Perturbation theory of short-range atomic interactions

1970 ◽  
Vol 317 (1531) ◽  
pp. 545-574 ◽  
Keyword(s):  
Perturbation Theory ◽  
Short Range ◽  
Similarity Transformation ◽  
Order Theory ◽  
First Order ◽  
Hartree Fock ◽  
First Order Theory ◽  
Atomic Interactions ◽  
Cusp Conditions ◽  
Molecular Calculations

A new united atom perturbation theory of the interaction of two atoms at small separations is described. The key feature is a similarity transformation of the Schrödinger equation which enables the cusp conditions to be satisfied at both nuclei and preserves the correct molecular symmetry. The first-order theory is examined in detail and compared with other united atom theories. Numerical calculations are presented for the ground states of the systems H + 2 , HeH 2+ HeH, He 2 and Li + He, based mainly on Hartree-Fock wavefunctions for the united atoms, and are compared with accurate molecular calculations. The agreement is remarkably good for separations up to 1 bohr.

An Experiment on Compressible-Flow Perturbations

1959 ◽  
Vol 26 (1) ◽  
pp. 114-119
Author(s):  
T. A. d’Ews Thomson ◽  
R. E. Meyer
Keyword(s):  
Perturbation Theory ◽  
Order Theory ◽  
Linear Perturbation ◽  
Pressure Gradients ◽  
Local Pressure ◽  
Supersonic Wind Tunnel ◽  
First Order ◽  
First Order Theory ◽  
Mach Number Distribution ◽  
Linear Perturbation Theory

Abstract The effect which a slight tilting of the liners of a supersonic wind-tunnel nozzle has on the Mach-number distribution in the test-rhombus is determined on the basis of the linear-perturbation theory of reference [1]. Experiments are reported which (a) confirm that the first-order subsonic and transonic perturbations of the flow may be neglected compared with the supersonic perturbations, and (b) indicate that appreciable effects not accounted for by the first-order theory occur when the flow possesses high local pressure gradients.

scholarly journals A first-order theory of Ulm type

Computability ◽  
2019 ◽  
Vol 8 (3-4) ◽  
pp. 347-358
Author(s):  
Matthew Harrison-Trainor
Keyword(s):  
Order Theory ◽  
First Order ◽  
First Order Theory

scholarly journals Quasi-decidability of a Fragment of the First-Order Theory of Real Numbers

2015 ◽  
Vol 57 (2) ◽  
pp. 157-185 ◽  
Author(s):  
Peter Franek ◽  
Stefan Ratschan ◽  
Piotr Zgliczynski
Keyword(s):  
Order Theory ◽  
Real Numbers ◽  
First Order ◽  
First Order Theory

The spectrum of resplendency

1990 ◽  
Vol 55 (2) ◽  
pp. 626-636
Author(s):  
John T. Baldwin
Keyword(s):  
Homogeneous Model ◽  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Uncountable Cardinal ◽  
Recursive Theory ◽  
Finite Language

AbstractLet T be a complete countable first order theory and λ an uncountable cardinal. Theorem 1. If T is not superstable, T has 2λ resplendent models of power λ. Theorem 2. If T is strictly superstable, then T has at least min(2λ, ℶ2) resplendent models of power λ. Theorem 3. If T is not superstable or is small and strictly superstable, then every resplendent homogeneous model of T is saturated. Theorem 4 (with Knight). For each μ ∈ ω ∪ {ω, 2ω} there is a recursive theory in a finite language which has μ resplendent models of power κ for every infinite κ.

Sign in / Sign up

Export Citation Format

Share Document