ElementProperties

Class Methods

`__init__`()
`get_corrected_rydberg_constant`([unit])	Return the corrected Rydberg constant in the desired unit.
`is_allowed_shell`(n, l, s_tot)	Check if the quantum numbers describe an allowed shell.

Class Attributes and Properties

`additional_allowed_shells`	Additional allowed shells (n, l), which (n, l) is smaller than the ground state shell.
`alpha_closed_shell_core`	Static dipole polarizability (a.u.) of the core including the closed-shell electrons.
`mass_core_u`	The mass of the ionic core in unified atomic mass units (u).
`net_charge`	Net charge of the ionic core seen by the Rydberg electron (1 for neutral atoms, 2 for singly-charged ions).
`nuclear_dipole`	Nuclear dipole moment of the species.
`r_c_dipole_operator`	Cutoff radius (a.u.) of the core-polarization corrected electric-dipole operator (see alpha_closed_shell_core).
`reduced_mass_au`	The reduced mass mu in atomic units.
`s_c`	Total spin of the core electrons (0 for alkali atoms, 0.5 for alkaline earth atoms).
`s_r`	Total spin of the rydberg electron (always 0.5).
`species`	The short name of the atomic species.
`Z`	Atomic number of the species.
`i_c`	Nuclear spin.
`number_valence_electrons`	Number of valence electrons (i.e. 1 for alkali atoms and 2 for alkaline earth atoms).
`mass_number`	Mass number A (i.e. number of nucleons) of the isotope.
`atomic_mass_u`	Relative atomic mass of the neutral atom in unified atomic mass units (u).
`ground_state_shell`	Shell (n, l) describing the electronic ground state configuration.
`core_electron_configuration`	Electron configuration of the core electrons, e.g. 4p6 for Rb or 5s for Sr.

class rydstate.species.ElementProperties(*args: object, **kwargs: object)[source]

Base class for all element properties classes.

For the electronic ground state configurations and sorted shells, see e.g. https://www.webelements.com/atoms.html

Parameters:

args (object)
kwargs (object)

Return type:

CachedT

species: ClassVar[str]: The short name of the atomic species.

Z: ClassVar[int]: Atomic number of the species.

net_charge: ClassVar[int] = 1: Net charge of the ionic core seen by the Rydberg electron (1 for neutral atoms, 2 for singly-charged ions).

i_c: ClassVar[float]: Nuclear spin.

number_valence_electrons: ClassVar[int]: Number of valence electrons (i.e. 1 for alkali atoms and 2 for alkaline earth atoms).

mass_number: ClassVar[int]: Mass number A (i.e. number of nucleons) of the isotope.

atomic_mass_u: ClassVar[float]

Relative atomic mass of the neutral atom in unified atomic mass units (u).

I.e. the mass including all Z electrons and their binding energies.

If not said otherwise, the values are taken from Table I (the atomic mass table) of the AME2020 atomic mass evaluation (M. Wang et al., Chin. Phys. C 45, 030003 (2021), https://doi.org/10.1088/1674-1137/abddaf). Concretely, we use the unrounded version of that table, which is published as the text file https://www-nds.iaea.org/amdc/ame2020/mass_1.mas20.txt, where the last column holds the atomic mass.

ground_state_shell: ClassVar[tuple[int, int]]: Shell (n, l) describing the electronic ground state configuration.

additional_allowed_shells: ClassVar[list[tuple[int, int]]] = []: Additional allowed shells (n, l), which (n, l) is smaller than the ground state shell.

core_electron_configuration: ClassVar[str]: Electron configuration of the core electrons, e.g. 4p6 for Rb or 5s for Sr.

nuclear_dipole: ClassVar[float] = 0.0: Nuclear dipole moment of the species.

alpha_closed_shell_core: ClassVar[float] = 0.0: Static dipole polarizability (a.u.) of the core including the closed-shell electrons. It is used for the electric-dipole moment correction due to the core, see e.g. Weisheit Phys. Rev. A 5, 1621, 1972 (https://link.aps.org/doi/10.1103/PhysRevA.5.1621). The core-polarization corrected electric-dipole operator is d(r) = r - alpha_core/r^2 * (1 - exp(-(r/r_c)^3)). This is also used for model potentials including the core-polarization term, see e.g. PotentialMarinescu1994.

r_c_dipole_operator: ClassVar[float | None] = None: Cutoff radius (a.u.) of the core-polarization corrected electric-dipole operator (see alpha_closed_shell_core). The default None means no correction is applied (i.e. the bare electric-dipole operator d(r) = r is used). If not said otherwise, r_c is fitted to the NIST ASD line strengths of the principal series (ground state -> np_j).

property s_c: float: Total spin of the core electrons (0 for alkali atoms, 0.5 for alkaline earth atoms).

property s_r: float: Total spin of the rydberg electron (always 0.5).

is_allowed_shell(n, l, s_tot)[source]

Check if the quantum numbers describe an allowed shell.

I.e. whether the shell is above the ground state shell.

Parameters:

n (int) – Principal quantum number
l (int | Unknown) – Orbital angular momentum quantum number. If it is unknown (as it is the case for the perturber channels of the MQDT models), the shell configuration is only restricted to n being equal to or above the ground state shell.
s_tot (float | Unknown) – Total spin quantum number

Return type:

bool

Returns:

True if the quantum numbers specify a shell equal to or above the ground state shell, False otherwise.

get_corrected_rydberg_constant(unit=None)[source]

Return the corrected Rydberg constant in the desired unit.

Overloads:

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

Parameters:

unit (str | None)

Return type:

PlainQuantity[float] | float

The corrected Rydberg constant is defined as

\[R_M = R_\infty \frac{m_{Core}}{m_{Core} + m_e}\]

where \(R_\infty\) is the Rydberg constant for infinite nuclear mass, \(m_{Core}\) is the mass of the core, and \(m_e\) is the mass of the electron.

Parameters:: unit (str | None) – Desired unit for the corrected Rydberg constant. Default None returns a Pint quantity.
Returns:: Corrected Rydberg constant in the desired unit.
Return type:: PlainQuantity[float] | float

property mass_core_u: float

The mass of the ionic core in unified atomic mass units (u).

The core is the neutral atom stripped of the Rydberg electron and of all further electrons that are missing for an ion, i.e. of net_charge electrons in total. (The binding energies of these electrons are neglected, they only contribute on the order of 1e-8 u.)

property reduced_mass_au: float

The reduced mass mu in atomic units.

The reduced mass in atomic units \(\mu / m_e\) is given by

\[\frac{\mu}{m_e} = \frac{m_{Core}}{m_{Core} + m_e} = \frac{1}{1 + m_e / m_{Core}}\]

where \(m_{Core}\) is given by mass_core_u.