line_profile¶

line_profile.py — High-level LineProfile class for Stark-Zeeman calculations.

Typical usage:

import numpy as np
from starkzee.line_profile import LineProfile

lp = LineProfile(n_u=3, n_l=2, B=100.0, Ne_m3=1e23, Te_ev=5.0, species='H')

# Supply a grid in any of: energy [eV], wavelength [nm],
# frequency [THz], or wavenumber [cm⁻¹].
lp.compute_profile(np.linspace(1.80, 2.00, 2000), grid_type='energy_ev')
lp.compute_profile(np.linspace(620, 660, 2000),   grid_type='wavelength_nm')
lp.compute_profile(np.linspace(450, 490, 2000),   grid_type='frequency_thz')
lp.compute_profile(np.linspace(15000, 16000, 2000), grid_type='wavenumber_cm')

# Results are always available in all unit systems
lp.energies_ev          # energy grid [eV]
lp.detuning_ev          # E - E0       [eV]
lp.wavelengths_nm       # wavelength grid [nm]
lp.frequencies_thz      # frequency grid [THz]
lp.wavenumbers_cm       # wavenumber grid [cm⁻¹]
lp.detuning_nm          # λ - λ0       [nm]
lp.detuning_thz         # f - f0       [THz]
lp.detuning_cm          # ν̃ - ν̃0     [cm⁻¹]
lp.profile_pi           # π component
lp.profile_sig_plus     # σ+ component
lp.profile_sig_minus    # σ- component
lp.profile              # intensity at view_angle_deg (default 90°)
lp.profile_transverse   # π + 0.5*(σ+ + σ-)  (90° observation)
lp.profile_parallel     # σ+ + σ-             (0° observation)

# Discrete transitions at a single field configuration
lp.compute_discrete(Fz=0.0, Fx=1e8)
lp.discrete.energy_ev    # transition energies [eV]
lp.discrete.detuning_ev  # detuning from E0   [eV]
lp.discrete.wavelength_nm
lp.discrete.frequency_thz
lp.discrete.wavenumber_cm
lp.discrete.q            # polarization (0, +1, -1)
lp.discrete.strength     # \|d_q\|²  [a₀²]

class starkzee.line_profile.DiscreteTransitions(energy_ev, q, strength, upper_idx, lower_idx, E0)[source]¶

Bases: object

Discrete Stark-Zeeman dipole transitions at a single (B, Fz, Fx) configuration.

energy_ev¶

Transition energies E_upper − E_lower [eV], sorted ascending.

Type:: ndarray

detuning_ev¶

Detuning from the field-free line center [eV].

Type:: ndarray

wavelength_nm¶

Photon wavelength for each transition [nm].

Type:: ndarray

frequency_thz¶

Photon frequency [THz].

Type:: ndarray

wavenumber_cm¶

Photon wavenumber [cm⁻¹].

Type:: ndarray

q¶

Polarization index: 0 = π, +1 = σ+, −1 = σ−.

Type:: ndarray of int

strength¶

Dipole matrix element squared |d_q(i→j)|² [a₀²].

Type:: ndarray

upper_idx¶

Upper eigenstate index (0 … 2n_u²−1).

Type:: ndarray of int

lower_idx¶

Lower eigenstate index (0 … 2n_l²−1).

Type:: ndarray of int

class starkzee.line_profile.LineProfile(n_u, n_l, B, Ne_m3, Te_ev, species='H', Ti_ev=None, view_angle_deg=90)[source]¶

Bases: object

Stark-Zeeman line profile for a single hydrogenic n_u → n_l transition.

Stores all input parameters and computed results as attributes. Call compute_profile() to run the static profile solver and compute_discrete() to enumerate the discrete eigenstate transitions at a specific field configuration.

Parameters:

n_u (int) – Upper and lower principal quantum numbers.
n_l (int) – Upper and lower principal quantum numbers.
B (float) – Magnetic field [T].
Ne_m3 (float) – Electron density [m⁻³].
Te_ev (float) – Electron temperature [eV].
species (str, optional) – Emitting species: 'H' / 'hydrogen', 'D' / 'deuterium', or 'T' / 'tritium'. Default is 'H'.
Ti_ev (float, optional) – Ion temperature [eV]. When supplied, compute_profile() applies thermal Doppler broadening automatically after the static Stark-Zeeman calculation. Default is None (no Doppler broadening).
view_angle_deg (float, optional) – Default observation angle relative to B [degrees]. Used by compute_profile() to set lp.profile via the Stokes formula. Can be overridden per-call in compute_profile(). Default is 90 (perpendicular to B).

GRID_TYPES = ('energy_ev', 'wavelength_nm', 'frequency_thz', 'wavenumber_cm')¶: Accepted values for the grid_type parameter of compute_profile().

compute_profile(grid, grid_type='energy_ev', view_angle_deg=None, **kwargs)[source]¶

Compute the static Stark-Zeeman profile on the supplied grid.

Parameters:

grid (array-like) – Spectral axis values in the units specified by grid_type.
grid_type (str, optional) –
Unit system of grid. One of:

'energy_ev'
Photon energy [eV] (default).

'wavelength_nm'
Vacuum wavelength [nm].

'frequency_thz'
Photon frequency [THz].

'wavenumber_cm'
Wavenumber [cm⁻¹].
view_angle_deg (float, optional) – Observation angle relative to B [degrees] for this call. When given, overrides the class-level default for lp.profile; the class attribute is not modified. When omitted, falls back to self.view_angle_deg (default 90).
**kwargs – Forwarded to calculate_static_profile() (num_f, num_mu, use_screening, quadratic_zeeman, fine_structure, frequency_dependent_width).

Returns:

Allows method chaining.

Return type:

self

Notes

After this call all spectral-axis attributes are populated regardless of which grid_type was supplied: energies_ev, wavelengths_nm, frequencies_thz, wavenumbers_cm, and the corresponding detuning_* arrays.

compute_discrete(Fz=0.0, Fx=0.0, **kwargs)[source]¶

Enumerate discrete eigenstate transitions at field (Fz, Fx) [V/m].

All keyword arguments are forwarded to discrete_transitions() (quadratic_zeeman, fine_structure, min_strength).

Returns self to allow method chaining.

property profile_transverse¶: π + 0.5*(σ+ + σ−) — total intensity at 90° to B.

property profile_parallel¶: σ+ + σ− — total intensity along B (0°).

profile_at_angle(theta_deg)[source]¶

Total intensity at observation angle theta_deg relative to B.

Uses the standard Stokes formula:: I(θ) = I_π sin²θ + ½(I_σ+ + I_σ−)(1 + cos²θ)