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The ALPHA algorithm to evaluate the exact, tree-level matrix elements is reviewed in the context of multi-parton processes in QCD.
Implementation of our asymptotic expressions in this algorithm increases its efficiency substantially because the numerically expensive evaluation of the exact matrix elements is needed only for the neighboring particles.
The spin-angular part for these matrix elements is typically based on standard quantities such as matrix elements of the unit tensor, the (reduced) coefficients of fractional parentage as well as a number of other reduced matrix elements concerning various products of electron creation and annihilation operators.
The simplified model of 12-pulse rectifier that only considers the primary matrix elements is proposed by comparing the values and distribution of admittance matrix elements under positive-sequence and negative-sequence voltages and analyzing the harmonic production process of the AC current of rectifier.
The importance of asymmetric structure design to achieve considerable values of transition dipole matrix elements is demonstrated.
Quenching of the Mn L2 peak intensity due to multiple scattering effects and effects beyond dipole approximation in inelastic transition matrix elements is not considered.
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The Hamiltonian matrix elements were obtained in the numerical localized orbital basis set implementation39,40 within GGA.
In proportional counters the matrix elements are non-zero over a large area.
For selected uncorrelated atomic configurations, dipole matrix elements were calculated using the prescription described in ref. 36.
The Hamiltonian matrix elements were obtained using models with periodic boundary conditions imposed both along and across the interface.
Such a formulation leads to certain transcendental eigenvalue problems where the matrix elements are transcendental functions.
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