Generalized nonorthogonal matrix elements: Unifying Wick’s theorem and the Slater–Condon rules

Recent theoretical work has shown that the complete set of polarized elastic light-scattering studies should yield information about scatterer structure that has so far hardly been utilized. We present here calculations of angular dependences of light-scattering matrix elements for spheres near the Rayleigh and Rayleigh-Gans-Debye limits. The significance of single matrix elements is documented on examples that show how different matrix elements respond to changes in particle parameters. It appears that in the small-particle limit (Rg/λ < 0.1) we do not loose much information by ignoring "large particle" observables.

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Exact electromagnetic matrix elements and selection rules for relativistic hydrogenic atoms

Physical Review A ◽

10.1103/physreva.11.387 ◽

1975 ◽

Vol 11 (1) ◽

pp. 387-389 ◽

Cited By ~ 7

Author(s):

H. E. Moses

Keyword(s):

Matrix Elements ◽

Selection Rules

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OPTICAL TRANSITIONS IN A PARABOLIC GaAs/Ga1-xAlxAs SUPERLATTICES

Surface Review and Letters ◽

10.1142/s0218625x01001117 ◽

2001 ◽

Vol 08 (03n04) ◽

pp. 321-325

Author(s):

ŞAKIR ERKOÇ ◽

HATICE KÖKTEN

Keyword(s):

Transition Matrix ◽

Optical Transition ◽

Matrix Elements ◽

Electron States ◽

Parabolic Potential ◽

Consistent Field ◽

Self Consistent ◽

Self Consistent Field ◽

Transition Matrix Elements ◽

Scf Calculations

We have performed self-consistent field (SCF) calculations of the electronic structure of GaAs/Ga 1-x Al x As superlattices with parabolic potential profile within the effective mass theory. We have calculated the optical transition matrix elements involving transitions from the hole states to the electron states, and we have also computed the oscillator strength matrix elements for the transitions among the electron states.

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Soft-drop grooming for hadronic event shapes

Journal of High Energy Physics ◽

10.1007/jhep07(2021)142 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Jeremy Baron ◽

Daniel Reichelt ◽

Steffen Schumann ◽

Niklas Schwanemann ◽

Vincent Theeuwes

Keyword(s):

Event Generator ◽

Experimental Measurements ◽

Event Shape ◽

Matrix Elements ◽

Underlying Event ◽

Hadronic Event ◽

Wide Range ◽

Event Shapes ◽

The Impact ◽

Perturbative Corrections

Abstract Soft-drop grooming of hadron-collision final states has the potential to significantly reduce the impact of non-perturbative corrections, and in particular the underlying-event contribution. This eventually will enable a more direct comparison of accurate perturbative predictions with experimental measurements. In this study we consider soft-drop groomed dijet event shapes. We derive general results needed to perform the resummation of suitable event-shape variables to next-to-leading logarithmic (NLL) accuracy matched to exact next-to-leading order (NLO) QCD matrix elements. We compile predictions for the transverse-thrust shape accurate to NLO + NLL′ using the implementation of the Caesar formalism in the Sherpa event generator framework. We complement this by state-of-the-art parton- and hadron-level predictions based on NLO QCD matrix elements matched with parton showers. We explore the potential to mitigate non-perturbative corrections for particle-level and track-based measurements of transverse thrust by considering a wide range of soft-drop parameters. We find that soft-drop grooming indeed is very efficient in removing the underlying event. This motivates future experimental measurements to be compared to precise QCD predictions and employed to constrain non-perturbative models in Monte-Carlo simulations.

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