unzhakov
33ed4f7e44
- Add proper type annotations to all source files - Fix return types for numpy operations (np.asarray with dtype=np.float64) - Add type ignores for untyped scipy/pandas imports - Fix parameter type annotations (Callable, Sequence, Optional, etc.) - Add TYPE_CHECKING imports for forward references - Fix fitter.py attribute access issues (model_values, residuals, chi2_per_dof) - Add cw_extractor.py module-level type: ignore for complex scientific code - Update pyproject.toml to exclude notebooks from mypy - Run black and ruff for formatting and linting
284 lines
9.7 KiB
Python
284 lines
9.7 KiB
Python
# components/radiative.py
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import numpy as np
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from scipy.special import spence # type: ignore[import-untyped]
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from beta_spectrum.base import SpectrumComponent
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from beta_spectrum.constants import (
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MP_MEV,
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ME_MEV,
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ALPHA,
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HBAR_C_MEV_FM,
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EULER_GAMMA,
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R0_FM,
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)
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class RadiativeCorrection(SpectrumComponent):
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"""
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Outer radiative correction R(W, W0) = 1 + delta_1 + delta_2.
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Implements:
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- delta_1: O(alpha) universal Sirlin function g(W, W0) from
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Sirlin (1967) Eq. (20b), with endpoint soft-photon resummation
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per Sirlin (1987) Eq. (53).
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- delta_2: O(Z*alpha^2) finite nuclear size correction from
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Sirlin (1987) Eq. (1-10), using the modified Gaussian model.
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This is the INCLUSIVE correction suitable for:
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- Magnetic spectrometers
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- Detectors where bremsstrahlung is not detected
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- Precision at 1% level or worse
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The O(Z^2*alpha^3) correction is neglected for Z < 30 (spec Section 5).
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Inner radiative corrections are absorbed into effective coupling constants
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and are not part of the spectrum shape calculation.
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"""
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def __init__(
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self,
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W0: float,
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Z: int = 0,
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A: int | None = None,
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use_endpoint_resummation: bool = True,
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delta_cut: float = 1e-3,
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):
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"""
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Args:
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W0: Endpoint energy in natural units m_e=c=h_bar=1
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Z: Nuclear charge of daughter nucleus
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A: Mass number (optional, affects nuclear model correction)
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use_endpoint_resummation: Apply Eq.(53) to handle ln(W0 - W) divergence
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delta_cut: Only apply resummation when (W0 - W) < delta_cut (spec Section 3.4)
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"""
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self.W0 = W0
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self.Z = Z
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self.A = A
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self.use_endpoint_resummation = use_endpoint_resummation
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self.delta_cut = delta_cut
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self.m_p = MP_MEV / ME_MEV # ~1836.15 (proton mass in m_e units)
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self.gamma_E = EULER_GAMMA # Euler-Mascheroni constant
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# Precompute constant terms
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self._outer_normalization = ALPHA / (2.0 * np.pi) # ~0.00116
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self._subtraction_term = 3.0 * np.log(self.m_p / (2.0 * self.W0))
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# Precompute O(Z*alpha^2) energy-independent nuclear part if A is given
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self._delta_F = self._compute_nuclear_model_correction(Z, A)
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def __call__(self, W: np.ndarray) -> np.ndarray:
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"""
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Calculate R(W, W0) = 1 + delta_1(W, W0) + delta_2(Z, W).
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Args:
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W: Electron total energy array (in natural m_e=c=h_bar=1 units)
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Returns:
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Radiative correction factor array
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"""
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W = np.asarray(W, dtype=float)
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# Avoid numerical issues exactly at endpoint W0
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eps = 1e-9
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mask_finite = W < (self.W0 - eps)
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delta_R = np.zeros_like(W, dtype=float)
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if np.any(mask_finite):
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W_finite = W[mask_finite]
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# O(alpha) correction (Sirlin 1967)
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delta_1 = self._delta_1(W_finite)
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# O(Z*alpha^2) correction (Sirlin 1987)
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delta_2 = self._delta_2(W_finite)
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delta_R_finite = delta_1 + delta_2
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delta_R[mask_finite] = delta_R_finite
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return np.asarray(1.0 + delta_R, dtype=np.float64)
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def _delta_1(self, W: np.ndarray) -> np.ndarray:
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"""
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O(alpha) universal Sirlin function g(W, W0) per Sirlin (1967) Eq. (20b).
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g(W, W0) = 3*ln(m_p/(2*W0)) - 3/4
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+ 4*(tanh_inv_beta/beta - 1)*[(W0-W)/(3W) - 3/2 + ln(2*(W0-W))]
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+ (4/beta)*L(2*beta/(1+beta))
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+ (tanh_inv_beta/beta)*[2*(1+beta^2) + (W0-W)^2/(6*W^2) - 4*tanh_inv_beta]
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where L(x) = -Li_2(x) is the Spence function (dilogarithm).
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The correction is delta_1 = (alpha/2pi) * (g(W, W0) - subtraction_term).
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The subtraction_term cancels the constant part in the Hayen reformulation.
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"""
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beta = self._safe_beta(W)
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tanh_inv_beta_beta = self._safe_tanh_inv_beta_over_beta(beta)
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# Dilogarithm term: L(2*beta/(1+beta)) = -Li_2(2*beta/(1+beta))
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arg = 2.0 * beta / (1.0 + beta)
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arg = np.minimum(arg, 1.0 - 1e-12) # Avoid numerical problems at arg=1
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dilog_term = (4.0 / beta) * spence(1.0 - arg)
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# arctanh factor: (tanh^{-1}(beta)/beta) - 1
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atanh_factor = tanh_inv_beta_beta - 1.0
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# Energy difference
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delta_W = self.W0 - W
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delta_W = np.where(delta_W > 0, delta_W, 1e-12)
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if self.use_endpoint_resummation:
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# Apply soft-photon resummation from Sirlin (1987)
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# Replace C(beta)*ln(W0-W) with C(beta)*((W0-W)^{t(beta)}-1)/t(beta)
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# Only near endpoint: (W0 - W) < delta_cut (spec Section 3.4)
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t_beta = (2.0 * ALPHA / np.pi) * atanh_factor
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small_t = np.abs(t_beta) < 1e-6
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resummed_log = np.empty_like(delta_W)
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resummed_log[:] = np.log(delta_W)
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near_endpoint = delta_W < self.delta_cut
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if np.any(near_endpoint):
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resummed_log[near_endpoint] = (
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np.power(delta_W[near_endpoint], t_beta[near_endpoint]) - 1.0
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) / t_beta[near_endpoint]
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small_t_mask = near_endpoint & small_t
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resummed_log[small_t_mask] = np.log(delta_W[small_t_mask])
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log_term = np.log(2.0) + resummed_log
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else:
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log_term = np.log(2.0 * delta_W)
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# Energy-dependent term
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term2 = 4.0 * atanh_factor * (delta_W / (3.0 * W) - 1.5 + log_term)
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# Beta-dependent term (no divergence)
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term3 = tanh_inv_beta_beta * (
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2.0 * (1.0 + beta**2)
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+ (delta_W**2) / (6.0 * W**2)
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- 4.0 * tanh_inv_beta_beta
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)
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# Leading constant
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const_term = -0.75
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g_func = const_term + dilog_term + term2 + term3
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return np.asarray(
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self._outer_normalization * (g_func - self._subtraction_term),
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dtype=np.float64,
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)
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def _delta_2(self, W: np.ndarray) -> np.ndarray:
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"""
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O(Z*alpha^2) finite nuclear size correction per Sirlin (1987).
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delta_2(Z, W) = Z * alpha^2 * (Delta_1_4(W) + Delta_F)
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where:
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- Delta_1_4(W) = ln(m_p) - (5/12)*ln(2*W) + 43/18
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(energy-dependent relativistic part)
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- Delta_F(Z, A) = nuclear-structure-dependent part from modified
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Gaussian model (Eq. 10 of Sirlin 1987)
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For Z=0, this correction is zero.
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"""
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if self.Z == 0:
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return np.zeros_like(W)
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# Energy-dependent part: Delta_1^0(W) + Delta_4(W)
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# From Sirlin 1987 relativistic limit
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Delta_1_4 = np.log(self.m_p) - (5.0 / 12.0) * np.log(2.0 * W) + 43.0 / 18.0
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# Total O(Z*alpha^2) correction
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delta_2 = self.Z * ALPHA**2 * (Delta_1_4 + self._delta_F)
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return np.asarray(delta_2, dtype=np.float64)
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def _compute_nuclear_model_correction(self, Z: int, A: int | None) -> float:
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"""
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Compute the nuclear-structure-dependent part Delta_F of the O(Z*alpha^2) correction.
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Uses the modified Gaussian model from Sirlin (1987) Eq. (10):
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Delta_F = ln(Lambda/M) - kappa_1(Z)
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where:
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- Lambda = sqrt(6)/a, with a = r_0 * A^{1/3} (rms charge radius)
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- M = proton mass
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- kappa_1(Z) = 0.5 * [gamma_E + ln(3/(2*k^2)) + 2*alpha/(2+3*alpha)]
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- k^2 = (3/2) * (2+5*alpha)/(2+3*alpha)
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- alpha = (Z-2)/3
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- r_0 = 1.2 fm (Wilkinson)
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If A is not specified, returns 0 (no nuclear model correction).
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"""
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if A is None:
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return 0.0
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# Nuclear radius from Wilkinson's r_0
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a_fm = R0_FM * A ** (1.0 / 3.0) # rms charge radius in fm
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a_me = a_fm / (HBAR_C_MEV_FM / ME_MEV) # convert to m_e^{-1} units
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# Lambda = sqrt(6)/a
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Lambda = np.sqrt(6.0) / a_me
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# M/Lambda ratio for the log term
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M_over_Lambda = self.m_p / Lambda
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# kappa_1(Z) from Sirlin 1987
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alpha_param = (Z - 2.0) / 3.0
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k_sq = 1.5 * (2.0 + 5.0 * alpha_param) / (2.0 + 3.0 * alpha_param)
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kappa_1 = 0.5 * (
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self.gamma_E
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+ np.log(3.0 / (2.0 * k_sq))
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+ 2.0 * ALPHA / (2.0 + 3.0 * ALPHA)
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)
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delta_F = float(np.log(M_over_Lambda) - kappa_1)
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return delta_F
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def _safe_beta(self, W: np.ndarray) -> np.ndarray:
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"""
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Compute beta = p/W = sqrt(1 - 1/W^2) with safe handling near threshold.
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At W=1 (threshold), beta=0. We use a floor to avoid division by zero.
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"""
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beta = np.sqrt(np.maximum(1.0 - 1.0 / W**2, 0.0))
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beta = np.maximum(beta, 1e-12)
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return beta
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def _safe_tanh_inv_beta_over_beta(self, beta: np.ndarray) -> np.ndarray:
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"""
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Compute tanh^{-1}(beta)/beta with numerical stability for small beta.
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For beta < 1e-6, use Taylor expansion:
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tanh^{-1}(beta)/beta = 1 + beta^2/3 + beta^4/5 + ...
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For beta >= 1e-6, use the direct formula:
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tanh^{-1}(beta)/beta = 0.5 * ln((1+beta)/(1-beta)) / beta
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Per spec Section 3.3, this avoids division by zero and loss of precision.
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"""
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result = np.empty_like(beta)
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small_beta = beta < 1e-6
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# Taylor series for small beta: 1 + beta^2/3 + beta^4/5 + beta^6/7
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beta_sq = beta**2
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result[small_beta] = (
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1.0
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+ beta_sq[small_beta] / 3.0
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+ beta_sq[small_beta] ** 2 / 5.0
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+ beta_sq[small_beta] ** 3 / 7.0
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)
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# Direct computation for larger beta
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not_small = ~small_beta
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if np.any(not_small):
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result[not_small] = (
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0.5
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* np.log((1.0 + beta[not_small]) / (1.0 - beta[not_small]))
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/ beta[not_small]
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)
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return result
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