arXiv subjects

Jacek Komasa

Publications and source records attributed to Jacek Komasa.

At least 19 recordsLinked to original sources

arXiv2025

Electron-nucleus Araki-Sucher correction in the hydrogen molecule isotopologues

The quantum electrodynamic Araki-Sucher correction arising from the interaction between electrons and nuclei is calculated for rovibrational energy levels of the hydrogen molecule and its isotopologues. The corresponding expectation value $\langle r_{en}^{-3}\rangle$ is evaluated across a wide range of internuclear distances using the Born-Oppenheimer approximation. The electronic wave function is represented as a linear combination of explicitly correlated Gaussian basis functions. This correction contributes approximately tenths of a megahertz (about $10^{-5}$cm$^{-1}$) to the dissociation energy of rovibrational levels and to the transitions between them. Given recent spectroscopic measurements with an accuracy of 10 kHz, this correction is necessary to achieve sub-MHz agreement between theory and experiment.

physics.chem-ph↗

arXiv2024

Integrals for relativistic nonadiabatic energies of H$_2$ in exponential basis

Accurate predictions for hydrogen molecular levels require the treatment of electrons and nuclei on an equal footing. While nonrelativistic theory has been effectively formulated this way, calculation of relativistic and quantum electrodynamic effects using an exponential basis with explicit correlations that ensure well-controlled numerical precision is much more challenging. In this work, we derive a complete set of integrals for the relativistic correction and demonstrate their application to several of the lowest rovibrational levels. Together with similar advancements for quantum electrodynamic corrections, this will improve the accuracy beyond $10^{-9}$ and hopefully explain discrepancies with recent experimental values.

physics.chem-ph↗

arXiv2023

Leading-order QED effects in the ground electronic state of molecular hydrogen

We perform highly accurate calculations of the leading order QED correction to the ground electronic state of molecular hydrogen. Numerical results are obtained for a grid of the internuclear distances $R=0-10$ au with the relative precision of about $10^{-8}$. The major numerical uncertainty of previous QED results [K. Piszczatowski et al., JCTC $\textbf{5}$, 3039 (2009)] has been eliminated. Nevertheless, the discrepancy with measurements in HD at the level of 1.9 $σ$ persists.

physics.atom-ph↗

arXiv2022

Nuclear magnetic shielding in HD and HT

We perform a calculation of the nuclear magnetic shielding in HD and HT molecules, with complete and perturbative accounts for nuclear masses. From the difference in shielding, we obtain the deuteron and triton magnetic moments in agreement with the CODATA value, with the accuracy limited only by nuclear magnetic resonance measurements. Most importantly, our calculations indicate a potential for improved determination of nuclear magnetic moments.

physics.atom-ph↗

arXiv2021

Nonrelativistic energy of tritium-containing hydrogen molecule isotopologues

The nonrelativistic energy of low lying rovibrational levels of HT, DT, and \T\ is determined to an absolute accuracy of $10^{-7}-10^{-8}$ cm$^{-1}$ using the variational method with the four-body nonadiabatic James-Coolidge functions. The new results increase the accuracy of the nonrelativistic component of the energy levels by several orders of magnitude. As a consequence, the total transition energies are improved by at least an order of magnitude.

physics.chem-ph↗

arXiv2021

Fine and hyperfine splitting of the low-lying states of $^9$Be

We perform accurate calculations of energy levels as well as fine and hyperfine splittings of the lowest $^{1,3}\!P_J$, $^{3}\!S_1$, $^{3}\!P^e_J$, and $^{1,3}\!D_J$ excited states of the $^9$Be atom using explicitly correlated Gaussian functions and report on the breakdown of the standard hyperfine structure theory. Because of the strong hyperfine mixing, which prevents the use of common hyperfine constants, we formulate a description of the fine and hyperfine structure that is valid for an arbitrary coupling strength and may have wide applications in many other atomic systems.

physics.atom-ph↗

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↗

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

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↗

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↗

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↗

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

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

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↗