scholarly journals The Role of the Pauli Exclusion Principle in Nuclear Physics Models

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 738
Author(s):  
Josué R. M. Berriel-Aguayo ◽  
Peter O. Hess
Keyword(s):  
Nuclear Structure ◽  
Nuclear Physics ◽  
Pauli Exclusion Principle ◽  
Cluster Models ◽  
Exclusion Principle ◽  
Practical Reasons ◽  
Algebraic Models ◽  
Fermion Systems ◽  
Basic Concepts

The Pauli Exclusion Principle (PEP) is one of the most basic concepts in physics, but also the most difficult to implement in many-fermion systems, which are common in nuclear physics. To investigate the consequences of ignoring the PEP, we discuss several algebraic models in nuclear structure physics, in particular cluster models. Sometimes they tend to ignore the Pauli Exclusion Principle for practical reasons, leading to flawed interpretations. Though at first sight there seems to be an agreement to experiment, often it is due to the limited number of states known experimentally. We discuss several models which include or not the PEP, illustrating through their differences the importance of the PEP. This contribution is also a review of recently published results.

Quantum Constraints in π Systems: The Role of the Pauli Antisymmetry Principle for π Electronic Properties

1997 ◽  
Vol 52 (10) ◽  
pp. 717-726
Author(s):  
Michael C. Böhm ◽  
Johannes Schütt
Keyword(s):  
Hard Core ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Nearest Neighbour ◽  
Charge Fluctuations ◽  
Fermionic Systems ◽  
Ring Atom ◽  
Quantum Statistical ◽  
The Many

Abstract It is demonstrated that the Pauli antisymmetry principle (PAP) is without influence in the π electron subspace of polyenes and (4n + 2) annulenes (n = 0, 1, 2...) as long as the hoppings are restricted to nearest-neighbour centers. Here the π electrons behave like a hard core bosonic (hcb) ensemble where fermionic on-site and bosonic intersite properties are combined. In 4n and (2n + 1) annulenes (n = 1,2, 3...) π electron jumps between the first and last ring atom lead to a Pauli antisymmetry-based destabilization. The second quantum constraint in fermionic systems is the Pauli exclusion principle (PEP). In the many-electron basis adopted in the present work it is possible to treat the PAP and PEP as two decoupled constraints. The electronic destabilization due to the PEP is enhanced with increasing size of the system. The influence of the PAP and PEP on the π electrons is discussed in terms of π energies and charge fluctuations. The model Hamiltonians adopted are of the Hückel molecular orbital (HMO) and Pariser-Parr-Pople (PPP) type. We suggest quantum statistical definitions of the quantities "aromaticity" and "antiaromaticity", qualitative descriptors which are widely employed in the chemical literature.

scholarly journals The nuclei 12C, 16O and the role of the Pauli Exclusion Principle

2019 ◽  
Vol 1308 ◽  
pp. 012011
Author(s):  
P. O. Hess ◽  
M. Berriel-Aguayo ◽  
L. J. Chávez-Nuñez
Keyword(s):  
Pauli Exclusion Principle ◽  
Exclusion Principle

scholarly journals BULK AND EDGE EXCITATIONS IN A ν=1 QUANTUM HALL FERROMAGNET

2001 ◽  
Vol 15 (19n20) ◽  
pp. 2747-2760
Author(s):  
RASHMI RAY
Keyword(s):  
Hilbert Space ◽  
Quantum Hall ◽  
Pauli Exclusion Principle ◽  
Collective Excitations ◽  
Exclusion Principle ◽  
Collective Coordinates ◽  
Fermion Systems ◽  
Effective Lagrangian ◽  
The Many ◽  
Finite Extent

In this article, we shall focus on the collective dynamics of the fermions in a ν=1 quantum Hall droplet. Specifically, we propose to look at the quantum Hall ferromagnet. In this system, the electron spins are ordered in the ground state due to the exchange part of the Coulomb interaction and the Pauli exclusion principle. The low energy excitations are ferromagnetic magnons. To provide a means for describing these magnons, we shall discuss a method of introducing collective coordinates in the Hilbert space of many-fermion systems. These collective coordinates are bosonic in nature. They map a part of the fermionic Hilbert space into a bosonic Hilbert space. Using this technique, we shall interpret the magnons as bosonic collective excitations in the Hilbert space of the many-electron Hall system. By considering a Hall droplet of finite extent, we shall also obtain the effective Lagrangian governing the spin collective excitations at the edge of the sample.

1. Matter from the inside

2014 ◽  
pp. 1-21
Author(s):  
Peter Atkins
Keyword(s):  
Quantum Mechanics ◽  
General Structure ◽  
Valence Bond ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Molecular Orbital Theory ◽  
Orbital Theory ◽  
Covalent Bonds ◽  
Bond Theory

‘Matter from the inside’ shows that one way to understand how a physical chemist thinks and contributes to chemistry is to start at the atom's interior and then travel out into the world of bulk matter. It begins with the electronic structure of atoms, introduces the role of quantum mechanics in accounting for electron arrangement, and outlines Schrödinger's model of s-, p-, d-, and f-orbitals and the Pauli exclusion principle. Physical chemistry accounts for the general structure of the Periodic Table. The radius, ionization energy, and electron affinity properties of atoms are then considered along with ionic and covalent bonds, and the quantum mechanics of bonds, including valence-bond theory and molecular orbital theory.

scholarly journals The key role of the Silicon Drift Detectors in testing the Pauli Exclusion Principle for electrons: the VIP-2 experiment

2020 ◽  
Vol 1548 ◽  
pp. 012033
Author(s):  
L De Paolis ◽  
A Amirkhani ◽  
S Bartalucci ◽  
S Bertolucci ◽  
M Bazzi ◽  
...  
Keyword(s):  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Silicon Drift Detectors

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.

Programming the Common Market: The Making and Failure of a ‘Dirigiste’ Europe, 1957–1967

2021 ◽  
pp. 1-15
Author(s):  
Hugo Canihac
Keyword(s):  
European Integration ◽  
European Economic Community ◽  
Early Years ◽  
Practical Reasons ◽  
Economic Governance ◽  
Economic Community ◽  
European Economic ◽  
History Of ◽  
The Common

This article contributes to the debate about the history of the political economy of the European Economic Community (EEC). It retraces the efforts during the early years of the EEC to implement a form of ‘European economic programming’, that is, a more ‘dirigiste’ type of economic governance than is usually associated with European integration. Based on a variety of archives, it offers a new account of the making and failure of this project. It argues that, at the time, the idea of economic programming found many supporters, but its implementation largely failed for political as well as practical reasons. In so doing, it also brings to light the role of economists during the early years of European integration.

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