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Absence of a Scott Correction for the Total Binding Energy of Noninteracting Fermions in a Smooth Potential Well

Citation

Huxtable, Barton Duane (1988) Absence of a Scott Correction for the Total Binding Energy of Noninteracting Fermions in a Smooth Potential Well. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/87FQ-5X29. https://resolver.caltech.edu/CaltechETD:etd-09062005-101909

Abstract

It is shown, for V in a particular class of smooth functions, that the total binding energy, E(Z), of Z noninteracting Fermions in the potential well Z4/3V(Z1/3x), obeys E(Z) = cTF(V)Z7/3 + 0(Z5/3) as Z → ∞. Here cTF(V) is the coefficient predicted by the Thomas-Fermi theory. This result is consistent with the conjectured Scott correction, which occurs at order Z2, to the total binding energy of an atom of atomic number Z. This correction is thought to arise only because V(x) ~ - |x|1 near x - 0 in the atomic problem, and so V is not a smooth function.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Atomic physics; quantum mechanics; Scott correction; semi-classical approximation; Thomas-Fermi theory
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Simon, Barry M.
Thesis Committee:
  • Simon, Barry M. (chair)
  • Barnes, Charles A.
  • Cross, Michael Clifford
  • Koonin, Steven E.
Defense Date:16 June 1987
Non-Caltech Author Email:bhuxtable (AT) usersystems.com
Funders:
Funding AgencyGrant Number
NSFUNSPECIFIED
Earle C. Anthony FellowshipUNSPECIFIED
CaltechUNSPECIFIED
Record Number:CaltechETD:etd-09062005-101909
Persistent URL:https://resolver.caltech.edu/CaltechETD:etd-09062005-101909
DOI:10.7907/87FQ-5X29
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3349
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:06 Sep 2005
Last Modified:29 Jan 2020 01:18

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