions and Hartree–Fock equation at finite temperature". Physica A: Statistical Mechanics and its Applications 334, nr 1-2 (marzec 2004): 151–59. http://dx.doi.org/10.1016/j.physa.2003.10.071.

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30

Ebeling, Werner, Heidi Reinholz i Gerd Röpke. "Hydrogen, helium and lithium plasmas at high pressures". European Physical Journal Special Topics 229, nr 22-23 (grudzień 2020): 3403–31. http://dx.doi.org/10.1140/epjst/e2020-000066-6.

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AbstractThe equations of state (EoS) and other thermodynamic properties of plasmas of the light elements H, He, and Li, are calculated using inverted fugacity expansions. Fugacity expansions are known as an alternative to density expansions but show often an inferior convergence. If, however, the inversion can be solved, the fugacity representations may be very efficient. In particular, the contributions of deeply bound states are included in the fugacity expansion in a very effective way. The mathematical problems on nonlinearity connected with the inversion of fugacities to densities are reduced to solvable algebraic problems. The inversion of fugacities to densities is solved separately for two density regions: (i) In the low density, non-degenerate region we consider ring contributions describing screening effects and ladder contributions describing bound state formation. (ii) In the high density, degenerate region the electrons are described by the Fermi–Dirac distribution. Hartree–Fock contributions and Pauli blocking have to be taken into account. The ions are considered as classical, strongly correlated subsystem eventually forming a Wigner lattice. We solve the inversion problem for each of the regions. Near the crossing point, the separate solutions are connected to each other, either by smooth concatenation at the crossing point or by Padé approximations.
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31

Bunge, C. F., R. J'auregui i E. Ley-Koo. "Article". Canadian Journal of Physics 76, nr 6 (1.06.1998): 421–44. http://dx.doi.org/10.1139/p98-023.

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When the one-body part of the relativistic Hamiltonian H is asum of one-electron Dirac Hamiltonians, relativistic configurationinteraction (CI) calculations are carried out on an ad hocbasis of positive-energy orbitals, {u+j; j=1,2,...,m}, andmore recently, with the full bases of positive-energy andnegative-energy orbitals, {u+j ,u-j ;j=1,2,...,m}. Therespective eigenproblems,H+C+k=E+kC+k, k=1,2,..., N(m),andHCk=EkCk ; k=1,2,...,N(2m)are related throughE+k <= Ek+N(2m)-N(m)establishing a new variational principle for relativistic calculationsof electronic structures.In this paper, on the basis of Brillouin's theorem and a relativisticmulticonfiguration Hartree-Fock (RMCHF) expansion in the{u+j, u-j; j=1,2,...,m} basis, we develop equations to annihilatethe coefficients of all single excitations to obtain very accurateRMCHF solutions.Moreover, after nullifying the coefficients of single excitations,the above inequality among energies becomes an equality,leading to a particular instance of an exact decoupling ofpositive-energy and negative-energy orbitals, irrespective of anyad hoc choice of potentials, hence rigorously justifying, forthe first time, the absence of explicit projection operators in allcurrent relativistic work where one-electron Dirac Hamiltoniansare involved.We present, also for the first time, relativistic Hartree-Fockapproximations for the ground states of He through Ar, which areaccurate to six decimals in a.u., and which converge to thenonrelativistic results when the speed of light c -> infinity.This accuracy was obtained by means of compact Slater-type orbitalexpansions through a direct translation of nonrelativistic Hartree-Fockwithout need to reoptimize nonlinear parameters. Our SCFequations are also valid for any open shells and for anyexcited states within a given symmetry, as exemplified withapplications to odd-parity, J = 1/2, 1s22s22p2np statesof neutral nitrogen. PACS Nos.: 31.10+z, 11.80Fv, 31.20Tz, 31.30Jv
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32

Dorne, Anaïs, Bijaya K. Sahoo i Anders Kastberg. "Relativistic Coupled-Cluster Calculations of Isotope Shifts for the Low-Lying States of Ca II in the Finite-Field Approach". Atoms 9, nr 2 (3.05.2021): 26. http://dx.doi.org/10.3390/atoms9020026.

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We have evaluated the isotope shift (IS) constants of the first five low-lying fine-structure states of the singly charged calcium ion (Ca II) by adopting a finite-field (FF) approach in the relativistic coupled-cluster (RCC), a method developed by us and by using a code also developed by us. A similar previous calculation using singles and doubles approximation RCC theory (RCCSD method), gives results for the individual states in the FF approach that deviate substantially, while the differential values (the shifts of the spectral lines) agree reasonably well with other theoretical results and with experiments. However, we find a contrasting trend from the FF approach using our RCCSD method although calculations with the Dirac–Hartree–Fock (DHF) method shows good agreement. Our results also show that inclusion of partial triple excitations in the perturbative approach (RCCSD(T) method) through energy derivation lessens accuracy, but these results can be improved when triple excitations are included in the wave function that determines the RCC equations. The differences between the RCCSD and RCCSD(T) results demonstrate the importance of triple excitations in evaluating energies and IS constants for Ca II. Finally, we also present ab initio values of IS’s between the S–P, S–D, and D–P transitions in the DHF, and RCCSD and RCCSD(T) approximations and this is compared to the previously reported values (theoretical as well as experimental).
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33

Paturel, Éric. "Solutions of the Dirac-Fock equations without projector". Journées équations aux dérivées partielles, 2000, 1–10. http://dx.doi.org/10.5802/jedp.576.

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34

MAHATO, DIBYENDU, Lalita Sharma, Saumyashree Baral, Subhasish Saha, Jobin Jose i Rajesh Srivastava. "Study of electron impact elastic scattering from Kr@C60 and Xe@C60 using a fully relativistic approach". Journal of Physics B: Atomic, Molecular and Optical Physics, 22.06.2022. http://dx.doi.org/10.1088/1361-6455/ac7b59.

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Abstract In the present work, a detailed study has been reported on electron impact elastic scattering from Krypton (Kr) and Xenon (Xe) atoms when confined in two different types of C60 potentials viz. (a) hard annular square well (ASW) and (b) diffused Gaussian annular square well (GASW). The Dirac equations are solved using these potentials for encaged Kr and Xe in C60. First, bound state Dirac-Fock wave functions of these encaged Kr and Xe atoms are found by utilizing modified general relativistic atomic structure package (GRASP) and thereafter, the charge densities and static potentials of the endohedral Kr@C60 and Xe@C60 are obtained. Further, using these, the Dirac equations are solved by the relativistic partial wave phase shift analysis method and the scattering amplitudes in terms of phase shifts are obtained. Thereafter, the differential and integrated cross sections are calculated. The electron elastic differential and integrated cross section of Kr@C60 and Xe@C60 along with the C60 are calculated in the range of 0.1-15 eV incident electron energies. Presently, no experimental and theoretical results are available to compare our electron scattering cross section results from Kr@C60 and Xe@C60; thus, we have shown the cross section results obtained from ASW and GASW potential and compared them.
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35

Furusawa, Shun, Hajime Togashi, Kohsuke Sumiyoshi, Koichi Saito, Shoichi Yamada i Hideyuki Suzuki. "Nuclear statistical equilibrium equation of state with a parametrized Dirac–Brückner Hartree–Fock calculation". Progress of Theoretical and Experimental Physics 2020, nr 1 (1.01.2020). http://dx.doi.org/10.1093/ptep/ptz135.

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Abstract We calculate new equations of state (EOSs) for astrophysical simulations in the framework of the extended nuclear statistical equilibrium, in which we minimize the free energy density for the full ensemble of nuclei in a hot and dense stellar environment. To evaluate bulk and surface energies of heavy nuclei and free energies of uniformly distributed nucleons, we use fitting formulae for the interaction energies and single-nucleon potentials at zero temperature of a Dirac–Brückner Hartree–Fock (DBHF) theory, one of the modern approaches to describe homogeneous nuclear matter. We find that the DBHF EOS exhibits larger mass fractions for medium-mass nuclei and smaller mass fractions for the other nuclei than the EOS obtained using the variational method (VM), another modern model for homogeneous nuclear matter. This effect is due to the more deeply bound energy for symmetric nuclear matter and the larger symmetry energy encoded in the DBHF EOS. At supra-nuclear densities, the DBHF EOS exhibits characteristics of a larger free energy, a higher pressure, and a larger neutron chemical potential of neutron-rich matter, which lead to a larger radius of cold neutron stars than that obtained by the VM EOS.
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36

Kupliauskienė, Alicija. "Theoretical study of 4p5nln'l'LSJstates of Sr ion excited by electron impact on Sr atom". Lithuanian Journal of Physics 58, nr 3 (5.11.2018). http://dx.doi.org/10.3952/physics.v58i3.3810.

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Calculations of energy levels and electron-impact excitation cross sections of the Auger autoionizing states 4p5nln'l'(nl= 4d, 5s, 5p; n'l'= 4d, 5s, 5p, 5d, 6s, 6p, 6d, 7s, 7p) of Sr ion were performed. A large-scale configuration interaction method on the basis of the solutions of Dirac–Fock–Slater equations was used. The cross sections of electron-impact simultaneous ionization and excitation, and Auger decay of the electron-impact excited states of Sr atom to the 4p-core excited autoionizing states of Sr ion were calculated for the first time and used to estimate the intensity of ejected electron lines. Tentative identification of the Auger electron lines of Sr ion registered in a number of experiments is presented.
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