A statistical approach to perturbation theory and inverse‐energy‐weighted sum rules

1981 ◽  
Vol 22 (12) ◽  
pp. 2961-2967 ◽  
Author(s):  
Thirumala Raya Halemane
Keyword(s):  
Perturbation Theory ◽  
Statistical Approach ◽  
Sum Rules ◽  
Weighted Sum

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.

Breakdown of Asymptotic Sum Rules in Perturbation Theory

1969 ◽  
Vol 22 (18) ◽  
pp. 978-981 ◽  
Author(s):  
Stephen L. Adler ◽  
Wu-Ki Tung
Keyword(s):  
Perturbation Theory ◽  
Sum Rules

Generalized isospin sum rule: an application to magnetic transitions

1984 ◽  
Vol 62 (8) ◽  
pp. 764-770 ◽  
Author(s):  
John A. Montgomery ◽  
Kwang-Bock Yoo ◽  
Herbert Überall ◽  
B. Bosco
Keyword(s):  
Magnetic Dipole ◽  
Electron Scattering ◽  
Sum Rules ◽  
Experimental Results ◽  
Weighted Sum ◽  
Magnetic Transitions ◽  
Sum Rule ◽  
Numerical Predictions ◽  
Magnetic Dipole Transitions ◽  
Special Case

Energy-weighted sum rules with separated isospin contributions for arbitrary operators and multipolarities are developed for photonuclear and electron-scattering transitions. The Kurath sum rule is contained as a special case. Applying the sum rule to magnetic dipole transitions, ensuing numerical predictions for non-self-conjugate nuclei are compared with experimental results.

scholarly journals Improved calculation of the γ*γ → π process at low Q2 using LCSR’s and renormalization-group summation

2022 ◽  
Vol 258 ◽  
pp. 03003
Author(s):  
Sergey Mikhailov ◽  
Alexandr Pimikov ◽  
N.G. Stefanis
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Transition Form Factor ◽  
Sum Rules ◽  
Power Series Expansion ◽  
Transition Form ◽  
Analytic Perturbation Theory ◽  
Fixed Order ◽  
Best Fit ◽  
Good Agreement

We study two versions of lightcone sum rules to calculate the γ*γ → π0 transition form factor (TFF) within QCD. While the standard version is based on fixed-order perturbation theory by means of a power-series expansion in the strong coupling, the new method incorporates radiative corrections by renormalization-group summation and generates an expansion within a generalized fractional analytic perturbation theory involving only analytic couplings. Using this scheme, we determine the relative nonperturbative parameters and the first two Gegenbauer coefficients of the pion distribution amplitude (DA) to obtain TFF predictions in good agreement with the preliminary BESIII data, while the best-fit pion DA satisfies the most recent lattice constraints on the second moment of the pion DA at the three-loop level.

scholarly journals The influence of the nuclear surface diffuseness on the transition charge densities.

2019 ◽  
Vol 3 ◽  
pp. 104
Author(s):  
T. S. Kosmas ◽  
J. D. Vergados
Keyword(s):  
Sum Rules ◽  
Form Factors ◽  
Scattering Data ◽  
Nuclear Surface ◽  
Weighted Sum ◽  
Transition Form ◽  
Charge Densities ◽  
Nuclear Ground State ◽  
Surface Diffuseness ◽  
Model Approach

Proton partial occupancies of the nuclear surface orbits are used in a modified shell model approach to study isoscalar dipole transition charge densities and form factors for self-conjugate nuclei. The energy-weighted sum-rules of Harakeh-Dieperink for both the transition form factor and transition charge density are modified so as fractional occupation probabilities of the states may be used. The partial occupancies of the surface n/j-levels are determined by fitting to the experimental inelastic scattering data and compared with those found previously in the study of nuclear ground state properties

scholarly journals The strong coupling from $e^+e^-\to$~hadrons

2019 ◽  
Author(s):  
Diogo Boito ◽  
Maarten Golterman ◽  
Alex Keshavarzi ◽  
Kim Maltman ◽  
Daiskuke Nomura ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Strong Coupling ◽  
Sum Rules ◽  
Finite Energy ◽  
Order Perturbation ◽  
Decay Data ◽  
Systematic Effects ◽  
Fixed Order ◽  
Charm Mass ◽  
Good Agreement

We use a new compilation of the hadronic RR-ratio from available data for the process e^+e^-\toe+e−→ hadrons below the charm mass to determine the strong coupling \alpha_sαs, using finite-energy sum rules. Quoting our results at the \tauτ mass to facilitate comparison to the results obtained from similar analyses of hadronic \tauτ-decay data, we find \alpha_s(m_\tau^2)=0.298\pm 0.016\pm 0.006αs(mτ2)=0.298±0.016±0.006 in fixed-order perturbation theory, and \alpha_s(m_\tau^2)=0.304\pm 0.018\pm 0.006αs(mτ2)=0.304±0.018±0.006 in contour-improved perturbation theory, where the first error is statistical, and the second error combines various systematic effects. These values are in good agreement with a recent determination from the OPAL and ALEPH data for hadronic \tauτ decays. We briefly compare the R(s)R(s)-based analysis with the \tauτ-based analysis.

Logarithmic perturbation theory for a spiked oscillator and sum rules

2005 ◽  
Vol 103 (1) ◽  
pp. 19-24 ◽  
Author(s):  
S. K. Bandyopadhyay ◽  
K. Bhattacharyya
Keyword(s):  
Perturbation Theory ◽  
Sum Rules

scholarly journals Energy Weighted Sum Rules for Spin-Dependent Excitations of Nuclei

1980 ◽  
Vol 63 (5) ◽  
pp. 1599-1607 ◽  
Author(s):  
S. Nishizaki ◽  
K. Ando
Keyword(s):  
Sum Rules ◽  
Weighted Sum
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