arXiv subjects

Rajmund Krivec

Publications and source records attributed to Rajmund Krivec.

4 recordsLinked to original sources

arXiv2022

Fock expansion for two-electron atoms. High order angular coefficients

The Fock expansion, which describes the properties of two-electron atoms near the nucleus, is studied. The angular Fock coefficients $ψ_{k,p}(α,θ)$ with the maximum possible value of subscript $p$ are calculated on examples of the coefficients with $5\leq k \leq 10$. The presented technique makes it possible to calculate such angular coefficients for any arbitrarily large $k$. The mentioned coefficients being leading in the logarithmic power series representing the Fock expansion may be indispensable for the development of simple methods for calculating the helium-like electronic structure. The theoretical results obtained are verified by other suitable methods. The Wolfram Mathematica is used extensively.

physics.atom-ph↗

arXiv2020

The collinear helium atom and two-electron ions

Collinear configurations of the helium-like atomic systems, relevant, e.g., for the quasifree mechanism of the double photoionization of helium, are studied, parameterized by the single scalar parameter $-1\leq λ\leq1$ ("collinear parameter") where $λ=0$ corresponds to the electron-nucleus ($\textbf{e-n}$) coalescence and $λ=1$ corresponds to the electron-electron ($\textbf{e-e}$) coalescence. In general, $λ>0$ corresponds to the \textbf{n-e-e} configuration, and $λ<0$ to the \textbf{e-n-e} configuration. Simple mathematical representations of the expectation values of the Dirac delta function relevant for the collinear configurations are derived and calculated from fully three-body dynamics without approximation for the two-electron atomic wave functions with nuclear charge $1\leq Z\leq5$. Simple formulas for calculating the expectation values of the kinetic and potential energy operators in collinear configurations are derived. Unusual physical properties of the \textbf{n-e-e} collinear configurations found for certain ranges of $λ$ are presented. The first few angular Fock coefficients for collinear configurations are derived as functions of $λ$. Highly accurate model wave functions describing the ground states of the two-electron atoms with collinear arrangement of the particles are constructed. All results are illustrated by tables and figures.

physics.atom-ph↗

arXiv2019

Averaged electron densities of the helium-like atoms

Different kinds of averaging of the wavefunctions/densities of the two-electron atomic systems are investigated. Using the Pekeris-like method, the ground state wave functions $Ψ$ of the helium-like atoms with nucleus charge $1\leq Z\leq5$ are calculated in a few coordinate systems including the hyperspherical coordinates $\left\{R,α,θ\right\}$. The wave functions $Ψ_{av}(R)$ of the hyperspherical radius $R$ are calculated numerically by averaging $Ψ$ over the hyperspherical angles $α$ and $θ$. The exact analytic representations for the relative derivatives $Ψ_{av}'(0)/Ψ_{av}(0)$ and $Ψ_{av}''(0)/Ψ_{av}(0)$ are derived. Analytic approximations very close to the actual $Ψ_{av}(R)$ are obtained. Using actual wave functions $Ψ$, the one-electron densities $ρ(r)$ are calculated as functions of the electron-nucleus distance $r$. The relevant derivatives $ρ'(0)/ρ(0)$ and $ρ''(0)/ρ(0)$ characterizing the behavior of $ρ(r)$ near the nucleus are calculated numerically. Very accurate analytical approximations, representing the actual one-electron density both near the nucleus and far away from it, are derived. All the analytical and numerical results are supplemented with tables and graphs.

physics.atom-ph↗

arXiv2017

On detecting Higgs coupling in transitions of light atoms

In light of the known Higgs mass and the current constraints on the quark-lepton Higgs coupling, we derive conditions for extracting upper limits on the lepton-nucleon Higgs coupling from light atoms and ions, assuming the availability of locally precise two- and three-body methods might be beneficial. A recent work has proposed to extract these limits in heavy atoms where the Higgs term is enhanced by $\approx 10^3 AZ$, due to both the large coupling modifier and large $A$, $Z$, and assuming sufficiently precise relativistic electron wave functions. We first revisit the old idea of using the Lamb shift in light muonic ions where the coupling is enhanced by about $201^3 AZ^3$ primarily due to the concentration of the muon wave function at the origin, the muon coupling modifier already being close to 1. For the muonic helium an experimental precision below 0.1 ppm is required to reach the constraints on Higgs couplings. However, theoretical uncertainty is large due to nuclear potential dependence of the finite size terms enhanced by the small muon orbit, and their elimination by using several states is precluded due to the Lamb shift being the only precisely measurable state. In normal (electronic) light systems transitions between low-lying states lie near the optical region allowing precise experiments, and extraction may be possible by eliminating the finite-size, polarization and Zemach moment terms from a set of transitions, e.g. $1S-2S$ and improved $2^3S-2^3P$ and $2^1S-2^3S$ in ${\rm He}^+$, while isotope shifts could be used if additional transitions are measured as precisely.

hep-ph↗