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#

Module#

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

Bases: AlkaliAtom

Properties of caesium atoms

I: float = 3.5#: Nuclear spin

Z: int = 55#: Atomic number

a1: List[float] = [3.49546309, 4.69366096, 4.32466196, 3.01048361]#: model potential parameters from [1]

a2: List[float] = [1.475338, 1.71398344, 1.61365288, 1.40000001]#: model potential parameters from [1]

a3: List[float] = [-9.72143084, -24.6562428, -6.7012885, -3.20036138]#: model potential parameters from [1]

a4: List[float] = [0.02629242, -0.09543125, -0.74095193, 0.00034538]#: model potential parameters from [1]

abundance: float = 1.0#: relative isotope abundance

alphaC: float = 15.644#: model potential parameters from [1]

alpha_d_eff: float = 15.79#: ion core dipole polarisability

alpha_q_eff: float = 38.7#

//doi.org/10.1364/JOSA.71.000423

Type:: Effective core polarisabilities from https

dipoleMatrixElementFile: str = 'cs_dipole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

elementName: str = 'Cs133'#: Human-readable element name

extraLevels: List[Tuple[int, int, float]] = [(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: float = -0.00039885395#: Nuclear g-factor [17]

gL: float = 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.

groundStateN: int = 6#: principal quantum number for the ground state

hyperfineStructureData: str = 'cs_hfs_data.csv'#: source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 3.8939057274321813#: (eV), Ref. [10].

levelDataFromNIST: str = 'cs_NIST_level_data.ascii'#: location of stored NIST values of measured energy levels in eV

literatureDMEfilename: str = 'caesium_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 = 2.206946954537107e-25#: atomic mass in kg

meltingPoint: float = 301.59#: in K

minQuantumDefectN: int = 12#: minimal quantum number for which quantum defects can be used; uses measured energy levels otherwise

quadrupoleMatrixElementFile: str = 'cs_quadrupole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

quantumDefect = [[[4.0493532, 0.2391, 0.06, 11, -209, 0.0], [3.5915871, 0.36273, 0.0, 0.0, 0.0, 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]], [[4.0493532, 0.2391, 0.06, 11, -209, 0.0], [3.5590676, 0.37469, 0.0, 0.0, 0.0, 0.0], [2.4663144, 0.01381, -0.392, -1.9, 0.0, 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]]]#

//doi.org/10.1103/PhysRevA.93.013424 \(F_{5/2}\) and \(G_{7/2}\) are from [2], while \(D_{3/2}\) are from [11],

Note

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

Type:: quantum defects for \(S_{1/2}\), \(nP_{1/2}\), \(nP_{3/2}\), \(D_{5/2}\) are from https

rc: List[float] = [1.9204693, 2.13383095, 0.93007296, 1.99969677]#: model potential parameters from [1]

scaledRydbergConstant = 13.60563696419653#: in eV

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

Bases: Caesium

support for American English spelling

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

Bases: AlkaliAtom

Properties of hydrogen atoms

Z: int = 1#: Atomic number

a1: List[float] = [0.0, 0.0, 0.0, 0.0]#: Model potential parameters fitted from experimental observations for different l (electron angular momentum)

dipoleMatrixElementFile: str = 'h_dipole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

groundStateN: int = 1#: principal quantum number for the ground state

ionisationEnergy = 13.598433#: (eV), Ref. [13].

levelDataFromNIST: str = 'h_NIST_level_data.ascii'#: location of stored NIST values of measured energy levels in eV

mass: float = 1.673532840653473e-27#: source NIST, Atomic Weights and Isotopic Compositions [15]

minQuantumDefectN: int = 8#: minimal quantum number for which quantum defects can be used; uses measured energy levels otherwise

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

quadrupoleMatrixElementFile: str = 'h_quadrupole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

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

Bases: AlkaliAtom

Properties of lithium 6 atoms

I: float = 1.0#: Nuclear spin

Z: int = 3#: Atomic number

a1: List[float] = [2.47718079, 3.45414648, 2.51909839, 2.51909839]#: model potential parameters from [1]

a2: List[float] = [1.84150932, 2.5515108, 2.4371245, 2.4371245]#: model potential parameters from [1]

a3: List[float] = [-0.02169712, -0.21646561, 0.32505524, 0.32505524]#: model potential parameters from [1]

a4: List[float] = [-0.11988362, -0.06990078, 0.1060243, 0.1060243]#: model potential parameters from [1]

a_q_eff = 0.04579#

//doi.org/10.1103/PhysRevA.16.1141

Type:: (Effective) core plarisabiltiesm from https

abundance: float = 0.0759#: source NIST, Atomic Weights and Isotopic Compositions [15]

alphaC: float = 0.1923#: model potential parameters from [1]

alpha_d_eff: float = 0.1883#: ion core dipole polarisability

dipoleMatrixElementFile: str = 'li6_dipole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

elementName: str = 'Li6'#: Human-readable element name

extraLevels: List[Tuple[int, int, float]] = []#: levels that are for smaller principal quantum number (n) than ground level, but are above in energy due to angular part

gL: float = 0.999908799883342#: Electron Orbital g-factor

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.

groundStateN: int = 2#: principal quantum number for the ground state

hyperfineStructureData: str = 'li6_hfs_data.csv'#: source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 5.391719434894345#: ionisationEnergy in eV

levelDataFromNIST: str = 'li_NIST_level_data.ascii'#: location of stored NIST values of measured energy levels in eV

mass: float = 9.988346558882577e-27#: source NIST, Atomic Weights and Isotopic Compositions [15]

meltingPoint: float = 453.68999999999994#: in K

minQuantumDefectN: int = 4#: minimal quantum number for which quantum defects can be used; uses measured energy levels otherwise

quadrupoleMatrixElementFile: str = 'li6_quadrupole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

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: List[float] = [0.61340824, 0.61566441, 2.34126273, 2.34126273]#: model potential parameters from [1]

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

Bases: AlkaliAtom

Properties of lithium 7 atoms

I: float = 1.5#: Nuclear spin

Z: int = 3#: Atomic number

a1: List[float] = [2.47718079, 3.45414648, 2.51909839, 2.51909839]#: model potential parameters from [1]

a2: List[float] = [1.84150932, 2.5515108, 2.4371245, 2.4371245]#: model potential parameters from [1]

a3: List[float] = [-0.02169712, -0.21646561, 0.32505524, 0.32505524]#: model potential parameters from [1]

a4: List[float] = [-0.11988362, -0.06990078, 0.1060243, 0.1060243]#: model potential parameters from [1]

abundance: float = 0.9241#: source NIST, Atomic Weights and Isotopic Compositions [15]

alphaC: float = 0.1923#: model potential parameters from [1]

alpha_d_eff: float = 0.1883#: ion core dipole polarisability

alpha_q_eff: float = 0.04579#

//doi.org/10.1103/PhysRevA.16.1141

Type:: (Effective) core plarisabiltiesm from https

dipoleMatrixElementFile: str = 'li7_dipole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

elementName: str = 'Li7'#: Human-readable element name

extraLevels: List[Tuple[int, int, float]] = []#: levels that are for smaller principal quantum number (n) than ground level, but are above in energy due to angular part

gL: float = 0.9999218101994961#: Electron Orbital g-factor

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.

groundStateN: int = 2#: principal quantum number for the ground state

hyperfineStructureData: str = 'li7_hfs_data.csv'#: source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 5.391719#: (eV) NIST Ref. [14].

levelDataFromNIST: str = 'li_NIST_level_data.ascii'#: location of stored NIST values of measured energy levels in eV

mass: float = 1.1650347814151284e-26#: source NIST, Atomic Weights and Isotopic Compositions [15]

meltingPoint: float = 453.68999999999994#: in K

minQuantumDefectN: int = 4#: minimal quantum number for which quantum defects can be used; uses measured energy levels otherwise

quadrupoleMatrixElementFile: str = 'li7_quadrupole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

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: List[float] = [0.61340824, 0.61566441, 2.34126273, 2.34126273]#: model potential parameters from [1]

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

Bases: 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: AlkaliAtom

Properties of potassium 39 atoms

I: float = 1.5#: Nuclear spin

Z: int = 19#: Atomic number

a1: List[float] = [3.56079437, 3.65670429, 4.12713694, 1.42310446]#: model potential parameters from [1]

a2: List[float] = [1.83909642, 1.67520788, 1.79837462, 1.27861156]#: model potential parameters from [1]

a3: List[float] = [-1.74701102, -2.07416615, -1.69935174, 4.77441476]#: model potential parameters from [1]

a4: List[float] = [-1.03237313, -0.89030421, -0.98913582, -0.94829262]#: model potential parameters from [1]

abundance: float = 0.932581#: source NIST, Atomic Weights and Isotopic Compositions [15]

alphaC: float = 5.331#: model potential parameters from [1]

alpha_d_eff: float = 5.49#: ion core dipole polarisability

alpha_q_eff: float = 18#

//doi.org/10.1103/PhysRevA.100.012501

Type:: (Effective) core plarisabiltiesm from https

dipoleMatrixElementFile: str = 'k_dipole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

elementName: str = 'K39'#: Human-readable element name

extraLevels: List[Tuple[int, int, float]] = [(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

gL: float = 0.9999859207462916#: Electron Orbital g-factor

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.

groundStateN: int = 4#: principal quantum number for the ground state

hyperfineStructureData: str = 'k39_hfs_data.csv'#: source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 4.340663718336421#: (eV), weighted average of values in Ref. [12].

levelDataFromNIST: str = 'k_NIST_level_data.ascii'#: location of stored NIST values of measured energy levels in eV

literatureDMEfilename: str = 'potassium_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 = 6.470075689059882e-26#: source NIST, Atomic Weights and Isotopic Compositions [15]

meltingPoint: float = 336.65#: in K

quadrupoleMatrixElementFile: str = 'k_quadrupole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

quantumDefect = [[[2.18020826, 0.134534, 0.0952, 0.0021, 0.0, 0.0], [1.71392626, 0.23114, 0.1948, 0.3683, 0.0, 0.0], [0.27698453, -1.02691, -0.665, 10.9, 0.0, 0.0], [0.0094576, -0.0446, 0.0, 0.0, 0.0, 0.0], [0.002408, -0.0209, 0.0, 0.0, 0.0, 0.0]], [[2.18020826, 0.134534, 0.0952, 0.0021, 0.0, 0.0], [1.71087854, 0.23233, 0.1961, 0.3716, 0.0, 0.0], [0.27715665, -1.02493, -0.64, 10.0, 0.0, 0.0], [0.0094576, -0.0446, 0.0, 0.0, 0.0, 0.0], [0.002408, -0.0209, 0.0, 0.0, 0.0, 0.0]]]#

//doi.org/10.1103/PhysRevA.100.012501

Type:: p1/2 and p3/2, s1/2, d3/2, d5/2 and f and g (centre of manifold) from https

rc: List[float] = [0.83167545, 0.85235381, 0.83216907, 6.50294371]#: model potential parameters from [1]

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

Bases: AlkaliAtom

Properties of potassium 40 atoms

I: float = 4#: Nuclear spin

Z: int = 19#: Atomic number

a1: List[float] = [3.56079437, 3.65670429, 4.12713694, 1.42310446]#: model potential parameters from [1]

a2: List[float] = [1.83909642, 1.67520788, 1.79837462, 1.27861156]#: model potential parameters from [1]

a3: List[float] = [-1.74701102, -2.07416615, -1.69935174, 4.77441476]#: model potential parameters from [1]

a4: List[float] = [-1.03237313, -0.89030421, -0.98913582, -0.94829262]#: model potential parameters from [1]

abundance: float = 0.000117#: source NIST, Atomic Weights and Isotopic Compositions [15]

alphaC: float = 5.331#: model potential parameters from [1]

alpha_d_eff: float = 5.49#: ion core dipole polarisability

alpha_q_eff: float = 18#

//doi.org/10.1103/PhysRevA.100.012501

Type:: (Effective) core plarisabiltiesm from https

dipoleMatrixElementFile: str = 'k_dipole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

elementName: str = 'K40'#: Human-readable element name

extraLevels: List[Tuple[int, int, float]] = [(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

gL: float = 0.9999862731474772#: Electron Orbital g-factor

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.

groundStateN: int = 4#: principal quantum number for the ground state

hyperfineStructureData: str = 'k40_hfs_data.csv'#: source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 4.340663718336421#: (eV), weighted average of values in Ref. [12].

levelDataFromNIST: str = 'k_NIST_level_data.ascii'#: location of stored NIST values of measured energy levels in eV

literatureDMEfilename: str = 'potassium_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 = 6.636178030489023e-26#: source NIST, Atomic Weights and Isotopic Compositions [15]

meltingPoint: float = 336.65#: in K

quadrupoleMatrixElementFile: str = 'k_quadrupole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

//doi.org/10.1103/PhysRevA.100.012501

Type:: p1/2 and p3/2, s1/2, d3/2, d5/2 and f and g (centre of manifold) from https

rc: List[float] = [0.83167545, 0.85235381, 0.83216907, 6.50294371]#: model potential parameters from [1]

scaledRydbergConstant = 13.605506359647544#: in eV

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

Bases: AlkaliAtom

Properties of potassium 41 atoms

I: float = 1.5#: Nuclear spin

Z: int = 19#: Atomic number

a1: List[float] = [3.56079437, 3.65670429, 4.12713694, 1.42310446]#: model potential parameters from [1]

a2: List[float] = [1.83909642, 1.67520788, 1.79837462, 1.27861156]#: model potential parameters from [1]

a3: List[float] = [-1.74701102, -2.07416615, -1.69935174, 4.77441476]#: model potential parameters from [1]

a4: List[float] = [-1.03237313, -0.89030421, -0.98913582, -0.94829262]#: model potential parameters from [1]

abundance: float = 0.067302#: source NIST, Atomic Weights and Isotopic Compositions [15]

alphaC: float = 5.331#: model potential parameters from [1]

alpha_d_eff: float = 5.49#: ion core dipole polarisability

alpha_q_eff: float = 18#

//doi.org/10.1103/PhysRevA.100.012501

Type:: (Effective) core plarisabiltiesm from https

dipoleMatrixElementFile: str = 'k_dipole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

elementName: str = 'K41'#: Human-readable element name

extraLevels: List[Tuple[int, int, float]] = [(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

gL: float = 0.999986607532609#: Electron Orbital g-factor

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.

groundStateN: int = 4#: principal quantum number for the ground state

hyperfineStructureData: str = 'k41_hfs_data.csv'#: source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 4.340663718336421#: (eV), weighted average of values in Ref. [12].

levelDataFromNIST: str = 'k_NIST_level_data.ascii'#: location of stored NIST values of measured energy levels in eV

literatureDMEfilename: str = 'potassium_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 = 6.8018711175017e-26#: source NIST, Atomic Weights and Isotopic Compositions [15]

meltingPoint: float = 336.65#: in K

quadrupoleMatrixElementFile: str = 'k_quadrupole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

//doi.org/10.1103/PhysRevA.100.012501

Type:: p1/2 and p3/2, s1/2, d3/2, d5/2 and f and g (centre of manifold) from https

rc: List[float] = [0.83167545, 0.85235381, 0.83216907, 6.50294371]#: model potential parameters from [1]

scaledRydbergConstant = 13.605510909189032#: in eV

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

Bases: 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: AlkaliAtom

Properites of rubidium 85 atoms

I: float = 2.5#: Nuclear spin

Z: int = 37#: Atomic number

a1: List[float] = [3.69628474, 4.44088978, 3.78717363, 2.39848933]#: model potential parameters from [1]

a2: List[float] = [1.64915255, 1.92828831, 1.57027864, 1.76810544]#: model potential parameters from [1]

a3: List[float] = [-9.86069196, -16.7959777, -11.6558897, -12.0710678]#: model potential parameters from [1]

a4: List[float] = [0.19579987, -0.8163314, 0.52942835, 0.77256589]#: model potential parameters from [1]

abundance: float = 0.7217#: source NIST, Atomic Weights and Isotopic Compositions [15]

alphaC: float = 9.076#: model potential parameters from [1]

alpha_d_eff: float = 9.089#: ion core dipole polarisability

alpha_q_eff: float = 16.8#

//doi.org/10.1103/PhysRevA.102.062818

Type:: Effective core polarisabilities from https

dipoleMatrixElementFile: str = 'rb_dipole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

elementName: str = 'Rb85'#: Human-readable element name

extraLevels: List[Tuple[int, int, float]] = [(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: float = -0.00029364#: Nuclear g-factor [18]

gL: float = 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.

groundStateN: int = 5#: principal quantum number for the ground state

hyperfineStructureData: str = 'rb85_hfs_data.csv'#: source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 4.177126524885211#: (eV) Ref. [16]

levelDataFromNIST: str = 'rb_NIST_level_data.ascii'#: location of stored NIST values of measured energy levels in eV

literatureDMEfilename: str = 'rubidium_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 = 1.4099934427170326e-25#: source NIST, Atomic Weights and Isotopic Compositions [15]

meltingPoint: float = 312.46#: in K

minQuantumDefectN: int = 8#: minimal quantum number for which quantum defects can be used; uses measured energy levels otherwise

quadrupoleMatrixElementFile: str = 'rb_quadrupole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

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: List[float] = [1.66242117, 1.50195124, 4.86851938, 4.79831327]#: model potential parameters from [1]

scaledRydbergConstant = 13.605605222241762#: in eV

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

Bases: AlkaliAtom

Properites of rubidium 87 atoms

I: float = 1.5#: Nuclear spin

Z: int = 37#: Atomic number

a1: List[float] = [3.69628474, 4.44088978, 3.78717363, 2.39848933]#: model potential parameters from [1]

a2: List[float] = [1.64915255, 1.92828831, 1.57027864, 1.76810544]#: model potential parameters from [1]

a3: List[float] = [-9.86069196, -16.7959777, -11.6558897, -12.0710678]#: model potential parameters from [1]

a4: List[float] = [0.19579987, -0.8163314, 0.52942835, 0.77256589]#: model potential parameters from [1]

abundance: float = 0.2783#: source NIST, Atomic Weights and Isotopic Compositions [15]

alphaC: float = 9.076#: model potential parameters from [1]

alpha_d_eff: float = 9.089#: ion core dipole polarisability

alpha_q_eff: float = 16.8#

//doi.org/10.1103/PhysRevA.102.062818

Type:: Effective core polarisabilities from https

dipoleMatrixElementFile: str = 'rb_dipole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

elementName: str = 'Rb87'#: Human-readable element name

extraLevels: List[Tuple[int, int, float]] = [(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: float = -0.0009951414#: Nuclear g-factor [19]

gL: float = 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.

groundStateN: int = 5#: principal quantum number for the ground state

hyperfineStructureData: str = 'rb87_hfs_data.csv'#: source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 4.177127322752153#: (eV) Ref. [6]

levelDataFromNIST: str = 'rb_NIST_level_data.ascii'#: location of stored NIST values of measured energy levels in eV

literatureDMEfilename: str = 'rubidium_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 = 1.4431608971954693e-25#: source NIST, Atomic Weights and Isotopic Compositions [15]

meltingPoint: float = 312.46#: in K

minQuantumDefectN: int = 8#: minimal quantum number for which quantum defects can be used; uses measured energy levels otherwise

quadrupoleMatrixElementFile: str = 'rb_quadrupole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

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: List[float] = [1.66242117, 1.50195124, 4.86851938, 4.79831327]#: model potential parameters from [1]

scaledRydbergConstant = 13.605607242421279#: in eV (M_ion core = m_atomic - m_electron)

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

Bases: AlkaliAtom

Properties of sodium 23 atoms

I: float = 1.5#: Nuclear spin

Z: int = 11#: Atomic number

a1: List[float] = [4.82223117, 5.08382502, 3.53324124, 1.11056646]#: model potential parameters from [1]

a2: List[float] = [2.45449865, 2.18226881, 2.48697936, 1.05458759]#: model potential parameters from [1]

a3: List[float] = [-1.12255048, -1.19534623, -0.75688448, 1.73203428]#: model potential parameters from [1]

a4: List[float] = [-1.42631393, -1.03142861, -1.27852357, -0.09265696]#: model potential parameters from [1]

abundance: float = 1.0#: source NIST, Atomic Weights and Isotopic Compositions [15]

alphaC: float = 0.9448#: model potential parameters from [1]

alpha_d_eff: float = 0.998#: ion core dipole polarisability

alpha_q_eff: float = 0.351#

//doi.org/10.1103/PhysRevA.38.4985

Type:: (Effective) core plarisabiltiesm from https

dipoleMatrixElementFile: str = 'na23_dipole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

elementName: str = 'Na23'#: Human-readable element name

extraLevels: List[Tuple[int, int, float]] = []#: levels that are for smaller principal quantum number (n) than ground level, but are above in energy due to angular part

gL: float = 0.9999761380854973#: Electron Orbital g-factor

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.

groundStateN: int = 3#: principal quantum number for the ground state

hyperfineStructureData: str = 'na23_hfs_data.csv'#: source of HFS magnetic dipole and quadrupole constants

ionisationEnergy = 5.139075593905028#: (eV) from Ref. [12]

levelDataFromNIST: str = 'na_NIST_level_data.ascii'#: location of stored NIST values of measured energy levels in eV

literatureDMEfilename: str = 'sodium_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 = 3.81754100782179e-26#: source NIST, Atomic Weights and Isotopic Compositions [15]

meltingPoint: float = 370.94399999999996#: in K

quadrupoleMatrixElementFile: str = 'na23_quadrupole_matrix_elements.npy'#: location of hard-disk stored dipole matrix elements

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: List[float] = [0.45489422, 0.45798739, 0.71875312, 28.6735059]#: model potential parameters from [1]

scaledRydbergConstant = 13.605368465104466#: (eV)