ElementPropertiesYtterbium174

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

Z	Atomic number of the species.
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.
atomic_mass_u	Relative atomic mass of the neutral atom in unified atomic mass units (u).
core_electron_configuration	Electron configuration of the core electrons, e.g. 4p6 for Rb or 5s for Sr.
ground_state_shell	Shell (n, l) describing the electronic ground state configuration.
i_c	Nuclear spin.
mass_core_u	The mass of the ionic core in unified atomic mass units (u).
mass_number	Mass number A (i.e. number of nucleons) of the isotope.
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.
number_valence_electrons	Number of valence electrons (i.e. 1 for alkali atoms and 2 for alkaline earth atoms).
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.

class rydstate.species.ytterbium.ElementPropertiesYtterbium174(*args: object, **kwargs: object)

Parameters:

• args (object)

• kwargs (object)

Return type:

CachedT

species: ClassVar[str] = 'Yb174'

The short name of the atomic species.

i_c: ClassVar[float] = 0

Nuclear spin.

mass_number: ClassVar[int] = 174

Mass number A (i.e. number of nucleons) of the isotope.

atomic_mass_u: ClassVar[float] = 173.938867545

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.

nuclear_dipole: ClassVar[float] = 0.0

Nuclear dipole moment of the species.

Z: ClassVar[int] = 70

Atomic number of the species.

additional_allowed_shells: ClassVar = [(5, 2), (5, 3), (5, 4)]

Additional allowed shells (n, l), which (n, l) is smaller than the ground state shell.

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.

core_electron_configuration: ClassVar[str] = '4f14.6s'

Electron configuration of the core electrons, e.g. 4p6 for Rb or 5s for Sr.

get_corrected_rydberg_constant(unit=None)

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

ground_state_shell: ClassVar[tuple[int, int]] = (6, 0)

Shell (n, l) describing the electronic ground state configuration.

is_allowed_shell(n, l, s_tot)

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.

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.)

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).

number_valence_electrons: ClassVar[int] = 2

Number of valence electrons (i.e. 1 for alkali atoms and 2 for alkaline earth atoms).

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 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.

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).