Physical Review A

Rydberg levels of lithium

Richard J. Drachman, A. K. Bhatia

Published Apr 1, 1995• 45 citations

Abstract

The electrostatic fine structure for singly excited lithium is accurately calculated using an effective potential method that has proven to be very useful for helium. Relevant properties of the two-electron ${\mathrm{Li}}^{+}$ ionic core with finite nuclear mass are determined from variational wave functions. From these, non- relativistic level shifts are obtained analytically, and the leading relativistic correction is applied. A comparison with recent experimental results is made.

DOI: 10.1103/physreva.51.2926

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Physical Review A

Rydberg levels of lithium

Richard J. Drachman, A. K. Bhatia

Published Apr 1, 1995• 45 citations

Publisher

Abstract

{\mathrm{Li}}^{+}

ionic core with finite nuclear mass are determined from variational wave functions. From these, non- relativistic level shifts are obtained analytically, and the leading relativistic correction is applied. A comparison with recent experimental results is made.

DOI: 10.1103/physreva.51.2926

Related papers

Accuracy limits on the description of the lowest S excitation in the Li atom using explicitly correlated Gaussian basis functions

Monika Stanke, Jacek Komasa, Dariusz Kędziera +2 more

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Physical Review ANov 14, 200828 citations

Theoretical study of helium Rydberg states

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Resonance measurements of d−f and d−g intervals in lithium Rydberg states

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In this work, the ground-state energy of the lithium atom is systematically investigated using both time-independent perturbation theory and the variational method to provide a comprehensive pedagogical analysis of many-body atomic systems. The unperturbed Hamiltonian is initially constructed by neglecting electron-electron interactions, treating the system as three independent hydrogen-like electrons to yield a zeroth-order energy baseline of -275.51 eV. The antisymmetric fermionic nature of the exact wave function is rigorously enforced through the Slater determinant formalism. First-order perturbation theory is applied to evaluate static inter-electronic repulsion using exact Coulomb and exchange integrals, refining the energy state to -192.01 eV. To account for dynamical electronic correlation, second-order perturbation theory is computed numerically for virtual single-electron s-orbital transitions, leading to a total perturbative energy of -196.36 eV. A brief discussion of two-electron excitations is also included to encapsulate further physical realism within the framework. Furthermore, a non-orthogonal two-parameter variational approach is employed to model the shell-specific shielding effect. By optimizing the effective nuclear charges, the variational method establishes a superior upper bound energy of -201.187 eV. The results of both methods are comprehensively contrasted against each other and the reference baseline to provide critical insights into the nature of electron correlation and screening in multi-electron atoms.In this work, the ground-state energy of the lithium atom is systematically investigated using both time-independent perturbation theory and the variational method to provide a comprehensive pedagogical analysis of many-body atomic systems. The unperturbed Hamiltonian is initially constructed by neglecting electron-electron interactions, treating the system as three independent hydrogen-like electrons to yield a zeroth-order energy baseline of -275.51 eV. The antisymmetric fermionic nature of the exact wave function is rigorously enforced through the Slater determinant formalism. First-order perturbation theory is applied to evaluate static inter-electronic repulsion using exact Coulomb and exchange integrals, refining the energy state to -192.01 eV. To account for dynamical electronic correlation, second-order perturbation theory is computed numerically for virtual single-electron s-orbital transitions, leading to a total perturbative energy of -196.36 eV. A brief discussion of two-electron excitations is also included to encapsulate further physical realism within the framework. Furthermore, a non-orthogonal two-parameter variational approach is employed to model the shell-specific shielding effect. By optimizing the effective nuclear charges, the variational method establishes a superior upper bound energy of -201.187 eV. The results of both methods are comprehensively contrasted against each other and the reference baseline to provide critical insights into the nature of electron correlation and screening in multi-electron atoms.

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Determination of dipole and quadrupole polarizabilities of Ba+ by measurement of the fine structure of high- L n=9 and 10 Rydberg states of barium

Erica L. Snow, M. A. Gearba, R. A. Komara +2 more

The fine structure of high-angular-momentum $n=9$ and 10 Rydberg states of barium has been measured precisely, using the resonant excitation Stark ionization spectroscopy method. Optical transitions corresponding to $(n,{n}^{\ensuremath{'}})=(10,30)$, (9,17), and (9,20) were induced with a Doppler-tuned ${\mathrm{CO}}_{2}$ laser, determining the fine-structure energies corresponding to all $n=9$ and 10 levels with $L\ensuremath{\geqslant}6$. The pattern of these fine-structure energies conforms closely with an effective potential model, by comparison with which the dipole and quadrupole polarizabilities of ${\mathrm{Ba}}^{+}$ can be determined. Combining our data with earlier measurements made it possible to deduce, in addition, the portion of ${\ensuremath{\alpha}}_{2}$ due to the lowest excited $D$ state of ${\mathrm{Ba}}^{+}$ . Our best estimates of these three properties are ${\ensuremath{\alpha}}_{1}=124.30(16){a}_{0}^{3}$, ${\ensuremath{\alpha}}_{2}=2462(361){a}_{0}^{5}$, and ${\ensuremath{\alpha}}_{2}^{0}=1828(88){a}_{0}^{5}$.The fine structure of high-angular-momentum $n=9$ and 10 Rydberg states of barium has been measured precisely, using the resonant excitation Stark ionization spectroscopy method. Optical transitions corresponding to $(n,{n}^{\ensuremath{'}})=(10,30)$, (9,17), and (9,20) were induced with a Doppler-tuned ${\mathrm{CO}}_{2}$ laser, determining the fine-structure energies corresponding to all $n=9$ and 10 levels with $L\ensuremath{\geqslant}6$. The pattern of these fine-structure energies conforms closely with an effective potential model, by comparison with which the dipole and quadrupole polarizabilities of ${\mathrm{Ba}}^{+}$ can be determined. Combining our data with earlier measurements made it possible to deduce, in addition, the portion of ${\ensuremath{\alpha}}_{2}$ due to the lowest excited $D$ state of ${\mathrm{Ba}}^{+}$. Our best estimates of these three properties are ${\ensuremath{\alpha}}_{1}=124.30(16){a}_{0}^{3}$, ${\ensuremath{\alpha}}_{2}=2462(361){a}_{0}^{5}$, and ${\ensuremath{\alpha}}_{2}^{0}=1828(88){a}_{0}^{5}$.

Physical Review AFeb 25, 200529 citations

THEORETICAL STUDY OF THE FINE-STRUCTURE INVERSIONS IN nf RYDBERG STATES OF ALKALI ATOMS

YAN JUN, Peihong Zhang, Xiao‐Min Tong +2 more

Based on the Relativistic Multichannel Theory,we have systematically studied the fine structure of nf Rydberg states of alkali atoms. Our calculated differences between the quantum defects μj+ and μj- are in good agreement with measured values, namely normal for Li and Na while inverted for Rb and Cs. We also predict a normal fine-structure for K and an inverted one for Fr, which still have no experimental data currently. Our theoretical calculation shows that the exchange between excited electron and core electrons is responsible for the inversion, which is a purely relativistic effect, while electron correlation is unimportant.Based on the Relativistic Multichannel Theory,we have systematically studied the fine structure of nf Rydberg states of alkali atoms. Our calculated differences between the quantum defects μj+ and μj- are in good agreement with measured values, namely normal for Li and Na while inverted for Rb and Cs. We also predict a normal fine-structure for K and an inverted one for Fr, which still have no experimental data currently. Our theoretical calculation shows that the exchange between excited electron and core electrons is responsible for the inversion, which is a purely relativistic effect, while electron correlation is unimportant.

Acta Physica SinicaJan 1, 199623 citations

{\mathrm{Li}}^{+}

We have performed very accurate quantum-mechanical calculations for the two lowest

S

states of the lithium atom in order to determine the transition energy. In the nonrelativistic part of the calculations performed using the variational method, we explicitly included the nuclear motion. The nonrelativistic wave function was expanded in terms of explicitly correlated Gaussian functions. Next, this wave function was used to calculate the leading ${\ensuremath{\alpha}}^{2}$ relativistic correction ($\ensuremath{\alpha}$ is the fine-structure constant) and the ${\ensuremath{\alpha}}^{3}$ QED correction. We also estimated the ${\ensuremath{\alpha}}^{4}$ QED correction by calculating its dominating component. The results obtained with Gaussians are compared with the most accurate results obtained recently with the Hylleraas-type basis functions.

Using a laser-excitation, optical-detection scheme, we have observed microwave transitions from the

\mathrm{nd}

to the

\mathrm{nf}

and

\mathrm{ng}

orbital levels in lithium states with principal quantum number

n

from 7 to 11. These measurements yield precise values for the

d

f

, and

g

state fine-structure intervals as well as $d\ensuremath{-}f$ and $d\ensuremath{-}g$ energy separations. Within the accuracy of these measurements, the fine structures are found to be hydrogenic. The dipole polarizability of the

{\mathrm{Li}}^{+}

core is determined from the $d\ensuremath{-}f$ and $d\ensuremath{-}g$ energy splittings. The $d\ensuremath{-}f$ intervals are compared to pseudopotential calculations.

The fine structure of high-angular-momentum

n=9

and 10 Rydberg states of barium has been measured precisely, using the resonant excitation Stark ionization spectroscopy method. Optical transitions corresponding to $(n,{n}^{\ensuremath{'}})=(10,30)$, (9,17), and (9,20) were induced with a Doppler-tuned

{\mathrm{CO}}_{2}

laser, determining the fine-structure energies corresponding to all

n=9

and 10 levels with $L\ensuremath{\geqslant}6$. The pattern of these fine-structure energies conforms closely with an effective potential model, by comparison with which the dipole and quadrupole polarizabilities of

{\mathrm{Ba}}^{+}

can be determined. Combining our data with earlier measurements made it possible to deduce, in addition, the portion of ${\ensuremath{\alpha}}_{2}$ due to the lowest excited

D

state of

{\mathrm{Ba}}^{+}

. Our best estimates of these three properties are ${\ensuremath{\alpha}}_{1}=124.30(16){a}_{0}^{3}$, ${\ensuremath{\alpha}}_{2}=2462(361){a}_{0}^{5}$, and ${\ensuremath{\alpha}}_{2}^{0}=1828(88){a}_{0}^{5}$.