Compare SQDT low lying matrix elements to udel

docs/examples.rst

@@ -45,6 +45,7 @@ Some comparisons to old versions of pairinteraction, ARC and NIST data.
    examples/comparisons/compare_z_min_cutoff.ipynb
    examples/comparisons/compare_nist_energy_levels_data.ipynb
    examples/comparisons/compare_nist_matrix_elements.ipynb
+   examples/comparisons/compare_udel_portal_matrix_elements.ipynb
    examples/comparisons/compare_model_potentials.ipynb
    examples/comparisons/compare_whittaker.ipynb
 

docs/examples/comparisons/compare_nist_matrix_elements.ipynb

@@ -240,6 +240,74 @@
     "plt.show()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Independent check: $5p_j \\rightarrow 6d_{j'}$\n",
+    "\n",
+    "The cutoff $r_c$ was fitted to the principal series $5s_{1/2} \\rightarrow np_j$ only,\n",
+    "so transitions between two *excited* states are an independent test of the dressed operator.\n",
+    "NIST ASD lists three E1 lines connecting the $4p^6\\,5p$ and $4p^6\\,6d$ configurations."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "        transition       bare    dressed       NIST   (|<5p_j||d||6d_j'>| in e a0)\n",
+      "  5p_1/2 -> 6d_3/2     1.0322     1.0830     1.1798   (ratios to NIST: 0.875 / 0.918)\n",
+      "  5p_3/2 -> 6d_5/2     1.4684     1.5332     1.6580   (ratios to NIST: 0.886 / 0.925)\n",
+      "  5p_3/2 -> 6d_3/2     0.4920     0.5135     0.5577   (ratios to NIST: 0.882 / 0.921)\n"
+     ]
+    }
+   ],
+   "source": [
+    "# {((n, j) lower, (n, j) upper): S in (e a0)^2}\n",
+    "# from https://physics.nist.gov/PhysRefData/ASD/lines_form.html (retrieved 2026-07-28)\n",
+    "nist_s_5p_6d = {\n",
+    "    ((5, 0.5), (6, 1.5)): 1.392,  # 620.63092 nm\n",
+    "    ((5, 1.5), (6, 2.5)): 2.749,  # 629.83252 nm\n",
+    "    ((5, 1.5), (6, 1.5)): 3.11e-1,  # 629.92245 nm\n",
+    "}\n",
+    "\n",
+    "print(f\"{'transition':>18} {'bare':>10} {'dressed':>10} {'NIST':>10}   (|<5p_j||d||6d_j'>| in e a0)\")\n",
+    "for ((n_low, j_low), (n_up, j_up)), line_strength in nist_s_5p_6d.items():\n",
+    "    lower = rydstate.RydbergStateSQDTAlkali(\"Rb\", n_low, l=1, j=j_low)\n",
+    "    upper = rydstate.RydbergStateSQDTAlkali(\"Rb\", n_up, l=2, j=j_up)\n",
+    "    bare = upper.calc_reduced_matrix_element(lower, \"electric_dipole_rydberg\", unit=\"e a0\")\n",
+    "    dressed = upper.calc_reduced_matrix_element(lower, \"electric_dipole\", unit=\"e a0\")\n",
+    "    nist = np.sqrt(line_strength)\n",
+    "    transition = f\"{n_low}p_{2 * j_low:1.0f}/2 -> {n_up}d_{2 * j_up:1.0f}/2\"\n",
+    "    print(\n",
+    "        f\"{transition:>18} {abs(bare):10.4f} {abs(dressed):10.4f} {nist:10.4f}\"\n",
+    "        f\"   (ratios to NIST: {abs(bare) / nist:.3f} / {abs(dressed) / nist:.3f})\"\n",
+    "    )"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Unlike for the principal series, the shielding correction *increases* these matrix elements, by $4-5\\%$.\n",
+    "The $-\\alpha_c/r^2 (1 - e^{-(r/r_c)^3})$ term contributes only at small $r$ (a few $r_c$), so its sign relative to\n",
+    "the bare integral decides whether it shields or enhances: the $5s \\rightarrow np$ integrals are dominated by a\n",
+    "single sign and are shielded, whereas the $5p \\rightarrow 6d$ integrals suffer a strong cancellation between an\n",
+    "inner positive and an outer negative lobe, and the small-$r$ correction adds to the surviving remainder --- the\n",
+    "same enhancement already seen for the $np \\rightarrow 4d, 5d$ channels above.\n",
+    "\n",
+    "The correction moves all three lines towards NIST, but a deficit of $\\approx 8\\%$ remains.\n",
+    "That deficit is a property of the *reference*, not of the operator: the NIST ASD line strengths for these three\n",
+    "lines are about 10% larger than the high-precision values tabulated by the UD atomic data portal,\n",
+    "far outside the portal's stated uncertainty. Measured against the portal, the dressed operator agrees to\n",
+    "$\\approx 1.5\\%$ --- see the direct comparison in [compare_udel_portal_matrix_elements.ipynb](compare_udel_portal_matrix_elements.ipynb)."
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -255,7 +323,7 @@
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   {
    "cell_type": "code",
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    "outputs": [
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@@ -306,7 +374,7 @@
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+   "execution_count": 7,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2026-07-27T11:05:51.131147Z",
@@ -373,7 +441,7 @@
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@@ -400,7 +468,7 @@
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    "outputs": [
     {