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Mariusz Puchalski

Publications and source records attributed to Mariusz Puchalski.

At least 37 records · Page 2Linked to original sources
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

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

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↗
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

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

Frequency-dependent polarizability of helium including relativistic effects with nuclear recoil terms

Future metrology standards will be partly based on physical quantities computed from first principles rather than measured. In particular, a new pressure standard can be established if the dynamic polarizability of helium can be determined from theory with an uncertainty smaller than 0.2 ppm. We present calculations of the frequency-dependent part of this quantity including relativistic effects with full account of leading nuclear recoil terms and using highly optimized explicitly correlated basis sets. A particular emphasis is put on uncertainty estimates. At the He-Ne laser wavelength of 632.9908 nm, the computed polarizability value of 1.391 811 41 a.u. has uncertainty of 0.1 ppm that is two orders of magnitude smaller than those of the most accurate polarizability measurements. We also obtained an accurate expansion of the helium refractive index in powers of density.

physics.atom-ph↗
arXiv2014

On the empirical dipole polarizability of He from spectroscopy of HeH$^{+}$

Using a long-range polarization potential for HeH$^{+}$, we can obtain an empirical value for the Boltzmann constant $k_{B}$ with an order of magnitude greater precision than the previous best experimental value based on the dipole polarizability of $^{4}$He. We find that relativistic and QED effects of order $α_{\rm FS}^{3}$ in the fine structure constant are crucial in the quadrupole polarizability in order to fit the dipole polarizbility with this precision using the polarization potential. By calculating finite-mass corrections for $^{3}$He, we also present theoretical values for the dipole and quadrupole polarizabilities of $^{3}$He with 9 and 7 digits of precision respectively.

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↗
arXiv2013

Testing quantum electrodynamics in the lowest singlet states of beryllium atom

High-precision results are reported for the energy levels of $2{^1S}$ and $2{^1P}$ states of the beryllium atom. Calculations are performed using fully correlated Gaussian basis sets and taking into account the relativistic, quantum electrodynamics (QED), and finite nuclear mass effects. Theoretical predictions for the ionization potential of the beryllium ground state $75\,192.699(7) \icm$ and the $2{^1P} \rightarrow 2{^1S}$ transition energy $42\,565.441(11) \icm$ are compared to the known but less accurate experimental values. The accuracy of the four-electron computations approaches that achieved for the three-electron atoms, which enables determination of the nuclear charge radii and precision tests of QED.

physics.atom-ph↗
arXiv2010

Applications of four-body exponentially correlated functions

We demonstrate the applicability of four-body exponentially correlated functions for the accurate calculations of relativistic effects in lithium-like atoms and present results for matrix elements of various operators which involve negative powers of interparticle distances.

physics.atom-ph↗
arXiv2009

Ground state of Li and Be$^+$ using explicitly correlated functions

We compare the explicitly correlated Hylleraas and exponential basis sets in the evaluations of ground state of Li and Be$^+$. Calculations with Hylleraas functions are numerically stable and can be performed with the large number of basis functions. Our results for ground state energies $-7.478 060 323 910 10(32)$, $-14.324 763 176 790 43(22)$ of Li and Be$^+$ correspondingly, are the most accurate to date. When small basis set is considered, explicitly correlated exponential functions are much more effective. With only 128 functions we obtained about $10^{-9}$ relative accuracy, but the severe numerical instabilities make this basis costly in the evaluation.

physics.atom-ph↗
arXiv2009

Relativistic, QED, and nuclear mass effects in the magnetic shielding of $^3$He

The magnetic shielding $σ$ of $^3$He is studied. The complete relativistic corrections of order $O(α^2)$, leading QED corrections of order $O(α^3 \lnα)$, and finite nuclear mass effects of order $O(m/m_{\rm N})$ are calculated with high numerical precision. The resulting theoretical predictions for $σ= 59.967~43(10)\cdot 10^{-6}$ are the most accurate to date among all elements and support the use of $^3$He as a NMR standard.

physics.chem-ph↗