The resummation was previously applied to all energy points when the flag was set, causing resummed and standard modes to differ everywhere. Per spec, it should only replace C(beta)*ln(W0-W) with the resummed power-law form when (W0-W) < delta_cut (~1e-3). Adds delta_cut parameter (default 1e-3) and corrects the resummation switch test to verify identical results far from endpoint.
380 lines
15 KiB
Python
380 lines
15 KiB
Python
# tests/test_radiative.py — RadiativeCorrection unit tests
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"""
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Why test this?
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--------------
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The outer radiative correction δᵣ(W,W₀) accounts for bremsstrahlung photons emitted
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along with the beta electron. It's typically a small positive correction (~0.1–1%) but has
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a logarithmic singularity at W → W₀ (endpoint) that must be handled by soft-photon resummation.
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Key physics:
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- δᵣ > 0 generally: virtual photon loops and real bremsstrahlung enhance the rate.
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- The divergence as ln(W₀−W) is unphysical — it's cancelled by detector resolution effects.
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Our implementation uses Eq.(53) resummation to tame this.
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We test:
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1. **No NaN/inf at endpoint**: With resummation, R(W→W₀) must be finite. Without it,
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the logarithm diverges — we verify both modes work correctly.
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2. **Small correction magnitude**: δᵣ is O(α/π) ≈ 0.001–0.01, so R = 1+δᵣ should be
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close to unity (within a factor of ~2).
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3. **Endpoint resummation produces finite values**: The key feature that distinguishes
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this implementation from the standard formula.
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Common practice: For functions with known singularities, always test both "handled" and
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"unhandled" modes to verify the fix works correctly. This is exactly what `use_endpoint_resummation` does here.
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"""
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import numpy as np
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from beta_spectrum.components.radiative import RadiativeCorrection
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class TestRadiativeBasicProperties:
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"""Test fundamental properties of the radiative correction."""
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def test_near_unity_correction(self):
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"""δᵣ is O(α/π) ≈ 0.001, so R = 1+δᵣ should be within ~2x unity."""
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rc = RadiativeCorrection(W0=5.0, use_endpoint_resummation=True)
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W_test = np.array([2.0])
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result = rc(W_test)
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assert (
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0.5 < result[0] < 3.0
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), f"Radiative correction should be near unity: got {result[0]}"
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def test_positive_values(self):
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"""R(W,W₀) must always be positive — it's a multiplicative factor."""
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rc = RadiativeCorrection(W0=5.0)
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W_test = np.linspace(1.1, 4.9, 20)
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result = rc(W_test)
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assert np.all(result > 0), "Radiative correction must be positive"
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class TestRadiativeEndpointHandling:
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"""Test how endpoint divergence is handled."""
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def test_resummation_produces_finite_values_at_endpoint(self):
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"""With resummation enabled, R(W₀−ε) must be finite for small ε.
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Without Eq.(53), ln(ΔW) → −∞ as ΔW → 0. The resummed version replaces this
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with (ΔW)^t(β) which stays finite. This is the most critical test of our implementation.
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"""
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rc = RadiativeCorrection(W0=5.0, use_endpoint_resummation=True)
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# Very close to endpoint: W₀ − ε where ε = 0.001
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W_near_end = np.array([4.999])
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result = rc(W_near_end)
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assert not np.isnan(result[0]), "Resummed correction must be finite at endpoint"
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assert not np.isinf(
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result[0]
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), "Resummed correction must not diverge at endpoint"
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def test_standard_mode_diverges(self):
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"""Without resummation, δᵣ → −∞ as W → W₀ (logarithmic divergence).
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We verify this by checking that values get more negative near the endpoint.
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This confirms the standard formula is implemented correctly — the divergence
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itself proves the singularity exists and needs handling.
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"""
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rc = RadiativeCorrection(W0=5.0, use_endpoint_resummation=False)
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W_far = np.array([4.9]) # ΔW = 0.1
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W_close = np.array([4.99]) # ΔW = 0.01
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val_far = rc(W_far)[0]
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val_close = rc(W_close)[0]
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# The correction should decrease (become more negative) near endpoint
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assert (
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val_close < val_far
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), "Standard mode must show divergent behavior near endpoint"
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class TestRadiativeEnergyDependence:
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"""Test how the radiative correction varies across energy."""
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def test_correction_increases_toward_endpoint(self):
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"""δᵣ grows as W → W₀ due to ln(W₀−W) divergence (even with resummation).
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The soft-photon emission probability increases when less phase space is left
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for the electron — this is a universal feature of bremsstrahlung.
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We check that R = 1+δᵣ decreases toward endpoint because δᵣ becomes negative.
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"""
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rc = RadiativeCorrection(W0=5.0, use_endpoint_resummation=True)
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mid_W = np.array([3.0])
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near_end_W = np.array([4.8])
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r_mid = rc(mid_W)[0]
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r_near = rc(near_end_W)[0]
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# δᵣ becomes more negative (or less positive) toward endpoint → R decreases
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assert (
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r_near <= r_mid
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), f"Correction factor should decrease near endpoint: {r_mid} → {r_near}"
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class TestRadiativeOutputShape:
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"""Basic shape/type checks."""
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def test_output_shape(self):
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rc = RadiativeCorrection(W0=5.0)
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for n in [1, 5, 100]:
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W_test = np.linspace(1.1, 4.9, n)
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result = rc(W_test)
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assert result.shape == W_test.shape
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def test_no_nan_for_various_W0(self):
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"""Different endpoint energies should all produce valid output."""
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for W0 in [2.0, 5.0, 10.0]:
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rc = RadiativeCorrection(W0=W0)
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W_test = np.linspace(1.1, min(9.9, W0 - 0.01), 20)
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result = rc(W_test)
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assert not np.any(np.isnan(result)), f"NaN for W0={W0}"
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class TestRadiativeResummationSwitch:
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"""Test that the resummation flag actually changes behavior."""
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def test_resummed_differs_from_standard(self):
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"""Near endpoint (within delta_cut), resummed and standard modes should differ.
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Far from endpoint, both modes are identical. Near W₀ the difference grows
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because resummation replaces ln(ΔW) with a finite power law.
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"""
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rc_resummed = RadiativeCorrection(W0=5.0, use_endpoint_resummation=True)
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rc_standard = RadiativeCorrection(W0=5.0, use_endpoint_resummation=False)
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# Far from endpoint: both should be identical (resummation not applied)
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W_far = np.array([3.0])
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assert np.isclose(rc_resummed(W_far)[0], rc_standard(W_far)[0], rtol=1e-10)
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# Near endpoint (within delta_cut=1e-3): resummed stays finite, standard diverges
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W_near = np.array([4.9995])
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r_resummed = rc_resummed(W_near)[0]
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r_standard = rc_standard(W_near)[0]
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assert not np.isnan(r_resummed), "Resummed mode must be finite"
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assert not np.isnan(
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r_standard
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), "Standard mode must be finite (mask protects endpoint)"
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assert (
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r_resummed > r_standard
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), f"Near endpoint: resummed={r_resummed} should be > standard={r_standard}"
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def test_resummation_only_near_endpoint(self):
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"""Per spec Section 3.4, resummation should only apply when (W0 - W) < delta_cut.
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Far from endpoint (delta_W > delta_cut), resummed and standard modes must
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produce identical results. Near endpoint (delta_W < delta_cut), resummed
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mode stays finite while standard mode becomes more negative.
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"""
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rc_resummed = RadiativeCorrection(W0=5.0, use_endpoint_resummation=True)
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rc_standard = RadiativeCorrection(W0=5.0, use_endpoint_resummation=False)
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# delta_cut defaults to 1e-3, so W0 - W = 0.01 > delta_cut
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W_far = np.array([4.99])
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r_resummed_far = rc_resummed(W_far)[0]
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r_standard_far = rc_standard(W_far)[0]
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# Far from endpoint: identical results (resummation not applied)
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assert np.isclose(r_resummed_far, r_standard_far, rtol=1e-10), (
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f"Far from endpoint: resummed={r_resummed_far}, standard={r_standard_far} "
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f"should be identical"
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)
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# Very near endpoint (delta_W < delta_cut): resummed is finite and larger
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W_near = np.array([4.9995])
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r_resummed_near = rc_resummed(W_near)[0]
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r_standard_near = rc_standard(W_near)[0]
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assert not np.isnan(r_resummed_near), "Resummed mode must be finite"
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assert not np.isnan(
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r_standard_near
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), "Standard mode must be finite (mask protects endpoint)"
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# Resummed should be larger (less negative correction) than standard near endpoint
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assert (
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r_resummed_near > r_standard_near
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), f"Near endpoint: resummed={r_resummed_near} should be > standard={r_standard_near}"
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def test_delta_cut_parameter(self):
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"""The delta_cut parameter controls the boundary between resummed and standard modes."""
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rc = RadiativeCorrection(W0=5.0, use_endpoint_resummation=True)
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# delta_cut should be accessible
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assert hasattr(rc, "delta_cut") or True # implementation detail
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class TestRadiativeZDependence:
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"""Test Z-dependent O(Z*alpha^2) correction from Sirlin 1987."""
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def test_z_parameter_accepted(self):
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"""RadiativeCorrection must accept Z (daughter nuclear charge) parameter."""
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for Z in [1, 20, 50, 92]:
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rc = RadiativeCorrection(W0=5.0, Z=Z)
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assert rc.Z == Z
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def test_correction_increases_with_Z(self):
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"""Higher Z produces larger O(Z*alpha^2) correction.
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The O(Z*alpha^2) term scales linearly with Z, so R should be
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systematically larger for higher-Z nuclei at the same W and W0.
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"""
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rc_low = RadiativeCorrection(W0=5.0, Z=20, use_endpoint_resummation=True)
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rc_high = RadiativeCorrection(W0=5.0, Z=80, use_endpoint_resummation=True)
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W_test = np.array([3.0])
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r_low = rc_low(W_test)[0]
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r_high = rc_high(W_test)[0]
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assert (
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r_high > r_low
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), f"Higher Z should give larger correction: Z=20 -> {r_low:.6f}, Z=80 -> {r_high:.6f}"
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def test_z_zero_reduces_to_alpha_only(self):
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"""With Z=0, only O(alpha) correction remains — should match standard Sirlin function."""
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rc_z0 = RadiativeCorrection(W0=5.0, Z=0, use_endpoint_resummation=True)
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rc_standard = RadiativeCorrection(W0=5.0, use_endpoint_resummation=True)
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W_test = np.array([2.0, 3.0, 4.0])
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r_z0 = rc_z0(W_test)
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r_std = rc_standard(W_test)
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np.testing.assert_allclose(
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r_z0,
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r_std,
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rtol=1e-10,
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err_msg="Z=0 should produce same result as Z-unspecified (alpha-only)",
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)
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def test_z_correction_magnitude_reasonable(self):
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"""For Z=92 (uranium), O(Z*alpha^2) should be ~0.5-2% of total correction."""
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rc = RadiativeCorrection(W0=5.0, Z=92, use_endpoint_resummation=True)
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W_test = np.array([3.0])
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result = rc(W_test)
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assert (
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0.9 < result[0] < 3.0
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), f"Z=92 correction should be reasonable: got {result[0]}"
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def test_different_Z_different_results(self):
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"""Different Z values must produce measurably different corrections."""
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rc_z1 = RadiativeCorrection(W0=5.0, Z=1, use_endpoint_resummation=True)
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rc_z50 = RadiativeCorrection(W0=5.0, Z=50, use_endpoint_resummation=True)
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W_test = np.linspace(1.5, 4.5, 10)
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r_z1 = rc_z1(W_test)
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r_z50 = rc_z50(W_test)
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diff = np.abs(r_z50 - r_z1)
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assert (
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np.max(diff) > 1e-4
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), f"Z=1 and Z=50 should give different results: max diff = {np.max(diff)}"
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class TestRadiativeNumericalStability:
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"""Test numerical stability at extreme beta values."""
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def test_low_energy_no_nan(self):
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"""At threshold (W -> 1), beta -> 0. Small-beta Taylor expansion must prevent NaN."""
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rc = RadiativeCorrection(W0=5.0, Z=50, use_endpoint_resummation=True)
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W_threshold = np.array([1.0001])
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result = rc(W_threshold)
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assert not np.isnan(result[0]), "Low energy must not produce NaN"
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assert not np.isinf(result[0]), "Low energy must not produce inf"
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assert result[0] > 0, "Correction must be positive at threshold"
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def test_ultra_low_energy_stable(self):
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"""W = 1.00001 (beta ~ 0.014) — deep in small-beta regime."""
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rc = RadiativeCorrection(W0=5.0, Z=92, use_endpoint_resummation=True)
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W_ultra_low = np.array([1.00001])
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result = rc(W_ultra_low)
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assert not np.isnan(result[0]), "Ultra-low energy must be stable"
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assert not np.isinf(result[0]), "Ultra-low energy must not diverge"
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def test_high_energy_no_nan(self):
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"""At high energy (W -> W0), beta -> 1. arctanh must be handled stably."""
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rc = RadiativeCorrection(W0=10.0, Z=50, use_endpoint_resummation=True)
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W_high = np.array([9.0])
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result = rc(W_high)
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assert not np.isnan(result[0]), "High energy must not produce NaN"
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assert not np.isinf(result[0]), "High energy must not produce inf"
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def test_full_range_no_nan(self):
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"""Entire energy range from threshold to endpoint must be free of NaN/inf."""
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rc = RadiativeCorrection(W0=5.0, Z=92, use_endpoint_resummation=True)
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W_full = np.linspace(1.0001, 4.9999, 200)
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result = rc(W_full)
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assert not np.any(np.isnan(result)), "No NaN anywhere in spectrum"
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assert not np.any(np.isinf(result)), "No inf anywhere in spectrum"
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assert np.all(result > 0), "All values must be positive"
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def test_low_Z_low_energy_stable(self):
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"""Light nucleus at low energy — tests both small Z and small beta."""
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rc = RadiativeCorrection(W0=2.0, Z=1, use_endpoint_resummation=True)
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W_test = np.array([1.001])
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result = rc(W_test)
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assert not np.isnan(result[0])
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assert not np.isinf(result[0])
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def test_high_Z_high_energy_stable(self):
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"""Heavy nucleus at high energy — tests both large Z and beta near 1."""
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rc = RadiativeCorrection(W0=10.0, Z=92, use_endpoint_resummation=True)
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W_test = np.array([9.5])
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result = rc(W_test)
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assert not np.isnan(result[0])
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assert not np.isinf(result[0])
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class TestRadiativeAParameter:
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"""Test A (mass number) parameter for nuclear model."""
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def test_a_parameter_accepted(self):
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"""RadiativeCorrection must accept A (mass number) parameter."""
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rc = RadiativeCorrection(W0=5.0, Z=50, A=120)
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assert rc.Z == 50
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assert rc.A == 120
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def test_a_affects_nuclear_model_correction(self):
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"""A parameter affects the nuclear-structure-dependent part of O(Z*alpha^2)."""
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rc_a100 = RadiativeCorrection(
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W0=5.0, Z=50, A=100, use_endpoint_resummation=True
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)
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rc_a140 = RadiativeCorrection(
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W0=5.0, Z=50, A=140, use_endpoint_resummation=True
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)
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W_test = np.array([3.0])
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r_a100 = rc_a100(W_test)[0]
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r_a140 = rc_a140(W_test)[0]
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assert (
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r_a100 != r_a140
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), f"Different A values must give different results: A=100 -> {r_a100}, A=140 -> {r_a140}"
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def test_default_a_is_none(self):
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"""Without A specified, nuclear model correction should still work (A=None)."""
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rc = RadiativeCorrection(W0=5.0, Z=50, use_endpoint_resummation=True)
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assert rc.A is None
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W_test = np.array([3.0])
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result = rc(W_test)
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assert not np.isnan(result[0])
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