arXiv:physics/0108047 · Physical Review A

High-accuracy relativistic many-body calculations of van der Waals coefficients C6 for alkaline-earth-metal atoms

S. G. Porsev, Andrei Derevianko

Published Jan 11, 2002• 83 citations

Abstract

Relativistic many-body calculations of van der Waals coefficients ${C}_{6}$ for dimers correlating to two ground-state alkaline-earth-metal atoms at large internuclear separations are reported. The following values and uncertainties were determined: ${C}_{6}=214(3)$ for Be, 627(12) for Mg, 2221(15) for Ca, 3170(196) for Sr, and 5160(74) for Ba in atomic units.

DOI: 10.1103/physreva.65.020701

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Semiempirical calculation of van der Waals coefficients for alkali-metal and alkaline-earth-metal atoms

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High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C 6, C 8, and C 10 for alkaline-earth dimers

S. G. Porsev, Andrei Derevianko

The static and dynamic electric dipole, quadrupole, and octupole polarizabilities of the alkaline-earth atoms (beryllium, magnesium, calcium, strontium, and barium) in the ground state were calculated. The dynamic polarizabilities obtained were used to calculate the van der Waals coefficients C 6, C 8, and C 10 of alkaline-earth metal dimers for the interaction of two like atoms in the ground state. The results are compared with other theoretical and experimental data.

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arXiv:physics/0108047 · Physical Review A

High-accuracy relativistic many-body calculations of van der Waals coefficients C6 for alkaline-earth-metal atoms

S. G. Porsev, Andrei Derevianko

Published Jan 11, 2002• 83 citations

arXiv HTML PDF

Abstract

Relativistic many-body calculations of van der Waals coefficients

{C}_{6}

for dimers correlating to two ground-state alkaline-earth-metal atoms at large internuclear separations are reported. The following values and uncertainties were determined:

{C}_{6}=214(3)

for Be, 627(12) for Mg, 2221(15) for Ca, 3170(196) for Sr, and 5160(74) for Ba in atomic units.

DOI: 10.1103/physreva.65.020701

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Semiempirical calculation of van der Waals coefficients for alkali-metal and alkaline-earth-metal atoms

J. Mitroy, M. W. J. Bromley

The van der Waals coefficients, ${C}_{6},{C}_{8},$ and ${C}_{10}$ for the alkali-metal (Li, Na, K, and Rb) and alkaline-earth-metal (Be, Mg, Ca, and Sr) atoms are estimated by a combination of ab initio and semiempirical methods. Polarizabilities and atom-wall coefficients are given as a diagnostic check, and the lowest order nonadiabatic dispersion coefficient, ${D}_{8}$ and the three-body coefficient, ${C}_{9}$ are also presented. The dispersion coefficients are in agreement with the available relativistic many-body perturbation theory calculations. The contribution from the core was included by using constrained sum rules involving the core polarizability and Hartree-Fock expectation values to estimate the f-value distribution.The van der Waals coefficients, ${C}_{6},{C}_{8},$ and ${C}_{10}$ for the alkali-metal (Li, Na, K, and Rb) and alkaline-earth-metal (Be, Mg, Ca, and Sr) atoms are estimated by a combination of ab initio and semiempirical methods. Polarizabilities and atom-wall coefficients are given as a diagnostic check, and the lowest order nonadiabatic dispersion coefficient, ${D}_{8}$ and the three-body coefficient, ${C}_{9}$ are also presented. The dispersion coefficients are in agreement with the available relativistic many-body perturbation theory calculations. The contribution from the core was included by using constrained sum rules involving the core polarizability and Hartree-Fock expectation values to estimate the f-value distribution.

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We derive the relativistic formulas for the van der Waals coefficients of Yb--alkali-metal dimers that correlate to ground and excited separated-atom limits. We calculate ${C}_{6}$ and ${C}_{8}$ coefficients of particular experimental interest. We also derive a semiempirical formula that expresses the ${C}_{8}$ coefficient of heteronuclear $A+B$ dimers in terms of the ${C}_{6}$ and ${C}_{8}$ coefficients of homonuclear dimers and the static dipole and quadrupole polarizabilities of the atomic states $A$ and $B$ . We report results of calculation of the ${C}_{6}$ coefficients for the Yb-Rb ${}^{3}{P}_{1}^{o}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and ${}^{1}{S}_{0}+5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}^{o}$ dimers, and the ${C}_{8}$ coefficients for the Yb-Li ${}^{1}{S}_{0}+2s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and Yb-Rb ${}^{1}{S}_{0}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ dimers. Uncertainties are estimated for all predicted properties.We derive the relativistic formulas for the van der Waals coefficients of Yb--alkali-metal dimers that correlate to ground and excited separated-atom limits. We calculate ${C}_{6}$ and ${C}_{8}$ coefficients of particular experimental interest. We also derive a semiempirical formula that expresses the ${C}_{8}$ coefficient of heteronuclear $A+B$ dimers in terms of the ${C}_{6}$ and ${C}_{8}$ coefficients of homonuclear dimers and the static dipole and quadrupole polarizabilities of the atomic states $A$ and $B$. We report results of calculation of the ${C}_{6}$ coefficients for the Yb-Rb ${}^{3}{P}_{1}^{o}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and ${}^{1}{S}_{0}+5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}^{o}$ dimers, and the ${C}_{8}$ coefficients for the Yb-Li ${}^{1}{S}_{0}+2s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and Yb-Rb ${}^{1}{S}_{0}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ dimers. Uncertainties are estimated for all predicted properties.

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The long-range part of the interatomic interactions plays a substantial role in the collisional dynamics of ultracold gases. Here, we report on the calculation of the isotropic and anisotropic ${C}_{6}$ coefficients characterizing the van der Waals interaction between dysprosium or erbium atoms in the two lowest energy levels and the ground-state alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba) atoms. The calculations are done using the integral of dynamic dipole polarizabilities at so-called imaginary frequencies of the two interacting atoms. For all atom pairs, we find that the isotropic ${C}_{6}$ coefficients are two or three orders of magnitude larger than the anisotropic ones. Those coefficients are essential for modeling collisional properties of heteronuclear quantum mixtures containing highly magnetic dysprosium or erbium atoms and alkali-metal or alkaline-earth-metal atoms.The long-range part of the interatomic interactions plays a substantial role in the collisional dynamics of ultracold gases. Here, we report on the calculation of the isotropic and anisotropic ${C}_{6}$ coefficients characterizing the van der Waals interaction between dysprosium or erbium atoms in the two lowest energy levels and the ground-state alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba) atoms. The calculations are done using the integral of dynamic dipole polarizabilities at so-called imaginary frequencies of the two interacting atoms. For all atom pairs, we find that the isotropic ${C}_{6}$ coefficients are two or three orders of magnitude larger than the anisotropic ones. Those coefficients are essential for modeling collisional properties of heteronuclear quantum mixtures containing highly magnetic dysprosium or erbium atoms and alkali-metal or alkaline-earth-metal atoms.

arXiv:2311.17745Physical Review AJan 18, 20240 citations

Accurate relativistic many-body calculations of van der Waals coefficients C8 and C10 for alkali-metal dimers

S. G. Porsev, Andrei Derevianko

We consider long-range interactions between two alkali-metal atoms in their respective ground states. We extend the previous relativistic many-body calculations of C6 dispersion coefficients [Phys. Rev. Lett. 82, 3589 (1999)] to higher-multipole coefficients C8 and C10. Special attention is paid to usually omitted contribution of core-excited states. We calculate this contribution within relativistic random-phase approximation and demonstrate that for heavy atoms core excitations contribute as much as 10% to the dispersion coefficients. We tabulate results for both homonuclear and heteronuclear dimers and estimate theoretical uncertainties. The estimated uncertainties for C8 coefficients range from 0.5% for Li2 to 4% for Cs2.We consider long-range interactions between two alkali-metal atoms in their respective ground states. We extend the previous relativistic many-body calculations of C6 dispersion coefficients [Phys. Rev. Lett. 82, 3589 (1999)] to higher-multipole coefficients C8 and C10. Special attention is paid to usually omitted contribution of core-excited states. We calculate this contribution within relativistic random-phase approximation and demonstrate that for heavy atoms core excitations contribute as much as 10% to the dispersion coefficients. We tabulate results for both homonuclear and heteronuclear dimers and estimate theoretical uncertainties. The estimated uncertainties for C8 coefficients range from 0.5% for Li2 to 4% for Cs2.

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Two-dipole and three-dipole dispersion coefficients for interaction of alkaline-earth-metal atoms with alkaline-earth-metal atoms and alkaline-earth-metal ions

Neelam Shukla, Bindiya Arora, Lalita Sharma +1 more

Apropos of the growing interest in the study of long-range interactions for their applications in cold-atom physics, we perform theoretical calculations for the two-dipole ${C}_{6}$ and three-dipole ${C}_{9}$ dispersion coefficients involving alkaline-earth-metal atoms with alkaline-earth-metal atoms and alkaline-earth-metal ions. The ${C}_{6}$ and ${C}_{9}$ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated ${C}_{6}$ coefficients for the considered alkaline-earth-metal atoms are compared with previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the ${C}_{6}$ coefficients for alkaline-earth-metal atoms with alkaline-earth-metal ions and the ${C}_{9}$ coefficients we perform separate fitting calculations and compare the results. Our calculations match in an excellent manner with the fitting calculations. We also report the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth-metal ions, i.e., ${\mathrm{Be}}^{+}, {\mathrm{Mg}}^{+}, {\mathrm{Ca}}^{+}, {\mathrm{Sr}}^{+}$ , and ${\mathrm{Ba}}^{+}$ , as well as the alkaline-earth-metal atoms, i.e., Be, Mg, Ca, Sr, and Ba. These show good agreement when compared with the available experimental results.Apropos of the growing interest in the study of long-range interactions for their applications in cold-atom physics, we perform theoretical calculations for the two-dipole ${C}_{6}$ and three-dipole ${C}_{9}$ dispersion coefficients involving alkaline-earth-metal atoms with alkaline-earth-metal atoms and alkaline-earth-metal ions. The ${C}_{6}$ and ${C}_{9}$ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated ${C}_{6}$ coefficients for the considered alkaline-earth-metal atoms are compared with previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the ${C}_{6}$ coefficients for alkaline-earth-metal atoms with alkaline-earth-metal ions and the ${C}_{9}$ coefficients we perform separate fitting calculations and compare the results. Our calculations match in an excellent manner with the fitting calculations. We also report the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth-metal ions, i.e., ${\mathrm{Be}}^{+}, {\mathrm{Mg}}^{+}, {\mathrm{Ca}}^{+}, {\mathrm{Sr}}^{+}$, and ${\mathrm{Ba}}^{+}$, as well as the alkaline-earth-metal atoms, i.e., Be, Mg, Ca, Sr, and Ba. These show good agreement when compared with the available experimental results.

Physical Review AAug 27, 20208 citations

High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C 6, C 8, and C 10 for alkaline-earth dimers

S. G. Porsev, Andrei Derevianko

Journal of Experimental and Theoretical PhysicsFeb 1, 2006125 citations

Relativistic many-body calculations of van der Waals coefficients

{C}_{6}

for dimers correlating to two ground-state alkaline-earth-metal atoms at large internuclear separations are reported. The following values and uncertainties were determined:

{C}_{6}=214(3)

for Be, 627(12) for Mg, 2221(15) for Ca, 3170(196) for Sr, and 5160(74) for Ba in atomic units.

The van der Waals coefficients,

{C}_{6},{C}_{8},

and

{C}_{10}

for the alkali-metal (Li, Na, K, and Rb) and alkaline-earth-metal (Be, Mg, Ca, and Sr) atoms are estimated by a combination of ab initio and semiempirical methods. Polarizabilities and atom-wall coefficients are given as a diagnostic check, and the lowest order nonadiabatic dispersion coefficient,

{D}_{8}

and the three-body coefficient,

{C}_{9}

are also presented. The dispersion coefficients are in agreement with the available relativistic many-body perturbation theory calculations. The contribution from the core was included by using constrained sum rules involving the core polarizability and Hartree-Fock expectation values to estimate the f-value distribution.

We derive the relativistic formulas for the van der Waals coefficients of Yb--alkali-metal dimers that correlate to ground and excited separated-atom limits. We calculate

{C}_{6}

and

{C}_{8}

coefficients of particular experimental interest. We also derive a semiempirical formula that expresses the

{C}_{8}

coefficient of heteronuclear

A+B

dimers in terms of the

{C}_{6}

and

{C}_{8}

coefficients of homonuclear dimers and the static dipole and quadrupole polarizabilities of the atomic states

A

and

B

. We report results of calculation of the

{C}_{6}

coefficients for the Yb-Rb

{}^{3}{P}_{1}^{o}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

and

{}^{1}{S}_{0}+5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}^{o}

dimers, and the

{C}_{8}

coefficients for the Yb-Li

{}^{1}{S}_{0}+2s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

and Yb-Rb

{}^{1}{S}_{0}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

dimers. Uncertainties are estimated for all predicted properties.

The long-range part of the interatomic interactions plays a substantial role in the collisional dynamics of ultracold gases. Here, we report on the calculation of the isotropic and anisotropic

{C}_{6}

coefficients characterizing the van der Waals interaction between dysprosium or erbium atoms in the two lowest energy levels and the ground-state alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba) atoms. The calculations are done using the integral of dynamic dipole polarizabilities at so-called imaginary frequencies of the two interacting atoms. For all atom pairs, we find that the isotropic

{C}_{6}

coefficients are two or three orders of magnitude larger than the anisotropic ones. Those coefficients are essential for modeling collisional properties of heteronuclear quantum mixtures containing highly magnetic dysprosium or erbium atoms and alkali-metal or alkaline-earth-metal atoms.

Apropos of the growing interest in the study of long-range interactions for their applications in cold-atom physics, we perform theoretical calculations for the two-dipole

{C}_{6}

and three-dipole

{C}_{9}

dispersion coefficients involving alkaline-earth-metal atoms with alkaline-earth-metal atoms and alkaline-earth-metal ions. The

{C}_{6}

and

{C}_{9}

coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated

{C}_{6}

coefficients for the considered alkaline-earth-metal atoms are compared with previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the

{C}_{6}

coefficients for alkaline-earth-metal atoms with alkaline-earth-metal ions and the

{C}_{9}

coefficients we perform separate fitting calculations and compare the results. Our calculations match in an excellent manner with the fitting calculations. We also report the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth-metal ions, i.e.,

{\mathrm{Be}}^{+}, {\mathrm{Mg}}^{+}, {\mathrm{Ca}}^{+}, {\mathrm{Sr}}^{+}

, and

{\mathrm{Ba}}^{+}

, as well as the alkaline-earth-metal atoms, i.e., Be, Mg, Ca, Sr, and Ba. These show good agreement when compared with the available experimental results.