RydbergStateMQDT

Class Methods

`__init__`(species, coefficients, ...)
`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_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.
`mqdt`	Return the MQDT object used to calculate this state.
`n`	Return the corresponding principal quantum number n of the state.
`norm`	Return the norm of the state (should be 1).
`nui`	Return the effective principal quantum numbers nui of the different channels.
`species`	The species of the Rydberg state.
`rydberg_kets`	The Rydberg kets that form the Rydberg state.
`nu`	The effective principal quantum number nu given in reference to the reference ionization threshold.
`f_tot`	The total angular momentum quantum number f_tot of the Rydberg state.

class rydstate.rydberg_state.RydbergStateMQDT(species, coefficients, rydberg_kets, nu, energy_au, model, potential_class)[source]

Parameters:

species (str)
coefficients (Sequence[float] | NDArray)
rydberg_kets (list[RydbergKet])
nu (float)
energy_au (float)
model (MQDTModel)
potential_class (type[Potential])

property mqdt: MQDT: Return the MQDT object used to calculate this state.

property nui: NDArray[Any]: Return the effective principal quantum numbers nui of the different channels.

property n: int

Return the corresponding principal quantum number n of the state.

We define the corresponding principal quantum number n for MQDT states via the nodes of the main contributing rydberg ket (nodes = n - l_r - 1). For TrivialModel states, the quantum defect is zero, so the channel dependent effective quantum number nui is already an integer and we simply round it to the nearest integer.

calc_exp_qn(qn)[source]

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

calc_std_qn(qn)[source]

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)

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

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).

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 species of the Rydberg state.

rydberg_kets: list[RydbergKet]: The Rydberg kets that form the Rydberg state.

nu: float: The effective principal quantum number nu given in reference to the reference ionization threshold.

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