arXiv:1605.05040 · Physical Review A

Relativistic semiempirical-core-potential calculations of Sr+ using Laguerre and Slater spinors

Jun Jiang, Jim Mitroy, Yongjun Cheng, M. W. J. Bromley

Published Dec 23, 2016• 25 citations

Abstract

A relativistic description of the structure of heavy alkali-metal atoms and alkali-like ions using S-spinors and L-spinors is developed. The core wave function is defined by a Dirac-Fock calculation using an S-spinor basis. The S-spinor basis is then supplemented with a large set of L-spinors for calculation of the valence wave function in a frozen-core model. The numerical stability of the L-spinor approach is demonstrated by computing the energies and decay rates of several low-lying hydrogen eigenstates, along with the polarizabilities of a $Z=60$ hydrogenic ion. The approach is then applied to calculate the dynamic polarizabilities of the $5s, 4d$, and $5p$ states of ${\mathrm{Sr}}^{+}$. The magic wavelengths at which the Stark shifts between different pairs of transitions are 0 are computed. Determination of the magic wavelengths for the $5s\ensuremath{\rightarrow}4{d}_{\frac{3}{2}}$ and $5s\ensuremath{\rightarrow}4{d}_{\frac{5}{2}}$ transitions near 417 nm (near the wavelength for the $5s\ensuremath{\rightarrow}5{p}_{j}$ transitions) would allow determination of the oscillator strength ratio for the $5s\ensuremath{\rightarrow}5{p}_{\frac{1}{2}}$ and $5s\ensuremath{\rightarrow}5{p}_{\frac{3}{2}}$ transitions.

DOI: 10.1103/physreva.94.062514

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arXiv:1605.05040 · Physical Review A

Relativistic semiempirical-core-potential calculations of Sr+ using Laguerre and Slater spinors

Jun Jiang, Jim Mitroy, Yongjun Cheng, M. W. J. Bromley

Published Dec 23, 2016• 25 citations

arXiv HTML PDF

Abstract

Z=60

hydrogenic ion. The approach is then applied to calculate the dynamic polarizabilities of the

5s, 4d

, and

5p

states of

{\mathrm{Sr}}^{+}

. The magic wavelengths at which the Stark shifts between different pairs of transitions are 0 are computed. Determination of the magic wavelengths for the

5s\ensuremath{\rightarrow}4{d}_{\frac{3}{2}}

and

5s\ensuremath{\rightarrow}4{d}_{\frac{5}{2}}

transitions near 417 nm (near the wavelength for the

5s\ensuremath{\rightarrow}5{p}_{j}

transitions) would allow determination of the oscillator strength ratio for the

5s\ensuremath{\rightarrow}5{p}_{\frac{1}{2}}

and

5s\ensuremath{\rightarrow}5{p}_{\frac{3}{2}}

transitions.

DOI: 10.1103/physreva.94.062514

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Relativistic coupled-cluster calculations of the polarizabilities of atomic thallium

Yong-Bo Tang, Ningning Gao, Bing-Qiong Lou +1 more

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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

Long-range interactions between the alkali-metal atoms and alkaline earth ions

Jasmeet Kaur, D. K. Nandy, Bindiya Arora +1 more

Accurate knowledge of interaction potentials among the alkali atoms and alkaline earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali atoms with the Ca $^+$ , Ba $^+$ , Sr $^+$ , and Ra $^+$ alkaline earth ions systematically which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation $R$ . Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above mentioned systems which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representation of the interaction potentials versus $R$ are given among all the considered atoms and ions.Accurate knowledge of interaction potentials among the alkali atoms and alkaline earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali atoms with the Ca$^+$, Ba$^+$, Sr$^+$, and Ra$^+$ alkaline earth ions systematically which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation $R$. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above mentioned systems which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representation of the interaction potentials versus $R$ are given among all the considered atoms and ions.

arXiv:1409.7154Sep 25, 20140 citations

Z=60

hydrogenic ion. The approach is then applied to calculate the dynamic polarizabilities of the

5s, 4d

, and

5p

states of

{\mathrm{Sr}}^{+}

. The magic wavelengths at which the Stark shifts between different pairs of transitions are 0 are computed. Determination of the magic wavelengths for the

5s\ensuremath{\rightarrow}4{d}_{\frac{3}{2}}

and

5s\ensuremath{\rightarrow}4{d}_{\frac{5}{2}}

transitions near 417 nm (near the wavelength for the

5s\ensuremath{\rightarrow}5{p}_{j}

transitions) would allow determination of the oscillator strength ratio for the

5s\ensuremath{\rightarrow}5{p}_{\frac{1}{2}}

and

5s\ensuremath{\rightarrow}5{p}_{\frac{3}{2}}

transitions.

Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the

6p

7s

7p

8s

8p

, and

6d

states and the dynamic dipole polarizabilities of the

6p

and

7s

states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the

7{s}_{1/2}

7{p}_{1/2}

8{p}_{1/2}

, and

8{p}_{3/2}

states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the

6{p}_{1/2}

7s

and

6{p}_{3/2}

7s

transitions in the range of 488--1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the

7{s}_{1/2}

7{p}_{1/2}

and

7{s}_{1/2}

7{p}_{3/2}

transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the

6{p}_{1/2}

7{p}_{1/2}

transition, are also evaluated and compared with available theoretical and experimental values.

n{D}_{3/2,\phantom{\rule{0.16em}{0ex}}5/2}

states with large principal quantum numbers up to

n=50

. The calculations are performed within an effective one-electron approximation, based on the Dirac-Fock Hamiltonian with a semiempirical core-polarization potential. The obtained results are compared with those from a simpler semiempirical approach and with available experimental data.

{\mathrm{Cs}}_{2}

. Numerical stability in a wide range of molecular geometries is achieved at the cost of a very moderate loss of accuracy for low-lying states and negligibly small deviations of the computational scheme from strict size consistency. The adiabatic potential energy curves computed for the

(2,3){0}^{+}

(RbCs) and

(1,2){0}_{u}^{+}

(

{\mathrm{Cs}}_{2}

) states are converted into ``quasidiabatic'' potentials and effective spin-orbit-coupling functions via projection of the scalar relativistic states onto the subsets of fully relativistic states. A detailed comparison of the present ab initio results with their experimental and preceding theoretical counterparts is performed.

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 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.

^+

, Ba

^+

, Sr

^+

, and Ra

^+

alkaline earth ions systematically which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation

R

. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above mentioned systems which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representation of the interaction potentials versus

R

are given among all the considered atoms and ions.