Alkali atom data

arc.alkali_atom_data

This module specifies properties of individual alkali metals.

Hydrogen([preferQuantumDefects, cpp_numerov])

Properties of hydrogen atoms

Lithium6([preferQuantumDefects, cpp_numerov])

Properties of lithium 6 atoms

Lithium7([preferQuantumDefects, cpp_numerov])

Properties of lithium 7 atoms

Sodium([preferQuantumDefects, cpp_numerov])

Properties of sodium 23 atoms

Potassium([preferQuantumDefects, cpp_numerov])

backward compatibility: before only one class for Potassium existed and it corresponded to Potassium 39

Potassium39([preferQuantumDefects, cpp_numerov])

Properties of potassium 39 atoms

Potassium40([preferQuantumDefects, cpp_numerov])

Properties of potassium 40 atoms

Potassium41([preferQuantumDefects, cpp_numerov])

Properties of potassium 41 atoms

Rubidium([preferQuantumDefects, cpp_numerov])

backward compatibility: before there was only one Rubidium class, and that one corresponded to Rubidium85

Rubidium85([preferQuantumDefects, cpp_numerov])

Properites of rubidium 85 atoms

Rubidium87([preferQuantumDefects, cpp_numerov])

Properites of rubidium 87 atoms

Caesium([preferQuantumDefects, cpp_numerov])

Properties of caesium atoms

This module specifies properties of individual alkali metals.

If you want to change e.g. coefficients used for model potential, quantum defects, or other numerical values, this is the place to look at.

How to delete precalculated dipole/quadrupole matrix elements values and/or start a new database? To delete precalculated values, simply delete files, whose names are stated in dipoleMatrixElementFile, quadrupoleMatrixElementFile and precalculatedDB variables for the corresponding atom type, from data/ folder. Alternatively, if you want to keep old values, but want to also start completely new calculation of dipole matrix elements (e.g. because you changed parameters of energy levels significantly or model potential parameters), simply set new values for dipoleMatrixElementFile, quadrupoleMatrixElementFile and precalculatedDB variables.

Note that by default isotopes of Rubidium and Potassium are sharing precalculated dipole and quadrupole matrix elements. This is because the small energy level differences typically don’t change this matrix elements within a typical accuracy.

Data sources

1(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54)

M. Marinescu, H. R. Sadeghpour, and A. Dalgarno, Phys.Rev.A 49, 982 (1994) https://doi.org/10.1103/PhysRevA.49.982

2

K.-H. Weber and Craig J. Sansonetti, Phys.Rev.A 35, 4650 (1987)

3(1,2,3,4,5,6,7,8,9)

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

4(1,2)

Wenhui Li, I. Mourachko, M. W. Noel, and T. F. Gallagher, Phys. Rev. A 67, 052502 (2003) https://doi.org/10.1103/PhysRevA.67.052502

5(1,2)

Jianing Han, Yasir Jamil, D. V. L. Norum, Paul J. Tanner, and T. F. Gallagher, Phys. Rev. A 74, 054502 (2006) https://doi.org/10.1103/PhysRevA.74.054502

6

Markus Mack, Florian Karlewski, Helge Hattermann, Simone Hockh, Florian Jessen, Daniel Cano, and Jozsef Fortagh, Phys. Rev. A 83, 052515 (2011), https://doi.org/10.1103/PhysRevA.83.052515

7

K. Afrousheh, P. Bohlouli-Zanjani, J. A. Petrus, and J. D. D. Martin, Phys. Rev. A 74, 062712 (2006) https://doi.org/10.1103/PhysRevA.74.062712

8

K. Moore, A. Duspayev, R. Cardman, and G. Raithel, Phys. Rev. A 102, 062817 (2020), https://doi.org/10.1103/PhysRevA.102.062817

9(1,2)

P. Goy, J. Liang, M. Gross, and S. Haroche, Phys. Rev. A 34, 2889 (1986) https://doi.org/10.1103/PhysRevA.34.2889

10

Johannes Deiglmayr, Holger Herburger, Heiner Sassmannshausen, Paul Jansen, Hansjurg Schmutz, Frederic Merkt, Phys. Rev. A 93, 013424 (2016) https://doi.org/10.1103/PhysRevA.93.013424

11

C. -J. Lorenzen, and K. Niemax, Z. Phys. A 315, 127 (1984) https://doi.org/10.1007/BF01419370

12(1,2,3,4,5,6,7,8,9,10,11,12)
  1. -J. Lorenzen, and K. Niemax, Physica Scripta 27, 300 (1983)

13

NIST, P. Mohr and S. Kotochigova, unpublished calculations (2000). The wavelengths for the Balmer-alpha and Balmer-beta transitions at 6563 and 4861 \(\unicode{xC5}\) include only the stronger components of more extensive fine structures.

14
    1. Kelly, J. Phys. Chem. Ref. Data 16, Suppl. 1 (1987).

15(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)

J. S. Coursey, D. J. Schwab, J. J. Tsai, and R. A. Dragoset, (2015), Atomic Weights and Isotopic Compositions (version 4.1). Online Available: http://physics.nist.gov/Comp (2017, March, 14). National Institute of Standards and Technology, Gaithersburg, MD.

16

B. Sanguinetti, H. O. Majeed, M. L. Jones and B. T. H. Varcoe, J. Phys. B 42, 165004 (2009) http://iopscience.iop.org/article/10.1088/0953-4075/42/16/165004/meta

17(1,2)

D. Steck, Cesium D Line Data v2.2.1 https://steck.us/alkalidata/cesiumnumbers.1.6.pdf

18(1,2)

D. Steck, Rubidium 85 D Line Data v2.2.1 https://steck.us/alkalidata/rubidium85numbers.pdf

19(1,2)

D. Steck, Rubidium 87 D Line Data v2.2.1 https://steck.us/alkalidata/rubidium87numbers.pdf

20
  1. Feiertag, A. Sahm, and G. zu Putlitz, Z. Phys. 255, 93 (1972)

21
  1. Arrimondo, M. Inguscio and P. Violino, Rev. Mod. Phys. 49, 31 (1977)

Module

class Caesium(preferQuantumDefects=True, cpp_numerov=True)[source]

Bases: arc.alkali_atom_functions.AlkaliAtom

Properties of caesium atoms

a1 = [3.49546309, 4.69366096, 4.32466196, 3.01048361]

model potential parameters from 1

a2 = [1.475338, 1.71398344, 1.61365288, 1.40000001]

model potential parameters from 1

a3 = [-9.72143084, -24.6562428, -6.7012885, -3.20036138]

model potential parameters from 1

a4 = [0.02629242, -0.09543125, -0.74095193, 0.00034538]

model potential parameters from 1

alphaC = 15.644

model potential parameters from 1

extraLevels = [[5, 2, 2.5], [5, 2, 1.5], [5, 3, 3.5], [5, 3, 2.5], [5, 4, 4.5], [5, 4, 3.5], [4, 3, 3.5], [4, 3, 2.5]]

levels that are for smaller n than ground level, but are above in energy due to angular part

gI = -0.00039885395

Nuclear g-factor 17

gL = 0.99999587

Electron orbital g-factor 17

getPressure(temperature)[source]

Pressure of atomic vapour at given temperature.

Uses equation and values from 3. Values from table 2. (accuracy +- 5%) are used for Cs in solid phase. Values from table 3. (accuracy +-1 %) are used for Cs in liquid phase.

hyperfineStructureData = 'cs_hfs_data.csv'

source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 3.893905726389478

(eV), Ref. 10.

meltingPoint = 301.59

in K

quantumDefect = [[[4.04935665, 0.2377037, 0.255401, 0.00378, 0.25486, 0.0], [3.5915895, 0.360926, 0.41905, 0.64388, 1.45035, 0.0], [2.4754562, 0.00932, -0.43498, -0.76358, -18.0061, 0.0], [0.03341424, -0.198674, 0.28953, -0.2601, 0.0, 0.0], [0.00703865, -0.049252, 0.01291, 0.0, 0.0, 0.0]], [[4.04935665, 0.2377037, 0.255401, 0.00378, 0.25486, 0.0], [3.5589599, 0.392469, -0.67431, 22.3531, -92.289, 0.0], [2.46631524, 0.013577, -0.37457, -2.1867, -1.5532, -56.6739], [0.03341424, -0.198674, 0.28953, -0.2601, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]

quantum defects for \(S_{1/2}\), \(nP_{1/2}\), \(D_{5/2}\), \(F_{5/2}\) and \(G_{7/2}\) are from 2, while quantum defects for \(nP_{3/2}\),:math:D_{3/2} are from 11,

Note

f_7/2 quantum defects are PUT TO BE EXACTLY the same as f_5/2 (~10MHz difference?!)

rc = [1.9204693, 2.13383095, 0.93007296, 1.99969677]

model potential parameters from 1

scaledRydbergConstant = 13.605636960556954

in eV

class Cesium(preferQuantumDefects=True, cpp_numerov=True)[source]

Bases: arc.alkali_atom_data.Caesium

support for American English spelling

class Hydrogen(preferQuantumDefects=True, cpp_numerov=True)[source]

Bases: arc.alkali_atom_functions.AlkaliAtom

Properties of hydrogen atoms

ionisationEnergy = 13.598433

(eV), Ref. 13.

mass = 1.6735328383153192e-27

source NIST, Atomic Weights and Isotopic Compositions 15

potential(l, s, j, r)[source]

returns total potential that electron feels

Total potential = core potential + Spin-Orbit interaction

Parameters
  • l (int) – orbital angular momentum

  • s (float) – spin angular momentum

  • j (float) – total angular momentum

  • r (float) – distance from the nucleus (in a.u.)

Returns

potential (in a.u.)

Return type

float

class Lithium6(preferQuantumDefects=True, cpp_numerov=True)[source]

Bases: arc.alkali_atom_functions.AlkaliAtom

Properties of lithium 6 atoms

a1 = [2.47718079, 3.45414648, 2.51909839, 2.51909839]

model potential parameters from 1

a2 = [1.84150932, 2.5515108, 2.4371245, 2.4371245]

model potential parameters from 1

a3 = [-0.02169712, -0.21646561, 0.32505524, 0.32505524]

model potential parameters from 1

a4 = [-0.11988362, -0.06990078, 0.1060243, 0.1060243]

model potential parameters from 1

abundance = 0.0759

source NIST, Atomic Weights and Isotopic Compositions 15

alphaC = 0.1923

model potential parameters from 1

getPressure(temperature)[source]

Pressure of atomic vapour at given temperature.

Uses equation and values from 3. Values from table 3. (accuracy +-1 %) are used both for liquid and solid phase of Li.

hyperfineStructureData = 'li6_hfs_data.csv'

source of HFS magnetic dipole and quadrupole constants

mass = 9.988346544927492e-27

source NIST, Atomic Weights and Isotopic Compositions 15

meltingPoint = 453.68999999999994

in K

quantumDefect = [[[0.3995101, 0.029, 0.0, 0.0, 0.0, 0.0], [0.0471835, -0.024, 0.0, 0.0, 0.0, 0.0], [0.002129, -0.01491, 0.1759, -0.8507, 0.0, 0.0], [-7.7e-05, 0.021856, -0.4211, 2.3891, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[0.3995101, 0.029, 0.0, 0.0, 0.0, 0.0], [0.047172, -0.024, 0.0, 0.0, 0.0, 0.0], [0.002129, -0.01491, 0.1759, -0.8507, 0.0, 0.0], [-7.7e-05, 0.021856, -0.4211, 2.3891, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]

quantum defects for \(nS\) and \(nP\) are from Ref. 9 . Quantum defects for \(D_j\) and \(F_j\) are from Ref. 12 (note that this defects in Ref. 12 are for Li7, differences are expected not be too big).

rc = [0.61340824, 0.61566441, 2.34126273, 2.34126273]

model potential parameters from 1

class Lithium7(preferQuantumDefects=True, cpp_numerov=True)[source]

Bases: arc.alkali_atom_functions.AlkaliAtom

Properties of lithium 7 atoms

a1 = [2.47718079, 3.45414648, 2.51909839, 2.51909839]

model potential parameters from 1

a2 = [1.84150932, 2.5515108, 2.4371245, 2.4371245]

model potential parameters from 1

a3 = [-0.02169712, -0.21646561, 0.32505524, 0.32505524]

model potential parameters from 1

a4 = [-0.11988362, -0.06990078, 0.1060243, 0.1060243]

model potential parameters from 1

abundance = 0.9241

source NIST, Atomic Weights and Isotopic Compositions 15

alphaC = 0.1923

model potential parameters from 1

getPressure(temperature)[source]

Pressure of atomic vapour at given temperature (in K).

Uses equation and values from 3. Values from table 3. (accuracy +-1 %) are used for both liquid and solid phase of Li.

hyperfineStructureData = 'li7_hfs_data.csv'

source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 5.391719

(eV) NIST Ref. 14.

mass = 1.1650347797874157e-26

source NIST, Atomic Weights and Isotopic Compositions 15

meltingPoint = 453.68999999999994

in K

quantumDefect = [[[0.3995101, 0.029, 0.0, 0.0, 0.0, 0.0], [0.047178, -0.024, 0.0, 0.0, 0.0, 0.0], [0.002129, -0.01491, 0.1759, -0.8507, 0.0, 0.0], [-7.7e-05, 0.021856, -0.4211, 2.3891, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[0.3995101, 0.029, 0.0, 0.0, 0.0, 0.0], [0.0471665, -0.024, 0.0, 0.0, 0.0, 0.0], [0.002129, -0.01491, 0.1759, -0.8507, 0.0, 0.0], [-7.7e-05, 0.021856, -0.4211, 2.3891, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]

quantum defects for \(nS\) and \(nP\) states are from Ref. 9. Quantum defects for \(D_j\) and \(F_j\) states are from 12.

rc = [0.61340824, 0.61566441, 2.34126273, 2.34126273]

model potential parameters from 1

class Potassium(preferQuantumDefects=True, cpp_numerov=True)[source]

Bases: arc.alkali_atom_data.Potassium39

backward compatibility: before only one class for Potassium existed and it corresponded to Potassium 39

class Potassium39(preferQuantumDefects=True, cpp_numerov=True)[source]

Bases: arc.alkali_atom_functions.AlkaliAtom

Properties of potassium 39 atoms

a1 = [3.56079437, 3.65670429, 4.12713694, 1.42310446]

model potential parameters from 1

a2 = [1.83909642, 1.67520788, 1.79837462, 1.27861156]

model potential parameters from 1

a3 = [-1.74701102, -2.07416615, -1.69935174, 4.77441476]

model potential parameters from 1

a4 = [-1.03237313, -0.89030421, -0.98913582, -0.94829262]

model potential parameters from 1

abundance = 0.932581

source NIST, Atomic Weights and Isotopic Compositions 15

alphaC = 5.331

model potential parameters from 1

extraLevels = [[3, 2, 2.5], [3, 2, 1.5]]

levels that are for smaller n than ground level, but are above in energy due to angular part

getPressure(temperature)[source]

Pressure of atomic vapour at given temperature.

Uses equation and values from 3. Values from table 2. (accuracy +- 5%) are used for Na in solid phase. Values from table 3. (accuracy +-1 %) are used for Na in liquid phase.

hyperfineStructureData = 'k39_hfs_data.csv'

source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 4.340663717174086

(eV), weighted average of values in Ref. 12.

mass = 6.470075680020302e-26

source NIST, Atomic Weights and Isotopic Compositions 15

meltingPoint = 336.65

in K

quantumDefect = [[[2.1801985, 0.13558, 0.0759, 0.117, -0.206, 0.0], [1.713892, 0.233294, 0.16137, 0.5345, -0.234, 0.0], [0.27697, -1.024911, -0.709174, 11.839, -26.689, 0.0], [0.010098, -0.100224, 1.56334, -12.6851, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[2.1801985, 0.13558, 0.0759, 0.117, -0.206, 0.0], [1.710848, 0.235437, 0.11551, 1.1015, -2.0356, 0.0], [0.277158, -1.025635, -0.59201, 10.0053, -19.0244, 0.0], [0.010098, -0.100224, 1.56334, -12.6851, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]

quantum defects from Ref. 12.

rc = [0.83167545, 0.85235381, 0.83216907, 6.50294371]

model potential parameters from 1

class Potassium40(preferQuantumDefects=True, cpp_numerov=True)[source]

Bases: arc.alkali_atom_functions.AlkaliAtom

Properties of potassium 40 atoms

a1 = [3.56079437, 3.65670429, 4.12713694, 1.42310446]

model potential parameters from 1

a2 = [1.83909642, 1.67520788, 1.79837462, 1.27861156]

model potential parameters from 1

a3 = [-1.74701102, -2.07416615, -1.69935174, 4.77441476]

model potential parameters from 1

a4 = [-1.03237313, -0.89030421, -0.98913582, -0.94829262]

model potential parameters from 1

abundance = 0.000117

source NIST, Atomic Weights and Isotopic Compositions 15

alphaC = 5.331

model potential parameters from 1

extraLevels = [[3, 2, 2.5], [3, 2, 1.5]]

levels that are for smaller n than ground level, but are above in energy due to angular part

getPressure(temperature)[source]

Pressure of atomic vapour at given temperature.

Uses equation and values from 3. Values from table 2. (accuracy +- 5%) are used for Na in solid phase. Values from table 3. (accuracy +-1 %) are used for Na in liquid phase.

hyperfineStructureData = 'k40_hfs_data.csv'

source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 4.340663717174086

(eV), weighted average of values in Ref. 12.

mass = 6.636178021217375e-26

source NIST, Atomic Weights and Isotopic Compositions 15

meltingPoint = 336.65

in K

quantumDefect = [[[2.1801985, 0.13558, 0.0759, 0.117, -0.206, 0.0], [1.713892, 0.233294, 0.16137, 0.5345, -0.234, 0.0], [0.27697, -1.024911, -0.709174, 11.839, -26.689, 0.0], [0.010098, -0.100224, 1.56334, -12.6851, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[2.1801985, 0.13558, 0.0759, 0.117, -0.206, 0.0], [1.710848, 0.235437, 0.11551, 1.1015, -2.0356, 0.0], [0.277158, -1.025635, -0.59201, 10.0053, -19.0244, 0.0], [0.010098, -0.100224, 1.56334, -12.6851, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]

quantum defects from Ref. 12.

rc = [0.83167545, 0.85235381, 0.83216907, 6.50294371]

model potential parameters from 1

scaledRydbergConstant = 13.605506356008

in eV

class Potassium41(preferQuantumDefects=True, cpp_numerov=True)[source]

Bases: arc.alkali_atom_functions.AlkaliAtom

Properties of potassium 41 atoms

a1 = [3.56079437, 3.65670429, 4.12713694, 1.42310446]

model potential parameters from 1

a2 = [1.83909642, 1.67520788, 1.79837462, 1.27861156]

model potential parameters from 1

a3 = [-1.74701102, -2.07416615, -1.69935174, 4.77441476]

model potential parameters from 1

a4 = [-1.03237313, -0.89030421, -0.98913582, -0.94829262]

model potential parameters from 1

abundance = 0.067302

source NIST, Atomic Weights and Isotopic Compositions 15

alphaC = 5.331

model potential parameters from 1

extraLevels = [[3, 2, 2.5], [3, 2, 1.5]]

levels that are for smaller n than ground level, but are above in energy due to angular part

getPressure(temperature)[source]

Pressure of atomic vapour at given temperature.

Uses equation and values from 3. Values from table 2. (accuracy +- 5%) are used for Na in solid phase. Values from table 3. (accuracy +-1 %) are used for Na in liquid phase.

hyperfineStructureData = 'k41_hfs_data.csv'

source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 4.340663717174086

(eV), weighted average of values in Ref. 12.

mass = 6.801871107998557e-26

source NIST, Atomic Weights and Isotopic Compositions 15

meltingPoint = 336.65

in K

quantumDefect = [[[2.1801985, 0.13558, 0.0759, 0.117, -0.206, 0.0], [1.713892, 0.233294, 0.16137, 0.5345, -0.234, 0.0], [0.27697, -1.024911, -0.709174, 11.839, -26.689, 0.0], [0.010098, -0.100224, 1.56334, -12.6851, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[2.1801985, 0.13558, 0.0759, 0.117, -0.206, 0.0], [1.710848, 0.235437, 0.11551, 1.1015, -2.0356, 0.0], [0.277158, -1.025635, -0.59201, 10.0053, -19.0244, 0.0], [0.010098, -0.100224, 1.56334, -12.6851, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]

quantum defects from Ref. 12.

rc = [0.83167545, 0.85235381, 0.83216907, 6.50294371]

model potential parameters from 1

scaledRydbergConstant = 13.605510905549485

in eV

class Rubidium(preferQuantumDefects=True, cpp_numerov=True)[source]

Bases: arc.alkali_atom_data.Rubidium85

backward compatibility: before there was only one Rubidium class, and that one corresponded to Rubidium85

class Rubidium85(preferQuantumDefects=True, cpp_numerov=True)[source]

Bases: arc.alkali_atom_functions.AlkaliAtom

Properites of rubidium 85 atoms

a1 = [3.69628474, 4.44088978, 3.78717363, 2.39848933]

model potential parameters from 1

a2 = [1.64915255, 1.92828831, 1.57027864, 1.76810544]

model potential parameters from 1

a3 = [-9.86069196, -16.7959777, -11.6558897, -12.0710678]

model potential parameters from 1

a4 = [0.19579987, -0.8163314, 0.52942835, 0.77256589]

model potential parameters from 1

abundance = 0.7217

source NIST, Atomic Weights and Isotopic Compositions 15

alphaC = 9.076

model potential parameters from 1

extraLevels = [[4, 2, 2.5], [4, 2, 1.5], [4, 3, 3.5], [4, 3, 2.5]]

levels that are for smaller n than ground level, but are above in energy due to angular part

gI = -0.00029364

Nuclear g-factor 18

gL = 0.99999354

Electron orbital g-factor 18

getPressure(temperature)[source]

Pressure of atomic vapour at given temperature.

Uses equation and values from 3. Values from table 2. (accuracy +- 5%) are used for Rb in solid phase. Values from table 3. (accuracy +-1 %) are used for Rb in liquid phase.

hyperfineStructureData = 'rb85_hfs_data.csv'

source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 4.177126523766669

(eV) Ref. 16

mass = 1.409993440747079e-25

source NIST, Atomic Weights and Isotopic Compositions 15

meltingPoint = 312.46

in K

quantumDefect = [[[3.1311804, 0.1784, 0.0, 0.0, 0.0, 0.0], [2.6548849, 0.29, 0.0, 0.0, 0.0, 0.0], [1.34809171, -0.60286, 0.0, 0.0, 0.0, 0.0], [0.0165192, -0.085, 0.0, 0.0, 0.0, 0.0], [0.003999, -0.0202, 0.0, 0.0, 0.0, 0.0]], [[3.1311804, 0.1784, 0.0, 0.0, 0.0, 0.0], [2.6416737, 0.295, 0.0, 0.0, 0.0, 0.0], [1.34646572, -0.596, 0.0, 0.0, 0.0, 0.0], [0.0165437, -0.086, 0.0, 0.0, 0.0, 0.0], [0.003999, -0.0202, 0.0, 0.0, 0.0, 0.0]]]

quantum defects for \(nF\) states are from 5. Quantum defects for \(nG\) states are from 8. All other quantum defects are from from 4

rc = [1.66242117, 1.50195124, 4.86851938, 4.79831327]

model potential parameters from 1

scaledRydbergConstant = 13.605605218602195

in eV

class Rubidium87(preferQuantumDefects=True, cpp_numerov=True)[source]

Bases: arc.alkali_atom_functions.AlkaliAtom

Properites of rubidium 87 atoms

a1 = [3.69628474, 4.44088978, 3.78717363, 2.39848933]

model potential parameters from 1

a2 = [1.64915255, 1.92828831, 1.57027864, 1.76810544]

model potential parameters from 1

a3 = [-9.86069196, -16.7959777, -11.6558897, -12.0710678]

model potential parameters from 1

a4 = [0.19579987, -0.8163314, 0.52942835, 0.77256589]

model potential parameters from 1

abundance = 0.2783

source NIST, Atomic Weights and Isotopic Compositions 15

alphaC = 9.076

model potential parameters from 1

extraLevels = [[4, 2, 2.5], [4, 2, 1.5], [4, 3, 3.5], [4, 3, 2.5]]

levels that are for smaller n than ground level, but are above in energy due to angular part

gI = -0.0009951414

Nuclear g-factor 19

gL = 0.99999369

Electron orbital g-factor 19

getPressure(temperature)[source]

Pressure of atomic vapour at given temperature.

Uses equation and values from 3. Values from table 2. (accuracy +- 5%) are used for Rb in solid phase. Values from table 3. (accuracy +-1 %) are used for Rb in liquid phase.

hyperfineStructureData = 'rb87_hfs_data.csv'

source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 4.177127321633609

(eV) Ref. 6

mass = 1.4431608951791763e-25

source NIST, Atomic Weights and Isotopic Compositions 15

meltingPoint = 312.46

in K

quantumDefect = [[[3.1311804, 0.1784, 0.0, 0.0, 0.0, 0.0], [2.6548849, 0.29, 0.0, 0.0, 0.0, 0.0], [1.34809171, -0.60286, 0.0, 0.0, 0.0, 0.0], [0.0165192, -0.085, 0.0, 0.0, 0.0, 0.0], [0.00405, 0.0, 0.0, 0.0, 0.0, 0.0]], [[3.1311804, 0.1784, 0.0, 0.0, 0.0, 0.0], [2.6416737, 0.295, 0.0, 0.0, 0.0, 0.0], [1.34646572, -0.596, 0.0, 0.0, 0.0, 0.0], [0.0165437, -0.086, 0.0, 0.0, 0.0, 0.0], [0.00405, 0.0, 0.0, 0.0, 0.0, 0.0]]]

quantum defects for \(nF\) states are from 5. Quantum defects for \(nG\) states are from 7. All other quantum defects are from from 4

rc = [1.66242117, 1.50195124, 4.86851938, 4.79831327]

model potential parameters from 1

scaledRydbergConstant = 13.60560723878171

in eV (M_ion core = m_atomic - m_electron)

class Sodium(preferQuantumDefects=True, cpp_numerov=True)[source]

Bases: arc.alkali_atom_functions.AlkaliAtom

Properties of sodium 23 atoms

a1 = [4.82223117, 5.08382502, 3.53324124, 1.11056646]

model potential parameters from 1

a2 = [2.45449865, 2.18226881, 2.48697936, 1.05458759]

model potential parameters from 1

a3 = [-1.12255048, -1.19534623, -0.75688448, 1.73203428]

model potential parameters from 1

a4 = [-1.42631393, -1.03142861, -1.27852357, -0.09265696]

model potential parameters from 1

abundance = 1.0

source NIST, Atomic Weights and Isotopic Compositions 15

alphaC = 0.9448

model potential parameters from 1

getPressure(temperature)[source]

Pressure of atomic vapour at given temperature.

Uses equation and values from 3. Values from table 2. (accuracy +- 5%) are used for Na in solid phase. Values from table 3. (accuracy +-1 %) are used for Na in liquid phase.

hyperfineStructureData = 'na23_hfs_data.csv'

source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 5.139075592528896

(eV) from Ref. 12

mass = 3.8175410024881635e-26

source NIST, Atomic Weights and Isotopic Compositions 15

meltingPoint = 370.94399999999996

in K

quantumDefect = [[[1.347964, 0.060673, 0.0233, -0.0085, 0.0, 0.0], [0.85538, 0.11363, 0.0384, 0.1412, 0.0, 0.0], [0.015543, -0.08535, 0.7958, -4.0513, 0.0, 0.0], [0.001453, 0.017312, -0.7809, 7.021, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], [[1.347964, 0.060673, 0.0233, -0.0085, 0.0, 0.0], [0.854565, 0.114195, 0.0352, 0.1533, 0.0, 0.0], [0.015543, -0.08535, 0.7958, -4.0513, 0.0, 0.0], [0.001453, 0.017312, -0.7809, 7.021, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]]

Quantum defects are from Ref. 12. Note that we are using modified Rydberg-Ritz formula. In literature both modified and non-modified coefficients appear. For more details about the two equations see page 301. of Ref. 12.

rc = [0.45489422, 0.45798739, 0.71875312, 28.6735059]

model potential parameters from 1

scaledRydbergConstant = 13.60536846146495

(eV)