RydbergStateAlkali

Class Methods

__init__(species, n, l[, j, f, m])	Initialize the Rydberg state.
calc_matrix_element(other, operator, q[, unit])	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).
get_energy([unit])	Get the energy of the Rydberg state.
get_nu()	Get the effective principal quantum number nu (for alkali atoms also known as n*) for the Rydberg state.

Class Attributes and Properties

angular	The angular/spin state of the Rydberg electron.
radial	The radial state of the Rydberg electron.
species

class rydstate.RydbergStateAlkali(species, n, l, j=None, f=None, m=None)

Initialize the Rydberg state.

Parameters:

• species (str | SpeciesObject) – Atomic species.

• n (int) – Principal quantum number of the rydberg electron.

• l (int) – Orbital angular momentum quantum number of the rydberg electron.

• j (float | None) – Angular momentum quantum number of the rydberg electron.

• f (float | None) – Total angular momentum quantum number of the atom (rydberg electron + core) Optional, only needed if the species supports hyperfine structure (i.e. species.i_c is not None or 0).

• m (float | None) – Total magnetic quantum number. Optional, only needed for concrete angular matrix elements.

species: SpeciesObject

property angular: AngularKetLS

The angular/spin state of the Rydberg electron.

property radial: RadialState

The radial state of the Rydberg electron.

get_nu()

Get the effective principal quantum number nu (for alkali atoms also known as n*) for the Rydberg state.

Return type:

float

calc_matrix_element(other, operator, q, unit=None)

Calculate the matrix element.

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

\[\left\langle self || r^k_radial \hat{O}_{k_angular} || other \right\rangle\]

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 (Self) – The other Rydberg state for which to calculate the matrix element.

• operator (Literal['magnetic_dipole', 'electric_dipole', 'electric_quadrupole', 'electric_octupole', 'electric_quadrupole_zero']) – The operator for which to calculate the matrix element.

• q (int) – The component of the operator.

• 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.

Return type:

Union[PlainQuantity[float], float]

Returns:

The matrix element for the given operator.

calc_reduced_matrix_element(other, operator, unit=None)

Calculate the reduced matrix element.

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 (Self) – The other Rydberg state for which to calculate the matrix element.

• operator (Literal['magnetic_dipole', 'electric_dipole', 'electric_quadrupole', 'electric_octupole', 'electric_quadrupole_zero']) – The operator for which to calculate the matrix element.

• 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.

Return type:

Union[PlainQuantity[float], float]

Returns:

The reduced matrix element for the given operator.

calc_reduced_overlap(other)

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

Return type:

float

Parameters:

other (RydbergStateBase)

get_energy(unit=None)

Get the energy of the Rydberg state.

The energy is defined as

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

where mu = R_M/R_infty is the reduced mass and nu the effective principal quantum number.

Return type:

Union[PlainQuantity[float], float]

Parameters:

unit (str | None)