Dangers of the ``Average Energy Approximation'' in Perturbation Theory

1960 ◽  
Vol 32 (4) ◽  
pp. 1263-1263 ◽  
Author(s):  
A. D. McLachlan
Keyword(s):  
Perturbation Theory ◽  
Average Energy ◽  
Energy Approximation

The chemical shift. I. Approximate theory and application to first row binary fluorides

1970 ◽  
Vol 48 (22) ◽  
pp. 3498-3503 ◽  
Author(s):  
F. G. Herring
Keyword(s):  
Perturbation Theory ◽  
Chemical Shift ◽  
Chemical Shifts ◽  
Average Energy ◽  
Approximate Theory ◽  
Hartree Fock ◽  
Nuclear Shielding ◽  
Energy Approximation

Starting from the approximations of the i.n.d.o.-l.c.a.o.-s.c.f. method and using approximate Hartree–Fock perturbation theory, a method has been developed whereby the nuclear shielding of a nucleus for a first row element may be estimated. The method avoids the use of the average energy approximation. The method is demonstrated by calculating the 19F chemical shifts in the first row binary fluorides relative to the fluorine molecule.

scholarly journals Anisotropic and isotropic triple-dipole dispersion energy coefficients for all three-body interactions involving He, Ne, Ar, Kr, Xe, H2, N2, and CO

1996 ◽  
Vol 74 (6) ◽  
pp. 1180-1186 ◽  
Author(s):  
Sean A.C. McDowell ◽  
Ashok Kumar ◽  
William J. Meath
Keyword(s):  
Input Data ◽  
Average Energy ◽  
Interaction Energies ◽  
Tabular Form ◽  
Rare Gases ◽  
Dispersion Energy ◽  
Interacting Species ◽  
Energy Approximation ◽  
Dipole Oscillator ◽  
Three Body

Formulae for the computation of isotropic and anisotropic dipolar dispersion energy coefficients, for two-body and three-body interactions involving H2, N2, CO, and the rare gases, are presented in an average energy approximation. These coefficients are computed to within 1% of the reliable values for these coefficients, which are obtained by using the relevant dipole oscillator strength distributions, with the exception of a few that are recorded in tabular form. The input data required for these formulae are the isotropic and anisotropic polarizabilities and average energies for the interacting species. The results provide the first reliable anisotropic triple-dipole dispersion energy coefficients for interactions involving molecules. Key words: non-additive, anisotropic, interaction energies, triple-dipole dispersion energies.

CHIRAL PERTURBATION THEORY AT THE QUARK LEVEL

1992 ◽  
Vol 07 (29) ◽  
pp. 7305-7338 ◽  
Author(s):  
A.N. IVANOV ◽  
M. NAGY ◽  
N.I. TROITSKAYA
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Final State Interaction ◽  
Low Energy ◽  
Chiral Perturbation ◽  
Final State ◽  
Large N ◽  
Quark Level ◽  
Energy Approximation

The chiral perturbation theory is developed at the quark level within the extended Nambu-Jona-Lasinio model, which we used for the low-energy approximation of QCD in the leading order of the large N expansion. In terms of constituent-quark loop diagrams we analyze all of the main low-energy effects caused by the first order corrections in the current-quark-mass expansions. For the correct description of the η→3π decays we confirm the important role of the final-state interaction quoted by Gasser and Leutwyler.

THE $K_L^0\to \pi ^0 \gamma \gamma$ DECAY IN CHIRAL PERTURBATION THEORY BASED ON THE EXTENDED NAMBU-JONA-LASINIO MODEL

1992 ◽  
Vol 07 (21) ◽  
pp. 5115-5129 ◽  
Author(s):  
ANDREI N. IVANOV
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chiral Limit ◽  
Decay Amplitude ◽  
Low Energy ◽  
Chiral Perturbation ◽  
Photon Exchange ◽  
Two Photon ◽  
Energy Approximation ◽  
Gamma Decay

The [Formula: see text] decay is analyzed within chiral perturbation theory based on the extended Nambu-Jona-Lasinio model, which is used as a low energy approximation of QCD. The two-photon spectrum of the [Formula: see text] decay and the value of the probability [Formula: see text] are obtained in good agreement with experimental data. It is shown that the CP-conserving two-photon exchange contribution to the [Formula: see text] decay mplitude is negligibly small compared to that of the CP-violating one-photon exchange. Also presented is the derivation of the low-energy theorem for the [Formula: see text] decay amplitude in the chiral limit.

Article

1998 ◽  
Vol 76 (4) ◽  
pp. 483-489 ◽  
Author(s):  
Sean AC McDowell ◽  
W J Meath
Keyword(s):  
Average Energy ◽  
Rare Gases ◽  
Dispersion Energy ◽  
Interacting Species ◽  
Energy Approximation ◽  
Three Body

Average energy approximations for the anisotropic triple-dipole dispersion energy coefficients are tested using reliable results for these coefficients, which are available for all interactions involving the rare gases, H2, N2, CO, O2, and NO. The original average energy approximation does not reproduce any of the anisotropic coefficients to within their estimated uncertainties. More recently derived average energy approximation formulae, requiring the isotropic and anisotropic polarizabilities and average energies for the interacting species as input, reproduce all but 69 of the 680 isotropic and anisotropic coefficients considered to within their estimated uncertainties.Key words: nonadditive, three-body interactions, dispersion energies.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Stopping-power determination for compound by EELS

1994 ◽  
Vol 52 ◽  
pp. 948-949 ◽  
Author(s):  
David C. Joy ◽  
Suichu Luo ◽  
John R. Dunlap ◽  
Dick Williams ◽  
Siqi Cao
Keyword(s):  
Energy Loss ◽  
Electron Energy ◽  
Electron Energy Loss Spectroscopy ◽  
Materials Science ◽  
Average Energy ◽  
Stopping Power ◽  
Accurate Information ◽  
Power Calculation ◽  
Coulomb Collisions ◽  
Electron Energy Loss

In Physics, Chemistry, Materials Science, Biology and Medicine, it is very important to have accurate information about the stopping power of various media for electrons, that is the average energy loss per unit pathlength due to inelastic Coulomb collisions with atomic electrons of the specimen along their trajectories. Techniques such as photoemission spectroscopy, Auger electron spectroscopy, and electron energy loss spectroscopy have been used in the measurements of electron-solid interaction. In this paper we present a comprehensive technique which combines experimental and theoretical work to determine the electron stopping power for various materials by electron energy loss spectroscopy (EELS ). As an example, we measured stopping power for Si, C, and their compound SiC. The method, results and discussion are described briefly as below.The stopping power calculation is based on the modified Bethe formula at low energy:where Neff and Ieff are the effective values of the mean ionization potential, and the number of electrons participating in the process respectively. Neff and Ieff can be obtained from the sum rule relations as we discussed before3 using the energy loss function Im(−1/ε).

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