arXiv subjects

Krzysztof Pachucki

Publications and source records attributed to Krzysztof Pachucki.

At least 109 records · Page 6Linked to original sources

arXiv2009

Nonadiabatic corrections to rovibrational levels of H$_2$

The leading nonadiabatic corrections to rovibrational levels of a diatomic molecule are expressed in terms of three functions of internuclear distance: corrections to the adiabatic potential, the effective nuclear mass, and the effective moment of inertia. The resulting radial Schrödinger equation for nuclear motion is solved numerically yielding accurate nonadiabatic energies for all rovibrational levels of H$_2$ molecule in excellent agreement with previous calculations by Wolniewicz.

physics.chem-ph↗

arXiv2008

Relativistic, QED, and finite nuclear mass corrections for low-lying states of Li and Be$^+$

Accurate results for nonrelativistic energy, relativistic, QED, and finite nuclear mass corrections are obtained for $2^1S_{1/2}$, $3^1S_{1/2}$ and $2^1P_{1/2}$ states of the Li atom and Be$^+$ ion. Our computational approach uses the Hylleraas basis set with the analytic integration and recursion relations. From comparison of experimental results for the isotope shifts to theoretical predictions including nuclear polarizabilities, we obtain nuclear charge radii for Li and Be isotopes.

physics.atom-ph↗

arXiv2008

Electric dipole rovibrational transitions in HD molecule

The rovibrational electric dipole transitions in the ground electronic state of the HD molecule are studied. A simple, yet rigorous formula is derived for the transition rates in terms of the electric dipole moment function $D(R)$, which is calculated in a wide range of $R$. Our numerical results for transition rates are in moderate agreement with experiments and previous calculations, but are at least an order of magnitude more accurate.

physics.chem-ph↗

arXiv2008

Nonadiabatic corrections to the wave function and energy

Nonadiabatic corrections in molecules composed of a few atoms are considered. It is demonstrated that a systematic perturbative expansion around the adiabatic solution is possible, with the expansion parameter being the electron-nucleus mass ratio to the power 3/4. Closed form formulae for the leading corrections to the wave function and to the energy are derived. Their applicability is demonstrated by a comparison of numerical results for the hydrogen molecule with the former nonadiabatic calculations and the experimental values. Good agreement with the recent experiment is achieved for the ground state dissociation energy of both H$_2$ and D$_2$.

physics.chem-ph↗

arXiv2008

Singular Hylleraas three-electron integrals

Calculations of the leading quantum electrodynamics effects in few electron systems involve singular matrix elements of the inter-electronic distances of the form $1/r_i^3$ and $1/r_{ij}^3$. Integrals that result when the nonrelativistic wave function is represented with a Hylleraas basis representation are studied. Recursion relations for various powers of the electron coordinates and the master integrals are derived in a form suited for high precision numerical evaluations.

physics.atom-ph↗

arXiv2008

Ortho-para transition in molecular hydrogen

The radiative ortho-para transition in the molecular hydrogen is studied. This highly forbidden transition is very sensitive to relativistic and subtle nonadiabatic effects. Our result for the transition rate in the ground vibrational level $Γ(J=1\to J=0) = 6.20(62)\cdot 10^{-14} \iyr$ is significantly lower in comparison to all the previous approximate calculations. Experimental detection of such a weak line by observation of, for example, the cold interstellar molecular hydrogen is at present unlikely.

physics.chem-ph↗

arXiv2007

Helium energy levels including $m α^6$ corrections

The $m α^6$ correction to energy is expressed in terms of an effective Hamiltonian $H^{(6)}$ for an arbitrary state of helium. Numerical calculations are performed for $n=2$ levels, and the previous result for the $2^3P$ centroid is corrected. While the resulting theoretical predictions for the ionization energy are in moderate agreement with experimental values for $2^3S_1$, $2^3P$, and $2^1S_0$ states, they are in significant disagreement for the singlet state $2^1P_1$.

physics.atom-ph↗

arXiv2007

Nuclear vector polarizability correction to hyperfine splitting

The interaction of orbital electrons with the charge and magnetic moment of the nucleus polarizes it, and the detailed description requires a careful treatment of the nuclear vector polarizability. We present a complete and closed form expression for the resulting contribution to hyperfine splitting in light atomic systems.

physics.atom-ph↗

arXiv2006

$α^4$ Ry corrections to singlet states of helium

Corrections of order $α^4$Ry are calculated for the singlet states $1^1S_0$ and $2^1S_0$ of the helium atom. The result for $1^1S_0$ state is in slight disagreement with that of Korobov and Yelkhovsky in [Phys. Rev. Lett. {\bf 87}, 193003 (2001)]. The results obtained lead to a significant improvement of transition frequencies between low lying levels of the helium atom. In particular theoretical predictions for the $2^1S_0 - 1^1S_0$ transition are found to be in disagreement with experimental values.

physics.atom-ph↗

arXiv2006

Improved theory of helium fine structure

Improved theoretical predictions for the fine-structure splitting of $2^3P_J$ levels in helium are obtained by the calculation of contributions of order $α^5 Ry$. New results for transition frequencies, $ν_{01} = 29 616 943.01(17)$ kHz and $ν_{12} = 2 291 161.13(30)$ kHz disagree significantly with the experimental values, indicating an outstanding problem in bound state QED.

physics.atom-ph↗

arXiv2006

Nonrelativistic QED approach to the Lamb shift

We calculate the one- and two-loop corrections of order alpha(Zalpha)^6 and alpha^2(Zalpha)^6 respectively, to the Lamb shift in hydrogen-like systems using the formalism of nonrelativistic quantum electrodynamics. We obtain general results valid for all hydrogenic states with nonvanishing orbital angular momentum and for the normalized difference of S-states. These results involve the expectation value of local effective operators and relativistic corrections to Bethe logarithms. The one-loop correction is in agreement with previous calculations for the particular cases of S, P, and D states. The two-loop correction in the order alpha^2(Zalpha)^6 includes the pure two-loop self-energy and all diagrams with closed fermion loops. The obtained results allow one to obtain improved theoretical predictions for all excited hydrogenic states.

physics.atom-ph↗

arXiv2006

Calculation of the One- and Two-Loop Lamb Shift for Arbitrary Excited Hydrogenic States

General expressions for quantum electrodynamic corrections to the one-loop self-energy [of order alpha(Zalpha)^6] and for the two-loop Lamb shift [of order alpha^2(Zα)^] are derived. The latter includes all diagrams with closed fermion loops. The general results are valid for arbitrary excited non-S hydrogenic states and for the normalized Lamb shift difference of S states, defined as Delta_n = n^3 DeltaE(nS) - DeltaE(1S). We present numerical results for one-loop and two-loop corrections for excited S, P and D states. In particular, the normalized Lamb shift difference of S states is calculated with an uncertainty of order 0.1 kHz.

physics.atom-ph↗

arXiv2006

Ground state wave function and energy of the lithium atom

Highly accurate nonrelativistic ground-state wave function and energy of the lithium atom is obtained in the Hylleraas basis set. The leading relativistic corrections,as represented by Breit-Pauli Hamiltonian, are obtained in fair agreement with the former results. The calculational method is based on the analytical evaluation of Hylleraas integrals with the help of recursion relations.

physics.atom-ph↗

arXiv2005

Relativistic corrections to the long range interaction between closed shell atoms

The complete $O(α^2)$ correction to the long range interaction between neutral closed shell atoms is obtained, the relation to the asymptotic expansion of the known short range interaction at the atomic scale is presented and a general interaction potential which is valid in the whole range of the inter atomic distances is constructed.

physics.atom-ph↗

arXiv2005

Complete two-loop correction to the bound-electron g factor

Within a systematic approach based on the dimensionally regularized nonrelativistic quantum electrodynamics, we derive the complete result for the two-loop correction to order $(α/π)^2 (Z α)^4$ for the $g$ factor of an electron bound in an $nS$ state of a hydrogenlike ion. The results obtained significantly improve the accuracy of the theoretical predictions for the hydrogenlike carbon and oxygen ions and influence the value of the electron mass inferred from $g$ factor measurements.

physics.atom-ph↗

arXiv2005

One-loop self-energy correction in a strong binding field

A new scheme for the numerical evaluation of the one-loop self-energy correction to all orders in Z αis presented. The scheme proposed inherits the attractive features of the standard potential-expansion method but yields a partial-wave expansion that converges more rapidly than in the other methods reported in the literature.

physics.atom-ph↗

arXiv2004

Higher-order effective Hamiltonian for light atomic systems

We present the derivation of the effective higher-order Hamiltonian, which gives $m α^6$ contribution to energy levels of an arbitrary light atom. The derivation is based on the Foldy-Wouthuysen transformation of the one-particle Dirac Hamiltonian followed by perturbative expansion of the many particle Green function. The obtained results can be used for the high precision calculation of relativistic effects in atomic systems.

physics.atom-ph↗

arXiv2004

Recursion relations for Hylleraas three-electron integral

Recursion relations for Hylleraas three-electron integral are obtained in a closed form by using integration by parts identities. Numerically fast and well stable algorithm for the calculation of the integral with high powers of inter-electronic coordinates is presented.

physics.atom-ph↗