{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ratios of light nuclei in the statistical model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import special\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formulas for the particle density $n$:"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the formula for the particle density $n_i$ from the lecture (slide 6 of chapter 5):\n",
    "\n",
    "$$ \n",
    "n_i = g_i \\frac{4 \\pi}{(2 \\pi)^3} \\int_0^{\\infty} \\frac{p^2\\,\\mathrm dp}{\\exp\\left(\\frac{\\sqrt{p^2+m^2}-\\mu}{T}\\right) \\pm 1}\n",
    " = \n",
    "\\frac{g_i}{2 \\pi^2} m^2 T \\sum \\limits_{k=1}^{\\infty} \\frac{(\\mp 1)^{k+1}}{k} e^{k \\mu / T} \n",
    "K_2\\left( \\frac{k m}{T}\\right)\n",
    "$$\n",
    "\n",
    "Here the upper sign is for fermions and the lower signs for bosons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def n_hadron_general(T, mu, m, g, sign, nsum):\n",
    "    \"\"\"\n",
    "    Hadron density in a simple statistical mode (vanashing baryo-chemical potential)\n",
    "    T: temperature\n",
    "    mu: baryo-chemical potential\n",
    "    m: hadron mass\n",
    "    g: degeneracy\n",
    "    sign: + for bosons, - for fermions\n",
    "    nsum: number of terms to add up\n",
    "    \"\"\"\n",
    "    sum = 0\n",
    "    for k in range(1, nsum+1):\n",
    "        sum += T*g/(2*np.pi**2) * sign**(k+1)/k * m**2 * np.exp(k * mu / T) * special.kn(2,k*m/T)\n",
    "    return sum"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Boltzmann approximation takes only the first term of the sum (which is the same for bosons and for fermions):\n",
    "\n",
    "$$\n",
    "n_i = \n",
    "\\frac{g_i}{2 \\pi^2} m^2 T e^{\\mu / T} \n",
    "K_2\\left( \\frac{m}{T}\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def n_hadron_boltzmann(T, mu, m, g):\n",
    "    \"\"\"\n",
    "    Take only first term of the sum in n_hadron_general.\n",
    "    First term is the same for bosons and fernions (independent of the sign)\n",
    "    \"\"\"\n",
    "    return n_hadron_general(T, mu, m, g, 1, 1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Large argument approximation of the Bessel function:\n",
    "    \n",
    "$$ K_\\nu(x) \\approx \\sqrt{\\frac{\\pi}{2 x}} e^{-x} $$ \n",
    "\n",
    "This gives\n",
    "\n",
    "$$ n_i = \\frac{g}{(2 \\pi)^{3/2}} (m T)^{3/2} e^{-m/T}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def n_hadron_approx_bessel(T, mu, m, g):\n",
    "    return g/(2*np.pi)**(3/2) * (m * T)**(3/2) * np.exp(mu/T) * np.exp(-m/T)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot particle density per degree of freedom for different approximations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12f8cb250>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mval = np.linspace(0.1, 2, 1000)\n",
    "n_had_gen_bose = n_hadron_general(0.156, 0, mval, 1, 1, 20)\n",
    "n_had_boltz = n_hadron_boltzmann(0.156, 0, mval, 1)\n",
    "n_had_approx_bessel = n_hadron_approx_bessel(0.156, 0, mval, 1)\n",
    "# plt.yscale('log')\n",
    "plt.xlabel('m (GeV)')\n",
    "plt.ylabel(\"density per d.o.f\")\n",
    "plt.plot(mval, n_had_gen_bose, label='quantum statistics')\n",
    "plt.plot(mval, n_had_boltz, label='Boltzmann approx.')\n",
    "plt.plot(mval, n_had_approx_bessel, label='large argument approx')\n",
    "plt.legend()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate densities for d, ${}^3$He, and ${}^4$He"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define nuclear masses (in GeV)\n",
    "m_d = 1.8756\n",
    "m_he3 = 2.8084\n",
    "m_he4 = 3.7274"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_he3_gen/n_d_gen:  2.9446E-03\n",
      "n_he4_gen/n_d_gen:  6.0723E-06\n"
     ]
    }
   ],
   "source": [
    "n_d_gen = n_hadron_general(0.156, 0, m_d, 3, +1, 20)\n",
    "n_he3_gen = n_hadron_general(0.156, 0, m_he3, 2, -1, 20)\n",
    "n_he4_gen = n_hadron_general(0.156, 0, m_he4, 1, +1, 20)\n",
    "print(\"n_he3_gen/n_d_gen: \", '{:.4E}'.format(n_he3_gen/n_d_gen))\n",
    "print(\"n_he4_gen/n_d_gen: \", '{:.4E}'.format(n_he4_gen/n_d_gen))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_he3_approx/n_d_approx:  3.0905E-03\n",
      "n_he4_approx/n_d_approx:  6.5310E-06\n"
     ]
    }
   ],
   "source": [
    "n_d_boltz = n_hadron_approx_bessel(0.156, 0, m_d, 3)\n",
    "n_he3_boltz = n_hadron_approx_bessel(0.156, 0, m_he3, 2)\n",
    "n_he4_boltz = n_hadron_approx_bessel(0.156, 0, m_he4, 1)\n",
    "print(\"n_he3_approx/n_d_approx: \", '{:.4E}'.format(n_he3_boltz/n_d_boltz))\n",
    "print(\"n_he4_approx/n_d_approx: \", '{:.4E}'.format(n_he4_boltz/n_d_boltz))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ALICE data (read off by eye):\n",
    "\n",
    "$n_{He3} / n_{d} = 3 \\cdot 10^{-3}$\n",
    "\n",
    "$n_{He4} / n_{d} = 1 \\cdot 10^{-5}$\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.10.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}