arXiv:1307.2656 · Physical Review A

Long-range interaction coefficients for ytterbium dimers

S. G. Porsev, Marianna S. Safronova, Andrei Derevianko, Charles W. Clark

Published Jan 24, 2014• 35 citations

Abstract

We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the $6{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}$, $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$, and $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the ${C}_{6}$ coefficients for the Yb-Yb ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}$ and ${}^{3}{P}_{0}^{o}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$ dimers and ${C}_{8}$ coefficients for the ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}$ and ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ dimers.

DOI: 10.1103/physreva.89.012711

Related papers

Relativistic many-body calculations of van der Waals coefficients for Yb-Li and Yb-Rb dimers

S. G. Porsev, Marianna S. Safronova, Andrei Derevianko +1 more

arXiv:1401.6585Physical Review AFeb 6, 201415 citations

Long range interactions of ytterbium in mixed quantum gases

S. G. Porsev, Marianna S. Safronova, Andrei Derevianko +1 more

We present methods for accurate evaluation of van der Waals coefficients of dimers with excited atoms that have a strong decay channel. We calculate C_6 coefficients for the Yb-Yb 1S_0+ 3P_{0,1}, 3P_0+3P_0 and Yb-Rb 3P_1+5s, 1S_0+ 5p_{1/2} dimers and C_8 coefficients for the Yb-Yb 1S_0+1S_0, 1S_0+3P_1 and Yb-Rb 1S_0+5s dimers. We evaluate uncertainties of all properties.

arXiv:1307.2654Jul 10, 20130 citations

Relativistic calculations of C6 and C8 coefficients for strontium dimers

S. G. Porsev, Marianna S. Safronova, Charles W. Clark

arXiv:1409.5985Physical Review ANov 18, 201413 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

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.

Journal of Experimental and Theoretical PhysicsFeb 1, 2006125 citations

Dipole polarizabilities of excited alkali-metal atoms and long-range interactions of ground- and excited-state alkali-metal atoms with helium atoms

Cheng Zhu, A. Dalgarno, S. G. Porsev +1 more

Physical Review ASep 30, 200441 citations

Dispersion coefficients for alkali-metal dimers

M. Marinescu, H. R. Sadeghpour, A. Dalgarno

Physical Review AFeb 1, 1994377 citations

arXiv:1307.2656 · Physical Review A

Long-range interaction coefficients for ytterbium dimers

S. G. Porsev, Marianna S. Safronova, Andrei Derevianko, Charles W. Clark

Published Jan 24, 2014• 35 citations

arXiv HTML PDF

Abstract

We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the

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

6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}

, and

6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}

states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the

{C}_{6}

coefficients for the Yb-Yb

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}

and

{}^{3}{P}_{0}^{o}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}

dimers and

{C}_{8}

coefficients for the

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

and

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

dimers.

DOI: 10.1103/physreva.89.012711

Related papers

Relativistic many-body calculations of van der Waals coefficients for Yb-Li and Yb-Rb dimers

S. G. Porsev, Marianna S. Safronova, Andrei Derevianko +1 more

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.

arXiv:1401.6585Physical Review AFeb 6, 201415 citations

Long range interactions of ytterbium in mixed quantum gases

S. G. Porsev, Marianna S. Safronova, Andrei Derevianko +1 more

arXiv:1307.2654Jul 10, 20130 citations

Relativistic calculations of C6 and C8 coefficients for strontium dimers

S. G. Porsev, Marianna S. Safronova, Charles W. Clark

The electric-dipole and quadrupole polarizabilities of the $5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ state and the ${C}_{6}$ and ${C}_{8}$ coefficients for the ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}$ and ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ dimers of strontium are calculated using a high-precision relativistic approach that combines configuration interaction and linearized coupled-cluster methods. Our recommended values of the long-range dispersion coefficients for the ${0}_{u}$ and ${1}_{u}$ energy levels are ${C}_{6}({0}_{u})=3771(32)$ a.u. and ${C}_{6}({1}_{u})=4001(33)$ a.u., respectively. They are in good agreement with recent results from experimental photoassociation data. We also calculate ${C}_{8}$ coefficients for Sr dimers, which are needed for precise determination of long-range interaction potential. We confirm the experimental value for the magic wavelength, where the Stark shift on the ${}^{1}{S}_{0}\text{\ensuremath{-}}{}^{3}{P}_{1}^{o}$ transition vanishes. The accuracy of calculations is analyzed and uncertainties are assigned to all quantities reported in this work.The electric-dipole and quadrupole polarizabilities of the $5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ state and the ${C}_{6}$ and ${C}_{8}$ coefficients for the ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}$ and ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ dimers of strontium are calculated using a high-precision relativistic approach that combines configuration interaction and linearized coupled-cluster methods. Our recommended values of the long-range dispersion coefficients for the ${0}_{u}$ and ${1}_{u}$ energy levels are ${C}_{6}({0}_{u})=3771(32)$ a.u. and ${C}_{6}({1}_{u})=4001(33)$ a.u., respectively. They are in good agreement with recent results from experimental photoassociation data. We also calculate ${C}_{8}$ coefficients for Sr dimers, which are needed for precise determination of long-range interaction potential. We confirm the experimental value for the magic wavelength, where the Stark shift on the ${}^{1}{S}_{0}\text{\ensuremath{-}}{}^{3}{P}_{1}^{o}$ transition vanishes. The accuracy of calculations is analyzed and uncertainties are assigned to all quantities reported in this work.

arXiv:1409.5985Physical Review ANov 18, 201413 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

Dipole polarizabilities of excited alkali-metal atoms and long-range interactions of ground- and excited-state alkali-metal atoms with helium atoms

Cheng Zhu, A. Dalgarno, S. G. Porsev +1 more

The scalar and tensor dynamic polarizabilities of the first excited $^{2}P_{1∕2,3∕2}$ states of the alkali-metal atoms $\mathrm{Na}$ , $\mathrm{K}$ , and $\mathrm{Rb}$ are calculated using relativistic many-body perturbation theory. Comparison with experimental measurements of the static polarizabilities suggests that the errors in the theoretical predictions do not exceed 1%. The dynamic polarizabilities at imaginary frequencies are employed to calculate the long-range van der Waals coefficients for the interaction of ground-state helium atoms with the excited alkali-metal atoms to a probable error of less than 2%.The scalar and tensor dynamic polarizabilities of the first excited $^{2}P_{1∕2,3∕2}$ states of the alkali-metal atoms $\mathrm{Na}$, $\mathrm{K}$, and $\mathrm{Rb}$ are calculated using relativistic many-body perturbation theory. Comparison with experimental measurements of the static polarizabilities suggests that the errors in the theoretical predictions do not exceed 1%. The dynamic polarizabilities at imaginary frequencies are employed to calculate the long-range van der Waals coefficients for the interaction of ground-state helium atoms with the excited alkali-metal atoms to a probable error of less than 2%.

Physical Review ASep 30, 200441 citations

Dispersion coefficients for alkali-metal dimers

M. Marinescu, H. R. Sadeghpour, A. Dalgarno

Knowledge of the long-range interaction between atoms and molecules is of fundamental importance for low-energy and low-temperature collisions. The electronic interaction between the charge distributions of two ground-state alkali-metal atoms can be expanded in inverse powers of R, the internuclear distance. The coefficients ${\mathit{C}}_{6}$ , ${\mathit{C}}_{8}$ , and ${\mathit{C}}_{10}$ of, respectively, the ${\mathit{R}}^{\mathrm{\ensuremath{-}}6}$, ${\mathit{R}}^{\mathrm{\ensuremath{-}}8}$, and ${\mathit{R}}^{\mathrm{\ensuremath{-}}10}$ terms are calculated by integrating the products of the dynamic electric multipole polarizabilities of the individual atoms at imaginary frequencies, which are in turn obtained by solving two coupled inhomogeneous differential equations. Precise one-electron model potentials are developed to represent the motion of the valence electron in the field of the closed alkali-metal positive-ion core. The numerical results for the static multipole polarizabilities for the alkali-metal atoms and the coefficients ${\mathit{C}}_{6}$ , ${\mathit{C}}_{8}$ , and ${\mathit{C}}_{10}$ for homonuclear and heteronuclear alkali-metal diatoms are compared with other calculations.Knowledge of the long-range interaction between atoms and molecules is of fundamental importance for low-energy and low-temperature collisions. The electronic interaction between the charge distributions of two ground-state alkali-metal atoms can be expanded in inverse powers of R, the internuclear distance. The coefficients ${\mathit{C}}_{6}$, ${\mathit{C}}_{8}$, and ${\mathit{C}}_{10}$ of, respectively, the ${\mathit{R}}^{\mathrm{\ensuremath{-}}6}$, ${\mathit{R}}^{\mathrm{\ensuremath{-}}8}$, and ${\mathit{R}}^{\mathrm{\ensuremath{-}}10}$ terms are calculated by integrating the products of the dynamic electric multipole polarizabilities of the individual atoms at imaginary frequencies, which are in turn obtained by solving two coupled inhomogeneous differential equations. Precise one-electron model potentials are developed to represent the motion of the valence electron in the field of the closed alkali-metal positive-ion core. The numerical results for the static multipole polarizabilities for the alkali-metal atoms and the coefficients ${\mathit{C}}_{6}$, ${\mathit{C}}_{8}$, and ${\mathit{C}}_{10}$ for homonuclear and heteronuclear alkali-metal diatoms are compared with other calculations.

Physical Review AFeb 1, 1994377 citations

We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the

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

6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}

, and

6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}

{C}_{6}

coefficients for the Yb-Yb

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}

and

{}^{3}{P}_{0}^{o}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}

dimers and

{C}_{8}

coefficients for the

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

and

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

dimers.

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 electric-dipole and quadrupole polarizabilities of the

5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}

state and the

{C}_{6}

and

{C}_{8}

coefficients for the

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

and

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

dimers of strontium are calculated using a high-precision relativistic approach that combines configuration interaction and linearized coupled-cluster methods. Our recommended values of the long-range dispersion coefficients for the

{0}_{u}

and

{1}_{u}

energy levels are

{C}_{6}({0}_{u})=3771(32)

a.u. and

{C}_{6}({1}_{u})=4001(33)

a.u., respectively. They are in good agreement with recent results from experimental photoassociation data. We also calculate

{C}_{8}

coefficients for Sr dimers, which are needed for precise determination of long-range interaction potential. We confirm the experimental value for the magic wavelength, where the Stark shift on the ${}^{1}{S}_{0}\text{\ensuremath{-}}{}^{3}{P}_{1}^{o}$ transition vanishes. The accuracy of calculations is analyzed and uncertainties are assigned to all quantities reported in this work.

The scalar and tensor dynamic polarizabilities of the first excited

^{2}P_{1∕2,3∕2}

states of the alkali-metal atoms

\mathrm{Na}

\mathrm{K}

, and

\mathrm{Rb}

are calculated using relativistic many-body perturbation theory. Comparison with experimental measurements of the static polarizabilities suggests that the errors in the theoretical predictions do not exceed 1%. The dynamic polarizabilities at imaginary frequencies are employed to calculate the long-range van der Waals coefficients for the interaction of ground-state helium atoms with the excited alkali-metal atoms to a probable error of less than 2%.

{\mathit{C}}_{6}

{\mathit{C}}_{8}

, and

{\mathit{C}}_{10}

of, respectively, the ${\mathit{R}}^{\mathrm{\ensuremath{-}}6}$, ${\mathit{R}}^{\mathrm{\ensuremath{-}}8}$, and ${\mathit{R}}^{\mathrm{\ensuremath{-}}10}$ terms are calculated by integrating the products of the dynamic electric multipole polarizabilities of the individual atoms at imaginary frequencies, which are in turn obtained by solving two coupled inhomogeneous differential equations. Precise one-electron model potentials are developed to represent the motion of the valence electron in the field of the closed alkali-metal positive-ion core. The numerical results for the static multipole polarizabilities for the alkali-metal atoms and the coefficients

{\mathit{C}}_{6}

{\mathit{C}}_{8}

, and

{\mathit{C}}_{10}

for homonuclear and heteronuclear alkali-metal diatoms are compared with other calculations.