diff --git a/examples/notebooks/alpha_ca48_ambiguity.ipynb b/examples/notebooks/alpha_ca48_ambiguity.ipynb index f06d6546..c6a0e9f6 100644 --- a/examples/notebooks/alpha_ca48_ambiguity.ipynb +++ b/examples/notebooks/alpha_ca48_ambiguity.ipynb @@ -31,8 +31,11 @@ " import subprocess\n", " import urllib.request\n", "\n", + " # matplotlib 3.10.0-3.10.1, which Colab preinstalls, mangles an RGBA tuple\n", + " # passed as a facecolor to ax.hist -- it breaks the corner plots below\n", + " packages = [\"jitr\", \"dynesty\", \"corner\", \"matplotlib>=3.10.3\"]\n", " subprocess.run(\n", - " [sys.executable, \"-m\", \"pip\", \"install\", \"-q\", \"jitr\", \"dynesty\", \"corner\"],\n", + " [sys.executable, \"-m\", \"pip\", \"install\", \"-q\", *packages],\n", " check=True,\n", " )\n", " RAW = \"https://raw.githubusercontent.com/beykyle/jitr/main/examples/notebooks/\"\n", diff --git a/examples/notebooks/alpha_ca_calibration.ipynb b/examples/notebooks/alpha_ca_calibration.ipynb index 5ba72ee2..948ac86a 100644 --- a/examples/notebooks/alpha_ca_calibration.ipynb +++ b/examples/notebooks/alpha_ca_calibration.ipynb @@ -31,8 +31,11 @@ " import subprocess\n", " import urllib.request\n", "\n", + " # matplotlib 3.10.0-3.10.1, which Colab preinstalls, mangles an RGBA tuple\n", + " # passed as a facecolor to ax.hist -- it breaks the corner plots below\n", + " packages = [\"jitr\", \"dynesty\", \"corner\", \"matplotlib>=3.10.3\"]\n", " subprocess.run(\n", - " [sys.executable, \"-m\", \"pip\", \"install\", \"-q\", \"jitr\", \"dynesty\", \"corner\"],\n", + " [sys.executable, \"-m\", \"pip\", \"install\", \"-q\", *packages],\n", " check=True,\n", " )\n", " RAW = \"https://raw.githubusercontent.com/beykyle/jitr/main/examples/notebooks/\"\n", diff --git a/examples/notebooks/chex_jitr_validation.ipynb b/examples/notebooks/chex_jitr_validation.ipynb index 28699344..24e1865f 100644 --- a/examples/notebooks/chex_jitr_validation.ipynb +++ b/examples/notebooks/chex_jitr_validation.ipynb @@ -10,7 +10,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "id": "81bba3a5", "metadata": { "tags": [ @@ -44,15 +44,12 @@ "source": [ "## Comparison of quasi-elastic $(p,n)$ differential cross sections between jitR and CHEX\n", "\n", - "CHEX uses non-relativistic kinematics, so for a like-for-like comparison both the\n", - "entrance and exit channels are set up here with `relativistic=False`. jitR defaults\n", - "to the semi-relativistic (Ingemarsson) prescription, which changes the forward-angle\n", - "cross section at the ~10% level at this energy." + "CHEX uses non-relativistic kinematics, wheras jitR defaults to the semi-relativistic (Ingemarsson) prescription, so for a like-for-like comparison both the entrance and exit channels are set up here with `relativistic=False. " ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "id": "e6ba03f8", "metadata": {}, "outputs": [], @@ -64,7 +61,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "id": "fdd41822-23c4-4230-b119-fbced5089832", "metadata": {}, "outputs": [], @@ -74,7 +71,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "id": "38a6f920", "metadata": {}, "outputs": [], @@ -102,7 +99,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "id": "187d389a-88bf-4d76-bd1e-f9447d805c76", "metadata": {}, "outputs": [], @@ -114,7 +111,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "id": "adc61bc4-fd9f-459f-a496-424acd54d0be", "metadata": {}, "outputs": [], @@ -129,7 +126,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "id": "9c90f896-1b92-4c41-a1e7-1eab3392fdf1", "metadata": {}, "outputs": [], @@ -142,7 +139,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "id": "89e1f3fc-25cf-49e3-b7cd-a1faed13da22", "metadata": {}, "outputs": [ @@ -152,7 +149,7 @@ "ChannelKinematics(Elab=35, Ecm=34.27976496842483, mu=918.9637641236778, k=np.float64(1.2720279057856945), eta=np.float64(0.5343312852705087))" ] }, - "execution_count": 7, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -163,7 +160,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "id": "08d7aa13-c56e-4b0f-9862-f3621b9c6e33", "metadata": {}, "outputs": [ @@ -173,7 +170,7 @@ "ChannelKinematics(Elab=27.676442482181717, Ecm=27.106217022054977, mu=920.2073684974115, k=np.float64(1.1318942051723602), eta=np.float64(0.0))" ] }, - "execution_count": 8, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -184,19 +181,19 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 10, "id": "143ea4f8-9b66-4eb3-bbcf-22f8b3f1e1b4", "metadata": {}, "outputs": [], "source": [ - "channel_radius_fm = 16 # fm\n", + "channel_radius_fm = 12 # fm\n", "lmax = 20\n", "angles = np.linspace(0.01, np.pi, 180)" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 11, "id": "af4644ae-80d6-4b4a-8afb-ea9e467ddd51", "metadata": {}, "outputs": [ @@ -204,7 +201,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "35\n" + "25\n" ] } ], @@ -216,7 +213,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 12, "id": "dc19976d-76f7-4401-925e-dd4a8d3a6d50", "metadata": {}, "outputs": [], @@ -235,7 +232,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 13, "id": "f3dc176e-e2de-496e-b65b-d0d29b611267", "metadata": {}, "outputs": [ @@ -245,7 +242,7 @@ "48-Ca(p,n)48-Sc" ] }, - "execution_count": 12, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } @@ -256,7 +253,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 14, "id": "b8f93162-f9de-4e6a-a1a2-37d9e56d372c", "metadata": {}, "outputs": [], @@ -267,7 +264,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 15, "id": "4b3f74b9-4797-4efb-9528-1a501b5d4832", "metadata": {}, "outputs": [], @@ -280,7 +277,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 16, "id": "44c2b2fa-3420-4081-b3dc-6f46c1e98fe4", "metadata": {}, "outputs": [], @@ -292,7 +289,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 17, "id": "cd68ff12-8ff4-4c20-82ca-8072885e56a9", "metadata": {}, "outputs": [], @@ -308,7 +305,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 18, "id": "26813ce5-298e-4e6e-a767-391df2590723", "metadata": {}, "outputs": [], @@ -322,7 +319,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 19, "id": "e07a8f8d-b8d5-48d5-a085-03dadb12fba2", "metadata": {}, "outputs": [], @@ -352,23 +349,49 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 22, "id": "a2b503d1-5468-46bf-a884-ff5d0c8a719d", "metadata": {}, "outputs": [ { "data": { + "image/png": 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", "text/plain": [ - "" + "
" ] }, - "execution_count": 19, "metadata": {}, - "output_type": "execute_result" - }, + "output_type": "display_data" + } + ], + "source": [ + "plt.errorbar(\n", + " ca48_pn_ias[:, 0],\n", + " ca48_pn_ias[:, 1],\n", + " yerr=ca48_pn_ias[:, 2],\n", + " label=\"Jon et al., \",\n", + " linestyle=\"none\",\n", + " marker=\".\",\n", + ")\n", + "\n", + "plt.plot(workspace.angles * 180 / np.pi, xs, \"--\", label=\"JITR\")\n", + "plt.plot(xspn[\"theta\"], xspn[\"dxs\"], label=\"CHEX\", alpha=0.5)\n", + "plt.xlabel(r\"$\\theta$ [deg]\")\n", + "plt.ylabel(r\" $d \\sigma / \\Omega$ [mb/Sr]\")\n", + "plt.legend()\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "623d1c97-f9fe-42b5-bd6b-57375ad69834", + "metadata": {}, + "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -391,12 +414,15 @@ "plt.plot(xspn[\"theta\"], xspn[\"dxs\"], label=\"CHEX\", alpha=0.5)\n", "plt.xlabel(r\"$\\theta$ [deg]\")\n", "plt.ylabel(r\" $d \\sigma / \\Omega$ [mb/Sr]\")\n", - "plt.legend()" + "plt.legend()\n", + "plt.yscale(\"log\")\n", + "plt.tight_layout()\n", + "plt.show()" ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 21, "id": "22e9e190-1f57-41aa-b521-62e2f8d718d9", "metadata": {}, "outputs": [], diff --git a/examples/notebooks/chex_qepn_xs.txt b/examples/notebooks/chex_qepn_xs.txt index 20116bc3..ef294baf 100644 --- a/examples/notebooks/chex_qepn_xs.txt +++ b/examples/notebooks/chex_qepn_xs.txt @@ -1,180 +1,180 @@ - 0.0000000000000000 1.6752869555624581 - 1.0000000000000000 1.6804820601303603 - 2.0000000000000000 1.6960629667735683 - 3.0000000000000000 1.7220108448450666 - 4.0000000000000000 1.7582760924884138 - 5.0000000000000000 1.8047526571906038 - 6.0000000000000000 1.8612452512222577 - 7.0000000000000000 1.9274323428000764 - 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8.7147205737755792E-002 + 177.00000000000000 8.9445810953048557E-002 + 178.00000000000000 9.1127579056065153E-002 + 179.00000000000000 9.2152857826333631E-002 diff --git a/pyproject.toml b/pyproject.toml index cecabae3..96e36762 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -40,14 +40,13 @@ docs = [ ] examples = [ - "matplotlib", + "matplotlib>=3.10.3", "exfor_tools", "nbmake", "nbval", "ipykernel", "jupyter", "pytest", - "matplotlib", "black[jupyter]>=26.3.1", "dynesty>=3.0.0", "corner>=2.0.0", diff --git a/src/jitr/xs/quasielastic_pn.py b/src/jitr/xs/quasielastic_pn.py index b0308721..dd03b0f8 100644 --- a/src/jitr/xs/quasielastic_pn.py +++ b/src/jitr/xs/quasielastic_pn.py @@ -202,7 +202,7 @@ def __init__( ): if abs(m - mp) <= l and jp >= 0: ylm = sph_harm_y(l, int(m - mp), self.angles, 0) - cg0 = clebsch_gordan(l, 1 / 2, jp, m - mp, m, mp) + cg0 = clebsch_gordan(l, 1 / 2, jp, m - mp, mp, m) cg1 = clebsch_gordan(l, 1 / 2, jp, 0, m, m) self.geometric_factor[im, imp, l, ijp, :] = ( @@ -412,7 +412,7 @@ def xs( # TODO cast into a np.sum for im, m in enumerate([-0.5, 0.5]): for imp, mp in enumerate([-0.5, 0.5]): - for l in range(0, self.sys.lmax): + for l in range(0, self.sys.lmax + 1): for ijp, jp in enumerate([l + 0.5, l - 0.5]): if abs(m - mp) <= l and jp >= 0: Tmmp[im, imp, :] += ( diff --git a/tests/test_quasielastic_pn_spin_flip.py b/tests/test_quasielastic_pn_spin_flip.py new file mode 100644 index 00000000..758ba472 --- /dev/null +++ b/tests/test_quasielastic_pn_spin_flip.py @@ -0,0 +1,97 @@ +import numpy as np +import pytest + +from jitr.reactions import Reaction +from jitr.rmatrix import Solver +from jitr.xs.quasielastic_pn import Workspace + + +def _woods_saxon(rgrid: np.ndarray, depth: complex, R: float, a: float) -> np.ndarray: + return np.asarray(depth / (1 + np.exp((rgrid - R) / a)), dtype=np.complex128) + + +def _thomas(rgrid: np.ndarray, depth: complex, R: float, a: float) -> np.ndarray: + # derivative Woods-Saxon form factor used for spin-orbit coupling + x = np.exp((rgrid - R) / a) + return np.asarray(-depth * x / (1 + x) ** 2 / (a * rgrid), dtype=np.complex128) + + +@pytest.fixture(scope="module") +def workspace() -> Workspace: + reaction = Reaction((48, 20), (1, 1), (1, 0), (48, 21)) + kinematics_entrance = reaction.kinematics(35.0, relativistic=False) + kinematics_exit = reaction.kinematics_exit( + kinematics_entrance, 6.67, relativistic=False + ) + return Workspace( + reaction=reaction, + kinematics_entrance=kinematics_entrance, + kinematics_exit=kinematics_exit, + solver=Solver(35), + angles=np.linspace(0.05, np.pi - 0.05, 60), + lmax=15, + channel_radius_fm=14.0, + tmatrix_abs_tol=1e-12, + ) + + +def _potentials(workspace: Workspace) -> dict[str, np.ndarray]: + rgrid = workspace.radial_grid() + return { + "U_p_coulomb": _woods_saxon(rgrid, 8.0, 4.7, 0.3), + "U_p_central": _woods_saxon(rgrid, -50.0 - 8.0j, 4.4, 0.65), + "U_p_spin_orbit": _thomas(rgrid, 6.0 - 0.3j, 4.0, 0.6), + "U_n_central": _woods_saxon(rgrid, -46.0 - 8.0j, 4.4, 0.65), + "U_n_spin_orbit": _thomas(rgrid, 5.5 - 0.3j, 4.0, 0.6), + } + + +def _spin_amplitudes(workspace: Workspace, **potentials: np.ndarray) -> np.ndarray: + Tlj, _, _ = workspace.tmatrix(**potentials) + return np.einsum("abljt,lj->abt", workspace.geometric_factor, Tlj) + + +def test_spin_flip_geometric_factors_nonzero(workspace: Workspace) -> None: + gf = workspace.geometric_factor + for l in range(1, workspace.lmax + 1): + for ijp in range(2): + assert np.max(np.abs(gf[0, 1, l, ijp])) > 0 + assert np.max(np.abs(gf[1, 0, l, ijp])) > 0 + # s-wave cannot flip spin + np.testing.assert_array_equal(gf[0, 1, 0], 0) + np.testing.assert_array_equal(gf[1, 0, 0], 0) + + +def test_spin_flip_cancels_over_j(workspace: Workspace) -> None: + # CG orthogonality: for j-independent T_lj the spin-flip amplitude vanishes + gf = workspace.geometric_factor + scale = np.max(np.abs(gf)) + np.testing.assert_allclose(gf[0, 1].sum(axis=1), 0, atol=1e-12 * scale) + np.testing.assert_allclose(gf[1, 0].sum(axis=1), 0, atol=1e-12 * scale) + + +def test_no_spin_orbit_has_no_spin_flip(workspace: Workspace) -> None: + potentials = _potentials(workspace) + potentials.pop("U_p_spin_orbit") + potentials.pop("U_n_spin_orbit") + T = _spin_amplitudes(workspace, **potentials) + np.testing.assert_allclose(T[0, 1], 0, atol=1e-10 * np.max(np.abs(T))) + np.testing.assert_allclose(T[1, 0], 0, atol=1e-10 * np.max(np.abs(T))) + + +def test_spin_orbit_produces_spin_flip(workspace: Workspace) -> None: + potentials = _potentials(workspace) + T = _spin_amplitudes(workspace, **potentials) + xs = workspace.xs(**potentials) + + non_flip = workspace.xs_factor * 10 * (np.abs(T[0, 0]) ** 2 + np.abs(T[1, 1]) ** 2) + flip = workspace.xs_factor * 10 * (np.abs(T[0, 1]) ** 2 + np.abs(T[1, 0]) ** 2) + np.testing.assert_allclose(xs, non_flip + flip, rtol=1e-12) + + # parity: |T_{++}| = |T_{--}| and |T_{+-}| = |T_{-+}| in the scattering plane + np.testing.assert_allclose(np.abs(T[0, 0]), np.abs(T[1, 1]), rtol=1e-10) + np.testing.assert_allclose(np.abs(T[0, 1]), np.abs(T[1, 0]), rtol=1e-10) + + # spin-flip vanishes at 0 and 180 degrees but is sizable at intermediate angles + mid = (workspace.angles > np.pi / 4) & (workspace.angles < 3 * np.pi / 4) + assert np.mean(flip[mid] / xs[mid]) > 0.05 diff --git a/uv.lock b/uv.lock index 0f16799c..877f8077 100644 --- a/uv.lock +++ b/uv.lock @@ -1093,7 +1093,7 @@ dev = [ { name = "furo" }, { name = "ipykernel" }, { name = "jupyter" }, - { name = "matplotlib" }, + { name = "matplotlib", specifier = ">=3.10.3" }, { name = "mypy" }, { name = "myst-nb" }, { name = "nbmake" }, @@ -1117,7 +1117,7 @@ examples = [ { name = "exfor-tools" }, { name = "ipykernel" }, { name = "jupyter" }, - { name = "matplotlib" }, + { name = "matplotlib", specifier = ">=3.10.3" }, { name = "nbmake" }, { name = "nbval" }, { name = "pytest" },