RydbergStateSQDTDivalent

Class Methods

`__init__`(species, n, *, l, s[, j, f, m, ...])	Initialize the Rydberg state.
`calc_exp_qn`(qn)
`calc_matrix_element`(other, operator, q, *[, ...])	Calculate the matrix element.
`calc_reduced_matrix_element`(other, operator, *)	Calculate the reduced matrix element.
`calc_reduced_overlap`(other)	Calculate the reduced overlap <self\|other> (ignoring the magnetic quantum number m).
`calc_std_qn`(qn)
`get_binding_energy`([unit])	Get the binding energy of the Rydberg state, relative to its ionization energy.
`get_black_body_transition_rates`(temperature)	Calculate the black body transition rates of the Rydberg state.
`get_energy`([unit])	Get the energy of the Rydberg state.
`get_label`([fmt])	Label representing the state.
`get_lifetime`([temperature, ...])	Calculate the lifetime of the Rydberg state.
`get_spontaneous_transition_rates`([unit])	Calculate the spontaneous transition rates for the Rydberg state.
`to_coupling_scheme`(coupling_scheme)	Convert the Rydberg state to a different coupling scheme.

Class Attributes and Properties

`coefficients`	Return the channel coefficients as numpy array.
`norm`	Return the norm of the state (should be 1).
`nu`	The effective principal quantum number nu, defined with reference to the reference ionization energy.
`nui`	The effective principal quantum number nui, defined with reference to the ionization energy.
`radial`	The radial part of the Rydberg electron.
`rydberg_kets`
`species`	The atomic species of the Rydberg state.
`angular`	The angular/spin part of the Rydberg electron.
`n`	The principal quantum number n of the Rydberg state.
`f_tot`	The total angular momentum quantum number f_tot of the Rydberg state.

class rydstate.rydberg_state.RydbergStateSQDTDivalent(species, n, *, l, s, j=None, f=None, m=NotSet, sqdt=None, potential_class=None)[source]

Initialize the Rydberg state.

Parameters:

species (str) – Atomic species.
n (int) – Principal quantum number of the rydberg electron.
l (int) – Orbital angular momentum quantum number of the rydberg electron.
s (int) – Total electron spin quantum number, i.e. 0 for singlet and 1 for triplet states.
j (int | None) – Total electron angular momentum quantum number. Optional, if it is uniquely determined by l and s (i.e. for l = 0).
f (float | None) – Total angular momentum quantum number, including the nuclear spin. Optional, if it is uniquely determined by j (i.e. for species without nuclear spin).
m (float | NotSet) – Total magnetic quantum number. Optional, only needed for concrete angular matrix elements.
sqdt (SQDT | str | None) – The SQDT to use for the state. Either a string representing the tag of the SQDT class to use, or an instance of an SQDT class.
potential_class (type[Potential] | str | None) – The potential class to use for the radial ket. Either a string representing the tag of the potential class to use, or a potential class. If None, the default potential class for the species is used.

calc_exp_qn(qn)

Return type:: float
Parameters:: qn (str)

calc_matrix_element(other, operator, q, *, part='all', unit=None)

Calculate the matrix element.

Overloads:

self, other (RydbergState), operator (MatrixElementOperator), q (int), part (MatrixElementPart), unit (None) → PintFloat
self, other (RydbergState), operator (MatrixElementOperator), q (int), part (MatrixElementPart), unit (str) → float

Parameters:

other (RydbergState)
operator (Literal['magnetic_dipole', 'electric_monopole', 'electric_dipole', 'electric_quadrupole', 'electric_octupole', 'electric_quadrupole_zero', 'spherical', 'spherical_inner_valence', 'i_c', 's_c', 'l_c', 's_r', 'l_r', 's_tot', 'l_tot', 'j_c', 'j_r', 'j_tot', 'f_c', 'f_tot', 'identity_i_c', 'identity_s_c', 'identity_l_c', 'identity_s_r', 'identity_l_r', 'identity_s_tot', 'identity_l_tot', 'identity_j_c', 'identity_j_r', 'identity_j_tot', 'identity_f_c', 'identity_f_tot'])
q (int)
part (Literal['all', 'rydberg', 'inner_valence', 'closed_shell_core'])
unit (str | None)

Return type:

PlainQuantity[float] | float

Calculate the full matrix element between self and other, also considering the magnetic quantum numbers m of self and other.

\[\left\langle self | r^k_radial \hat{O}^{(k_{angular})}_q | other \right\rangle\]

where hat{O}^{(k_{angular})}_q is the operator of rank k_angular for which to calculate the matrix element. k_radial and k_angular are determined from the operator automatically.

Parameters:

other (RydbergState) – The other Rydberg state for which to calculate the matrix element.
operator (Literal['magnetic_dipole', 'electric_monopole', 'electric_dipole', 'electric_quadrupole', 'electric_octupole', 'electric_quadrupole_zero', 'spherical', 'spherical_inner_valence', 'i_c', 's_c', 'l_c', 's_r', 'l_r', 's_tot', 'l_tot', 'j_c', 'j_r', 'j_tot', 'f_c', 'f_tot', 'identity_i_c', 'identity_s_c', 'identity_l_c', 'identity_s_r', 'identity_l_r', 'identity_s_tot', 'identity_l_tot', 'identity_j_c', 'identity_j_r', 'identity_j_tot', 'identity_f_c', 'identity_f_tot']) – The operator for which to calculate the matrix element.
q (int) – The component of the operator.
part (Literal['all', 'rydberg', 'inner_valence', 'closed_shell_core']) – The part of the matrix element to calculate.
unit (str | None) – The unit to which to convert the radial matrix element. Can be “a.u.” for atomic units (so no conversion is done), or a specific unit. Default None will return a pint quantity.

Returns:

The matrix element for the given operator.

Return type:

PlainQuantity[float] | float

calc_reduced_matrix_element(other, operator, *, part='all', unit=None)

Calculate the reduced matrix element.

Overloads:

self, other (RydbergState), operator (MatrixElementOperator), part (MatrixElementPart), unit (None) → PintFloat
self, other (RydbergState), operator (MatrixElementOperator), part (MatrixElementPart), unit (str) → float

Parameters:

other (RydbergState)
operator (Literal['magnetic_dipole', 'electric_monopole', 'electric_dipole', 'electric_quadrupole', 'electric_octupole', 'electric_quadrupole_zero', 'spherical', 'spherical_inner_valence', 'i_c', 's_c', 'l_c', 's_r', 'l_r', 's_tot', 'l_tot', 'j_c', 'j_r', 'j_tot', 'f_c', 'f_tot', 'identity_i_c', 'identity_s_c', 'identity_l_c', 'identity_s_r', 'identity_l_r', 'identity_s_tot', 'identity_l_tot', 'identity_j_c', 'identity_j_r', 'identity_j_tot', 'identity_f_c', 'identity_f_tot'])
part (Literal['all', 'rydberg', 'inner_valence', 'closed_shell_core'])
unit (str | None)

Return type:

PlainQuantity[float] | float

Calculate the reduced matrix element between self and other (ignoring m quantum numbers)

\[\left\langle self || r^k_radial \hat{O}^{(k_{angular})} || other \right\rangle\]

where hat{O}^{(k_{angular})} is the operator of rank k_angular for which to calculate the matrix element. k_radial and k_angular are determined from the operator automatically.

Parameters:

other (RydbergState) – The other Rydberg state for which to calculate the matrix element.
operator (Literal['magnetic_dipole', 'electric_monopole', 'electric_dipole', 'electric_quadrupole', 'electric_octupole', 'electric_quadrupole_zero', 'spherical', 'spherical_inner_valence', 'i_c', 's_c', 'l_c', 's_r', 'l_r', 's_tot', 'l_tot', 'j_c', 'j_r', 'j_tot', 'f_c', 'f_tot', 'identity_i_c', 'identity_s_c', 'identity_l_c', 'identity_s_r', 'identity_l_r', 'identity_s_tot', 'identity_l_tot', 'identity_j_c', 'identity_j_r', 'identity_j_tot', 'identity_f_c', 'identity_f_tot']) – The operator for which to calculate the matrix element.
part (Literal['all', 'rydberg', 'inner_valence', 'closed_shell_core']) – The part of the matrix element to calculate.
unit (str | None) – The unit to which to convert the radial matrix element. Can be “a.u.” for atomic units (so no conversion is done), or a specific unit. Default None will return a pint quantity.

Returns:

The reduced matrix element for the given operator.

Return type:

PlainQuantity[float] | float

calc_reduced_overlap(other)

Calculate the reduced overlap <self|other> (ignoring the magnetic quantum number m).

Return type:: float
Parameters:: other (RydbergState)

calc_std_qn(qn)

Return type:: float
Parameters:: qn (str)

property coefficients: NDArray[Any]: Return the channel coefficients as numpy array.

get_binding_energy(unit=None)

Get the binding energy of the Rydberg state, relative to its ionization energy.

Overloads:

self, unit (None) → PintFloat
self, unit (str) → float

Parameters:

unit (str | None)

Return type:

PlainQuantity[float] | float

The binding energy is negative by convention, so it can be added directly to the ionization energy to obtain the total state energy.

The binding energy is given by

\[E = - \frac{Z^2 R_M}{\nu_i^2} = - \frac{1}{2} \frac{Z^2 \mu/m_e}{\nu_i^2} E_H\]

where \(R_M = R_\infty \mu/m_e\) is the mass corrected Rydberg constant, \(Z\) is the net charge of the ionic core seen by the Rydberg electron (note \(E_H = 2 R_\infty\)), \(\mu/m_e\) the reduced mass in atomic units and \(\nu_i\) the effective principal quantum number with reference to the ionization energy, see nui.

get_black_body_transition_rates(temperature, temperature_unit=None, unit=None)

Calculate the black body transition rates of the Rydberg state.

Overloads:

self (Self), temperature (PintFloat), temperature_unit (None), unit (None) → tuple[list[Self], PintArray]
self (Self), temperature (float), temperature_unit (str), unit (None) → tuple[list[Self], PintArray]
self (Self), temperature (PintFloat), temperature_unit (None), unit (str) → tuple[list[Self], NDArray]
self (Self), temperature (float), temperature_unit (str), unit (str) → tuple[list[Self], NDArray]

Parameters:

self (Self)
temperature (float | PlainQuantity[float])
temperature_unit (str | None)
unit (str | None)

Return type:

tuple[list[Self], NDArray[Any] | PlainQuantity[NDArray[Any]]]

The black body transition rates are given by the Einstein B coefficients, with a weight factor given by Planck’s law.

Parameters:

temperature (Union[float, PlainQuantity[float]]) – The temperature, for which to calculate the black body transition rates.
temperature_unit (str | None) – The unit of the temperature. Default None will assume the temperature is given as pint.Quantity.
unit (str | None) – The unit to which to convert the result. Default None will return a pint.Quantity.
self (Self)

Returns:

The relevant states and the transition rates.

Return type:

tuple[list[Self], NDArray[Any] | PlainQuantity[NDArray[Any]]]

get_energy(unit=None)

Get the energy of the Rydberg state.

Overloads:

self, unit (None) → PintFloat
self, unit (str) → float

Parameters:

unit (str | None)

Return type:

PlainQuantity[float] | float

The energy is defined as

\[E = - \frac{1}{2} \frac{\mu}{\nu^2} + E_{ionization}\]

where mu = R_M/R_infty is the reduced mass and nu the effective principal quantum number, and E_{ionization} is the reference ionization threshold of the species.

get_label(fmt='ket')

Label representing the state.

Parameters:: fmt (Literal['raw', 'ket', 'bra']) – The format of the label, i.e. whether to return the raw label, or the label in ket or bra notation.
Return type:: str
Returns:: The label of the state in the given format.

get_lifetime(temperature=None, temperature_unit=None, unit=None)

Calculate the lifetime of the Rydberg state.

Overloads:

self → PintFloat
self, temperature (PintFloat) → PintFloat
self, temperature (float), temperature_unit (str) → PintFloat
self, unit (str) → float
self, temperature (PintFloat), unit (str) → float
self, temperature (float), temperature_unit (str), unit (str) → float

Parameters:

temperature (float | PlainQuantity[float] | None)
temperature_unit (str | None)
unit (str | None)

Return type:

float | PlainQuantity[float]

The lifetime is the inverse of the sum of all transition rates.

Parameters:

temperature (Union[float, PlainQuantity[float], None]) – The temperature, for which to calculate the black body transition rates. Default None will not include black body transitions.
temperature_unit (str | None) – The unit of the temperature. Default None will assume the temperature is given as pint.Quantity.
unit (str | None) – The unit to which to convert the result. Default None will return a pint.Quantity.

Returns:

The lifetime of the state.

Return type:

float | PlainQuantity[float]

get_spontaneous_transition_rates(unit=None)

Calculate the spontaneous transition rates for the Rydberg state.

Overloads:

self (Self), unit (None) → tuple[list[Self], PintArray]
self (Self), unit (str) → tuple[list[Self], NDArray]

Parameters:

self (Self)
unit (str | None)

Return type:

tuple[list[Self], NDArray[Any] | PlainQuantity[NDArray[Any]]]

The spontaneous transition rates are given by the Einstein A coefficients.

Parameters:

unit (str | None) – The unit to which to convert the result. Default None will return a pint.Quantity.
self (Self)

Returns:

The relevant states and the transition rates.

Return type:

tuple[list[Self], NDArray[Any] | PlainQuantity[NDArray[Any]]]

property norm: float: Return the norm of the state (should be 1).

property nu: float

The effective principal quantum number nu, defined with reference to the reference ionization energy.

In contrast to nui, nu is defined with reference to the reference ionization energy (see reference_ionization_energy_au).

For states without hyperfine splitting, nui and nu are equal.

property nui: float

The effective principal quantum number nui, defined with reference to the ionization energy.

nui is defined with reference to the ionization energy of the Rydberg electron (see ionization_energy_au), i.e. via the binding energy

\[E = I - \frac{R_M}{\nu_i^2} = I_{\text{ref}} - \frac{R_M}{\nu^2}\]

where \(R_M = R_\infty \mu/m_e\) is the mass corrected Rydberg constant.

Therefore, nui is the quantum number that determines the radial wavefunction, see radial.

property radial: RadialKet: The radial part of the Rydberg electron.

property rydberg_kets: list[RydbergKet]

to_coupling_scheme(coupling_scheme)

Convert the Rydberg state to a different coupling scheme.

Parameters:: coupling_scheme (Literal['LS', 'JJ', 'FJ']) – The coupling scheme to which to convert the Rydberg state.
Return type:: RydbergState
Returns:: The Rydberg state in the new coupling scheme.

species: str: The atomic species of the Rydberg state.

angular: GenericT_AngularKet: The angular/spin part of the Rydberg electron.

n: int

The principal quantum number n of the Rydberg state.

For MQDT states, we define the corresponding principal quantum number n via the number of nodes in the radial wavefunction of the most dominant channel.

f_tot: float: The total angular momentum quantum number f_tot of the Rydberg state.