From 27adbdd5fe7e52d2f2b7e5c58515305e8fc619bf Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 16 May 2024 11:59:41 +0200
Subject: [PATCH 1/9] first draft of intro

---
 docs/hello.ipynb    |  51 ------
 docs/index.md       |   3 +-
 docs/intro.ipynb    | 263 ++++++++++++++++++++++++++
 docs/report-0.ipynb | 167 +++++++++++++++++
 pixi.lock           | 437 ++++++++++++++++++++++++++++++++++++++++++--
 pixi.toml           |   3 +
 6 files changed, 861 insertions(+), 63 deletions(-)
 delete mode 100644 docs/hello.ipynb
 create mode 100644 docs/intro.ipynb
 create mode 100644 docs/report-0.ipynb

diff --git a/docs/hello.ipynb b/docs/hello.ipynb
deleted file mode 100644
index cb1c2da..0000000
--- a/docs/hello.ipynb
+++ /dev/null
@@ -1,51 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "0",
-   "metadata": {},
-   "source": [
-    "# Starting document"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "1",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "print(\"Hello World!\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "2",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.12.3"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/docs/index.md b/docs/index.md
index ce8b6d0..e26c1a3 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -1,5 +1,6 @@
 # MyST-NB Quickstart
 
 ```{toctree}
-hello
+intro
+report-0
 ```
diff --git a/docs/intro.ipynb b/docs/intro.ipynb
new file mode 100644
index 0000000..f4f39ae
--- /dev/null
+++ b/docs/intro.ipynb
@@ -0,0 +1,263 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "::::{margin}\n",
+    ":::{card} Amplitude models for photoproduction reaction\n",
+    "PWA101(v2.0): Introduction\n",
+    "^^^\n",
+    "This document is a follow-up of PWA101 (v1.0) (temporarily see [here](https://compwa--217.org.readthedocs.build/report/999.html)),\n",
+    "as an introduction to Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model.\n",
+    "Now the focus is the use of symbolic expressions (computations) with `sympy` and the use of [ComPWA packages](https://compwa.github.io/) in general to illustrate the general process in PWA. This tutorial aims to equip readers with deeper understanding of PWA methodologies and full workflow in the context of hadron physics through a practical, hands-on example with symbolic expressions via [ComPWA](https://compwa.github.io/).\n",
+    "+++\n",
+    "✅&nbsp;[ComPWA/gluex-nstar#1](https://github.com/ComPWA/gluex-nstar/issues/1)\n",
+    ":::\n",
+    "::::"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "# # Amplitude Analysis 101 (v2.0)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "Address to the issue [ComPWA/gluex-nstar#1](https://github.com/ComPWA/gluex-nstar/issues/1), this document is PWA101(v2.0), which shows PWA methodologies and full workflow in the context of hadron physics with symbolic expressions via [ComPWA](https://compwa.github.io/)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "<!-- cspell:ignore Mathieu -->\n",
+    "This amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/) by Vincent Mathieu.\n",
+    "\n",
+    "The (photo-production) reaction is $ \\gamma p \\to \\eta \\pi^0 p$, it is described by a amplitude model with three possible resonances: $a_2$, $\\Delta^+$, and $N^*$. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "```{image} https://github.com/ComPWA/compwa-org/assets/17490173/ec6bf191-bd5f-43b0-a6cb-da470b071630\n",
+    ":width: 100%\n",
+    "```"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "The amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/), only the Breit-Wigner and Spherical harmonics terms are kept for doing PWA eventually, as shown in equation {eq}`BW_SH_label`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "$$\n",
+    "\\begin{eqnarray}\n",
+    "A^{12} &=& \\frac{\\sum a_m Y_2^m (\\Omega_1)}{s-m^2_{a_2}+im_{a_2} \\Gamma_{a_2}} \\\\\n",
+    "A^{23} &=& \\frac{\\sum b_m Y_1^m (\\Omega_2)}{s-m^2_{\\Delta}+im_{\\Delta} \\Gamma_{\\Delta}}  \\\\\n",
+    "\\\n",
+    "A^{31} &=& \\frac{c_0}{s-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}} \n",
+    "\\end{eqnarray}\n",
+    "$$ (BW_SH_label)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "where s is the Mandelstam variable, m is the mass, $\\Gamma$ is the width, Y is the spherical harmonics, $\\Omega$ is the decay angles (a pair of Euler angles), and a, b, and c are coefficients"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    ":::{note}\n",
+    "Mandelstam variables $s_{ij}=(p_i+p_j)^2$, $t_i=(p_a-p_i)^2$, and $u_i=(p_b-p_i)^2$.\n",
+    ":::\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "with  intensity $I$ and amplitude $A$:\n",
+    "\n",
+    "$$\n",
+    "\\begin{eqnarray}\n",
+    "I &=& |A|^2 \\nonumber \\\\\n",
+    "A &=& A^{12} + A^{23} + A^{31}  \\\\\n",
+    "\\end{eqnarray}\n",
+    "$$ (123_label)\n",
+    "\n",
+    "where $\\quad 1 \\equiv \\eta ; \\quad  2 \\equiv \\pi^0 ; \\quad 3 \\equiv p$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "10",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    ":::{note}\n",
+    "The choice of the amplitude model (equations (1) and (2)) for PWA in this tutorial consists of three resonances, and each of them are formed by two terms: Breit-Wigner with Spherical harmonics ($l = 2, 1, 0$).\n",
+    ":::"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "11",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    ":::{important}\n",
+    "The spin of $\\eta$ meson and $\\pi^0$ meson are all 0. But the spin of proton is not 0, it is spin-$\\frac{1}{2}$.\n",
+    "\n",
+    "In this amplitude model **spin** of baryon is simplified (not realistic):\n",
+    "$\\eta$, $\\pi^0$ and $p$ are all treated as spin-0 particles.\n",
+    "\n",
+    "This means that total intrinsic spin $s$ is ignored in this model,\n",
+    "the total angular momentum \n",
+    "$J$ of the system or any subsystems within this model will solely depend on the orbital angular momentum \n",
+    "$L$, characterized by quantum number $l$.\n",
+    "And this simplifies the use of spherical harmonics $Y_l^m(\\theta,\\phi)$,\n",
+    "since only the orbital angular momentum component is involved, and thus the combination of contribution is not considered (e.g. Clebsch-Gordan Coefficients).\n",
+    "\n",
+    "In our case: \n",
+    "- $A^{12}$ amplitude represents a d-wave interaction, as indicated by $l=2$.\n",
+    "    - The possible $m$ values are $−2,−1,0,1,2$. Each of these values corresponds to different orientations of the d-wave. The wave type is solely determined by $l$ and all these $m$ values still describe d-wave characteristics.\n",
+    "- $A^{23}$ amplitude represents a p-wave interaction, as indicated by $l=1$.\n",
+    "    - The possible $m$ values are $−1,0,1$. Each of these values corresponds to different orientations of the p-wave. Similarly, these values are all p-wave orientations.\n",
+    "- $A^{31}$ amplitude represents a s-wave interaction, as indicated by $l=0$.\n",
+    "    - The only possible $m$ value is 0, which is consistent with the spherical symmetry of s-waves.\n",
+    ":::"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "12",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/report-0.ipynb b/docs/report-0.ipynb
new file mode 100644
index 0000000..d89d699
--- /dev/null
+++ b/docs/report-0.ipynb
@@ -0,0 +1,167 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "::::{margin}\n",
+    ":::{card} Create a virtual particle that represents the state pγ in `QRules`\n",
+    "Report-0\n",
+    "^^^\n",
+    "+++\n",
+    "✅&nbsp;[ComPWA/gluex-nstar#5](https://github.com/ComPWA/gluex-nstar/issues/5)\n",
+    ":::\n",
+    "::::"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "# Virtual particle that represents the state pγ "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "Address to issue [ComPWA/gluex-nstar#5](https://github.com/ComPWA/gluex-nstar/issues/5), this section is an investigation of creating a virtual particle that represents the state $p \\gamma$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "As an example, create a virtual particle that represents state $e^+ e^-$ can be seen [here](https://qrules.readthedocs.io/0.10.x/usage/particle/#adding-custom-particle-definitions-through-python)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "from qrules.particle import load_pdg"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "particle_db = load_pdg()\n",
+    "print(\"Number of loaded particles:\", len(particle_db))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "particle_db.find(2212)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "particle_db.find(22)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/pixi.lock b/pixi.lock
index ba33ed9..02b31a0 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -38,6 +38,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/debugpy-1.8.1-py312h30efb56_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/decorator-5.1.1-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/defusedxml-0.7.1-pyhd8ed1ab_0.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/noarch/deprecated-1.2.14-pyh1a96a4e_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/distlib-0.3.8-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/docutils-0.21.2-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/entrypoints-0.4-pyhd8ed1ab_0.tar.bz2
@@ -67,6 +68,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/h11-0.14.0-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/h2-4.1.0-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/harfbuzz-8.4.0-h3d44ed6_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/hepunits-2.3.3-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/hpack-4.0.0-pyh9f0ad1d_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/httpcore-1.0.5-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/httpx-0.27.0-pyhd8ed1ab_0.conda
@@ -80,6 +82,8 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/importlib_resources-6.4.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/ipykernel-6.29.3-pyhd33586a_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/ipython-8.24.0-pyh707e725_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/ipython_genutils-0.2.0-py_1.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/noarch/ipywidgets-8.1.2-pyhd8ed1ab_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/isoduration-20.11.0-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/isort-5.13.2-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jax-0.4.26-pyhd8ed1ab_0.conda
@@ -91,10 +95,12 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/jsonschema-4.22.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jsonschema-specifications-2023.12.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jsonschema-with-format-nongpl-4.22.0-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter-1.0.0-pyhd8ed1ab_10.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter-cache-1.0.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter-lsp-2.2.5-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter-server-mathjax-0.2.6-pyh5bfe37b_1.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_client-8.6.1-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_client-7.4.9-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_console-6.6.3-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/jupyter_core-5.7.2-py312h7900ff3_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_events-0.10.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_server-2.14.0-pyhd8ed1ab_0.conda
@@ -105,6 +111,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-myst-2.4.2-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_pygments-0.3.0-pyhd8ed1ab_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_server-2.27.1-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_widgets-3.0.10-pyhd8ed1ab_0.conda
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+  timestamp: 1715499623651
 - kind: conda
   name: pandocfilters
   version: 1.5.0
@@ -3201,6 +3460,26 @@ packages:
   license_family: MIT
   size: 75191
   timestamp: 1712320447201
+- kind: conda
+  name: particle
+  version: 0.24.0
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/particle-0.24.0-pyhd8ed1ab_0.conda
+  sha256: 2471b4dde2640283c0c1dfba669b8c322e55c45269ff3dbf95c0cfb3b8ec0b50
+  md5: 58bfa493a4844538a140012c1d120360
+  depends:
+  - attrs >=19.2
+  - deprecated
+  - hepunits >=2.0.0
+  - importlib_resources >=2.0
+  - python >=3.7
+  - typing-extensions >=4.5
+  license: BSD-3-Clause
+  license_family: BSD
+  size: 163439
+  timestamp: 1713892152317
 - kind: conda
   name: pathspec
   version: 0.12.1
@@ -3361,6 +3640,21 @@ packages:
   license_family: BSD
   size: 270398
   timestamp: 1702399557137
+- kind: conda
+  name: prompt_toolkit
+  version: 3.0.42
+  build: hd8ed1ab_0
+  subdir: noarch
+  noarch: generic
+  url: https://conda.anaconda.org/conda-forge/noarch/prompt_toolkit-3.0.42-hd8ed1ab_0.conda
+  sha256: fd2185d501bf34cb4c121f2f5ade9157ac75e1644a9da81355c4c8f9c1b82d4d
+  md5: 85a2189ecd2fcdd86e92b2d4ea8fe461
+  depends:
+  - prompt-toolkit >=3.0.42,<3.0.43.0a0
+  license: BSD-3-Clause
+  license_family: BSD
+  size: 6846
+  timestamp: 1702399567048
 - kind: conda
   name: psutil
   version: 5.9.8
@@ -3521,6 +3815,21 @@ packages:
   license: Python-2.0
   size: 31991381
   timestamp: 1713208036041
+- kind: conda
+  name: python-constraint
+  version: 1.4.0
+  build: py_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/python-constraint-1.4.0-py_0.tar.bz2
+  sha256: 582f244b4f8703dd326e58b66b07aa34a6b211351bd141862ff20d25d680e6f0
+  md5: 34267ea9b6de472c4fc3cb73a5a10207
+  depends:
+  - python
+  license: BSD-2-Clause
+  license_family: BSD
+  size: 21336
+  timestamp: 1541423579379
 - kind: conda
   name: python-dateutil
   version: 2.9.0
@@ -3650,6 +3959,66 @@ packages:
   license_family: BSD
   size: 461684
   timestamp: 1715024520808
+- kind: conda
+  name: qrules
+  version: 0.10.1
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/qrules-0.10.1-pyhd8ed1ab_0.conda
+  sha256: 289fe3fd2ad41d086a39bc7e73336c467aaa24b29300ba104c93a914de80f2b3
+  md5: 00d71dbda539d5a5ef5f11cfa718a82c
+  depends:
+  - attrs >=20.1.0
+  - jsonschema
+  - particle
+  - python >=3.6
+  - python-constraint
+  - pyyaml
+  - tqdm >=4.24.0
+  - typing-extensions
+  license: GPL-3.0-or-later
+  license_family: GPL
+  size: 74164
+  timestamp: 1709326984310
+- kind: conda
+  name: qtconsole-base
+  version: 5.5.2
+  build: pyha770c72_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/qtconsole-base-5.5.2-pyha770c72_0.conda
+  sha256: 0e7e1fad227f3f4fa5c8cac23e8c49298d55158a85104d1b9d58795e68af0b5a
+  md5: 0f63ec743defb9de6728a98150a80839
+  depends:
+  - ipykernel >=4.1
+  - jupyter_client >=4.1
+  - jupyter_core
+  - packaging
+  - pygments
+  - python >=3.8
+  - qtpy >=2.4.0
+  - traitlets
+  license: BSD-3-Clause
+  license_family: BSD
+  size: 100292
+  timestamp: 1714943047487
+- kind: conda
+  name: qtpy
+  version: 2.4.1
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/qtpy-2.4.1-pyhd8ed1ab_0.conda
+  sha256: 925bf48e747af6ceff1b073c10b12fc94ef79c88a34729059d253e43466a33f1
+  md5: 7f391bd70d2abfb70f304ba5aa4e1261
+  depends:
+  - packaging
+  - python >=3.7
+  license: MIT
+  license_family: MIT
+  size: 61808
+  timestamp: 1698112171285
 - kind: conda
   name: re2
   version: 2023.09.01
@@ -4215,6 +4584,21 @@ packages:
   license_family: Apache
   size: 840527
   timestamp: 1708363299520
+- kind: conda
+  name: tqdm
+  version: 4.66.4
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/tqdm-4.66.4-pyhd8ed1ab_0.conda
+  sha256: 75342f40a69e434a1a23003c3e254a95dca695fb14955bc32f1819cd503964b2
+  md5: e74cd796e70a4261f86699ee0a3a7a24
+  depends:
+  - colorama
+  - python >=3.7
+  license: MPL-2.0 or MIT
+  size: 89452
+  timestamp: 1714855008479
 - kind: conda
   name: traitlets
   version: 5.14.3
@@ -4480,6 +4864,37 @@ packages:
   license_family: BSD
   size: 201426
   timestamp: 1697914826988
+- kind: conda
+  name: widgetsnbextension
+  version: 4.0.10
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/widgetsnbextension-4.0.10-pyhd8ed1ab_0.conda
+  sha256: 981b06c76a1a86bb84be09522768be0458274926b22f4b0225dfcdd30a6593e0
+  md5: 521f489e3babeddeec638c2add7e9e64
+  depends:
+  - python >=3.7
+  license: BSD-3-Clause
+  license_family: BSD
+  size: 886369
+  timestamp: 1707420479741
+- kind: conda
+  name: wrapt
+  version: 1.16.0
+  build: py312h98912ed_0
+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/wrapt-1.16.0-py312h98912ed_0.conda
+  sha256: dc8431b343961347ad93b33d2d8270e8c15d8825382f4f2540835c94aba2de05
+  md5: fa957a1c7bee7e47ad44633caf7be8bc
+  depends:
+  - libgcc-ng >=12
+  - python >=3.12,<3.13.0a0
+  - python_abi 3.12.* *_cp312
+  license: BSD-2-Clause
+  license_family: BSD
+  size: 62482
+  timestamp: 1699532968076
 - kind: conda
   name: xorg-kbproto
   version: 1.0.7
diff --git a/pixi.toml b/pixi.toml
index 8241a48..71c7429 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -21,9 +21,11 @@ sphinx-autobuild \
 
 [dependencies]
 black = ">=24.4.2,<24.5"
+ipywidgets = ">=8.1.2,<8.2"
 isort = ">=5.13.2,<5.14"
 jax = ">=0.4.26,<0.5"
 jaxlib = ">=0.4.23,<0.5"
+jupyter = ">=1.0.0,<1.1"
 jupyterlab = ">=4.2.0,<4.3"
 jupyterlab-git = ">=0.50.0,<0.51"
 jupyterlab-lsp = ">=5.1.0,<5.2"
@@ -34,6 +36,7 @@ pre-commit = ">=3.7.1,<3.8"
 pydata-sphinx-theme = ">=0.15.2,<0.16"
 python = ">=3.12.3,<3.13"
 python-graphviz = ">=0.20.3,<0.21"
+qrules = ">=0.10.1,<0.11"
 scipy = ">=1.13.0,<1.14"
 sphinx-autobuild = ">=2024.4.16,<2024.5"
 sympy = ">=1.12,<2"

From 5580c93275b75715bd13d12af34c8a650af3a76a Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 16 May 2024 15:15:40 +0200
Subject: [PATCH 2/9] Change of contents and dependency

---
 docs/conf.py                                |   9 +-
 docs/index.md                               |  20 +-
 docs/intro.ipynb                            | 263 ---------
 docs/{report-0.ipynb => pgamma-state.ipynb} |  20 +-
 docs/reaction.md                            |  73 +++
 pixi.lock                                   | 574 ++++++++++++++++++--
 pixi.toml                                   |   2 +
 7 files changed, 632 insertions(+), 329 deletions(-)
 delete mode 100644 docs/intro.ipynb
 rename docs/{report-0.ipynb => pgamma-state.ipynb} (89%)
 create mode 100644 docs/reaction.md

diff --git a/docs/conf.py b/docs/conf.py
index 159dd23..70fccf8 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -6,7 +6,14 @@
     "_build",
 ]
 extensions = ["myst_nb"]
-html_theme = "pydata_sphinx_theme"
+html_theme = "sphinx_book_theme"
 master_doc = "index"
+myst_enable_extensions = [
+    "amsmath",
+    "colon_fence",
+    "dollarmath",
+    "html_image",
+    "smartquotes",
+]
 nitpicky = True
 project = "GlueX N-Star"
diff --git a/docs/index.md b/docs/index.md
index e26c1a3..d0329a7 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -1,6 +1,20 @@
-# MyST-NB Quickstart
+# Amplitude Analysis 101 / PWA101 (v2.0)
+
+## Amplitude models for photoproduction reaction
+
+This document is a follow-up of PWA101 (v1.0) (temporarily see [here](https://compwa--217.org.readthedocs.build/report/999.html)),
+as an introduction to Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model.
+
+Now the focus is the use of symbolic expressions (computations) with the use of [ComPWA packages](https://compwa.github.io/), or CAS(Computer Algebra System)-assisted model building in general (the python package `SymPy` in this case) to illustrate the general process in PWA.
+
+This tutorial aims to equip readers with deeper understanding of PWA methodologies and full workflow in the context of hadron physics through a practical, hands-on example with symbolic expressions via [ComPWA](https://compwa.github.io/).
+
+Furthermore,
+address to the issue ✅&nbsp;[ComPWA/gluex-nstar#1](https://github.com/ComPWA/gluex-nstar/issues/1), this document is PWA101(v2.0), which shows PWA methodologies and full workflow in the context of hadron physics with symbolic expressions via [ComPWA](https://compwa.github.io/).
+
+# Table of contents:
 
 ```{toctree}
-intro
-report-0
+reaction
+pgamma-state
 ```
diff --git a/docs/intro.ipynb b/docs/intro.ipynb
deleted file mode 100644
index f4f39ae..0000000
--- a/docs/intro.ipynb
+++ /dev/null
@@ -1,263 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "0",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "::::{margin}\n",
-    ":::{card} Amplitude models for photoproduction reaction\n",
-    "PWA101(v2.0): Introduction\n",
-    "^^^\n",
-    "This document is a follow-up of PWA101 (v1.0) (temporarily see [here](https://compwa--217.org.readthedocs.build/report/999.html)),\n",
-    "as an introduction to Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model.\n",
-    "Now the focus is the use of symbolic expressions (computations) with `sympy` and the use of [ComPWA packages](https://compwa.github.io/) in general to illustrate the general process in PWA. This tutorial aims to equip readers with deeper understanding of PWA methodologies and full workflow in the context of hadron physics through a practical, hands-on example with symbolic expressions via [ComPWA](https://compwa.github.io/).\n",
-    "+++\n",
-    "✅&nbsp;[ComPWA/gluex-nstar#1](https://github.com/ComPWA/gluex-nstar/issues/1)\n",
-    ":::\n",
-    "::::"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "# # Amplitude Analysis 101 (v2.0)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "Address to the issue [ComPWA/gluex-nstar#1](https://github.com/ComPWA/gluex-nstar/issues/1), this document is PWA101(v2.0), which shows PWA methodologies and full workflow in the context of hadron physics with symbolic expressions via [ComPWA](https://compwa.github.io/)."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "<!-- cspell:ignore Mathieu -->\n",
-    "This amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/) by Vincent Mathieu.\n",
-    "\n",
-    "The (photo-production) reaction is $ \\gamma p \\to \\eta \\pi^0 p$, it is described by a amplitude model with three possible resonances: $a_2$, $\\Delta^+$, and $N^*$. "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "```{image} https://github.com/ComPWA/compwa-org/assets/17490173/ec6bf191-bd5f-43b0-a6cb-da470b071630\n",
-    ":width: 100%\n",
-    "```"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "The amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/), only the Breit-Wigner and Spherical harmonics terms are kept for doing PWA eventually, as shown in equation {eq}`BW_SH_label`."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "$$\n",
-    "\\begin{eqnarray}\n",
-    "A^{12} &=& \\frac{\\sum a_m Y_2^m (\\Omega_1)}{s-m^2_{a_2}+im_{a_2} \\Gamma_{a_2}} \\\\\n",
-    "A^{23} &=& \\frac{\\sum b_m Y_1^m (\\Omega_2)}{s-m^2_{\\Delta}+im_{\\Delta} \\Gamma_{\\Delta}}  \\\\\n",
-    "\\\n",
-    "A^{31} &=& \\frac{c_0}{s-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}} \n",
-    "\\end{eqnarray}\n",
-    "$$ (BW_SH_label)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "where s is the Mandelstam variable, m is the mass, $\\Gamma$ is the width, Y is the spherical harmonics, $\\Omega$ is the decay angles (a pair of Euler angles), and a, b, and c are coefficients"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "8",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    ":::{note}\n",
-    "Mandelstam variables $s_{ij}=(p_i+p_j)^2$, $t_i=(p_a-p_i)^2$, and $u_i=(p_b-p_i)^2$.\n",
-    ":::\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "with  intensity $I$ and amplitude $A$:\n",
-    "\n",
-    "$$\n",
-    "\\begin{eqnarray}\n",
-    "I &=& |A|^2 \\nonumber \\\\\n",
-    "A &=& A^{12} + A^{23} + A^{31}  \\\\\n",
-    "\\end{eqnarray}\n",
-    "$$ (123_label)\n",
-    "\n",
-    "where $\\quad 1 \\equiv \\eta ; \\quad  2 \\equiv \\pi^0 ; \\quad 3 \\equiv p$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "10",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    ":::{note}\n",
-    "The choice of the amplitude model (equations (1) and (2)) for PWA in this tutorial consists of three resonances, and each of them are formed by two terms: Breit-Wigner with Spherical harmonics ($l = 2, 1, 0$).\n",
-    ":::"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "11",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    ":::{important}\n",
-    "The spin of $\\eta$ meson and $\\pi^0$ meson are all 0. But the spin of proton is not 0, it is spin-$\\frac{1}{2}$.\n",
-    "\n",
-    "In this amplitude model **spin** of baryon is simplified (not realistic):\n",
-    "$\\eta$, $\\pi^0$ and $p$ are all treated as spin-0 particles.\n",
-    "\n",
-    "This means that total intrinsic spin $s$ is ignored in this model,\n",
-    "the total angular momentum \n",
-    "$J$ of the system or any subsystems within this model will solely depend on the orbital angular momentum \n",
-    "$L$, characterized by quantum number $l$.\n",
-    "And this simplifies the use of spherical harmonics $Y_l^m(\\theta,\\phi)$,\n",
-    "since only the orbital angular momentum component is involved, and thus the combination of contribution is not considered (e.g. Clebsch-Gordan Coefficients).\n",
-    "\n",
-    "In our case: \n",
-    "- $A^{12}$ amplitude represents a d-wave interaction, as indicated by $l=2$.\n",
-    "    - The possible $m$ values are $−2,−1,0,1,2$. Each of these values corresponds to different orientations of the d-wave. The wave type is solely determined by $l$ and all these $m$ values still describe d-wave characteristics.\n",
-    "- $A^{23}$ amplitude represents a p-wave interaction, as indicated by $l=1$.\n",
-    "    - The possible $m$ values are $−1,0,1$. Each of these values corresponds to different orientations of the p-wave. Similarly, these values are all p-wave orientations.\n",
-    "- $A^{31}$ amplitude represents a s-wave interaction, as indicated by $l=0$.\n",
-    "    - The only possible $m$ value is 0, which is consistent with the spherical symmetry of s-waves.\n",
-    ":::"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "12",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.12.3"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/docs/report-0.ipynb b/docs/pgamma-state.ipynb
similarity index 89%
rename from docs/report-0.ipynb
rename to docs/pgamma-state.ipynb
index d89d699..92e5d8e 100644
--- a/docs/report-0.ipynb
+++ b/docs/pgamma-state.ipynb
@@ -60,13 +60,21 @@
     "tags": []
    },
    "source": [
-    "As an example, create a virtual particle that represents state $e^+ e^-$ can be seen [here](https://qrules.readthedocs.io/0.10.x/usage/particle/#adding-custom-particle-definitions-through-python)."
+    "As an example of side note, create a virtual particle that represents state $e^+ e^-$ can be seen [here](https://qrules.readthedocs.io/0.10.x/usage/particle/#adding-custom-particle-definitions-through-python)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4",
+   "metadata": {},
+   "source": [
+    "`QRules` is used for this task"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4",
+   "id": "5",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -82,7 +90,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5",
+   "id": "6",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -99,7 +107,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6",
+   "id": "7",
    "metadata": {
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diff --git a/docs/reaction.md b/docs/reaction.md
new file mode 100644
index 0000000..0f8a6cd
--- /dev/null
+++ b/docs/reaction.md
@@ -0,0 +1,73 @@
+# Reaction and amplitude models
+
+<!-- cspell:ignore Mathieu -->
+<!-- This amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/) by Vincent Mathieu. -->
+
+## Reaction
+
+The (photo-production) reaction is $ \gamma p \to \eta \pi^0 p$, it is described by a amplitude model with three possible resonances: $a_2$, $\Delta^+$, and $N^*$.
+
+```{image} https://github.com/ComPWA/compwa-org/assets/17490173/ec6bf191-bd5f-43b0-a6cb-da470b071630
+:width: 100%
+```
+
+## Amplitude models
+
+The amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/), only the Breit-Wigner and Spherical harmonics terms are kept for doing PWA eventually, as shown in equation {eq}`BW_SH_label`.
+
+$$
+\begin{eqnarray}
+A^{12} &=& \frac{\sum a_m Y_2^m (\Omega_1)}{s-m^2_{a_2}+im_{a_2} \Gamma_{a_2}} \\
+A^{23} &=& \frac{\sum b_m Y_1^m (\Omega_2)}{s-m^2_{\Delta}+im_{\Delta} \Gamma_{\Delta}}  \\
+\
+A^{31} &=& \frac{c_0}{s-m^2_{N^*}+im_{N^*} \Gamma_{N^*}}
+\end{eqnarray}
+$$ (BW_SH_label)
+
+where s is the Mandelstam variable, m is the mass, $\Gamma$ is the width, Y is the spherical harmonics, $\Omega$ is the decay angles (a pair of Euler angles), and a, b, and c are coefficients
+
+:::{note}
+Mandelstam variables $s_{ij}=(p_i+p_j)^2$, $t_i=(p_a-p_i)^2$, and $u_i=(p_b-p_i)^2$.
+:::
+
+with  intensity $I$ and amplitude $A$:
+
+
+$$
+
+\begin{eqnarray}
+I &=& |A|^2 \nonumber \\
+A &=& A^{12} + A^{23} + A^{31} \\
+\end{eqnarray}
+
+$$
+(123_label)
+
+where $\quad 1 \equiv \eta ; \quad  2 \equiv \pi^0 ; \quad 3 \equiv p$
+
+:::{note}
+The choice of the amplitude model (equations (1) and (2)) for PWA in this tutorial consists of three resonances, and each of them are formed by two terms: Breit-Wigner with Spherical harmonics ($l = 2, 1, 0$).
+:::
+
+:::{important}
+The spin of $\eta$ meson and $\pi^0$ meson are all 0. But the spin of proton is not 0, it is spin-$\frac{1}{2}$.
+
+In this amplitude model **spin** of baryon is simplified (not realistic):
+$\eta$, $\pi^0$ and $p$ are all treated as spin-0 particles.
+
+This means that total intrinsic spin $s$ is ignored in this model,
+the total angular momentum
+$J$ of the system or any subsystems within this model will solely depend on the orbital angular momentum
+$L$, characterized by quantum number $l$.
+And this simplifies the use of spherical harmonics $Y_l^m(\theta,\phi)$,
+since only the orbital angular momentum component is involved, and thus the combination of contribution is not considered (e.g. Clebsch-Gordan Coefficients).
+
+In our case:
+- $A^{12}$ amplitude represents a d-wave interaction, as indicated by $l=2$.
+    - The possible $m$ values are $−2,−1,0,1,2$. Each of these values corresponds to different orientations of the d-wave. The wave type is solely determined by $l$ and all these $m$ values still describe d-wave characteristics.
+- $A^{23}$ amplitude represents a p-wave interaction, as indicated by $l=1$.
+    - The possible $m$ values are $−1,0,1$. Each of these values corresponds to different orientations of the p-wave. Similarly, these values are all p-wave orientations.
+- $A^{31}$ amplitude represents a s-wave interaction, as indicated by $l=0$.
+    - The only possible $m$ value is 0, which is consistent with the spherical symmetry of s-waves.
+:::
+$$
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   license_family: MIT
+  purls:
+  - pkg:pypi/ukkonen
   size: 14050
   timestamp: 1695549556745
 - kind: conda
@@ -4717,6 +5152,8 @@ packages:
   - python >=3.7
   license: MIT
   license_family: MIT
+  purls:
+  - pkg:pypi/uri-template
   size: 23999
   timestamp: 1688655976471
 - kind: conda
@@ -4734,6 +5171,8 @@ packages:
   - python >=3.7
   license: MIT
   license_family: MIT
+  purls:
+  - pkg:pypi/urllib3
   size: 94669
   timestamp: 1708239595549
 - kind: conda
@@ -4751,6 +5190,8 @@ packages:
   - python_abi 3.12.* *_cp312
   license: BSD-3-Clause
   license_family: BSD
+  purls:
+  - pkg:pypi/uvicorn
   size: 126964
   timestamp: 1710932152563
 - kind: conda
@@ -4768,6 +5209,9 @@ packages:
   - platformdirs <5,>=3.9.1
   - python >=3.8
   license: MIT
+  license_family: MIT
+  purls:
+  - pkg:pypi/virtualenv
   size: 3458445
   timestamp: 1715681264937
 - kind: conda
@@ -4785,6 +5229,8 @@ packages:
   - python_abi 3.12.* *_cp312
   license: MIT
   license_family: MIT
+  purls:
+  - pkg:pypi/watchfiles
   size: 1094669
   timestamp: 1701078026995
 - kind: conda
@@ -4800,6 +5246,8 @@ packages:
   - python >=3.8
   license: MIT
   license_family: MIT
+  purls:
+  - pkg:pypi/wcwidth
   size: 32709
   timestamp: 1704731373922
 - kind: conda
@@ -4815,6 +5263,8 @@ packages:
   - python >=3.5
   license: BSD-3-Clause
   license_family: BSD
+  purls:
+  - pkg:pypi/webcolors
   size: 18186
   timestamp: 1679900907305
 - kind: conda
@@ -4831,6 +5281,8 @@ packages:
   - python >=2.6
   license: BSD-3-Clause
   license_family: BSD
+  purls:
+  - pkg:pypi/webencodings
   size: 15600
   timestamp: 1694681458271
 - kind: conda
@@ -4846,6 +5298,8 @@ packages:
   - python >=3.8
   license: Apache-2.0
   license_family: APACHE
+  purls:
+  - pkg:pypi/websocket-client
   size: 47066
   timestamp: 1713923494501
 - kind: conda
@@ -4862,6 +5316,8 @@ packages:
   - python_abi 3.12.* *_cp312
   license: BSD-3-Clause
   license_family: BSD
+  purls:
+  - pkg:pypi/websockets
   size: 201426
   timestamp: 1697914826988
 - kind: conda
@@ -4877,6 +5333,8 @@ packages:
   - python >=3.7
   license: BSD-3-Clause
   license_family: BSD
+  purls:
+  - pkg:pypi/widgetsnbextension
   size: 886369
   timestamp: 1707420479741
 - kind: conda
@@ -4893,6 +5351,8 @@ packages:
   - python_abi 3.12.* *_cp312
   license: BSD-2-Clause
   license_family: BSD
+  purls:
+  - pkg:pypi/wrapt
   size: 62482
   timestamp: 1699532968076
 - kind: conda
@@ -5095,12 +5555,12 @@ packages:
 - kind: conda
   name: zeromq
   version: 4.3.5
-  build: h75354e8_3
-  build_number: 3
+  build: h75354e8_4
+  build_number: 4
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/zeromq-4.3.5-h75354e8_3.conda
-  sha256: c2f2db5d19b603546db025b47fb71765f8dda0a0fe8feb42bd4e6a46194a5590
-  md5: 1b0ea5d6674e4e7dde0537c890813edb
+  url: https://conda.anaconda.org/conda-forge/linux-64/zeromq-4.3.5-h75354e8_4.conda
+  sha256: bc9aaee39e7be107d7daff237435dfd8f791aca460a98583a36a263615205262
+  md5: 03cc8d9838ad9dd0060ab532e81ccb21
   depends:
   - krb5 >=1.21.2,<1.22.0a0
   - libgcc-ng >=12
@@ -5108,8 +5568,8 @@ packages:
   - libstdcxx-ng >=12
   license: MPL-2.0
   license_family: MOZILLA
-  size: 351803
-  timestamp: 1714545110790
+  size: 353229
+  timestamp: 1715607188837
 - kind: conda
   name: zipp
   version: 3.17.0
@@ -5123,6 +5583,8 @@ packages:
   - python >=3.8
   license: MIT
   license_family: MIT
+  purls:
+  - pkg:pypi/zipp
   size: 18954
   timestamp: 1695255262261
 - kind: conda
diff --git a/pixi.toml b/pixi.toml
index 71c7429..a2de7b2 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -21,6 +21,7 @@ sphinx-autobuild \
 
 [dependencies]
 black = ">=24.4.2,<24.5"
+graphviz = ">=9.0.0,<9.1"
 ipywidgets = ">=8.1.2,<8.2"
 isort = ">=5.13.2,<5.14"
 jax = ">=0.4.26,<0.5"
@@ -39,4 +40,5 @@ python-graphviz = ">=0.20.3,<0.21"
 qrules = ">=0.10.1,<0.11"
 scipy = ">=1.13.0,<1.14"
 sphinx-autobuild = ">=2024.4.16,<2024.5"
+sphinx-book-theme = ">=1.1.2,<1.2"
 sympy = ">=1.12,<2"

From e774af9aefbf6d12842d3a1442b5f4875e11f288 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 16 May 2024 17:39:43 +0200
Subject: [PATCH 3/9] pgamma virtual state generation!

---
 docs/pgamma-state.ipynb | 150 +++++++++++++++++++++++++++++++++++++---
 pixi.lock               |  17 +++++
 pixi.toml               |   1 +
 3 files changed, 157 insertions(+), 11 deletions(-)

diff --git a/docs/pgamma-state.ipynb b/docs/pgamma-state.ipynb
index 92e5d8e..b00a1db 100644
--- a/docs/pgamma-state.ipynb
+++ b/docs/pgamma-state.ipynb
@@ -84,7 +84,10 @@
    },
    "outputs": [],
    "source": [
-    "from qrules.particle import load_pdg"
+    "from qrules.particle import load_pdg\n",
+    "\n",
+    "particle_db = load_pdg()\n",
+    "print(\"Number of loaded particles:\", len(particle_db))"
    ]
   },
   {
@@ -100,24 +103,17 @@
    },
    "outputs": [],
    "source": [
-    "particle_db = load_pdg()\n",
-    "print(\"Number of loaded particles:\", len(particle_db))"
+    "particle_db.find(2212)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "id": "7",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
-    "particle_db.find(2212)"
+    "particle_db.find(\"p\")"
    ]
   },
   {
@@ -140,6 +136,16 @@
    "cell_type": "code",
    "execution_count": null,
    "id": "9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "particle_db.find(\"gamma\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "10",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -148,6 +154,128 @@
     "tags": []
    },
    "outputs": [],
+   "source": [
+    "from IPython.display import Math\n",
+    "\n",
+    "sigmas = particle_db.filter(\n",
+    "    lambda p: p.name.startswith(\"p\") and p.mass == 0.93827208816 and p.charge == 1\n",
+    ")\n",
+    "Math(\", \".join(p.latex for p in sigmas))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "11",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from IPython.display import Math\n",
+    "\n",
+    "sigmas = particle_db.filter(lambda p: p.name.startswith(\"gamma\"))\n",
+    "Math(\", \".join(p.latex for p in sigmas))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "12",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "proton = particle_db[\"p\"]\n",
+    "proton"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "13",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "gamma = particle_db[\"gamma\"]\n",
+    "gamma"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "14",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from qrules.particle import Particle, Spin\n",
+    "\n",
+    "pgamma = Particle(\n",
+    "    name=\"p\",\n",
+    "    latex=r\"p \\gamma\",\n",
+    "    spin=0.5,\n",
+    "    mass=4.101931071854584,\n",
+    "    charge=1,\n",
+    "    isospin=Spin(1 / 2, +1 / 2),\n",
+    "    baryon_number=1,\n",
+    "    parity=-1,\n",
+    "    pid=99999999,\n",
+    ")\n",
+    "pgamma"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "15",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pgamma_s3over2 = Particle(\n",
+    "    name=\"pgamma\",\n",
+    "    latex=R\"p \\gamma (s3/2)\",\n",
+    "    spin=1.5,\n",
+    "    mass=4.101931071854584,\n",
+    "    charge=1,\n",
+    "    isospin=Spin(1 / 2, +1 / 2),\n",
+    "    baryon_number=1,\n",
+    "    parity=-1,\n",
+    "    pid=99999999,\n",
+    ")\n",
+    "pgamma_s3over2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "16",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pgamma_s3over2.latex"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "17",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pgamma.latex"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "18",
+   "metadata": {},
+   "source": [
+    "The `pgamma` virtual state generated via `QRules` will be used in later stages!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "19",
+   "metadata": {},
+   "outputs": [],
    "source": []
   }
  ],
diff --git a/pixi.lock b/pixi.lock
index b8edcff..1f31ac1 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -111,6 +111,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-git-0.50.0-pyhd8ed1ab_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-lsp-5.1.0-pyhd8ed1ab_2.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-myst-2.4.2-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_code_formatter-2.2.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_pygments-0.3.0-pyhd8ed1ab_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_server-2.27.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_widgets-3.0.10-pyhd8ed1ab_0.conda
@@ -2320,6 +2321,22 @@ packages:
   - pkg:pypi/jupyterlab-myst
   size: 2127008
   timestamp: 1714146125212
+- kind: conda
+  name: jupyterlab_code_formatter
+  version: 2.2.1
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_code_formatter-2.2.1-pyhd8ed1ab_0.conda
+  sha256: 8873858a9d3b730a1d6a199be6d4fa67367837d6fa55aa8fe464040522cd906d
+  md5: d67b33450635a2ad1b55d48838eb1eca
+  depends:
+  - jupyter_server >=1.21,<3
+  - python >=3.7
+  license: MIT
+  license_family: MIT
+  size: 28923
+  timestamp: 1684681885304
 - kind: conda
   name: jupyterlab_pygments
   version: 0.3.0
diff --git a/pixi.toml b/pixi.toml
index a2de7b2..c8b913e 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -31,6 +31,7 @@ jupyterlab = ">=4.2.0,<4.3"
 jupyterlab-git = ">=0.50.0,<0.51"
 jupyterlab-lsp = ">=5.1.0,<5.2"
 jupyterlab-myst = ">=2.4.2,<2.5"
+jupyterlab_code_formatter = ">=2.2.1,<2.3"
 myst-nb = ">=1.1.0,<1.2"
 numpy = ">=1.26.4,<1.27"
 pre-commit = ">=3.7.1,<3.8"

From 7aa239afbd2a4c56ba32aa639abe3daecf1efd48 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Fri, 17 May 2024 17:24:40 +0200
Subject: [PATCH 4/9] ready to go draft of decay and gamma generation

---
 docs/index.md           |   4 +-
 docs/pgamma-state.ipynb | 285 +++++++++++++++++++++++++++++-----------
 docs/reaction.md        |  10 +-
 3 files changed, 216 insertions(+), 83 deletions(-)

diff --git a/docs/index.md b/docs/index.md
index d0329a7..b08e62e 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -1,11 +1,11 @@
 # Amplitude Analysis 101 / PWA101 (v2.0)
 
-## Amplitude models for photoproduction reaction
+## CAS-assisted Amplitude Models building for photoproduction reaction
 
 This document is a follow-up of PWA101 (v1.0) (temporarily see [here](https://compwa--217.org.readthedocs.build/report/999.html)),
 as an introduction to Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model.
 
-Now the focus is the use of symbolic expressions (computations) with the use of [ComPWA packages](https://compwa.github.io/), or CAS(Computer Algebra System)-assisted model building in general (the python package `SymPy` in this case) to illustrate the general process in PWA.
+Now the focus is the use of symbolic expressions (computations), with the use of [ComPWA packages](https://compwa.github.io/), or CAS(Computer Algebra System)-assisted model building in general (the python package `SymPy` in this case) to illustrate the general process in PWA.
 
 This tutorial aims to equip readers with deeper understanding of PWA methodologies and full workflow in the context of hadron physics through a practical, hands-on example with symbolic expressions via [ComPWA](https://compwa.github.io/).
 
diff --git a/docs/pgamma-state.ipynb b/docs/pgamma-state.ipynb
index b00a1db..d2ff38b 100644
--- a/docs/pgamma-state.ipynb
+++ b/docs/pgamma-state.ipynb
@@ -11,14 +11,7 @@
     "tags": []
    },
    "source": [
-    "::::{margin}\n",
-    ":::{card} Create a virtual particle that represents the state pγ in `QRules`\n",
-    "Report-0\n",
-    "^^^\n",
-    "+++\n",
-    "✅&nbsp;[ComPWA/gluex-nstar#5](https://github.com/ComPWA/gluex-nstar/issues/5)\n",
-    ":::\n",
-    "::::"
+    "# Virtual particle that represents the state pγ "
    ]
   },
   {
@@ -32,7 +25,7 @@
     "tags": []
    },
    "source": [
-    "# Virtual particle that represents the state pγ "
+    "Address to issue ✅&nbsp;[ComPWA/gluex-nstar#5](https://github.com/ComPWA/gluex-nstar/issues/5), this section is an investigation of creating a virtual particle that represents the state $p \\gamma$ in `QRules`"
    ]
   },
   {
@@ -46,21 +39,15 @@
     "tags": []
    },
    "source": [
-    "Address to issue [ComPWA/gluex-nstar#5](https://github.com/ComPWA/gluex-nstar/issues/5), this section is an investigation of creating a virtual particle that represents the state $p \\gamma$"
+    "As an example of side note, create a virtual particle that represents state $e^+ e^-$ can be seen [here](https://qrules.readthedocs.io/0.10.x/usage/particle/#adding-custom-particle-definitions-through-python)."
    ]
   },
   {
    "cell_type": "markdown",
    "id": "3",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
-    "As an example of side note, create a virtual particle that represents state $e^+ e^-$ can be seen [here](https://qrules.readthedocs.io/0.10.x/usage/particle/#adding-custom-particle-definitions-through-python)."
+    "## Finding particles"
    ]
   },
   {
@@ -68,7 +55,7 @@
    "id": "4",
    "metadata": {},
    "source": [
-    "`QRules` is used for this task"
+    "Our reaction is $p + \\gamma \\to \\eta + \\pi^0 + p$, so we can look for each of the reaction and decay particles"
    ]
   },
   {
@@ -90,10 +77,34 @@
     "print(\"Number of loaded particles:\", len(particle_db))"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "6",
+   "metadata": {},
+   "source": [
+    "The [`ParticleCollection`](https://qrules.readthedocs.io/0.10.x/api/qrules.particle/#qrules.particle.ParticleCollection) class offers some methods to search for particles by name or by PID, name, or other properties."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7",
+   "metadata": {},
+   "source": [
+    "### Proton"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8",
+   "metadata": {},
+   "source": [
+    "Search by Particle ID (PID) for proton:"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6",
+   "id": "9",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -106,36 +117,57 @@
     "particle_db.find(2212)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "10",
+   "metadata": {},
+   "source": [
+    "Search by Particle name for proton:"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7",
+   "id": "11",
    "metadata": {},
    "outputs": [],
    "source": [
-    "particle_db.find(\"p\")"
+    "particle_db.find(\"p\")\n",
+    "proton = particle_db[\"p\"]"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "id": "12",
+   "metadata": {},
    "outputs": [],
    "source": [
-    "particle_db.find(22)"
+    "from IPython.display import Math\n",
+    "\n",
+    "Math(proton.latex)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "13",
+   "metadata": {},
+   "source": [
+    "### $\\gamma$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "14",
+   "metadata": {},
+   "source": [
+    "similarly for $\\gamma$:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9",
+   "id": "15",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -145,63 +177,134 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "id": "16",
+   "metadata": {},
    "outputs": [],
    "source": [
-    "from IPython.display import Math\n",
-    "\n",
-    "sigmas = particle_db.filter(\n",
-    "    lambda p: p.name.startswith(\"p\") and p.mass == 0.93827208816 and p.charge == 1\n",
-    ")\n",
-    "Math(\", \".join(p.latex for p in sigmas))"
+    "gamma = particle_db[\"gamma\"]\n",
+    "Math(gamma.latex)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "17",
+   "metadata": {},
+   "source": [
+    "### $\\eta$"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11",
+   "id": "18",
    "metadata": {},
    "outputs": [],
    "source": [
-    "from IPython.display import Math\n",
-    "\n",
-    "sigmas = particle_db.filter(lambda p: p.name.startswith(\"gamma\"))\n",
-    "Math(\", \".join(p.latex for p in sigmas))"
+    "particle_db.find(\"eta\")"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12",
+   "id": "19",
    "metadata": {},
    "outputs": [],
    "source": [
-    "proton = particle_db[\"p\"]\n",
-    "proton"
+    "eta = particle_db[\"eta\"]\n",
+    "Math(gamma.latex)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "20",
+   "metadata": {},
+   "source": [
+    "### $\\pi^0$"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "13",
+   "id": "21",
    "metadata": {},
    "outputs": [],
    "source": [
-    "gamma = particle_db[\"gamma\"]\n",
-    "gamma"
+    "particle_db.find(\"pi0\")"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "14",
+   "id": "22",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pi0 = particle_db[\"pi0\"]\n",
+    "Math(pi0.latex)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "23",
+   "metadata": {},
+   "source": [
+    "# Adding custom particle"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "24",
+   "metadata": {},
+   "source": [
+    "We add the virtual particle $p\\gamma$ to represent the state of $p-\\gamma$ system in the photoproduction reaction.\n",
+    "See PWA101 (temporary [here](https://compwa--217.org.readthedocs.build/report/999.html)), the value of the mass of the system $m_{p\\gamma}$ in CM frame is about 4.102 GeV in this analysis.\n",
+    "\n",
+    "\n",
+    "We use `Particle` from `QRules` for adding custom particle, so that some quantum numbers we need to determine for the $p\\gamma$ virtual state particle:\n",
+    "\n",
+    "* (Total) Spin\n",
+    "    * $J_{p\\gamma} = \\frac{1}{2}$ or $\\frac{3}{2}$\n",
+    "      \n",
+    "      because $J_{p\\gamma}$ = from $|s_p-s_{\\gamma}|$ to $s_p + s_{\\gamma}$ = from $|\\frac{1}{2}-1|$ to $\\frac{1}{2} + 1$\n",
+    "      \n",
+    "* Mass\n",
+    "    * $m_{p\\gamma} = E_{p\\gamma} \\approx 4.102$\n",
+    "    \n",
+    "* Charge\n",
+    "    * $Q_{p\\gamma} = Q_p + Q_{\\gamma} = 1 $\n",
+    "      \n",
+    "* Isospin and $3^{rd}# component of isospin\n",
+    "    * $I_{p\\gamma} = I_p = \\frac{1}{2}$\n",
+    "    * $I_{3_{p\\gamma}} = I_{3_p} = +\\frac{1}{2}$\n",
+    "  \n",
+    "* Baryon Number\n",
+    "    * $B_{p\\gamma} = B_p  = 1$\n",
+    "\n",
+    "* Parity\n",
+    "    * $P_{p\\gamma} = P_p \\times P_{\\gamma} = +1 \\times (-1) = -1$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "25",
+   "metadata": {},
+   "source": [
+    "These quantum numbers provide a complete and accurate description of the virtual particle representing the p−γ system with a mass of 4.102 GeV.\n",
+    "The pγ virtual particle has two possibilities for the total spin, while the other quantum numbers are fixed."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "26",
+   "metadata": {},
+   "source": [
+    "We add the spin-$\\frac{1}{2}$ $p\\gamma$ virtual particle via `QRules` and named it $p\\gamma$ with a make-up pid number 99990"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "27",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -209,74 +312,104 @@
     "\n",
     "pgamma = Particle(\n",
     "    name=\"p\",\n",
-    "    latex=r\"p \\gamma\",\n",
+    "    latex=r\"p\\gamma (s1/2)\",\n",
     "    spin=0.5,\n",
     "    mass=4.101931071854584,\n",
     "    charge=1,\n",
     "    isospin=Spin(1 / 2, +1 / 2),\n",
     "    baryon_number=1,\n",
     "    parity=-1,\n",
-    "    pid=99999999,\n",
+    "    pid=99990,\n",
     ")\n",
     "pgamma"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "28",
+   "metadata": {},
+   "source": [
+    "We add the spin-$\\frac{3}{2}$ $p\\gamma$ virtual particle via `QRules` and named it $p\\gamma (s3/2)$ with a make-up pid number 99991"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "15",
+   "id": "29",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pgamma_s3over2 = Particle(\n",
+    "pgamma_j3over2 = Particle(\n",
     "    name=\"pgamma\",\n",
-    "    latex=R\"p \\gamma (s3/2)\",\n",
+    "    latex=R\"p\\gamma (s3/2)\",\n",
     "    spin=1.5,\n",
     "    mass=4.101931071854584,\n",
     "    charge=1,\n",
     "    isospin=Spin(1 / 2, +1 / 2),\n",
     "    baryon_number=1,\n",
     "    parity=-1,\n",
-    "    pid=99999999,\n",
+    "    pid=99991,\n",
     ")\n",
-    "pgamma_s3over2"
+    "pgamma_j3over2"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "16",
+   "id": "30",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pgamma_s3over2.latex"
+    "Math(pgamma.latex)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "17",
+   "id": "31",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pgamma.latex"
+    "Math(pgamma_j3over2.latex)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "18",
+   "id": "32",
    "metadata": {},
    "source": [
-    "The `pgamma` virtual state generated via `QRules` will be used in later stages!"
+    "The $`p\\gamma`$ virtual states generated via `QRules` will be used in later stages, both possible spin states $(J= \\frac{1}{2}$ and $\\frac{3}{2})$ should be taken into account if possible, otherwise simplified if necessary."
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "19",
+   "cell_type": "markdown",
+   "id": "33",
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "source": [
+    ":::{important}\n",
+    "It is possible to add any kind of custom Particle, as long as its quantum numbers comply with the [gellmann_nishijima()](https://qrules.readthedocs.io/0.10.x/api/qrules.conservation_rules/#qrules.conservation_rules.gellmann_nishijima) rule:\n",
+    ":::\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "34",
+   "metadata": {},
+   "source": [
+    ":::{note}\n",
+    "[Gell-Mann-Nishijima formula](https://en.wikipedia.org/wiki/Gell-Mann–Nishijima_formula):\n",
+    "$Q = I_3 + \\frac{1}{2}(B+S+C+B'+T)$\n",
+    "\n",
+    "where \n",
+    "Q is charge, \n",
+    "$I_3$ is Spin projection of isospin, \n",
+    " B is baryon number, \n",
+    " S is strangeness, \n",
+    " C is charmness, \n",
+    " B' is bottomness, and \n",
+    " T is topness.\n",
+    ":::\n"
+   ]
   }
  ],
  "metadata": {
diff --git a/docs/reaction.md b/docs/reaction.md
index 0f8a6cd..17f3519 100644
--- a/docs/reaction.md
+++ b/docs/reaction.md
@@ -1,17 +1,17 @@
-# Reaction and amplitude models
+# Reaction and Models
 
 <!-- cspell:ignore Mathieu -->
 <!-- This amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/) by Vincent Mathieu. -->
 
-## Reaction
+## Reaction with Resonances and Decay
 
-The (photo-production) reaction is $ \gamma p \to \eta \pi^0 p$, it is described by a amplitude model with three possible resonances: $a_2$, $\Delta^+$, and $N^*$.
+The (photo-production) reaction is $ \gamma p \to \eta \pi^0 p$, its decay is described by an amplitude model with three possible resonances: $a_2$, $\Delta^+$, and $N^*$.
 
 ```{image} https://github.com/ComPWA/compwa-org/assets/17490173/ec6bf191-bd5f-43b0-a6cb-da470b071630
 :width: 100%
 ```
 
-## Amplitude models
+## Amplitude Models
 
 The amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/), only the Breit-Wigner and Spherical harmonics terms are kept for doing PWA eventually, as shown in equation {eq}`BW_SH_label`.
 
@@ -24,7 +24,7 @@ A^{31} &=& \frac{c_0}{s-m^2_{N^*}+im_{N^*} \Gamma_{N^*}}
 \end{eqnarray}
 $$ (BW_SH_label)
 
-where s is the Mandelstam variable, m is the mass, $\Gamma$ is the width, Y is the spherical harmonics, $\Omega$ is the decay angles (a pair of Euler angles), and a, b, and c are coefficients
+where s is the Mandelstam variable, m is the mass, $\Gamma$ is the width, $Y^m_l$ is the spherical harmonics, $\Omega_i$ is the decay angles (a pair of Euler angles), and $a_i$, $b_i$, and $c_i$ are coefficients
 
 :::{note}
 Mandelstam variables $s_{ij}=(p_i+p_j)^2$, $t_i=(p_a-p_i)^2$, and $u_i=(p_b-p_i)^2$.

From 165b294585cb6b4e3bcdea435e3b66f4d400f7d7 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Fri, 24 May 2024 18:54:03 +0200
Subject: [PATCH 5/9] draft now for the transition

---
 docs/pgamma-state.ipynb | 133 ++++++++++++++++++++++++++++++++++++----
 pixi.toml               |   1 +
 2 files changed, 123 insertions(+), 11 deletions(-)

diff --git a/docs/pgamma-state.ipynb b/docs/pgamma-state.ipynb
index d2ff38b..2db8722 100644
--- a/docs/pgamma-state.ipynb
+++ b/docs/pgamma-state.ipynb
@@ -71,6 +71,7 @@
    },
    "outputs": [],
    "source": [
+    "from IPython.display import Math\n",
     "from qrules.particle import load_pdg\n",
     "\n",
     "particle_db = load_pdg()\n",
@@ -305,13 +306,19 @@
    "cell_type": "code",
    "execution_count": null,
    "id": "27",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "from qrules.particle import Particle, Spin\n",
     "\n",
     "pgamma = Particle(\n",
-    "    name=\"p\",\n",
+    "    name=\"pgamma\",\n",
     "    latex=r\"p\\gamma (s1/2)\",\n",
     "    spin=0.5,\n",
     "    mass=4.101931071854584,\n",
@@ -336,11 +343,17 @@
    "cell_type": "code",
    "execution_count": null,
    "id": "29",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "pgamma_j3over2 = Particle(\n",
-    "    name=\"pgamma\",\n",
+    "    name=\"pgammas3/2\",\n",
     "    latex=R\"p\\gamma (s3/2)\",\n",
     "    spin=1.5,\n",
     "    mass=4.101931071854584,\n",
@@ -357,7 +370,13 @@
    "cell_type": "code",
    "execution_count": null,
    "id": "30",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "Math(pgamma.latex)"
@@ -367,23 +386,51 @@
    "cell_type": "code",
    "execution_count": null,
    "id": "31",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "Math(pgamma_j3over2.latex)"
    ]
   },
   {
-   "cell_type": "markdown",
+   "cell_type": "code",
+   "execution_count": null,
    "id": "32",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
    "source": [
-    "The $`p\\gamma`$ virtual states generated via `QRules` will be used in later stages, both possible spin states $(J= \\frac{1}{2}$ and $\\frac{3}{2})$ should be taken into account if possible, otherwise simplified if necessary."
+    "particle_db.add(pgamma)"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "33",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "The $`p\\gamma`$ virtual states generated via `QRules` will be used in later stages, both possible spin states $(J= \\frac{1}{2}$ and $\\frac{3}{2})$ should be taken into account if possible, otherwise simplified if necessary."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "34",
    "metadata": {},
    "source": [
     ":::{important}\n",
@@ -393,8 +440,14 @@
   },
   {
    "cell_type": "markdown",
-   "id": "34",
-   "metadata": {},
+   "id": "35",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
     ":::{note}\n",
     "[Gell-Mann-Nishijima formula](https://en.wikipedia.org/wiki/Gell-Mann–Nishijima_formula):\n",
@@ -410,6 +463,64 @@
     " T is topness.\n",
     ":::\n"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "36",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "import qrules\n",
+    "\n",
+    "reaction1 = qrules.generate_transitions(\n",
+    "    initial_state=(\"pgamma\"),\n",
+    "    final_state=[\"eta\", \"pi0\", \"p\"],\n",
+    "    # allowed_intermediate_particles=[\"f(0)(980)\", \"f(0)(1500)\"],\n",
+    "    allowed_interaction_types=[\"strong\", \"EM\", \"weak\"],\n",
+    "    formalism=\"canonical-helicity\",\n",
+    "    particle_db=particle_db,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "37",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "import graphviz\n",
+    "\n",
+    "dot = qrules.io.asdot(reaction1, collapse_graphs=True)\n",
+    "graphviz.Source(dot)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "38",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
diff --git a/pixi.toml b/pixi.toml
index c8b913e..238cb6d 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -22,6 +22,7 @@ sphinx-autobuild \
 [dependencies]
 black = ">=24.4.2,<24.5"
 graphviz = ">=9.0.0,<9.1"
+ipython = ">=8.24.0,<8.25"
 ipywidgets = ">=8.1.2,<8.2"
 isort = ">=5.13.2,<5.14"
 jax = ">=0.4.26,<0.5"

From c25be43e7cb1c396d854dd30fe8395aeaab2c9d0 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Mon, 3 Jun 2024 16:09:37 +0200
Subject: [PATCH 6/9] add transition and graph

---
 docs/pgamma-state.ipynb | 78 +++++++++++++++++++++++++++++------------
 pixi.lock               | 38 ++++++++++++++++++++
 pixi.toml               |  1 +
 3 files changed, 95 insertions(+), 22 deletions(-)

diff --git a/docs/pgamma-state.ipynb b/docs/pgamma-state.ipynb
index 2db8722..b72ecc4 100644
--- a/docs/pgamma-state.ipynb
+++ b/docs/pgamma-state.ipynb
@@ -73,7 +73,9 @@
    "source": [
     "from IPython.display import Math\n",
     "from qrules.particle import load_pdg\n",
+    "from ampform.io import aslatex, improve_latex_rendering\n",
     "\n",
+    "improve_latex_rendering()\n",
     "particle_db = load_pdg()\n",
     "print(\"Number of loaded particles:\", len(particle_db))"
    ]
@@ -274,7 +276,7 @@
     "* Charge\n",
     "    * $Q_{p\\gamma} = Q_p + Q_{\\gamma} = 1 $\n",
     "      \n",
-    "* Isospin and $3^{rd}# component of isospin\n",
+    "* Isospin and $3^{rd}$ component of isospin\n",
     "    * $I_{p\\gamma} = I_p = \\frac{1}{2}$\n",
     "    * $I_{3_{p\\gamma}} = I_{3_p} = +\\frac{1}{2}$\n",
     "  \n",
@@ -352,8 +354,8 @@
    },
    "outputs": [],
    "source": [
-    "pgamma_j3over2 = Particle(\n",
-    "    name=\"pgammas3/2\",\n",
+    "pgamma2 = Particle(\n",
+    "    name=\"pgamma2\",\n",
     "    latex=R\"p\\gamma (s3/2)\",\n",
     "    spin=1.5,\n",
     "    mass=4.101931071854584,\n",
@@ -363,7 +365,7 @@
     "    parity=-1,\n",
     "    pid=99991,\n",
     ")\n",
-    "pgamma_j3over2"
+    "pgamma2"
    ]
   },
   {
@@ -395,7 +397,7 @@
    },
    "outputs": [],
    "source": [
-    "Math(pgamma_j3over2.latex)"
+    "Math(pgamma2.latex)"
    ]
   },
   {
@@ -415,8 +417,18 @@
    ]
   },
   {
-   "cell_type": "markdown",
+   "cell_type": "code",
+   "execution_count": null,
    "id": "33",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "particle_db.add(pgamma2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "34",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -430,7 +442,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "34",
+   "id": "35",
    "metadata": {},
    "source": [
     ":::{important}\n",
@@ -440,7 +452,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "35",
+   "id": "36",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -467,7 +479,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "36",
+   "id": "37",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -478,8 +490,9 @@
    "outputs": [],
    "source": [
     "import qrules\n",
+    "import graphviz\n",
     "\n",
-    "reaction1 = qrules.generate_transitions(\n",
+    "reaction1_all = qrules.generate_transitions(\n",
     "    initial_state=(\"pgamma\"),\n",
     "    final_state=[\"eta\", \"pi0\", \"p\"],\n",
     "    # allowed_intermediate_particles=[\"f(0)(980)\", \"f(0)(1500)\"],\n",
@@ -492,7 +505,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "37",
+   "id": "38",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -502,23 +515,44 @@
    },
    "outputs": [],
    "source": [
-    "import graphviz\n",
-    "\n",
-    "dot = qrules.io.asdot(reaction1, collapse_graphs=True)\n",
+    "dot = qrules.io.asdot(reaction1_all, collapse_graphs=True)\n",
+    "print(\"All interaction types\")\n",
     "graphviz.Source(dot)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "38",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "id": "39",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "reaction1 = qrules.generate_transitions(\n",
+    "    initial_state=(\"pgamma2\"),\n",
+    "    final_state=[\"eta\", \"pi0\", \"p\"],\n",
+    "    # allowed_intermediate_particles=[\"f(0)(980)\", \"f(0)(1500)\"],\n",
+    "    allowed_interaction_types=[\"strong\", \"EM\", \"weak\"],\n",
+    "    formalism=\"canonical-helicity\",\n",
+    "    particle_db=particle_db,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "40",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dot1 = qrules.io.asdot(reaction1, collapse_graphs=True)\n",
+    "graphviz.Source(dot1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "41",
+   "metadata": {},
    "outputs": [],
    "source": []
   }
diff --git a/pixi.lock b/pixi.lock
index 1f31ac1..6e93627 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -9,6 +9,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/_openmp_mutex-4.5-2_gnu.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/accessible-pygments-0.0.4-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/alabaster-0.7.16-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/ampform-0.15.4-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/anyio-4.3.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/argon2-cffi-23.1.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/argon2-cffi-bindings-21.2.0-py312h98912ed_4.conda
@@ -232,6 +233,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/scipy-1.13.0-py312hc2bc53b_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/send2trash-1.8.3-pyh0d859eb_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/setuptools-69.5.1-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/singledispatchmethod-1.0-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/six-1.16.0-pyh6c4a22f_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/smmap-5.0.0-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/sniffio-1.3.1-pyhd8ed1ab_0.conda
@@ -358,6 +360,27 @@ packages:
   - pkg:pypi/alabaster
   size: 18365
   timestamp: 1704848898483
+- kind: conda
+  name: ampform
+  version: 0.15.4
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/ampform-0.15.4-pyhd8ed1ab_0.conda
+  sha256: 624cff712efc18b9671a8252d619c0d09333145820d317730790ec56c7f22d3d
+  md5: b84e06a4afa0667bb831782d42aff262
+  depends:
+  - attrs >=20.1.0
+  - importlib-metadata
+  - python >=3.7
+  - qrules >=0.9.6
+  - singledispatchmethod
+  - sympy >=1.10
+  - typing-extensions
+  license: GPL-3.0-or-later
+  license_family: GPL
+  size: 76402
+  timestamp: 1716399533026
 - kind: conda
   name: anyio
   version: 4.3.0
@@ -4567,6 +4590,21 @@ packages:
   - pkg:pypi/setuptools
   size: 501790
   timestamp: 1713094963112
+- kind: conda
+  name: singledispatchmethod
+  version: '1.0'
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/singledispatchmethod-1.0-pyhd8ed1ab_0.tar.bz2
+  sha256: c743d4361e5512bccb902b16898ca2186091518c70be8a6c47c196c634048148
+  md5: e237d56c3f2fa2cb34d9dd0553590f94
+  depends:
+  - python >=2.7
+  license: MIT
+  license_family: MIT
+  size: 9246
+  timestamp: 1659474768029
 - kind: conda
   name: six
   version: 1.16.0
diff --git a/pixi.toml b/pixi.toml
index 238cb6d..a6442bd 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -20,6 +20,7 @@ sphinx-autobuild \
 """
 
 [dependencies]
+ampform = ">=0.15.4,<0.16"
 black = ">=24.4.2,<24.5"
 graphviz = ">=9.0.0,<9.1"
 ipython = ">=8.24.0,<8.25"

From da9e2d9fa819d9761a60e361f972bfd3ae6d3d48 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Tue, 4 Jun 2024 10:47:13 +0200
Subject: [PATCH 7/9] test diff transitions

---
 docs/pgamma-state.ipynb | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/docs/pgamma-state.ipynb b/docs/pgamma-state.ipynb
index b72ecc4..3bfab17 100644
--- a/docs/pgamma-state.ipynb
+++ b/docs/pgamma-state.ipynb
@@ -495,7 +495,7 @@
     "reaction1_all = qrules.generate_transitions(\n",
     "    initial_state=(\"pgamma\"),\n",
     "    final_state=[\"eta\", \"pi0\", \"p\"],\n",
-    "    # allowed_intermediate_particles=[\"f(0)(980)\", \"f(0)(1500)\"],\n",
+    "    allowed_intermediate_particles=[\"a(2)\", \"Delta\", \"N\"],\n",
     "    allowed_interaction_types=[\"strong\", \"EM\", \"weak\"],\n",
     "    formalism=\"canonical-helicity\",\n",
     "    particle_db=particle_db,\n",
@@ -530,7 +530,7 @@
     "reaction1 = qrules.generate_transitions(\n",
     "    initial_state=(\"pgamma2\"),\n",
     "    final_state=[\"eta\", \"pi0\", \"p\"],\n",
-    "    # allowed_intermediate_particles=[\"f(0)(980)\", \"f(0)(1500)\"],\n",
+    "    allowed_intermediate_particles=[\"a(2)\", \"Delta\", \"N\"],\n",
     "    allowed_interaction_types=[\"strong\", \"EM\", \"weak\"],\n",
     "    formalism=\"canonical-helicity\",\n",
     "    particle_db=particle_db,\n",

From 675cc078b1dc0583c3950096f81b1af477515f1a Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Tue, 4 Jun 2024 17:46:57 +0200
Subject: [PATCH 8/9] strong EM weak transition

---
 docs/pgamma-state.ipynb | 41 ++++++++++++++++++++++++++++++++++-------
 1 file changed, 34 insertions(+), 7 deletions(-)

diff --git a/docs/pgamma-state.ipynb b/docs/pgamma-state.ipynb
index 3bfab17..62a35f3 100644
--- a/docs/pgamma-state.ipynb
+++ b/docs/pgamma-state.ipynb
@@ -495,7 +495,7 @@
     "reaction1_all = qrules.generate_transitions(\n",
     "    initial_state=(\"pgamma\"),\n",
     "    final_state=[\"eta\", \"pi0\", \"p\"],\n",
-    "    allowed_intermediate_particles=[\"a(2)\", \"Delta\", \"N\"],\n",
+    "    # allowed_intermediate_particles=[\"a(2)\", \"Delta\", \"N\"],\n",
     "    allowed_interaction_types=[\"strong\", \"EM\", \"weak\"],\n",
     "    formalism=\"canonical-helicity\",\n",
     "    particle_db=particle_db,\n",
@@ -516,7 +516,6 @@
    "outputs": [],
    "source": [
     "dot = qrules.io.asdot(reaction1_all, collapse_graphs=True)\n",
-    "print(\"All interaction types\")\n",
     "graphviz.Source(dot)"
    ]
   },
@@ -527,11 +526,11 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "reaction1 = qrules.generate_transitions(\n",
-    "    initial_state=(\"pgamma2\"),\n",
+    "reaction1_strong_EM = qrules.generate_transitions(\n",
+    "    initial_state=(\"pgamma\"),\n",
     "    final_state=[\"eta\", \"pi0\", \"p\"],\n",
-    "    allowed_intermediate_particles=[\"a(2)\", \"Delta\", \"N\"],\n",
-    "    allowed_interaction_types=[\"strong\", \"EM\", \"weak\"],\n",
+    "    # allowed_intermediate_particles=[\"a(2)\", \"Delta\", \"N\"],\n",
+    "    allowed_interaction_types=[\"strong\", \"EM\"],\n",
     "    formalism=\"canonical-helicity\",\n",
     "    particle_db=particle_db,\n",
     ")"
@@ -544,7 +543,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "dot1 = qrules.io.asdot(reaction1, collapse_graphs=True)\n",
+    "dot1 = qrules.io.asdot(reaction1_strong_EM, collapse_graphs=True)\n",
     "graphviz.Source(dot1)"
    ]
   },
@@ -554,6 +553,34 @@
    "id": "41",
    "metadata": {},
    "outputs": [],
+   "source": [
+    "reaction1_strong = qrules.generate_transitions(\n",
+    "    initial_state=(\"pgamma\"),\n",
+    "    final_state=[\"eta\", \"pi0\", \"p\"],\n",
+    "    # allowed_intermediate_particles=[\"a(2)\", \"Delta\", \"N\"],\n",
+    "    allowed_interaction_types=[\"strong\"],\n",
+    "    formalism=\"canonical-helicity\",\n",
+    "    particle_db=particle_db,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "42",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dot1 = qrules.io.asdot(reaction1_strong, collapse_graphs=True)\n",
+    "graphviz.Source(dot1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "43",
+   "metadata": {},
+   "outputs": [],
    "source": []
   }
  ],

From 139807e655d6a12f878bdf39166718088b4fae0c Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Tue, 4 Jun 2024 18:05:40 +0200
Subject: [PATCH 9/9] add readthedoc yaml file

---
 .readthedocs.yaml | 13 +++++++++++++
 1 file changed, 13 insertions(+)
 create mode 100644 .readthedocs.yaml

diff --git a/.readthedocs.yaml b/.readthedocs.yaml
new file mode 100644
index 0000000..2d7e00c
--- /dev/null
+++ b/.readthedocs.yaml
@@ -0,0 +1,13 @@
+version: "2"
+
+build:
+  os: "ubuntu-22.04"
+  tools:
+    python: "3.12"
+
+python:
+  install:
+    - requirements: docs/requirements.txt
+
+sphinx:
+  configuration: docs/conf.py