arXiv subjects

Krzysztof Pachucki

Publications and source records attributed to Krzysztof Pachucki.

At least 55 records · Page 3Linked to original sources

arXiv2021

Hyperfine structure of the $2\,^3\!P$ state in $^9$Be and the nuclear quadrupole moment

We have performed accurate calculations of the hyperfine structure of the $2\,^3\!P$ state in the $^9$Be atom with the help of highly optimized, explicitly correlated functions, accounting for the leading finite nuclear mass, radiative, nuclear structure and relativistic effects. By comparison with measurements, we have determined the $^9$Be nuclear quadrupole moment to be $Q_{\rm N} = 0.05350(14)$ barns, which is not only the most accurate result, but also disagrees with previous determinations.

physics.atom-ph↗

arXiv2021

Nonradiative $α^7m$ QED effects in Lamb shift of helium triplet states

Theoretical predictions for the Lamb shift in helium are limited by unknown quantum electrodynamic effects of the order $α^7m$, where $α$ is the fine-structure constant and $m$ is the electron mass. We make an important step towards the complete calculation of these effects by deriving the most challenging part, which is induced by the virtual photon exchange between all three helium particles, the two electrons, and the nucleus. The complete calculation of the $α^7m$ effect including the radiative corrections will allow comparing of the nuclear charge radii determined from the electronic and muonic helium atoms and thus provide a stringent test of the Standard Model of fundamental interactions.

hep-ph↗

arXiv2021

Relativistic corrections to the Bethe logarithm for the $2^3S$ and $2^3P$ states of He

With this work we start a project of calculating the QED contribution of order $α^7m$ to the $2^3P$-$2^3S$ transition energy in helium, aiming for an accurate determination of the nuclear charge radius $r_E$ from measurements of the corresponding transition frequency. Together with the complementary determination of $r_E$ from muonic helium, this project will provide a stringent test of universality of electromagnetic interactions of leptons in the Standard Model. We report a calculation of the relativistic corrections to the Bethe logarithm for the $2^3S$ and $2^3P$ states, which is the most numerically demanding part of the project.

physics.atom-ph↗

arXiv2021

Radiative $\bm{α^7m}$ QED contribution to the helium Lamb shift

We present a derivation of the last unknown part of the $α^7m$ contribution to the Lamb shift of a two-electron atom, induced by the radiative QED effects beyond the Bethe logarithm. This derivation is performed in the framework of nonrelativistic quantum electrodynamics and is valid for the triplet (spin $S = 1$) atomic states. The obtained formulas are free from any divergences and are suitable for a numerical evaluation. This opens a way for a complete numerical calculation of the $α^7m$ QED effects in helium, which will allow an accurate determination of the nuclear charge radius from measurements of helium transition frequencies.

physics.atom-ph↗

arXiv2020

Hyperfine structure of the first rotational level in H$_2$, D$_2$ and HD molecules and the deuteron quadrupole moment

We perform the four-body calculation of the hyperfine structure in the first rotational state $J=1$ of the H$_2$, D$_2$, and HD molecules and determine the accurate value for the deuteron electric quadrupole moment $Q_d = 0.285\,699(15)(18)$ fm$^2$ in significant disagreement with former spectroscopic determinations. Our results for the hyperfine parameters agree very well with the currently most accurate molecular-beam magnetic resonance measurement performed several decades ago by N.F. Ramsey and coworkers. They also indicate the significance of previously neglected nonadiabatic effects. Moreover, a very good agreement with the recent calculation of $Q_d$ based on the chiral effective field theory, although much less accurate, indicates the importance of the spin dependence of nucleon interactions in the accurate description of nuclei.

physics.chem-ph↗

arXiv2020

QED calculation of the $\bf{2p}$ fine structure in Li-like ions

Large-scale {\em ab initio} QED calculations are performed for the $2p_{3/2}$--$2p_{1/2}$ fine-structure interval of Li-like ions with nuclear charges $Z = 5\,$--$\,92$. Improved theoretical predictions are obtained by combining together two complementary theoretical methods, namely, the approach that accounts for all orders in the binding nuclear strength and the nonrelativistic QED approach that accounts for all orders in the nonrelativistic electron-electron interaction. The resulting unified approach provides theoretical predictions which are more accurate than the available experimental results across the interval of the nuclear charges considered.

physics.atom-ph↗

arXiv2020

QED calculation of ionization energies of $1snd$ states in helium

Quantum electrodynamical (QED) calculations of ionization energies of the $1snd\,D$ states are performed for the helium atom. We reproduce the previously known relativistic and QED effects up to order $mα^5$ and extend the theory by calculating the complete $mα^6$ correction. The total contribution of the $mα^6$ effects is shown to be much smaller than previously estimated, due to a large cancelation between the radiative and non-radiative parts of this correction. As a result of our calculations, we confirm the previously reported deviations between measured transition energies and theoretical predictions for the $nD$--$2S$ and $nD$--$2P$ transitions. Possible reasons for this discrepancy are analyzed.

physics.atom-ph↗

arXiv2020

Hyperfine structure in the HD molecule

We investigate interactions between the proton spin, the deuteron spin, and the orbital angular momentum in the electronic ground state of the HD molecule. These interactions lead to hyperfine splittings of molecular energy levels. Our numerical results for the first rotational level agree well with the currently most accurate measurement performed by Ramsey {\em et al.} in the 1950s. Knowledge of the hyperfine structure of other levels is necessary for the accurate determination of rovibrational transition energies in spectroscopic measurements. We present theoretical predictions and share the numerical code used to perform numerical calculations. This work sets the ground for high precision spectroscopic tests of hyperfine interactions in molecular systems. In particular we determine the value of the deuteron quadrupole moment $Q = 0.2856(2)$ fm$^2$ and give outlook for improving its accuracy by three orders of magnitude.

physics.chem-ph↗

arXiv2020

Long-range asymptotics of exchange energy in the hydrogen molecule

The exchange energy, i.e. the splitting $ΔE$ between gerade and ungerade states in the hydrogen molecule has proven very difficult in numerical calculation at large internuclear distances $R$, while known results are sparse and highly inaccurate. On the other hand, there are conflicting analytical results in the literature concerning its asymptotics. In this work we develop a flexible and efficient numerical approach using explicitly correlated exponential functions and demonstrate highly accurate exchange energies for internuclear distances as large as 57.5 au. This approach may find further applications in calculations of inter-atomic interactions. In particular, our results support the asymptotics form $ΔE \sim R^{5/2}e^{-2R}$, but with the leading coefficient being $2\,σ$ away from the analytically derived value.

physics.atom-ph↗

arXiv2019

Equation of motion for a bound system of charged particles

We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of polarizabilities. Due to the lack of separation of the total momentum from the internal degrees of freedom, the notion of polarizability of the bound state immersed in the continuum spectrum of the global motion is nontrivial. We introduce a bound-continuum perturbation theory and obtain a complete formula for the equation of motion for a polarizable bound system, such as atom, ion, or the nucleus. This formula may find applications when high precision is sought and small effects due polarizabilities are important.

physics.atom-ph↗

arXiv2019

Rovibrational energy levels of the hydrogen molecule through nonadiabatic perturbation theory

We present an accurate theoretical determination of rovibrational energy levels of the hydrogen molecule and its isotopologues in its electronic ground state. We consider all significant corrections to the Born-Oppenheimer approximation, obtained within nonadiabatic perturbation theory, including the mixed nonadiabatic-relativistic effects. Quantum electrodynamic corrections in the leading $α^5\,m$ and the next-to-leading $α^6\,m$ orders, as well as finite nuclear size effect, are also taken into account but within the Born-Oppenheimer approximation only. Final results for the transition wavelength between rovibrational levels achieve accuracy of the order of $10^{-3}$--$10^{-7}$ cm$^{-1}$, and are provided by simple to use computer code.

physics.chem-ph↗

arXiv2019

Dissociation Energy of Molecular Hydrogen Isotopologues

The nonrelativistic energy together with relativistic and quantum electrodynamic corrections for all the molecular hydrogen isotopologues (D$_2$, T$_2$, HD, HT, DT) were evaluated without expansion in the electron-nucleus mass ratio. The obtained results significantly improve the uncertainty of theoretical predictions, reaching a value below 1 MHz for the total dissociation energy. We observe good agreement with the experimental value for D$_2$ and $3\,σ$ discrepancy for the HD molecule, while no experimental values for the dissociation energy of molecules involving tritium have yet been obtained.

physics.chem-ph↗

arXiv2019

Quantum electrodynamic corrections to the $1s3d$ states of the helium atom

We perform quantum electrodynamic calculations of the ionization energy of the $1s3d$ states of the $^4$He atom, including a complete evaluation of the $mα^6$ correction. We find a large contribution from the nonradiative part of this correction, which has not been accounted for in previous investigations. The additional contribution shifts theoretical predictions for ionization energies by about 10$\,σ$. Despite this shift, we confirm the previously reported systematic deviations between measured experimental results and theoretical predictions for transitions involving $3D$ states. The reason for these deviations remains unknown.

physics.atom-ph↗

arXiv2019

Refractive index and generalized polarizability

We investigate the role of retardation corrections to polarizability and to refractive index. We found that the classical electromagnetic theory of dielectrics requires corresponding modifications in terms of nonlocality of the dielectric constant. This nonlocality should be taken into account in the interpretation of accurate measurements of the optical refractivity.

physics.class-ph↗

arXiv2019

Nuclear Charge Radii of $^{10,11}$B

The first determination of the nuclear charge radius by laser spectroscopy for a five-electron system is reported. This is achieved by combining high-accuracy ab initio mass-shift calculations and a high-resolution measurement of the isotope shift in the $2s^2 2p\, ^2\mathrm{P}_{1/2} \rightarrow 2s^2 3s\, ^2\mathrm{S}_{1/2}$ ground state transition in boron atoms. Accuracy is increased by orders of magnitude for the stable isotopes $^{10,11}$B and the results are used to extract their difference in the mean-square charge radius $\langle r^2_\mathrm{c}\rangle^{11} - \langle r^2_\mathrm{c}\rangle^{10} = -0.49\,(12)\,\mathrm{fm}^2$. The result is qualitatively explained by a possible cluster structure of the boron nuclei and quantitatively used as a benchmark for new ab initio nuclear structure calculations using the no-core shell model and Green's function Monte Carlo approaches.

physics.atom-ph↗

arXiv2018

Nuclear-structure corrections to the hyperfine splitting in muonic deuterium

Nuclear structure corrections of orders $Zα\, E_F$ and $(Zα)^2 E_F$ are calculated for the hyperfine splitting of the muonic deuterium. The obtained results disagree with previous calculations and lead to a $5\,σ$ disagreement with the current experimental value of the $2S$ hyperfine splitting in $μ$D.

physics.atom-ph↗

arXiv2018

Nonadiabatic relativistic correction in H$_2$, D$_2$, and HD

We calculate the nonadiabatic relativistic correction to rovibrational energy levels of H$_2$, D$_2$, and HD molecules using the nonadiabatic perturbation theory. This approach allows one to obtain nonadiabatic corrections to all the molecular levels with the help of a single effective potential. The obtained results are in very good agreement with the previous direct calculation of nonadiabatic relativistic effects for dissociation energies and resolve the reported discrepancies of theoretical predictions with recent experimental results.

physics.atom-ph↗

arXiv2018

Theory of the Lamb shift in hydrogen and light hydrogen-like ions

Theoretical calculations of the Lamb shift provide the basis required for the determination of the Rydberg constant from spectroscopic measurements in hydrogen. The recent high-precision determination of the proton charge radius drastically reduced the uncertainty in the hydrogen Lamb shift originating from the proton size. As a result, the dominant theoretical uncertainty now comes from the two- and three-loop QED effects, which calls for further advances in their calculations. We review the present status of theoretical calculations of the Lamb shift in hydrogen and light hydrogen-like ions with the nuclear charge number up to $Z = 5$. Theoretical errors due to various effects are critically examined and estimated.

physics.atom-ph↗