unzhakov
0c5c53688d
Add implementation for the basic set of spectrum components: Primary ------- - Phase Space - Fermi Function Corrections ----------- - Atomic: - Screening - Atomic exchange - E/M and finite size: - Finite nucleus size and charge distribution - Radiative
98 lines
2.5 KiB
Python
98 lines
2.5 KiB
Python
import numpy as np
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from beta_spectrum.base import SpectrumComponent
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from beta_spectrum.utils import momentum
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from beta_spectrum.constants import ALPHA
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class ScreeningCorrection(SpectrumComponent):
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"""
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Atomic screning correction S(Z, W).
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Implements:
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- Ratio method (non-screened to screened F(Z,W)*p*W) using shifted energy W -> W_tilde
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- Smooth switching function to regularize low-energy behaviour
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S(W) = 1 + f(W) * (S_raw(W) - 1
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"""
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def __init__(
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self,
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fermi_function,
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V0: float = None,
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Ws: float = 1.01,
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Delta: float = 0.005,
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eps: float = 1e-6,
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C=0.015,
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):
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"""
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Parameters
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----------
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Z : nuclear charge
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fermi_function : callable
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Instance of FermiFunction class
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V0 : screening potential (in m_e units)
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If None, uses simple scaling law
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Ws : switching midpoint
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Delta : switching width
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eps : numerical floor for W_tilde
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"""
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self.fermi = fermi_function
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self.Z = fermi_function.Z
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self.Ws = Ws
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self.Delta = Delta
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self.eps = eps
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self._C = C
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self.V0 = V0 if V0 is not None else self._estimate_V0()
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# --------------------
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# Core evaluation
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# --------------------
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def __call__(self, W: np.ndarray) -> np.ndarray:
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W = np.asarray(W)
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# Energy shift by screening potential V0
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W_tilde = self._screened_energy(W)
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# Momenta
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p = momentum(W)
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p_tilde = momentum(W_tilde)
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# Fermi functions
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F = self.fermi(W)
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F_tilde = self.fermi(W_tilde)
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# Raw ratio model (for W >> V0)
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S_raw = (F_tilde / F) * (p_tilde * W_tilde) / (p * W)
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# Smooth switching
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f = self._switching_function(W)
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return 1.0 + f * (S_raw - 1.0)
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# --------------------
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# Helpers
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# --------------------
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def _screened_energy(self, W):
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"""
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Apply energy shift W -> W_tilde with safe numerical floor
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"""
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W_tilde = W - self.V0
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return np.maximum(W_tilde, 1.0 + self.eps)
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def _switching_function(self, W):
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"""
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Logistic switching function
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"""
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return 1.0 / (1.0 + np.exp((self.Ws - W) / self.Delta))
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def _estimate_V0(self):
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"""
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Simple scaling estimate for screening potential.
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V0 ~ alpha * Z^(4/3) * C
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C ~ 0.01-0.02 (tunable constant)
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"""
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return ALPHA * self.Z ** (4.0 / 3.0) * self._C
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