Simulation of the exclusion principle in the neutron−16O interaction through a repulsive term and application to a three-body calculation of theO16(d,p)17O reaction

G. W. Bund; K. Ueta

doi:10.1103/physrevc.51.2819

Simulation of the exclusion principle in the neutron−16O interaction through a repulsive term and application to a three-body calculation of theO16(d,p)17O reaction

Physical Review C ◽

10.1103/physrevc.51.2819 ◽

1995 ◽

Vol 51 (5) ◽

pp. 2819-2822 ◽

Cited By ~ 1

Author(s):

G. W. Bund ◽

K. Ueta

Keyword(s):

Exclusion Principle ◽

Three Body ◽

Repulsive Term

Download Full-text

Quantum Mechanics and the Periodic Table

The Periodic Table ◽

10.1093/oso/9780190914363.003.0014 ◽

2019 ◽

Author(s):

Eric Scerri

Keyword(s):

Quantum Mechanics ◽

Quantum Theory ◽

Periodic Table ◽

Chemical Properties ◽

Pauli Exclusion Principle ◽

Niels Bohr ◽

Exclusion Principle ◽

Old Quantum Theory ◽

Set Up ◽

Three Body

In chapter 7, the influence of the old quantum theory on the periodic system was considered. Although the development of this theory provided a way of reexpressing the periodic table in terms of the number of outer-shell electrons, it did not yield anything essentially new to the understanding of chemistry. Indeed, in several cases, chemists such as Irving Langmuir, J.D. Main Smith, and Charles Bury were able to go further than physicists in assigning electronic configurations, as described in chapter 8, because they were more familiar with the chemical properties of individual elements. Moreover, despite the rhetoric in favor of quantum mechanics that was propagated by Niels Bohr and others, the discovery that hafnium was a transition metal and not a rare earth was not made deductively from the quantum theory. It was essentially a chemical fact that was accommodated in terms of the quantum mechanical understanding of the periodic table. The old quantum theory was quantitatively impotent in the context of the periodic table since it was not possible to even set up the necessary equations to begin to obtain solutions for the atoms with more than one electron. An explanation could be given for the periodic table in terms of numbers of electrons in the outer shells of atoms, but generally only after the fact. But when it came to trying to predict quantitative aspects of atoms, such as the ground-state energy of the helium atom, the old quantum theory was quite hopeless. As one physicist stated, “We should not be surprised . . . even the astronomers have not yet satisfactorily solved the three-body problem in spite of efforts over the centuries.” A succession of the best minds in physics, including Hendrik Kramers, Werner Heisenberg, and Arnold Sommerfeld, made strenuous attempts to calculate the spectrum of helium but to no avail. It was only following the introduction of the Pauli exclusion principle and the development of the new quantum mechanics that Heisenberg succeeded where everyone else had failed.

Download Full-text

Contributions of Three-body Overlap Effects to the Force Fields in CaF2-type Shell-model Lattices

Zeitschrift für Naturforschung A ◽

10.1515/zna-1972-8-906 ◽

1972 ◽

Vol 27 (8-9) ◽

pp. 1196-1210

Author(s):

Ø. Ra

Keyword(s):

Force Field ◽

Shell Model ◽

Long Range ◽

Short Range ◽

Equations Of Motion ◽

Exclusion Principle ◽

Electronic Charge ◽

Short Range Force ◽

Model Equations ◽

Three Body

Abstract Due to the exclusion principle the distribution of electronic charge in an ionic crystal differs from a superposition of free-ion charge densities even in the simple Heitler-London picture. This charge density deformation engenders three-body long-range forces the influence of which on lattice vibrations is not accounted for by the usual Kellermann matrix. To obtain a better separation of long-range from short-range forces in CaF2 , SrF2, and BaF2 , i. e. to avoid absorbing long-range interactions in an adjustable short-range force field, explicit formulae are derived for three-body contributions to the shell-model equations of motion. The additional dynamical matrices pertain to arbitrary wavelengths. In adding to the force field terms which are not purely volume dependent the present descirption of three-body forces is somewhat at variance with recent work on alkali halide dynamics. The deviation from pure volume dependence originates in overlap charges residing in internuclear regions.

Download Full-text