Divalent atom data

Note

This is a completely new module added in ARC 3.0.0 version. See more at E. J. Robertson, N. Šibalić, R. M. Potvliege and M. P. A. Jones, *Computer Physics Communications* **261**, 107814 (2021) `https://doi.org/10.1016/j.cpc.2020.107814 .

Strontium88([preferQuantumDefects, cpp_numerov])	Properties of Strontium 88 atoms
Calcium40([preferQuantumDefects, cpp_numerov])	Properties of Calcium 40 atoms
Ytterbium174([preferQuantumDefects, cpp_numerov])	Properties of Ytterbium 174 atoms

Data sources

[1] (1,2)

J. A. Armstrong, J. J. Wynne and P. Esherick, “Bound, odd-parity J = 1 spectra of the alkaline earths: Ca, Sr, and Ba”, J. Opt. Soc. Am. 69, 211-230 (1979) https://doi.org/10.1364/JOSA.69.000211

[2]

R.Beigang, K.Lücke, A.Timmermann, P.J.West and D.Frölich, Determination of absolute level energies of 5sns1S0 and 5snd1D2 Rydberg series of Sr, Opt. Commun. 42, 19 (1982). https://doi.org/10.1016/0030-4018(82)90082-7

[3]

J. E. Sansonetti and G Nave, Wavelengths, Transition Probabilities, and Energy Levels for the Spectrum of Neutral Strontium (Sr I), Journal of Physical and Chemical Reference Data 39, 033103 (2010). https://doi.org/10.1063/1.3449176

[4]

Baig M, Yaseen M, Nadeem A, Ali R. and Bhatti S. Three-photon excitation of strontium Rydberg levels, Optics Communications 156, 279 (1998) https://doi.org/10.1016/S0030-4018(98)00467-2

[5] (1,2)

P. Esherick, J. J. Wynne and J A Armstrong, Spectroscopy of 3P0 states of alkaline earths, Optics Letters 1, 19 (1977). https://doi.org/10.1364/OL.1.000019

[6]

P Esherick, Bound, even-parity J = 0 and J = 2 spectra of Sr, Physical Review A 15, 1920 (1977). https://doi.org/10.1103/PhysRevA.15.1920

[7]

R. Beigang and D. Schmidt, Two-Channel MQDT Analysis of Bound 5snd 3D1,3 Rydberg States of Strontium, Physica Scripta 27, 172 (1983). https://doi.org/10.1088/0031-8949/27/3/005

[8]

J R. Rubbmark and S. A. Borgstr¨om, Rydberg Series in Strontium Found in Absorption by Selectively, Laser-Excited Atoms. Physica Scripta 18, 196 (1978) https://doi.org/10.1088/0031-8949/18/4/002

[9]

Beigang R, Lucke K, Schmidt D, Timmermann A. and West P. J, One-Photon Laser Spectroscopy of Rydberg Series from Metastable Levels in Calcium and Strontium, Phys. Scr. 26, 183 (1982) https://doi.org/10.1088/0031-8949/26/3/007

[10] (1,2,3)

L. Couturier, I. Nosske, F. Hu, C. Tan, C. Qiao, Y. H. Jiang, P. Chen and M. Weidemüller. Measurement of the strontium triplet Rydberg series by depletion spectroscopy of ultracold atoms Phys. Rev. A 99, 022503 (2019) https://doi.org/10.1103/PhysRevA.99.022503

[11]

H. Maeda, Y. Matsuo, M. Takami and A. Suzuki, Optical-microwave double-resonance spectroscopy of highly excited Rydberg states of ytterbium, Physical Review A 45, 1732 (1992) https://doi.org/10.1103/PhysRevA.45.1732

[12]

M. Aymar, A. Debarre and O. Robaux, Highly excited levels of neutral ytterbium. II. Multichannel quantum defect analysis of odd- and even-parity spectra, Journal of Physics B: Atomic and Molecular Physics 13, 1089 (1980) https://doi.org/10.1088/0022-3700/13/6/016

[13] (1,2)

H. Lehec, A. Zuliani, W. Maineult, E. Luc-Koenig, P. Pillet, P. Cheinet, F. Niyaz and T. F. Gallagher, Laser and microwave spectroscopy of even-parity Rydberg states of neutral ytterbium and multichannel-quantum-defect-theory analysis, Physical Review A 98, 062506 (2018) https://doi.org/10.1103/PhysRevA.98.062506

[14]

W. F. Meggers and J. L. Tech, J. Res. Natl. Bur. Stand. (U.S.) 83, 13 (1978). https://doi.org/10.6028/jres.083.003

[15]

Thomas R. Gentile, Barbara J. Hughey, Daniel Kleppner and Theodore W. Ducas, Microwave spectroscopy of calcium Rydberg states, Physical Review A 42, 440 (1990) https://doi.org/10.1103/PhysRevA.42.440

[16]

Masabumi Miyabe, Christopher Geppert, Masaaki Kato, Masaki Oba, Ikuo Wakaida, Kazuo Watanabe and Klaus D. A. Wendt, Determination of Ionization Potential of Calcium by High-Resolution Resonance Ionization Spectroscopy, Journal of the Physical Society of Japan 75, 034302 (2006) https://doi.org/10.1143/JPSJ.75.034302

[17]

Meija, Juris et al, “Atomic weights of the elements 2013 (IUPAC Technical Report)”, Pure and Applied Chemistry 88,265 (2016) https://doi.org/10.1515/pac-2015-0305.

[18]

B.B. Zelener, S. A. Saakyan,V. A. Sautenkov, E. V. Vilshanskaya, B. V. Zelener and V. E. Fortov, JETP Letters 110, 761 (2019) https://doi.org/10.1134/S0021364019240093

[19]

J. Sugar and C. Corliss, J. Phys. Chem. Ref. Data 14, Suppl. 2 (1985)

[20] (1,2,3)

C.B.Alcock, V.P.Itkin, M.K.Horrigan, Canadian Metallurgical Quarterly, 23, 309 (1984) http://dx.doi.org/10.1179/cmq.1984.23.3.309

[21] (1,2,3)

NIST Standard reference database, https://dx.doi.org/10.18434/T4FW23

class Calcium40(preferQuantumDefects=True, cpp_numerov=True)

Bases: DivalentAtom

Properties of Calcium 40 atoms

I: float = 0

Nuclear spin

Z: int = 20

Atomic number

defectFittingRange: dict = {'1F3': [20, 150], '1P1': [22, 55], '1S0': [22, 55], '3D1': [22, 55], '3D2': [22, 55], '3P1': [22, 55], '3P2': [8, 18], '3S1': [22, 55]}

Quantum defect principal quantum number fitting ranges for different series

dipoleMatrixElementFile: str = 'ca_dipole_matrix_elements.npy'

location of hard-disk stored dipole matrix elements

elementName: str = 'Ca40'

Human-readable element name

getPressure(temperature)

Pressure of atomic vapour at given temperature.

Calculates pressure based on Ref. [20] (accuracy +- 5%).

groundStateN: int = 4

principal quantum number for the ground state

ionisationEnergy = 6.11315492705687

eV Ref. [18]

levelDataFromNIST: str = 'ca_level_data.csv'

Sources Refs. [1], [5], [9], [15], [19]

literatureDMEfilename: str = 'calcium_literature_dme.csv'

Filename of the additional literature source values of dipole matrix elements. These additional values should be saved as reduced dipole matrix elements in J basis.

mass: float = 6.635944365077078e-26

Ref. [21]

meltingPoint: float = 1115.15

in K

quadrupoleMatrixElementFile: str = 'ca_quadrupole_matrix_elements.npy'

location of hard-disk stored dipole matrix elements

quantumDefect = [[[2.33793, -0.1142, 0.0, 0.0, 0.0, 0.0], [1.885584, -0.324, -23.8, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.09864, -1.29, 36, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[2.440956, 0.35, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.8833, -0.02, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[2.440956, 0.35, 0.0, 0.0, 0.0, 0.0], [1.964709, 0.228, 0.0, 0.0, 0.0, 0.0], [0.8859, 0.13, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[2.440956, 0.35, 0.0, 0.0, 0.0, 0.0], [1.9549, 2.5, -160.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]

Contains list of modified Rydberg-Ritz coefficients for calculating quantum defects for [[ \(^1S_{0},^1P_{1},^1D_{2},^1F_{3}\)], [ \(^3S_{1},^3P_{0},^3D_{1},^3F_{2}\)], [ \(^3S_{1},^3P_{1},^3D_{2},^3F_{3}\)], [ \(^3S_{1},^3P_{2},^3D_{3},^3F_{4}\)]].

scaledRydbergConstant = 13.605506488142115

eV Ref. [16]

class Strontium88(preferQuantumDefects=True, cpp_numerov=True)

Bases: DivalentAtom

Properties of Strontium 88 atoms

I: float = 0.0

Nuclear spin

Z: int = 38

Atomic number

alphaC: float = 15

Core polarizability

defectFittingRange: dict = {'1D2': [20, 50], '1F3': [10, 28], '1P1': [10, 29], '1S0': [14, 34], '3D1': [28, 50], '3D2': [28, 50], '3D3': [20, 37], '3F2': [10, 24], '3F3': [10, 24], '3F4': [10, 28], '3P0': [8, 15], '3P1': [8, 21], '3P2': [19, 41], '3S1': [15, 50]}

Quantum defect principal quantum number fitting ranges for different series

dipoleMatrixElementFile: str = 'sr_dipole_matrix_elements.npy'

location of hard-disk stored dipole matrix elements

elementName: str = 'Sr88'

Human-readable element name

extraLevels: List[Tuple[int, int, int, int]] = [(4, 2, 3, 1), (4, 2, 1, 1), (4, 3, 3, 0), (4, 3, 4, 1), (4, 3, 3, 1), (4, 3, 2, 1), (4, 2, 2, 0)]

levels that are for smaller principal quantum number (n) than ground level, but are above in energy due to angular part

getPressure(temperature)

Pressure of atomic vapour at given temperature.

Calculates pressure based on Ref. [20] (accuracy +- 5%).

groundStateN: int = 5

principal quantum number for the ground state

ionisationEnergy = 5.694867028492927

(eV) Ref. [10]

levelDataFromNIST: str = 'sr_level_data.csv'

Sources Refs. [1], [2], [3], [4], [5], [6], [7], [8] , [10]

literatureDMEfilename: str = 'strontium_literature_dme.csv'

Filename of the additional literature source values of dipole matrix elements. These additional values should be saved as reduced dipole matrix elements in J basis.

mass: float = 1.4597071472709626e-25

Ref. [21]

meltingPoint: float = 1050.15

in K

quadrupoleMatrixElementFile: str = 'sr_quadrupole_matrix_elements.npy'

location of hard-disk stored dipole matrix elements

quantumDefect = [[[3.269123, -0.177769, 3.4619, 0.0, 0.0, 0.0], [2.72415, -3.39, -220.0, 0.0, 0.0, 0.0], [2.384667, -42.03053, -619.0, 0.0, 0.0, 0.0], [0.090886, -2.4425, 61.896, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[3.3707725, 0.41979, -0.421377, 0.0, 0.0, 0.0], [2.88673, 0.433745, -1.8, 0.0, 0.0, 0.0], [2.675236, -13.23217, -4418.0, 0.0, 0.0, 0.0], [0.120588, -2.1847, 102.98, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[3.3707725, 0.41979, -0.421377, 0.0, 0.0, 0.0], [2.88265, 0.39398, -1.1199, 0.0, 0.0, 0.0], [2.661488, -16.8524, -6629.26, 0.0, 0.0, 0.0], [0.11899, -2.0446, 103.26, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[3.3707725, 0.41979, -0.421377, 0.0, 0.0, 0.0], [2.88163, -2.462, 145.18, 0.0, 0.0, 0.0], [2.655, -65.317, -13576.7, 0.0, 0.0, 0.0], [0.12, -2.37716, 118.97, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]

Contains list of modified Rydberg-Ritz coefficients for calculating quantum defects for [[ \(^1S_{0},^1P_{1},^1D_{2},^1F_{3}\)], [ \(^3S_{1},^3P_{0},^3D_{1},^3F_{2}\)], [ \(^3S_{1},^3P_{1},^3D_{2},^3F_{3}\)], [ \(^3S_{1},^3P_{2},^3D_{3},^3F_{4}\)]].

scaledRydbergConstant = 13.605608233294875

Ref. [10]

class Ytterbium174(preferQuantumDefects=True, cpp_numerov=True)

Bases: DivalentAtom

Properties of Ytterbium 174 atoms

I: float = 0

Nuclear spin

Z: int = 70

Atomic number

defectFittingRange: dict = {'1D2': [40, 80], '1P1': [35, 54], '1S0': [34, 80], '3D2': [35, 80]}

Quantum defect principal quantum number fitting ranges for different series

dipoleMatrixElementFile: str = 'yb_dipole_matrix_elements.npy'

location of hard-disk stored dipole matrix elements

elementName: str = 'Yb174'

Human-readable element name

getPressure(temperature)

Pressure of atomic vapour at given temperature.

Calculates pressure based on Ref. [20] (accuracy +- 5%).

groundStateN: int = 6

principal quantum number for the ground state

ionisationEnergy = 6.254143651293333

ionisationEnergy in eV

levelDataFromNIST: str = 'yb_level_data.csv'

Sources Refs. [11], [12], [13], [14]

literatureDMEfilename: str = 'ytterbium_literature_dme.csv'

Filename of the additional literature source values of dipole matrix elements. These additional values should be saved as reduced dipole matrix elements in J basis.

mass: float = 2.8883228326085627e-25

Ref. [21]

meltingPoint: float = 1092.15

in K

quadrupoleMatrixElementFile: str = 'yb_quadrupole_matrix_elements.npy'

location of hard-disk stored dipole matrix elements

quantumDefect = [[[4.278367, -5.60943, -258.5, 0.0, 0.0, 0.0], [3.953434, -10.58286, 728.1, 0.0, 0.0, 0.0], [2.7130117, -0.929878, -636.4, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [2.7485996, 0.0137, -106.55, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]

Contains list of modified Rydberg-Ritz coefficients for calculating quantum defects for [[ \(^1S_{0},^1P_{1},^1D_{2},^1F_{3}\)], [ \(^3S_{1},^3P_{0},^3D_{1},^3F_{2}\)], [ \(^3S_{1},^3P_{1},^3D_{2},^3F_{3}\)], [ \(^3S_{1},^3P_{2},^3D_{3},^3F_{4}\)]].

scaledRydbergConstant = 13.60565021310462

eV Ref. [13]