scholarly journals Distorted waves with exact nonlocal exchange: A canonical function approach

2006 ◽  
Vol 84 (3) ◽  
pp. 193-211
Author(s):  
K Fakhreddine ◽  
R J Tweed ◽  
G Nguyen Vien ◽  
C Tannous ◽  
J Langlois ◽  
...  
Keyword(s):  
Impact Ionization ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Triplet States ◽  
Canonical Function ◽  
S Wave ◽  
Hartree Fock ◽  
Low Energies ◽  
Distorted Waves ◽  
Scattering Lengths

The Canonical Function Method (CFM) is developed and applied, for the first time, to the distorted wave problem with exact nonlocal exchange. In electron impact ionization of hydrogenic systems, the latter originates from the Pauli exclusion principle that leads, in the Hartree–Fock approximation, to a radial Schrodinger equation of an integro-differential type. The application of the CFM with static and polarization potentials allows us to obtain the phaseshifts and scattering lengths in the s-wave singlet and triplet states at high (≥5 eV) and low energies (≤0.1 eV). The results are compared with those obtained by other methods based on exact exchange, local equivalent-exchange potentials and recently developed spectral integral equation methods (S-IEM). The accuracy, stability, and speed of convergence of the CFM are analysed and compare favorably with other methods including the highly accurate S-IEM. At very low energies, the CFM is superior to all known methods.PACS Nos.: 34.00.00, 34.50.–s, 03.65.–w, 02.60.Nm, 02.60.–x

PHASE TRANSITIONS IN SELF-GRAVITATING SYSTEMS

2006 ◽  
Vol 20 (22) ◽  
pp. 3113-3198 ◽  
Author(s):  
P. H. CHAVANIS
Keyword(s):  
Phase Transitions ◽  
Gaseous Phase ◽  
Binary Star ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Stellar Systems ◽  
Star Model ◽  
Low Energies ◽  
Gravitating Systems ◽  
Classical Particles

We discuss the nature of phase transitions in self-gravitating systems. We show the connection between the binary star model of Padmanabhan, the thermodynamics of stellar systems and the thermodynamics of self-gravitating fermions. We stress the inequivalence of statistical ensembles for systems with long-range interactions, like gravity. In particular, we contrast the microcanonical evolution of stellar systems from the canonical evolution of self-gravitating Brownian particles. At low energies, self-gravitating Hamiltonian systems experience a gravothermal catastrophe in the microcanonical ensemble. At low temperatures, self-gravitating Brownian systems experience an isothermal collapse in the canonical ensemble. For classical particles, the gravothermal catastrophe leads to a binary star surrounded by a hot halo while the isothermal collapse leads to a Dirac peak containing all the mass. For self-gravitating fermions, the collapse stops when quantum degeneracy comes into play through the Pauli exclusion principle. The end-product of the collapse is a fermion ball, resembling a cold white dwarf star, surrounded by a halo. We can thus describe a phase transition from a gaseous phase to a condensed phase. At high energies or high temperatures, the condensate can experience an explosion, reverse to the collapse, and return to the gaseous phase. Due to the existence of long-lived metastable states, the points of collapse and explosion differ. This leads to a notion of hysteretic cycle in microcanonical and canonical ensembles.

Hardness and HOMO-LUMO Gap Probed by the Helium Atom Pushing the Molecular Surface of the First-Row Hydride Molecules

2003 ◽  
Vol 68 (12) ◽  
pp. 2344-2354 ◽  
Author(s):  
Edyta Małolepsza ◽  
Lucjan Piela
Keyword(s):  
Helium Atom ◽  
Pauli Exclusion Principle ◽  
Structure Change ◽  
Molecular Surface ◽  
Exclusion Principle ◽  
Probe Position ◽  
Repulsion Energy ◽  
Ionic Dissociation ◽  
Probe Site ◽  
Homo Lumo

A molecular surface defined as an isosurface of the valence repulsion energy may be hard or soft with respect to probe penetration. As a probe, the helium atom has been chosen. In addition, the Pauli exclusion principle makes the electronic structure change when the probe pushes the molecule (at a fixed positions of its nuclei). This results in a HOMO-LUMO gap dependence on the probe site on the isosurface. A smaller gap at a given probe position reflects a larger reactivity of the site with respect to the ionic dissociation.

Identical Particles and Second Quantization: Occupation Number Representation

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Occupation Number ◽  
Annihilation Operator ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Number Representation ◽  
Second Quantization ◽  
Identical Particles ◽  
Fundamental Properties ◽  
Minimum Uncertainty ◽  
Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

scholarly journals THEORY OF COMPLEX SCATTERING LENGTHS

2001 ◽  
Vol 15 (03) ◽  
pp. 105-109
Author(s):  
M. S. HUSSEIN
Keyword(s):  
Scattering Length ◽  
Effective Range ◽  
Low Energies ◽  
T Matrix ◽  
Scattering Lengths ◽  
New Equation ◽  
Molecule Interaction ◽  
Complex Atom

We derive a generalized Low equation for the T-matrix appropriate for complex atom–molecule interaction. The properties of this new equation at very low energies are studied and the complex scattering length and effective range are derived.

scholarly journals Testing the Pauli Exclusion Principle for Electrons at LNGS

2015 ◽  
Vol 61 ◽  
pp. 552-559 ◽  
Author(s):  
H. Shi ◽  
S. Bartalucci ◽  
S. Bertolucci ◽  
C. Berucci ◽  
A.M. Bragadireanu ◽  
...  
Keyword(s):  
Pauli Exclusion Principle ◽  
Exclusion Principle

Thermonuclear plasma conditions in stellar interiors

1981 ◽  
Vol 300 (1456) ◽  
pp. 641-648
Keyword(s):  
Nuclear Reactions ◽  
Pauli Exclusion Principle ◽  
Significant Rise ◽  
Exclusion Principle ◽  
Reaction Products ◽  
Thermonuclear Reactions ◽  
Radiated Energy ◽  
Large Numbers ◽  
Stellar Interiors ◽  
Late Stages

Thermonuclear reactions provide the main source of radiated energy for stars and they are also believed to be responsible for the production of most of the heavy elements in the Universe. The thermonuclear plasma is confined by the force of gravitation and for most of a star’s history the reactions occur slowly and steadily. In some circumstances, the properties of a star change very rapidly and explosive nuclear reactions occur. In very dense stellar interiors the energy states available to electrons may be limited by the Pauli exclusion principle. When thermonuclear reactions start in such a degenerate gas, a rise in temperature is not accompanied by a significant rise in pressure and as a result there may be a runaway increase in reaction rate. In contrast, when reactions start in a non-degenerate gas, there is normally an effective thermostat. A star is usually opaque to reaction products, so that there is no problem in maintaining the reaction temperature, but at late stages of stellar evolution nuclear or elementary particle reactions may produce large numbers of neutrinos and antineutrinos that do escape.

scholarly journals Two-Cooper-pair problem and the Pauli exclusion principle

2010 ◽  
Vol 81 (17) ◽  
Author(s):  
Walter V. Pogosov ◽  
Monique Combescot ◽  
Michel Crouzeix
Keyword(s):  
Cooper Pair ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle

scholarly journals X rays on quantum mechanics: Pauli Exclusion Principle and collapse models at test

2015 ◽  
Vol 631 ◽  
pp. 012068 ◽  
Author(s):  
C Curceanu ◽  
S Bartalucci ◽  
A Bassi ◽  
S Bertolucci ◽  
C Berucci ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
X Rays ◽  
Collapse Models
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