Browsing by Author "Pachucki, Krzysztof"
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Item Bethe logarithm for the lithium atom from exponentially correlated Gaussian functions(AMERICAN PHYSICAL SOCIETY, 2003-10-27) Pachucki, Krzysztof; Komasa, JacekThe calculation of Bethe logarithm for the ground state of the lithium atom is presented. The Bethe logarithm is the main QED effect coming from the electron self-interaction, which has not been obtained yet. Both results for the infinite nuclear mass, ln k = 5.178 17(3), and the mass polarization correction, Delta ln k = 0.114(3), significantly improve the hitherto theoretical values for the lithium ground-state energy. They allow from one side to test the theory against precise measurements of transition frequencies and from the other side, to improve the accuracy of determination of the difference in the square of nuclear charge radii from the isotope-shift measurements. The applied calculational method is based on the well adapted explicitly correlated Gaussian basis set and can be extended to other few-electron atoms and molecules.Item Excitation energy of 9Be(American Physical Society, 2006-05) Pachucki, Krzysztof; Komasa, JacekThe high precision relativistic and radiative corrections to the energy of the excited 3 S-1 state of the beryllium atom are obtained. The nonrelativistic wave function, expanded in a basis of exponentially correlated Gaussian functions, yields the lowest upper bounds to the energy of 2 S-1 and 3 S-1 states. By means of the integral representation, a reference-quality Bethe logarithm has been obtained. The resulting theoretical 2 S-1-3 S-1 transition energy amounts to 54 677.78(45) cm(-1) and differs from the known experimental value by about 0.5 cm(-1).Item Nonadiabatic corrections to rovibrational levels of H2(American Institute of Physics, 2009) Pachucki, Krzysztof; Komasa, JacekThe 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 the H2 molecule. Results for states with J ≤ 10 are in excellent agreement with previous calculations by Wolniewicz, and for states with J>10 are new.Item On the acceleration of the convergence of singular operators in Gaussian basis sets(AMERICAN INSTITUTE OF PHYSICS, 2005-05-08) Pachucki, Krzysztof; Cencek, Wojciech; Komasa, JacekGaussian type wave functions do not reproduce the interparticle cusps which result in a slow convergence of the expectation values of the operators involved in calculations of the relativistic and QED energy corrections. Methods correcting this deficiency are the main topic discussed in this paper. Benchmark expectation values of the singular operators for several few-electron systems are presented.Item Ortho-para transition in molecular hydrogen(American Physical Society, 2008-03-14) Pachucki, Krzysztof; Komasa, JacekThe radiative ortho-para transition in 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→J=0)=6.20(62)×10−14 yr−1 is significantly lower in comparison to all the previous approximate calculations. Experimental detection of such a weak line by observation of, for example, cold interstellar molecular hydrogen is at present unlikely.Item Relativistic and QED Corrections for the Beryllium Atom(American Physical Society, 2004) Pachucki, Krzysztof; Komasa, JacekComplete relativistic and quantum electrodynamics corrections of order α2 Ry and α3 Ry are calculated for the ground state of the beryllium atom and its positive ion. A basis set of correlated Gaussian functions is used, with exponents optimized against nonrelativistic binding energies. The results for Bethe logarithms lnk0(Be)=5.750 34(3) and lnk0(Be+)=5.751 67(3) demonstrate the availability of high precision theoretical predictions for energy levels of the beryllium atom and light ions. Our recommended value of the ionization potential 75 192.514(80) cm-1 agrees with equally accurate available experimental values.Item Rovibrational levels of HD(ROYAL SOCIETY OF CHEMISTRY, 2010) Pachucki, Krzysztof; Komasa, JacekThe dissociation energies of all rotation-vibrational states of the molecular HD in the ground electronic state are calculated to a high accuracy by including nonadiabatic, relativistic alpha(2), and quantum electrodynamic alpha(3) effects, with approximate treatment of small higher order alpha(4), and finite nuclear size corrections. The obtained result for the ground molecular state of 36 405.7828(10) cm(-1) is in a small disagreement with the latest most precise experimental value.