Fix MF=4 Legendre angular distribution weighting

CHANGELOG.md

@@ -13,6 +13,7 @@ and this project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.
 
 ### Fixed
 
+* Correct Legendre weighting in the MF=4 angular distribution conversion ([#46](https://github.com/paulromano/endf-python/pull/46))
 * Fixing MF7/MT2 key name: LHTR → LTHR ([#37](https://github.com/paulromano/endf-python/pull/37))
 
 ## [0.1.12]

src/endf/mf4.py

@@ -119,6 +119,7 @@ def from_dict(cls, data: dict) -> AngleDistribution:
             mu = []
             for a_l in data['legendre']['a_l']:
                 coef = np.insert(a_l, 0, 1.0)
+                coef *= (2 * np.arange(coef.size) + 1) / 2
                 mu.append(Legendre(coef))
         elif LTT == 2 and LI == 0:
             energy = data['tabulated']['E']
@@ -129,6 +130,7 @@ def from_dict(cls, data: dict) -> AngleDistribution:
             mu_leg = []
             for a_l in data['legendre']['a_l']:
                 coef = np.insert(a_l, 0, 1.0)
+                coef *= (2 * np.arange(coef.size) + 1) / 2
                 mu_leg.append(Legendre(coef))
 
             # Then get tabulated

tests/test_mf4.py

@@ -0,0 +1,62 @@
+# SPDX-FileCopyrightText: 2026 OpenMC contributors
+# SPDX-License-Identifier: MIT
+
+import numpy as np
+from numpy.polynomial.legendre import leggauss
+import pytest
+from endf.function import Tabulated1D
+from endf.mf4 import AngleDistribution
+
+
+@pytest.mark.parametrize('ltt', [1, 3])
+def test_legendre_conversion(ltt):
+    coefficients = [np.array([]), np.array([0.2, 0.1]), np.array([-0.1])]
+    energy = np.array([1.e3, 1.e-5, 1.])
+    tabulated = Tabulated1D([-1., 0., 1.], [0.25, 0.5, 0.75])
+    data = {
+        'LTT': ltt,
+        'LI': 0,
+        'legendre': {'E': energy, 'a_l': coefficients},
+        'tabulated': {'E': np.array([1.e6]), 'mu': [tabulated]},
+    }
+    original_coefficients = [a_l.copy() for a_l in coefficients]
+    distribution = AngleDistribution.from_dict(data)
+    repeated = AngleDistribution.from_dict(data)
+
+    expected_energy = [1.e3, 1.e-5, 1., 1.e6] if ltt == 3 else [1.e3, 1.e-5, 1.]
+    np.testing.assert_array_equal(distribution.energy, expected_energy)
+    np.testing.assert_array_equal(repeated.energy, expected_energy)
+    np.testing.assert_array_equal(energy, [1.e3, 1.e-5, 1.])
+    assert len(distribution.mu) == len(repeated.mu) == len(expected_energy)
+
+    expected_coef = [[0.5], [0.5, 0.3, 0.25], [0.5, -0.15]]
+    expected_values = [[0.5, 0.5, 0.5], [0.45, 0.375, 1.05], [0.65, 0.5, 0.35]]
+    expected_moments = [[1., 0., 0.], [1., 0.2, 0.1], [1., -0.1, 0.]]
+    cosine, weights = leggauss(8)
+    basis = np.array([np.ones(8), cosine, (3 * cosine**2 - 1) / 2])
+    for i, density in enumerate(distribution.mu[:3]):
+        assert density.coef == pytest.approx(expected_coef[i], rel=0., abs=1.e-13)
+        assert density([-1., 0., 1.]) == pytest.approx(expected_values[i], rel=0., abs=1.e-13)
+        assert density(0.) == pytest.approx(expected_values[i][1], rel=0., abs=1.e-13)
+        moments = basis @ (weights * density(cosine))
+        assert moments == pytest.approx(expected_moments[i], rel=0., abs=1.e-13)
+        np.testing.assert_array_equal(coefficients[i], original_coefficients[i])
+        np.testing.assert_array_equal(density.coef, repeated.mu[i].coef)
+
+    if ltt == 3:
+        assert distribution.mu[-1] is repeated.mu[-1] is tabulated
+        np.testing.assert_array_equal(data['tabulated']['E'], [1.e6])
+        np.testing.assert_array_equal(tabulated.x, [-1., 0., 1.])
+        np.testing.assert_array_equal(tabulated.y, [0.25, 0.5, 0.75])
+        assert tabulated([-1., 0., 1.]) == pytest.approx([0.25, 0.5, 0.75])
+
+
+def test_tabulated_conversion():
+    energy = np.array([1.e6])
+    mu = [Tabulated1D([-1., 1.], [0.4, 0.6])]
+    data = {'LTT': 2, 'LI': 0, 'tabulated': {'E': energy, 'mu': mu}}
+
+    distribution = AngleDistribution.from_dict(data)
+
+    assert distribution.energy is energy
+    assert distribution.mu is mu