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Register a new userA new perturbation technique for eigenenergies of the screened coulomb potential
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The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem of the radial Shrodinger equation with the screened Coulomb potential is developed. Based upon h-expansions and new quantization conditions a novel procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained.
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The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein-Gordon equation with attractive real-analytic screened Coulomb potentials, contained time-component of a Lorentz four-vector and a Lorentz-scalar term, is developed. Based upon $hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues for the Hulthen potential containing the vector part as well as the scalar component are considered.
We obtain the quantized momentum eigenvalues, $P_n$, together with space-like coherent eigenstates for the space-like counterpart of the Schru007fodinger equation, the Feinberg-Horodecki equation, with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.
In this work we show the advantages of using the Coulomb-hole plus screened-exchange (COHSEX) approach in the calculation of potential energy surfaces. In particular, we demonstrate that, unlike perturbative $GW$ and partial self-consistent $GW$ approaches, such as eigenvalue-self-consistent $GW$ and quasi-particle self-consistent $GW$, the COHSEX approach yields smooth potential energy surfaces without irregularities and discontinuities. Moreover, we show that the ground-state potential energy surfaces (PES) obtained from the Bethe-Salpeter equation, within the adiabatic connection fluctuation dissipation theorem, built with quasi-particle energies obtained from perturbative COHSEX on top of Hartree-Fock (BSE@COHSEX@HF) yield very accurate results for diatomic molecules close to their equilibrium distance. When self-consistent COHSEX quasi-particle energies and orbitals are used to build the BSE equation the results become independent of the starting point. We show that self-consistency worsens the total energies but improves the equilibrium distances with respect to BSE@COHSEX@HF. This is mainly due to changes in the screening inside the BSE.
A new recursion procedure for deriving renormalized perturbation expansions for the one-dimensional anharmonic oscillator is offered. Based upon the $hbar$-expansions and suitable quantization conditions, the recursion formulae obtained have the same simple form both for ground and excited states and can be easily applied to any renormalization scheme. As an example, the renormalized expansions for the sextic anharmonic oscillator are considered.
An algorithm has been developed for the Geant4 Monte-Carlo package for the efficient computation of screened Coulomb interatomic scattering. It explicitly integrates the classical equations of motion for scattering events, resulting in precise tracking of both the projectile and the recoil target nucleus. The algorithm permits the user to plug in an arbitrary screening function, such as Lens-Jensen screening, which is good for backscattering calculations, or Ziegler-Biersack-Littmark screening, which is good for nuclear straggling and implantation problems. This will allow many of the applications of the TRIM and SRIM codes to be extended into the much more general Geant4 framework where nuclear and other effects can be included.
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