optmat.gas.two_photon_bound#

The bound two-photon levels of the noble gases (OEP 6, Phase 2a: curation only).

Below half the ionisation energy, two photons of a field can excite a noble gas’s ground state to an even-parity level. This module states what is curated about those levels, per gas (two_photon_bound_levels()):

the even levels with \(J = 0, 1, 2\) below the ionisation energy, from the NIST level lists held as returned (nist_asd_2026; helium’s singlets only). For one linear polarisation and equal photons, \(J = 0\) and 2 are reached; \(J = 1\) only with unequal photons or another polarisation;
each level’s curated two-photon strengths, calculated or measured, in one convention: \(\delta^{TP}\) per level (summed over \(M_J\)), parallel linear polarisation, equal photons, in atomic units, and the frequency-integrated cross section

\[\sigma_0^{(2)} = 2\pi^3 \alpha^2 a_0^4\, \omega_\mathrm{au}^2\, \delta^{TP},\]

with the line profile normalised in the two-photon angular frequency, for coherent light (TC-952). A measured \(\sigma_0^{(2)}\) is corrected for the photon statistics its source used;
each level’s curated photoionisation cross sections.

It is a record of facts with no evaluator. A line profile, the excited population and the (2+1) ionisation that follows need the theory OEP 6 asks for in Q9, and are deferred to its Phase 2b (TC-945). Helium’s and xenon’s strengths are checked against independent values (assessment = "checked"). Neon’s, argon’s and krypton’s are "unresolved", each with its reason.

Examples#

>>> xenon = two_photon_bound_levels("Xe")
>>> level = xenon.level("5p5.(2P*<3/2>).6p", "2[1/2]", 0)
>>> round(level.wavelength * 1e9, 2)  # the exciting photon's vacuum wavelength, nm
249.63
>>> [(s.source, s.kind) for s in xenon.strengths_of(level)]
[('henriksson_2005', 'calculated'), ('kroll_1990', 'measured')]

Module Attributes

`BOUND_DERIVATION_VERSION`	The version of the stored records' derivation.
`SIGMA0_PER_DELTA`	\(\sigma_0^{(2)} / (\omega_\mathrm{au}^2 \delta^{TP})\), m^4 (TC-952).

Functions

`sigma0_from_delta`(delta, omega)	Return the frequency-integrated cross section of a two-photon strength.
`two_photon_bound_levels`(gas)	Return what is curated about a noble gas's bound two-photon levels.

Classes

`BoundLevel`(configuration, term, j, energy, ...)	An even level below the ionisation energy, as NIST lists it.
`BoundPhotoionisation`(level, unassigned, ...)	A curated photoionisation cross section of an excited level.
`BoundStrength`(level, unassigned, dataset, ...)	A curated two-photon strength of a level, in the canonical convention.
`TwoPhotonBoundLevels`(gas, ...[, ...])	The bound two-photon levels of a noble gas and what is curated about them.

optmat.gas.two_photon_bound.BOUND_DERIVATION_VERSION: Final = 1#: The version of the stored records’ derivation.

class optmat.gas.two_photon_bound.BoundLevel(configuration, term, j, energy, printed, reach)[source]#

Bases: object

An even level below the ionisation energy, as NIST lists it.

Attributes:

configurationstr: NIST’s configuration, e.g. "5p5.(2P*<3/2>).6p".
termstr: NIST’s term, e.g. "2[1/2]".
jint: The total angular momentum.
energyfloat: Above the ground level, J.
printedstr: NIST’s level, cm^-1, as printed (with any brackets).
reachstr: "linear" (J = 0, 2: reached by two equal, linearly polarised photons) or "other" (J = 1: only with unequal photons or another polarisation).

configuration: str#

energy: float#

j: int#

property key: str#

The level as "configuration|term|J".

Returns:

str: The key the selection file uses.

printed: str#

reach: str#

term: str#

property wavelength: float#

The vacuum wavelength of each of two equal photons that reach it, m.

Returns:

float: \(2 hc / E\).

class optmat.gas.two_photon_bound.BoundPhotoionisation(level, unassigned, dataset, source, omega, sigma, use)[source]#

Bases: object

A curated photoionisation cross section of an excited level.

Attributes:

levelstr: The level’s key, or empty where unassigned.
unassignedstr: Why it is not assigned, or empty.
datasetstr: The curated dataset.
sourcestr: The source record.
omegatuple of float or None: The ionising photon’s angular frequency, rad/s; None where the source states none (a threshold value at an unstated energy).
sigmatuple of float: The cross section, m^2.
usestr: The dataset’s use.

dataset: str#

level: str#

omega: tuple[float | None, ...]#

sigma: tuple[float, ...]#

source: str#

unassigned: str#

use: str#

class optmat.gas.two_photon_bound.BoundStrength(level, unassigned, dataset, row, source, kind, delta, sigma0, convention, derived, reason)[source]#

Bases: object

A curated two-photon strength of a level, in the canonical convention.

Attributes:

levelstr: The level’s key (BoundLevel.key), or empty where unassigned.
unassignedstr: Why it is not assigned to a level, or empty.
datasetstr: The curated dataset.
rowstr: Its row.
sourcestr: The source record.
kindstr: "calculated" or "measured".
deltafloat or None: \(\delta^{TP}\) per level, a.u.: as printed, or derived from a cross section; None for an unassigned cross section.
sigma0float or None: \(\sigma_0^{(2)}\), m^4, at the level’s NIST photon frequency; None where unassigned.
conventionstr: How it was obtained: "per_level", "one_component" (times 4/3) or "sigma0".
derivedbool: True unless the stored quantity is as printed.
reasonstr: Why this level.

convention: str#

dataset: str#

delta: float | None#

derived: bool#

kind: str#

level: str#

reason: str#

row: str#

sigma0: float | None#

source: str#

unassigned: str#

optmat.gas.two_photon_bound.SIGMA0_PER_DELTA: Final = 2.589493367193569e-44#: \(\sigma_0^{(2)} / (\omega_\mathrm{au}^2 \delta^{TP})\), m^4 (TC-952).

class optmat.gas.two_photon_bound.TwoPhotonBoundLevels(gas, derivation_version, ionisation, levels, strengths, photoionisation, assessment, assessment_reason, input_digests=<factory>, *, status='user', status_reason='', modified=(), base='')[source]#

Bases: Identified

The bound two-photon levels of a noble gas and what is curated about them.

Attributes:

gasGas: The species.
derivation_versionint: BOUND_DERIVATION_VERSION when it was derived.
ionisationfloat: The ionisation energy, J.
levelstuple of BoundLevel: The even J = 0, 1, 2 levels below it, by energy.
strengthstuple of BoundStrength: The curated two-photon strengths.
photoionisationtuple of BoundPhotoionisation: The curated photoionisation cross sections of the levels.
assessmentstr: "checked" or "unresolved".
assessment_reasonstr: Why.
input_digestsMapping of str to str: SHA-256 digests of what it was derived from.

EVALUATION_VERSION: ClassVar[int] = 1#

IDENTITY_KIND: ClassVar[str] = 'two_photon_bound_levels'#

assessment: str#

assessment_reason: str#

derivation_version: int#

property digest: str#

The record’s digest, identity.digest.

Returns:

str: 64 hexadecimal digits.

gas: Gas#

input_digests: Mapping[str, str]#

ionisation: float#

level(configuration, term, j)[source]#

Return a listed level.

Parameters:

configurationstr: NIST’s configuration.
termstr: NIST’s term.
jint: The total angular momentum.

Returns:

BoundLevel: The level.

Raises:

DataError: If it is not listed.

levels: tuple[BoundLevel, ...]#

photoionisation: tuple[BoundPhotoionisation, ...]#

photoionisation_of(level)[source]#

Return the photoionisation cross sections assigned to a level.

Parameters:

levelBoundLevel: A listed level.

Returns:

tuple of BoundPhotoionisation: Its cross sections.

strengths: tuple[BoundStrength, ...]#

strengths_of(level)[source]#

Return the strengths assigned to a level.

Parameters:

levelBoundLevel: A listed level.

Returns:

tuple of BoundStrength: Its strengths, calculated and measured.

optmat.gas.two_photon_bound.sigma0_from_delta(delta, omega)[source]#

Return the frequency-integrated cross section of a two-photon strength.

Parameters:

deltafloat: \(\delta^{TP}\) per level, parallel linear polarisation, equal photons, atomic units.
omegafloat: The photon’s angular frequency, rad/s: half the level’s over hbar.

Returns:

float: \(\sigma_0^{(2)} = 2\pi^3\alpha^2 a_0^4 \omega_\mathrm{au}^2 \delta\), m^4, the profile normalised in the two-photon angular frequency, coherent light (TC-952).

Examples

>>> f"{sigma0_from_delta(1.0, AU_ANGULAR_FREQUENCY):.5e}"
'2.58949e-44'

optmat.gas.two_photon_bound.two_photon_bound_levels(gas)[source]#

Return what is curated about a noble gas’s bound two-photon levels.

Parameters:

gasGas or str: He, Ne, Ar, Kr or Xe.

Returns:

TwoPhotonBoundLevels: The record.

Raises:

UnavailableModelError: For any other gas.

Examples

>>> two_photon_bound_levels("He").assessment
'checked'