arXiv subjects
Publications and source records attributed to Krzysztof Pachucki.
We report an accurate determination of the nuclear magnetic dipole moments of $^{6,7}$Li from the measured ratio of the nuclear and the electron $g$-factors in atomic Li. The obtained results significantly improve upon the literature values and stress the importance of reliable theoretical calculations of the nuclear shielding corrections.
The nuclear polarizability effects in hyperfine splitting of light atomic systems are not well known. The only system for which they were previously calculated is the hydrogen atom, where these effects were shown to contribute about 5\% of the total nuclear correction. One generally expects the polarizability effects to become more pronounced for composite nuclei. In the present work we determine the nuclear polarizability correction to the hyperfine splitting in He$^+$ by comparing the effective Zemach radius deduced from the experimental hyperfine splitting with the Zemach radius obtained from the electron scattering. We obtain a surprising result that the nuclear polarizability of the helion yields just 3\% of the total nuclear correction, which is smaller than for the proton.
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.
We investigate the modification of the transverse electromagnetic interaction between two point-like particles when one particle acquires a finite size. It is shown that the correct treatment of such interaction cannot be accomplished within the Breit approximation but should be addressed within the QED. The complete QED formula is derived for the finite-size nuclear recoil, exact in the coupling strength parameter $Z\,α$. Numerical calculations are carried out for a wide range of $Z$ and verified against the $(Z\,α)^5$ contribution. The comparison with the $Z\,α$ expansion identifies the contribution of order $(Z\,α)^6$, which is linear in the nuclear radius and numerically dominates over the lower-order $(Z\,α)^5$ term.
We perform ab initio calculations of the QED effects of order $mα^7$ for the $2^3S$ and $2^3P$ states of He-like ions. The computed effects are combined with previously calculated energies from [V. A. Yerokhin and K. Pachucki, Phys. Rev. A 81, 022507 (2010)], thus improving the theoretical accuracy by an order of magnitude. The obtained theoretical values for the $2^3S$-$2^3P_{0,2}$ transition energies are in good agreement with available experimental results and with previous calculations performed to all orders in the nuclear binding strength parameter $Zα$. For the ionization energies, however, we find some inconsistency between the $Zα$-expansion and all-order calculations, which might be related to a similar discrepancy between the theoretical and experimental results for the ionization energies of helium [V. Patkóš et al., Phys. Rev. A 103, 042809 (2021)].
We consider leading $O(m/M)$ nuclear recoil corrections to the hyperfine splitting in light atomic systems. Due to the singularity of hyperfine interactions, the electromagnetic form factors of the nucleus have to be introduced as a function of the four-momentum square, which goes beyond the Hamiltonian description of the system. We present a compact formula for $O(Z\,α)$ recoil corrections and indicate the importance, especially for light atoms, of a more realistic description of the nuclear structure effects.
We perform a calculation of quantum electrodynamics effects in excited states with $l>1$ of arbitrary two-body systems up to $α^6\,μ$ order. The obtained results are valid for hadronic atoms, as long as the strong interaction effects are negligible. We demonstrate that for circular states with $l\sim n$, the effective expansion parameter is $Z\,α/n$, which extends the applicability of the derived formulas to heavy ions. Moreover, inclusion of higher-order terms is feasible, which indicates that accurate measurements of excited states of, for example, muonic or antiprotonic hydrogenic ions can be used to determine the fundamental constants and to search for the existence of yet unknown long-range interactions.
We report a calculation of relativistic corrections of order $mα^7$ to the Bethe logarithm for the $2^3S$ and $2^3P$ states of helium-like ions. The calculation is required for improving the accuracy of theoretical energies of helium-like ions and for checking the evaluation of the $mα^7$ effects in helium performed in [V. Patkóš, V. A. Yerokhin, K. Pachucki, Phys. Rev. A 103, 042809 (2021)], where a significant discrepancy with experimental results was found. The large-$Z$ limit of the relativistic Bethe logarithm is determined numerically, in excellent agreement with the analytical results obtained from the hydrogen theory.
A calculation of two-electron QED effects to all orders in the nuclear binding strength parameter $Zα$ is presented for the ground and $n = 2$ excited states of helium-like ions. After subtracting the first terms of the $Zα$ expansion from the all-order results, we identify the higher-order QED effects of order $mα^7$ and higher. Combining the higher-order remainder with the results complete through order $mα^6$ from [V. A. Yerokhin and K. Pachucki, Phys. Rev. A 81, 022507 (2010)], we obtain the most accurate theoretical predictions for the ground and non-mixing $n=2$ states of helium-like ions with $Z = 5-30$. For the mixing $2^1 P_1$ and $2^3 P_1$ states, we extend the previous calculation by evaluating the higher-order mixing correction and show that it defines the uncertainty of theoretical calculations in the $LS$ coupling for $Z > 10$.
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.
We report on accurate variational calculations of the Born-Oppenheimer potential for excited states of the hydrogen molecule with $Π$, $Δ$, and $Φ$ symmetries. The obtained potential energy curves reach the relative precision of $10^{-9}$ or better along internuclear distances of 0.01 -- 20 au. Calculations rely on recursive evaluation of two-center two-electron molecular integrals with exponential functions in arbitrary precision arithmetics. Our results for most of the states are the first ever reported, and for the previously calculated states constitute an improvement by several orders of magnitude.
The derivation of leading quantum electrodynamic corrections to the nuclear magnetic shielding in light hydrogen- and helium-like atomic systems is described in detail. The presented theoretical approach applies to any light atomic and molecular systems, enabling the determination of the magnetic moment of light nuclei with much higher precision than known presently.
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.
The leading quantum electrodynamic corrections to the nuclear magnetic shielding in one- and two-electron atomic systems are obtained in a complete form, and the shielding constants of $^1$H, $^3$He$^+$, and $^3$He are calculated to be $17.735\,436(3) \cdot 10^{-6}$, $35.507\,434(9)\cdot 10^{-6}$, and $59.967\,029(23)\cdot 10^{-6}$, respectively. These results are orders of magnitude more accurate than previous ones, and, with the ongoing measurement of the nuclear magnetic moment of $^3$He$^+$ and planned $^3$He$^{2+}$, they open the window for high-precision absolute magnetometry using $^3$He NMR probes. The presented theoretical approach is applicable to all other light atomic and molecular systems, which facilitates the improved determination of magnetic moments of any light nuclei.
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.
The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine-structure constant $α$. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, $r_1$, $r_2$ and $r = |\vec{r}_1-\vec{r}_2|$. The choice of the exponential basis functions of the form $\exp(-αr_1 -βr_2 -γr)$ allows us to construct an accurate and compact representation of the nonrelativistic wave function and to efficiently compute matrix elements of numerous singular operators representing relativistic and QED effects. Calculations of the leading QED effects of order $α^5m$ (where $m$ is the electron mass) are complemented with the systematic treatment of higher-order $α^6m$ and $α^7m$ QED effects.
We report on highly accurate calculations of Born-Oppenheimer potentials for excited $n\,Σ^{+}$ states of the hydrogen molecule for all possible combinations of singlet/triplet and gerade/ungerade symmetries up to $n=7$. A relative accuracy of $10^{-10}$ (0.00002 cm$^{-1}$) or better is achieved for all the internuclear distances and all the excited states under consideration -- an improvement with respect to the best results available in the literature by at least 6 orders of magnitude. Presented variational calculations rely on efficient evaluation of molecular integrals with the explicitly correlated exponential basis in arbitrary precision arithmetics.
We have derived the complete formula for the $α^7\,m$ contribution to energy levels of an arbitrary triplet state of the helium atom, performed numerical calculations for the $2^3S$ and $2^3P$ states, and thus improved the theoretical accuracy of ionization energies of these states by more than an order of magnitude. Using the nuclear charge radius extracted from the muonic helium Lamb shift, we obtain the theoretical prediction in excellent agreement with the measured $2^3S - 2^3P$ transition energy [X.~Zheng et al., Phys. Rev. Lett. {\bf 199}, 263002 (2017)]. At the same time we observe significant discrepancies with experiments for the $2^3S- 3^3D$ and $2^3P - 3^3D$ transitions.