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Krzysztof Pachucki

Publications and source records attributed to Krzysztof Pachucki.

At least 73 records · Page 4Linked to original sources
arXiv2018

Three-photon exchange nuclear structure correction in hydrogenic systems

The complete relativistic $O(α^2)$ nuclear structure correction to the energy levels of ordinary (electronic) and muonic hydrogen-like atoms is investigated. The elastic part of the nuclear structure correction is derived analytically. The resulting formula is valid for an arbitrary hydrogenic system and is much simpler than analogous expressions previously reported in the literature. The analytical result is verified by high-precision numerical calculations. The inelastic $O(α^2)$ nuclear structure correction is derived for the electronic and muonic deuterium atoms. The correction comes from a three-photon exchange between the nucleus and the bound lepton and has not been considered in the literature so far. We demonstrate that in the case of deuterium, the inelastic three-photon exchange contribution is of a similar size and of the opposite sign to the corresponding elastic part and, moreover, cancels exactly the model dependence of the elastic part. The obtained results affect the determination of nuclear charge radii from the Lamb shift in ordinary and muonic atoms.

physics.atom-ph↗
arXiv2017

Nonadiabatic rotational states of the hydrogen molecule

We present a new computational method for the determination of energy levels in four-particle systems like H$_2$, HD, and HeH$^+$ using explicitly correlated exponential basis functions and analytic integration formulas. In solving the Schrödinger equation, no adiabatic separation of the nuclear and electronic degrees of freedom is introduced. We provide formulas for the coupling between the rotational and electronic angular momenta, which enable calculations of arbitrary rotationally excited energy levels. To illustrate the high numerical efficiency of the method, we present results for various states of the hydrogen molecule. The relative accuracy to which we determined the nonrelativistic energy reached the level of $10^{-12}$-$10^{-13}$, which corresponds to an uncertainty of $10^{-7}$-$10^{-8}$ cm$^{-1}$.

physics.chem-ph↗
arXiv2017

One-loop binding corrections to the electron $g$ factor

We calculate the one-loop electron self-energy correction of order $α\,(Z\,α)^5$ to the bound electron $g$ factor. Our result is in agreement with the extrapolated numerical value and paves the way for the calculation of the analogous, but as yet unknown two-loop correction.

physics.atom-ph↗
arXiv2017

Testing fundamental interactions on the helium atom

We critically examine the current status of theoretical calculations of the energies, the fine structure, and the isotope shift of the lowest-lying states of helium, searching for unresolved discrepancies with experiments. Calculations are performed within the quantum electrodynamics expansion in powers of the fine structure constant $α$ and the electron-to-nucleus mass ratio $m/M$. For energies, theoretical results are complete through orders $α^6m$ and $α^6m^2/M$, with the resulting accuracy ranging from $0.5$ to $2$~MHz for the $n=2$ states. The fine-structure splitting of the $2^3P$ state is predicted with a much better accuracy, 1.7~kHz, as a consequence of a calculation of the next-order $α^7m$ effect. An excellent agreement of the theoretical predictions with the recent measurements of the fine structure provides one of the best tests of the bound-state QED in few-electron systems and determines the fine-structure constant $α$ with an accuracy of 31~ppb. The isotope shift between $^3$He and $^4$He is treated theoretically with a sub-kHz accuracy, which allows for a high-precision determination of the differences of the nuclear charge radii $δr^2$. Several such determinations, however, yield results that are in a 4$σ$ disagreement with each other, what remains unexplained. Apart from this, we find no significant discrepancies between theory and experiment for the helium atom. In the future, a calculation of the next-order $α^7m$ effect for energy levels will enable determinations of the nuclear charge radii from atomic transition frequencies with an accuracy better than 1\%. Combined with the complementary determinations from muonic atoms, this will provide a sensitive test of universality in electromagnetic interactions of leptons and contribute to the solution of the proton charge radius puzzle.

physics.atom-ph↗
arXiv2017

Relativistic corrections for the ground electronic state of molecular hydrogen

We recalculate the leading relativistic corrections for the ground electronic state of the hydrogen molecule using variational method with explicitly correlated functions which satisfy the interelectronic cusp condition. The new computational approach allowed for the control of the numerical precision which reached about 8 significant digits. More importantly, the updated theoretical energies became discrepant with the known experimental values and we conclude that the yet unknown relativistic recoil corrections might be larger than previously anticipated.

physics.chem-ph↗
arXiv2016

Complete $α^6\,m$ corrections to the ground state of H$_2$

We perform the calculation of all relativistic and quantum electrodynamic corrections of the order of $α^6\,m$ to the ground electronic state of a hydrogen molecule and present improved results for the dissociation and the fundamental transitions energies. These results open the window for the high-precision spectroscopy of H$_2$ and related low-energy tests of fundamental interactions.

physics.chem-ph↗
arXiv2016

Schrödinger equation solved for the hydrogen molecule with unprecedented accuracy

The hydrogen molecule can be used for determination of physical constants and for improved tests of the hypothetical long range force between hadrons, which requires a sufficiently accurate knowledge of the molecular levels. For this reason, we have undertaken a project of significant improvements in theoretical predictions of H$_2$ and perform the first step, which is the solution of the nonrelativistic Schrödinger equation to the unprecedented accuracy of $10^{-12}$. This will inspire, we hope, a parallel progress in the spectroscopy of the molecular hydrogen.

physics.chem-ph↗
arXiv2015

Explicitly correlated wave function for a boron atom

We present results of high-precision calculations for a boron atom's properties using wave functions expanded in the explicitly correlated Gaussian basis. We demonstrate that the well-optimized 8192 basis functions enable a determination of energy levels, ionization potential, and fine and hyperfine splittings in atomic transitions with nearly parts per million precision. The results open a window to a spectroscopic determination of nuclear properties of boron including the charge radius of the proton halo in the $^8$B nucleus.

physics.atom-ph↗
arXiv2015

Precision Test of Many-Body QED in the Be$^+$ $2p$ Fine Structure Doublet Using Short-Lived Isotopes

Absolute transition frequencies of the $2s\; ^2{\rm S}_{1/2} \rightarrow 2p\;^2\mathrm{P}_{1/2,3/2}$ transitions in Be$^+$ were measured for the isotopes $^{7,9-12}$Be. The fine structure splitting of the $2p$ state and its isotope dependence are extracted and compared to results of \textit{ab initio} calculations using explicitly correlated basis functions, including relativistic and quantum electrodynamics effects at the order of $m α^6$ and $m α^7 \ln α$. Accuracy has been improved in both the theory and experiment by 2 orders of magnitude, and good agreement is observed. This represents one of the most accurate tests of quantum electrodynamics for many-electron systems, being insensitive to nuclear uncertainties.

physics.atom-ph↗
arXiv2015

Theory of the helium isotope shift

Theory of the isotope shift of the centroid energies of light few-electron atoms is reviewed. Numerical results are presented for the isotope shift of the $2^3P$-$2^3S$ and $2^1S$-$2^3S$ transition energies of $^3$He and $^4$He. By comparing theoretical predictions for the isotope shift with the experimental results, the difference of the squares of the nuclear charge radii of $^3$He and $^4$He, $δR^2$, is determined with high accuracy.

physics.atom-ph↗
arXiv2015

Deuteron and triton magnetic moments from NMR spectra of the hydrogen molecule

We present a theory and calculations of the nuclear magnetic shielding with finite nuclear mass effects and determine magnetic moments of deuteron and triton using the known NMR spectra of HD and HT molecules. The results $μ_d = 0.857\,438\,234\,6(53)\;μ_N$ and $μ_t = 2.978\,962\,471(10)\;μ_N$ are more accurate and in a good agreement with the currently accepted values.

physics.chem-ph↗
arXiv2015

Nuclear structure effects in light muonic atoms

Nuclear structure corrections to energy levels of light muonic atoms are derived with particular attention to the nuclear mass dependence. The obtained result for the 2P-2S transition of 1.717(19) meV serves for determination of the nuclear charge radius from the spectroscopic measurement in muonic deuterium.

physics.atom-ph↗
arXiv2014

Electromagnetic moments of the bound system of charged particles

We consider a bound system of particles interacting via electromagnetic forces in an external electromagnetic field, including leading relativistic corrections. Each particle has a definite mass, charge, spin, and charge radius. We introduce suitable canonical transformations and a perturbation scheme to obtain a Hamiltonian which describes the global dynamics of the system. This enables the derivation of formulas for various electromagnetic moments, such as the magnetic dipole moment, the mean square charge radius, and the electric dipole polarizability.

physics.atom-ph↗
arXiv2014

Quantum electrodynamics corrections to the $2P$ fine splitting in Li

We consider quantum electrodynamics (QED) corrections to the fine splitting $E(2P_{3/2}) - E(2P_{1/2})$ in the Li atom. We derive complete formulas for the $m\,α^6$ and $m\,α^7\,\lnα$ contributions and calculate them numerically using highly optimized, explicitly correlated basis functions. The obtained results resolve disagreement between measurements and lay the foundations for investigation of QED effects in light, many-electron atoms.

physics.atom-ph↗
arXiv2014

Ground state hyperfine splitting in the Be$^+$ ion

Relativistic and QED corrections are calculated for the hyperfine splitting (hfs) in the $2S_{1/2}$ ground state of $^{9}$Be$^+$ ions with an exact account for electronic correlations. The achieved accuracy is sufficient to determine the finite nuclear size effects from the comparison to the experimental hfs value. The obtained results establish the ground to determine the neutron halo in $^{11}$Be.

physics.atom-ph↗
arXiv2013

Ground state hyperfine splitting in ^6,7Li atoms and the nuclear structure

Relativistic and QED corrections were calculated for hyperfine splitting of the $2S_{1/2}$ ground state in $^{6,7}$Li atoms with an exact account for electronic correlations. The resulting theoretical predictions achieved such a precision level that, by comparison with experimental values, they enable determination of the nuclear properties. In particular, the obtained results show that the $^7$Li nucleus, having a charge radius smaller than $^6$Li, has about a 40% larger Zemach radius. Together with known differences in the electric quadrupole and magnetic dipole moments, this calls for a deeper understanding of the Li nuclear structure.

physics.atom-ph↗