Nuclear Mass Corrections Research Articles

Finite nuclear mass correction to the hyperfine splitting in hydrogenic systems

Finite nuclear mass correction to the hyperfine splitting in hydrogenic systems

Nuclear mass and size corrections to the magnetic shielding

Nuclear mass and size corrections to the magnetic shielding

Tune-out wavelengths for the 2 3S1 state of the Li+ ion

Configuration interaction calculations are performed to determine the dipole polarizabilities and tune-out wavelengths for the $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}$ state in ${\mathrm{Li}}^{+}$ ion. The finite nuclear mass correction is given by including the mass shift operator in the Dirac-Coulomb-Breit Hamiltonian directly, while the QED correction to dynamic dipole polarizabilities is evaluated by using the perturbation theory. The tune-out wavelengths for the $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}\phantom{\rule{0.28em}{0ex}}({M}_{J}=0)$ and $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}\phantom{\rule{0.28em}{0ex}}({M}_{J}=\ifmmode\pm\else\textpm\fi{}1)$ states are 159.620 55(6) nm and 159.631 14(6) nm, respectively. And the QED correction for 159 nm tune-out wavelength is 43 ppm. In addition, we obtain the static dipole polarizability for the $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}\phantom{\rule{0.28em}{0ex}}({M}_{J}=\ifmmode\pm\else\textpm\fi{}1)$ state to be 46.857 03(4) a.u., in which the contribution from QED is 70 ppm. The 159 nm tune-out wavelength and the static dipole polarizability of $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}$ state might provide a test of atomic structure theory.

Symmetry-dependent analytical all-electron potential for helium atom

Electron–electron interaction is the origin of the many-body problems usually encountered in physics and chemistry. Helium atom and other two-electron systems are the simplest many-body systems in nature. The Schrödinger equation even for such simple systems cannot be solved exactly without resorting to approximate methods. In this study, we have suggested a symmetry-dependent analytical all-electron potential for helium atom derived using an alternative multipole expansion, a variational technique, and a mean-field approximation. We have calculated the non-relativistic groundstate energy for helium atom to be −2.90422284. The suggested all-electron potential has a local Coulomb potential with embedded nuclear charge screening effect in the leading term of the multipole potential. A non-local component of the potential emanates from the higher-order angular momentum terms of the multipole series expansion. The higher-order multipole interactions are fully included through the exchange correlation processes where the interacting electrons exchange their angular momenta via the operator. With the derived potential, the effects of the local long-range and non-local short-range components, and the finite nuclear mass corrections are tested. Our results are in reasonable agreement with literature values. Indeed with the finite nuclear mass correction, we obtain the groundstate energy of helium atom to be −2.90382769.

Energy difference between the lowest doublet and quartet states of the boron atom

The energies of the lowest $^2P_u$, $^4P_g$ and $2D_g$ states of the boron atom are calculated with $\mu$hartree accuracy, in the basis of symmetrized, explicitly correlated Gaussian lobe functions. Finite nuclear mass and scalar relativistic corrections are taken into account. This study contributes to the problem of the energy differences between doublet and quartet states of boron, which have not been measured to date. It is found that the $^2P_u\rightarrow^4P_g$ excitation energy, recommended in the Atomic Spectra Database, appears underestimated by more than 300~cm$^{-1}$.

Ab initio Potential Energy Curve for the Ground State of Beryllium Dimer.

This work concerns ab initio calculations of the complete potential energy curve and spectroscopic constants for the ground state X1Σ g+ of the beryllium dimer, Be2. High accuracy and reliability of the results is one of the primary goals of the paper. To this end, we apply large basis sets of Slater-type orbitals combined with high-level electronic structure methods including triple and quadruple excitations. The effects of the relativity are also fully accounted for in the theoretical description. For the first time the leading-order quantum electrodynamics effects are fully incorporated for a many-electron molecule. Influence of the finite nuclear mass corrections (post-Born-Oppenheimer effects) turns out to be completely negligible for this system. The predicted well-depth ( De = 934.6 ± 2.5 cm-1) and the dissociation energy ( D0 = 807.7 cm-1) are in a very good agreement with the most recent experimental data. We confirm the existence of the weakly bound twelfth vibrational level [Patkowski et al. Science 2009, 326, 1382] that it lies just below the onset of the continuum.

Relativistic full-configuration-interaction calculations of magic wavelengths for the 2 3S1→2 1S0 transition of helium isotopes

A large-scale full-configuration-interaction calculation based on Dirac-Coulomb-Breit (DCB) Hamiltonian is performed for the $2\,^1S_0$ and $2\,^3S_1$ states of helium. The operators of the normal and specific mass shifts are directly included in the DCB framework to take the finite nuclear mass correction into account. High-accuracy energies and matrix elements involved n (the main quantum number) up to 13 are obtained from one diagonalization of Hamiltonian. The dynamic dipole polarizabilities are calculated by using the sum rule of intermediate states. And a series of magic wavelengths with QED and hyperfine effects included for the $2\,^3S_1\rightarrow2\,^1S_0$ transition of helium are identified. In addition, the high-order Ac Stark shift determined by the dynamic hyperpolarizabilities at the magic wavelengths are also evaluated. Since the most promising magic wavelength for application in experiment is 319.8 nm, the high-accuracy magic wavelength of 319.815 3(6) nm of $^4$He is in good agreement with recent measurement value of 319.815 92(15) nm [Nature Physics (2018)/arXiv:1804.06693], and present magic wavelength of 319.830 2(7) nm for $^3$He would provide theoretical support for experimental designing an optical dipole trap to precisely determine the nuclear charge radius of helium in future.

General theory for Rydberg states of atoms: The nonrelativistic case

We carry out a complete derivation on nonrelativistic energies of atomic Rydberg states, including finite nuclear mass corrections. Several missing terms are found and a discrepancy is confirmed in the works of Drachman [in Long Range Casimir Forces: Theory and Recent Experiments on Atomic Systems, edited by F. S. Levin and D. A. Micha (Plenum, New York, 1993)] and Drake [Adv. At., Mol., Opt. Phys. 31, 1 (1993)]. As a benchmark, we present a detailed tabulation of different energy levels.

Higher-order recoil corrections for singlet states of the helium atom

A nuclear-charge-radius ``puzzle'' is raised by this study on the difference of the nuclear charge radii --- derived from high-precision atomic spectra --- between ${}^{4}$He and ${}^{3}$He, where it is shown that the last previously unknown nuclear mass correction to the atomic transitions is insufficient in explaining the discrepancy.

Tune-out wavelength around 413 nm for the helium23S1state including relativistic and finite-nuclear-mass corrections

The tune-out wavelength at 413 nm for the $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}$ state of helium is expected to be sensitive to finite nuclear mass, relativistic, and quantum electrodynamic (QED) corrections, which provides a scheme for testing atomic structure theory [J. Mitroy and L.-Y. Tang, Phys. Rev. A 88, 052515 (2013)]. In the present work, a large-scale full-configuration-interaction calculation based on both the Dirac-Coulomb-Breit Hamiltonian and the nonrelativistic Hamiltonian is performed for the dynamic dipole polarizabilities of helium in the $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}$ state. The tune-out wavelengths for the magnetic sublevels ${M}_{J}=0$ and ${M}_{J}=\ifmmode\pm\else\textpm\fi{}1$ are determined to be 413.0801(4) nm and 413.0859(4) nm, respectively, at sub-ppm accuracy, including finite nuclear mass and relativistic corrections. Our value for the ${M}_{J}=1$ sublevel agrees with the measured value of 413.0938(20)(9) nm [B. M. Henson et al., Phys. Rev. Lett. 115, 043004 (2015)] at the level of 19 ppm. The discrepancy between these two values is mainly due to the uncalculated QED contribution. Our current value confirms quantitatively the prediction of Mitroy and Tang. Also, for the state of $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}$ we find that the corrections due to finite nuclear mass and relativistic effects to the static dipole polarizability of 315.7227(4)${a}_{0}^{3}$ are about 600 ppm and 310 ppm, respectively, which are about 1.4 and 5.4 times larger than those for the ground state. A measurement at the level of 10 ppm for the static dipole polarizability of helium in $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}$ can be used to determine the transition matrix element between $2{\phantom{\rule{0.28em}{0ex}}}^{3}S$ and $2{\phantom{\rule{0.28em}{0ex}}}^{3}P$ at the level of ${10}^{\ensuremath{-}5}$.

Nuclear mass corrections to the Casimir-Polder interaction

We present a derivation of the finite nuclear mass corrections to the Casimir-Polder interaction between two atomic systems in the ground state. Equivalently, we show how the long-range asymptotics of the adiabatic correction is modified due to the finite speed of light. We show that in addition to the contribution resulting from the finite-mass correction to atomic polarizabilities, a further contribution exists.

Influence of electron correlation on transition energy of gold ions

By using the multi-configuration Dirac–Fock theory and an active space approach, we calculate transition energy, oscillator strength, and transition probability for 4s–4p of Cu-, Zn-, Ga-, and Ge-like gold ions where Breit interaction, quantum electrodynamics, and nuclear-mass corrections have been considered. Our calculation includes valence–valence, core–valence, and core–core correlations, and the contribution of the three kinds of electron correlation effects on transition energy are discussed in detail. Most earlier measurements and calculations focus on the fewer-electrons system of low-Z to medium-Z ions; the purpose of this paper is to verify that core–valence correlation is more important than valence–valence and core–core correlation in a multi-electron system of highly charged high-Z ions.

Relativistic configuration-interaction calculations of electric dipole [formula omitted] transitions for medium-charge Li-like ions

In this work, the multi-configuration Dirac–Fock and relativistic configuration-interaction methods have been used to calculate the transition wavelengths, electric dipole transition probabilities, line strengths, and absorption oscillator strengths for the 2s–3p, 2p–3s, and 2p–3d transitions in Li-like ions with nuclear charge Z=7–30. Our calculated values are in good agreement with previous experimental and theoretical results. We took the contributions from Breit interaction, finite nuclear mass corrections, and quantum electrodynamics corrections to the initial and final levels into account, and also found that the contributions from Breit interaction, self-energy, and vacuum polarization grow fast with increasing nuclear charge for a fixed configuration. The ratio of the velocity to length form of the transition rate (Av/Al) was used to estimate the accuracy of our calculations.

Relativistic configuration interaction calculations for the K α X-ray transitions of Co XV to Co XXVI ions

Relativistic configuration interaction calculations with the inclusion of the Breit interaction, quantum electrodynamics (QED) and finite nuclear mass corrections have been carried out in the extended optimal level scheme using multiconfiguration Dirac-Fock wave functions on the wavelengths, electric dipole rates, oscillator strengths and line strengths of cobalt ions with a single vacancy in the K shell. The calculated values are compared with the other available data on He-like to Be-like cobalt and are found to be in very good agreement with them. This confirms the present calculations. We predict new data for several levels where no other theoretical and/or experimental results are available. These data provide reference values for level lifetimes, charge state distribution and the average charge of cobalt plasmas.

Relativistic configuration interaction calculations on Kα X-ray satellites of magnesium ions

In this work, the multi-configuration Dirac-Fock (MCDF) and relativistic configuration interaction (RCI) methods have been used to calculate the transition wavelengths, electric dipole transition probabilities, line strengths and absorption oscillator strengths for the Kα X-ray from Mg III to Mg XI. We also take the contributions from the Breit interaction, finite nuclear mass corrections and quantum electrodynamics corrections to the initial and final levels, into account. The present values for Mg X and Mg XI were in good agreement with the previous experimental and theoretical results. The new data in this work provide reference values for the level lifetimes, charge state distributions, and average charge of magnesium plasmas.

Relativistic configuration interaction calculations on Kα x-ray satellites of sodium ions

In this paper, the multi-configuration Dirac–Fock and relativistic configuration interaction methods have been used to calculate the transition wavelengths, electric-dipole transition probabilities, line strengths and absorption oscillator strengths for Kα x-rays from Na II to Na X. We have also taken into account the contributions from the Breit interaction, finite nuclear mass corrections and quantum electrodynamics corrections to the initial and the final level. The present values for Na IX and Na X are in good agreement with previous theoretical and experimental results, and the new data for Na II to Na VIII were ascertained to be reliable by comparing the velocity rate to the length rate. These data provide reference values for the level lifetimes, charge state distributions and average charge of sodium plasmas.

Vibrationally averaged post Born-Oppenheimer isotopic dipole moment calculations approaching spectroscopic accuracy

We report an upgrade of the Dalton code to include post Born-Oppenheimer nuclear mass corrections in the calculations of (ro-)vibrational averages of molecular properties. These corrections are necessary to achieve an accuracy of 10(-4) debye in the calculations of isotopic dipole moments. Calculations on the self-consistent field level present this accuracy, while numerical instabilities compromise correlated calculations. Applications to HD, ethane, and ethylene isotopologues are implemented, all of them approaching the experimental values.

Pseudospectral calculation of helium wave functions, expectation values, and oscillator strength

The pseudospectral method is a powerful tool for finding highly precise solutions of Schr\"{o}dinger's equation for few-electron problems. We extend the method's scope to wave functions with non-zero angular momentum and test it on several challenging problems. One group of tests involves the determination of the nonrelativistic electric dipole oscillator strength for the helium $1^1$S $\to 2^1$P transition. The result achieved, $0.27616499(27)$, is comparable to the best in the literature. Another group of test applications is comprised of well-studied leading order finite nuclear mass and relativistic corrections for the helium ground state. A straightforward computation reaches near state-of-the-art accuracy without requiring the implementation of any special-purpose numerics. All the relevant quantities tested in this paper -- energy eigenvalues, S-state expectation values and bound-bound dipole transitions for S and P states -- converge exponentially with increasing resolution and do so at roughly the same rate. Each individual calculation samples and weights the configuration space wave function uniquely but all behave in a qualitatively similar manner. Quantum mechanical matrix elements are directly and reliably calculable with pseudospectral methods. The technical discussion includes a prescription for choosing coordinates and subdomains to achieve exponential convergence when two-particle Coulomb singularities are present. The prescription does not account for the wave function's non-analytic behavior near the three-particle coalescence which should eventually hinder the rate of the convergence. Nonetheless the effect is small in the sense that ignoring the higher-order coalescence does not appear to affect adversely the accuracy of any of the quantities reported nor the rate at which errors diminish.

Multiconfiguration Dirac-Fock results for forbidden transitions in the 2p 4 configuration

Abstract Relativistic configuration interaction calculations with the inclusion of the Breit interaction, quantum electrodynamics and finite nuclear mass corrections have been carried out in the extended optimal level scheme using multiconfiguration Dirac-Fock wavefunctions on the forbidden transition probabilities for the 2p 4 ground state configuration of the oxygen isoelectronic sequence for 8 ⩽ Z ⩽ 42. Electric quadrupole and magnetic dipole transition probabilities are reported for transitions between several of these levels. Our results are compared with those from other theories and experiments. Our energy levels are in better agreement with experiment than other theories.

Systematic multi-configuration Dirac-Fock calculations of the Kα and Kβ X-ray spectra of silicon ions

The transition energies, absorption oscillator strengths, line strengths and transition probabilities between computed levels are reported for the He-like to Ne-like Silicon ion sequences. Wavefunctions were determined relativistic configuration interaction (RCI) and multi-configuration Dirac-Fock (MCDF) technique included the Breit interaction, quantum electrodynamic (QED) corrections and nuclear mass corrections. The calculated values are in good agreement with the available experimental data and the recent theoretical values obtained from other methods. These data provide reference values for the level lifetimes, charge state distributions, and average charge of silicon plasmas.