From c9b13a0010238885ad8eae3cd1362de6d055e9c2 Mon Sep 17 00:00:00 2001 From: Vladimir Date: Tue, 12 Sep 2023 15:20:05 -0600 Subject: [PATCH] pres 5 --- area.png | Bin 0 -> 64910 bytes catodicos.png | Bin 0 -> 581448 bytes geiger.jpg | Bin 0 -> 71916 bytes linac.jpg | Bin 0 -> 27452 bytes montecarlo1.png | Bin 0 -> 10591 bytes notas3.pdf | Bin 1417087 -> 1440192 bytes notas3.tex | 22 +- pres5.pdf | Bin 0 -> 4028223 bytes pres5.tex | 704 ++++++++++++++++++++++++++++++++++++++++++++++++ pres5.tex~ | 627 ++++++++++++++++++++++++++++++++++++++++++ slac.png | Bin 0 -> 1528599 bytes tevatron.jpg | Bin 0 -> 223731 bytes 12 files changed, 1343 insertions(+), 10 deletions(-) create mode 100644 area.png create mode 100644 catodicos.png create mode 100644 geiger.jpg create mode 100644 linac.jpg create mode 100644 montecarlo1.png create mode 100644 pres5.pdf create mode 100644 pres5.tex create mode 100644 pres5.tex~ create mode 100644 slac.png create mode 100644 tevatron.jpg diff --git a/area.png 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zwI2eV^AW8_R5oRj^z9Y;F*5r^&HC-Q%eLm)?%Vi%sfROmA;xVWeNS!oCH7;XTvT0% z9*Htr-z&*bqijQ0yOz%kV`>I|cA$mS#L|@#^tY_tA{gk-LR;jkhr9{2tGTziq-}E F{{vw7iW>j` literal 0 HcmV?d00001 diff --git a/pres5.tex b/pres5.tex new file mode 100644 index 0000000..7961e33 --- /dev/null +++ b/pres5.tex @@ -0,0 +1,704 @@ +\documentclass[12pt]{beamer} +\usetheme{Berlin} +\usepackage[utf8]{inputenc} +\usepackage[spanish]{babel} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{graphicx} +\usepackage{braket} + +\usepackage{appendixnumberbeamer} + +%\setbeamerfont{page number in head}{size=\large} +%\setbeamertemplate{footline}{Diapositiva} +\setbeamertemplate{footline}[frame number] + +\newcommand{\backupbegin}{ + \newcounter{finalframe} + \setcounter{finalframe}{\value{framenumber}} +} + +\newcommand{\backupend}{ + \setcounter{framenumber}{\value{finalframe}} +} + +\author{Física Nuclear y subnuclear } +\title{Experimentos en física de partículas y nuclear} +%\setbeamercovered{transparent} +%\setbeamertemplate{navigation symbols}{} +%\logo{} +%\institute{} +%\date{} +%\subject{} +\begin{document} + +\begin{frame} +\titlepage +\end{frame} + +%\begin{frame}{Contenido} +% \tableofcontents +%\end{frame} +\section*{Paso de partículas a través de la materia} +\begin{frame}{Partículas cargadas} + \begin{itemize} + \item Interacción coulombiana + \item Electrones o el núcleo + \item Depositando energía + \item Sufriendo dispersiones + \end{itemize} +\end{frame} + +\begin{frame}{Partículas cargadas} + + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.7\linewidth]{frenamiento.png} + \caption{Esquema del paso de partículas a través de la materia} + \label{fig:frena} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Distribución} + \begin{itemize} + \item Suceden múltiples y pequeñas dispersiones + \item Tenemos una distribución en energía y ángulo para las prtículas que salen. + \item Rango $R_0$ + \end{itemize} + Grosor + \begin{equation} + x_{\rho} = x\rho [gr/cm^2] + \end{equation} +\end{frame} + +\begin{frame}{Detenciones} + \begin{itemize} + \item Una fracción sale, otra es ``atrapada'' + \item Camino libre medio + \end{itemize} + \begin{align*} + dN =& -N(x)\mu dx \\ + N(x)=& N(0)e^{-\mu x}, + \end{align*} +\end{frame} + +\begin{frame}{Partículas cargadas pesadas} + \begin{itemize} + \item Colisiones inelásticas con los electrones (las más) + \item Colisiones elásticas con el núcleo (las menos) + \item Otros procesos posibles + \begin{itemize} + \item Radiación Cherenkov + \item Reacciones nucleares + \item Bremsstrahlung + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame}{La división} + \begin{itemize} + \item Electrones y positrones + \item El resto de leptones, hadrones y núcleos ligeros + \item Núcleos pesados + \end{itemize} +\end{frame} + +\begin{frame}{Poder de frenamiento} + Pérdidas por ionización + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.65\linewidth]{bethe.png} + \caption{Poder de frenamiento másico para anti-muones en cobre como función de $\beta \gamma = p/Mc$ Tomada de PDG: P.A. Zyla et al. (Particle Data Group), to be published in Prog. Theor. Exp. Phys. 2020, 083C01 (2020).} + \label{fig:bethe} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Bethe-Bloch} + \begin{equation*} + W_{max} = \frac{2m_e c^2 \beta^2 \gamma^2}{1 + 2\gamma\frac{m_e}{M}+\left(\frac{m_e}{M}\right)^2} + \end{equation*} + + \begin{align*} + -\frac{dE}{dx} &= (4\pi N_A r_e^2 m_e c^2) z^2 \frac{Z}{A}\frac{1}{\beta^2} \times \\ + &\left[ \frac{1}{2} ln\left(\frac{2m_e c^2 \beta^2 \gamma^2 W_{max}}{I^2}\right) - \beta^2 -\frac{\delta(\beta \gamma)}{2}\right] + \end{align*} +\end{frame} + +\begin{frame}{Valores} + \begin{itemize} + \item $N_A$, $r_e$, $m_e$ y $c$ $\rightarrow$ $K=4\pi N_A r_e^2 m_e c^2$ + \item $z$ de partícula incidente + \item $Z$ y $A$ de los núcleos del medio + \item $\beta$ y $\gamma$ de la partícula incidente + \item $I$ potencial de ionización + \end{itemize} +\end{frame} + +\begin{frame}{Ecuación de Bethe-Bloch compacta} + \begin{equation} + -\frac{dE}{dx} = K z^2 \frac{Z}{A}\frac{1}{\beta^2}\left[ ln\left(\frac{2m_e c^2 \beta^2 \gamma^2}{I}\right) - \beta^2 - \frac{\delta(\beta \gamma)}{2}\right] + \end{equation} + + \begin{equation*} + K= 0.3071\ MeV mol^{-1}cm^2 + \end{equation*} + + \begin{equation*} + K/A= 0.3071\ MeV gr^{-1} cm^2\ (\text{con } A=1 gr/mol) + \end{equation*} + +\end{frame} + + +\begin{frame}{Pérdida de energía total} + + \begin{equation*} + \Delta E_{perdida} = -\rho \int_0^d \frac{dE}{dx} dx + \end{equation*} + +\end{frame} + +\begin{frame}{Un ejercicio} + \begin{itemize} + \item \textbf{Qué distancia recorre un protón de $10GeV$ de energía cinética en una barra de plomo de bastante grosor.} + \end{itemize} + \begin{align*} + \rho_{Pb}=& 11.34 \frac{gr}{cm^3} \\ + m_p =& 0.938GeV/c^2 + \end{align*} +\end{frame} + +\begin{frame}{Obteniendo valores relativistas I} + \begin{align*} + \gamma=& \frac{E_T}{E_R} \\ + =& \frac{E_K+E_R}{E_R} \text{ ya que }E_T=E_K+E_r \\ + =& \frac{E_k+m_pc^2}{m_pc^2} \text{ para el protón }E_R=M_pc^2 \\ + =& \frac{E_k}{m_pc^2}+1 \text{ distribuyendo la fracción} \\ + =& \frac{10GeV}{0.938GeV}+1 = \mathbf{10.6609}. + \end{align*} +\end{frame} + +\begin{frame}{Obteniendo valores relativistas II} + Para obtener $\beta=0.9963$ + \begin{equation*} + \gamma = \frac{1}{\sqrt{1-\beta^2}}. + \end{equation*} +\end{frame} + +\begin{frame}{Calculamos la pérdida} + \begin{align*} + -\left\langle\frac{dE}{dx}\right\rangle = -0.3071& \frac{MeVcm^2}{gr}\ (1)^2 \frac{82}{207}\frac{1}{(0.9963)^2} \\ + &\left[ ln\left(\frac{2(5.11e5 eV/c^2) c^2 (0.9963)^2 (11.6609)^2}{820eV}\right) - (0.9963)^2 \right] + \label{ec:bethe2fi} + \end{align*} + \begin{equation*} + ln\left(\frac{2(5.11e5 eV/c^2) c^2 (0.9963)^2 (11.6609)^2}{820eV}\right) = 12.033 + \end{equation*} + El resto + \begin{align*} + -\left\langle\frac{dE}{dx}\right\rangle =& -0.3071 \frac{MeVcm^2}{gr}\ (1)^2 \frac{82}{207}\frac{1}{(0.9963)^2} \left[12.033-0.9963^2 \right] \\ + =& -1.35309 \frac{MeVcm^2}{gr} +\end{align*} +\end{frame} + +\begin{frame}{Últimos detalles} + \begin{equation*} + \rho \left\langle\frac{dE}{dx}\right\rangle = (11.34\frac{gr}{cm^3})(1.3531\frac{MeVcm^2}{gr})=15.3441\frac{MeV}{cm} + \end{equation*} + + \begin{align*} + R =& \int_{E_0}^0 \frac{dE}{\left\langle \frac{dE}{dx} \right\rangle}=\int_{10GeV}^0 \frac{dE}{15.3441\frac{MeV}{cm}}\\ + =& \frac{1}{15.3441\frac{MeV}{cm}}\int_{10GeV}^0 dE = \frac{1}{15.3441\frac{MeV}{cm}} (10GeV) \\ + =& \frac{10000 MeV}{15.3441\frac{MeV}{cm}} = 651.7162 cm = 6.5171 m. + \end{align*} + +\end{frame} + +\begin{frame}{Dispersión múltiple: ángulos pequeños} + \begin{equation} + \theta_0 = \theta_{plano}^{rms} = \frac{1}{\sqrt{2}} \theta_{espacio}^{rms} + \end{equation} + + \begin{equation} + \theta_0 = \frac{13.6 MeV}{\beta c p} z \sqrt{\frac{x}{X_0}}\left[ 1 + 0.038 ln \left( \frac{x z^2}{X_0 \beta^2} \right) \right] + \end{equation} + +\end{frame} + +\begin{frame}{Longitud de radiación} + \begin{itemize} + \item La distancia para la cual la energía del electrón se reduce en $1/e$ + \item $7/9$ del camino libre medio de fotones para producción de pares + \end{itemize} + + \begin{equation*} + X_0 = 716.4\ \frac{gr}{cm^2} \frac{A}{Z(Z+1)ln\left({\frac{287}{\sqrt{Z}}}\right)} + \end{equation*} + +\end{frame} + +\begin{frame}{Radiación Cherenkov} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.3\linewidth]{cherenkov.jpg} + \caption{Cono de luz de Cherenkov. Imagen de dominio público realizada por Pieter Kuiper, tomada de \url{https://commons.wikimedia.org/wiki/File:Cherenkov2.svg}.} + \label{fig:cherenkov} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Cono de luz Cherenkov} + \begin{equation*} + v=\beta c = \frac{c}{n}, + \end{equation*} + \begin{equation*} + v_{part} > \frac{c}{n}. + \end{equation*} + \begin{equation} + cos \theta_C = \frac{1}{\beta n} + \label{cos:chen} + \end{equation} +\end{frame} + +\begin{frame}{Fotones} + \begin{itemize} + \item Efecto fotoeléctrico + \item Efecto Compton + \item Producciones de pares ($E>2m_e c^2$) + \end{itemize} + +\end{frame} + +\begin{frame}{Efecto fotoeléctrico} + \begin{equation*} + T_e = h\nu -I_B + \end{equation*} +\end{frame} + +\begin{frame}{Dispersión de Compton} + +\begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.7\linewidth]{compton.png} + \caption{Dispersión de Compton, el fotón es marcado por $\lambda = 1/\nu$. Imagen tomada de This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.} + \label{fig:frena} + \end{center} + \end{figure} + +\end{frame} + +\begin{frame}{Relaciones dispersión de Compton} + + \begin{equation} + h\nu'=\frac{h\nu}{1+\gamma (1-cos\theta)}, + \end{equation} + + \begin{equation*} + T_e = h\nu - h\nu'= h\nu \frac{\gamma (1-cos\theta)}{1+\gamma (1-cos\theta)} + \end{equation*} + Límite de Compton + \begin{equation} + T_{max} = h\nu \left( \frac{2\gamma}{1+2\gamma} \right) + \end{equation} + +\end{frame} + +\begin{frame}{Producción de pares} + + \begin{itemize} + \item Fotón crea un par electrón-positrón + \item Solo puede suceder dentro del medio + \item Conservación de la energía y el momento + \item Mínimo de energía de $2m_ec^2$ + \end{itemize} + +\end{frame} + +\begin{frame}{Camino libre medio para producción de pares} + \begin{equation*} + X_{pares} = \mu_{pares}^{-1} \approx \frac{9}{7} X_0 + \end{equation*} + + ?`Qué sucede con el positrón después? + +\end{frame} + +\begin{frame}{Coeficiente de absorción} + \begin{equation*} + \mu = n\sigma + \end{equation*} +\end{frame} + +\section*{Detectores} +\begin{frame}{Detectores de ionización} + \begin{itemize} + \item Funcionan en el mismo rango de Bethe-Bloch + \item Se aplica un campo eléctrico + \item Medio ionizable y químicamente estable (bajo potencial de ionización) + \item Eletrodos: ánodo y cátodo + \end{itemize} + +\end{frame} + +\begin{frame}{Detectores de ionización } + + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.6\linewidth]{regiones.jpg} + \caption{Regiones de operación de los detectores de ionización. Imagen adaptada de la original de \href{https://commons.wikimedia.org/wiki/User:Dougsim}{Doug Sim} con licencia \href{https://en.wikipedia.org/wiki/en:Creative_Commons}{Creative Commons Attribution-Share Alike 3.0 Unported}} + \label{fig:region} + \end{center} + \end{figure} + +\end{frame} + +\begin{frame}{Contadores de ionización} + \begin{itemize} + \item En la región de ionización + \item Poco sensible a los cambios de voltaje + \item Sin amplificación + \item Requiere filtros + \item Respuesta rápida + \end{itemize} +\end{frame} + +\begin{frame}{Contadores proporcionales} + \begin{itemize} + \item Región proporcional + \item Campos eléctricos intensos $\sim 10^4 V/cm$ + \item Hay amplificación $\sim 10^5$ + \end{itemize} +\end{frame} + + + +\begin{frame}{Cámaras multilámbricas} + \begin{itemize} + \item Diseñadas por George Charpak + \item Alambres de $10-50 \mu m$ separados por $2mm.$ + \item Cátodos a $1cm$ por encima y debajo + \end{itemize} +\end{frame} + +\begin{frame}{Cámara multialámbrica} + \begin{figure} + \begin{center} + \includegraphics[width=0.4\linewidth]{mwpc.png} + \caption{Líneas de campo en cámara multialámbrica. This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.} + \label{fig:frena} + \end{center} + \end{figure} + +\end{frame} + + +\begin{frame}{Detector Geiger-Muller} + \begin{itemize} + \item Funciona en el límite + \item Produce una descarga por cada partícula que produce una ionización + \end{itemize} + +\end{frame} + + +\begin{frame}{Detector Geiger-Müller} + \begin{figure} + \begin{center} + \includegraphics[width=0.5\linewidth]{geiger.jpg} + \caption{Detector Geiger-Müller. This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.} + \label{fig:frena} + \end{center} + \end{figure} + +\end{frame} + + +\begin{frame}{Detectores de centelleo} + \begin{itemize} + \item Excitaciones de los átomos del material + \item Al regresar al estado base: emiten un fotón + \item Centelladores orgánicos: antraceno, naftaleno + \item Centelladores inorgánicos: NaI, CsI dopados + \end{itemize} + +\end{frame} + +\begin{frame}{PMT} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.7\linewidth]{pmt_es.png} + \caption{Tubo fotomultiplicador. Imagen de \href{https://commons.wikimedia.org/wiki/User:Wiso}{Wiso} con licencia \href{https://creativecommons.org/licenses/by-sa/3.0/deed.en}{Creative Commons Attribution-Share Alike 3.0 Unported}} + \end{center} + \end{figure} + ?`Usos de centelladores? +\end{frame} + +\begin{frame}{Detector Cherenkov} + \begin{itemize} + \item Partículas cargadas, pero el proceso no es ionización + \item Viaja más rápido que la luz \emph{en el medio} $v>c/n$ o $\beta>1/n$. + \item $\cos\theta_c = \frac{1}{\beta n}$ + \end{itemize} +\end{frame} + +\begin{frame}{Detectores semiconductores} + \begin{itemize} + \item Semiconductores + \item Detectores de ionización + \item $200-300 \mu m$ de grosor + \end{itemize} +\end{frame} + +\begin{frame}{Calorímetro} + \begin{itemize} + \item Las partículas depositan toda su energía cinética + \item Centelladores, contadores de ionizción o proporcionles + \item Fotones: producción de pares + \item Hadrones: procesos fuertes + \item Problemáticos: neutrinos y $\pi^0$ + \end{itemize} + +\end{frame} + +\begin{frame}{Aceleradores} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.7\linewidth]{tevatron.jpg} + \caption{Foto del Tevatrón en Fermilab. Imagen de Fermilab, Reidar Hahn, del dominio público} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Partículas nuevas} + \begin{itemize} + \item De forma natural tenemos poca variedad + \item Partículas de mayor masa requiere mayor energía + \item ?`Límite?: posiblemente $\hbar c/G_g\approx 1.22\times 10^20 eV/c^2$ + \end{itemize} + +\end{frame} + +\begin{frame}{Estudios de estructura} + \begin{columns} + \begin{column}{0.48\textwidth} + \begin{equation*} + \lambda = \frac{h}{p} + \end{equation*} + + \begin{equation*} + \bar{\lambda}= \frac{\lambda}{2\pi} = \frac{\hbar}{p} + \end{equation*} + + \begin{equation*} + \bar{\lambda} \leq d + \end{equation*} + + \begin{equation*} + p \geq \frac{\hbar}{d} + \end{equation*} + + \begin{equation*} + E_{kin} = \frac{p^2}{2m_p} = \frac{\hbar^2}{2m_p d^2} + \end{equation*} + + \end{column} + \begin{column}{0.48\textwidth} + + \begin{equation*} + \frac{E_{kin}}{m_pc^2} = \frac{1}{2d^2} \left( \frac{\hbar}{m_pc} \right)^2 + \end{equation*} + + \begin{align*} + \bar{\lambda}_p =& \frac{\hbar}{m_pc} = \frac{\hbar c}{m_pc^2}\\ + &= \frac{197.3\ MeV\ fm}{938\ MeV} = 0.210\ fm. + \end{align*} + + \begin{align*} + \frac{E_{kin}}{m_pc^2} =& \frac{1}{2} \left( \frac{\bar{\lambda}_p}{d} \right)^2 = 0.02\\ + E_{kin} =& 0.02 m_pc^2 = 0.02\times 938 MeV + \end{align*} + \end{column} + \end{columns} + + +\end{frame} + +\begin{frame}{Aceleración} + \begin{itemize} + \item $E=Fd=q|E|d = qV$ + \end{itemize} + + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.5\linewidth]{catodicos.png} + \caption{Foto de un cinescopio de televisión. Imagen de JMPerez~commonswiki con licencia Creative Commons Attribution-Share Alike 3.0 Unported} + \end{center} + \end{figure} + +\end{frame} + +\begin{frame}{Conceptos útiles} + \begin{itemize} + \item \emph{Flujo}: la cantidad de partículas que cruzan un área unitaria perpendicular al eje del haz por unidad de tiempo + + \begin{equation} + \mathcal{F} = n_i v, + \end{equation} + + \begin{equation*} + dN = \mathcal{F}N\sigma d\Omega + \end{equation*} + + \item \emph{Luminosidad}: la cantidad de eventos por unidad de sección eficaz que tienen lugar en una sección de encuentro del haz por unidad de tiempo + + \begin{equation*} + \mathcal{L} = \frac{\mathcal{N}_s}{\sigma_{tot}}=\frac{N_1 N_2 f}{A}, + \end{equation*} + + \end{itemize} + +\end{frame} + +\begin{frame}{Generadores elestrostáticos} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.5\linewidth]{vandegraff.jpg} + \caption{Esquema de un generador Van de Graff. Tomado con fines educativos de Henley} + \label{fig:vandegraff} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Van de Graff} + \begin{itemize} + \item Llega a $30-40 MeV$ + \item Más energías con un Van de Graff tandem + \item Un tandem en el IFUNAM + \end{itemize} + +\end{frame} + +\begin{frame}{Acelerdores lineales} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.5\linewidth]{slac.png} + \caption{Foto del acelerador lineal de Stanford, 3 km de longitud. Imagen de Victor Blacus en dominio público} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Linac} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.6\linewidth]{linac.jpg} + \caption{Esquema de un acelerador lineal. Imagen adaptada de Chetvorno con licencia CC0} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Óptica del haz} + \begin{itemize} + \item Lentes magnéticas + \item Dipolos pueden deflectar + \item Cuadrupolos lo más parecido a una lente óptica + \end{itemize} + \begin{equation*} + \overrightarrow{F} = q\left( \overrightarrow{E} + \frac{1}{c} \overrightarrow{v}\times \overrightarrow{B} \right) + \end{equation*} +\end{frame} + +\begin{frame}{Ciclotrón} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.7\linewidth]{ciclotron.png} + \caption{Esquema de funcionamiento de un ciclotron. Imagen de Ernest O. Lawrence - U.S. Patent 1,948,384, de dominio público} + \label{fig:ciclotron} + \end{center} + \end{figure} + +\end{frame} + +\begin{frame}{Resonancia y energía} + \begin{equation*} + \frac{v}{r} = \frac{qB}{m} + \end{equation*} + + \begin{equation*} + \omega = \frac{v}{r} + \end{equation*} + + \begin{equation*} + \nu = \frac{\omega}{2\pi} = \frac{qB}{2\pi m} = \frac{1}{2\pi}\left( \frac{q}{m} \right) B + \end{equation*} + + \begin{align*} + T_{max}=& \frac{1}{2}mv_{max}^2 = \frac{1}{2} m \omega^2 R^2 \\ + =& \frac{1}{2} m \left( \frac{qB}{m} \right)^2 R^2 = \frac{(qBR)^2}{2m} + \end{align*} +\end{frame} + +\begin{frame}{Sincrotrón} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.7\linewidth]{sincrotron.jpg} + \caption{Modelo de un acelerador sincrotrón. Imagen de EPSIM 3D/JF Santarelli, Synchrotron Soleil} + \label{fig:ciclotron} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Método Monte Carlo} + \begin{itemize} + \item Tratamiento estadístico en experimentos + \item Integración numérica + \item Optimización + \end{itemize} +\end{frame} + +\begin{frame}{Áreas por Monte Carlo} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.5\linewidth]{area.png} + \caption{Ejemplo del cálculo de una área con Montecarlo. Imagen de Mysid Yoderj con licencia Creative Commons CC0 1.0 Universal Public Domain Dedication} + \label{fig:ciclotron} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Generando a partir de distribución estadística} + \begin{itemize} + \item Valores al azar pero bajo cierta distribución + \end{itemize} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.5\linewidth]{montecarlo1.png} + \caption{Ejemplo de integración Monte Carlo. Imagen de Femizban con licencia Creative Commons Attribution-Share Alike 4.0 International} + \label{fig:ciclotron} + \end{center} + \end{figure} + +\end{frame} + +\begin{frame}{Números pseudo-aleatorios} + \begin{itemize} + \item Para acercarnos a la naturaleza necesitamos lo más aleatorio + \item Las computadoras no pueden generar números aleatorios + \item Mecanismos pseudo-aleatorios + \item Complementos verdadero-aleatorios + \end{itemize} +\end{frame} + +\begin{frame}{Paso de partículas a través de la materia} + \begin{itemize} + \item Los valores calculados por pedazos + \item Propagación de la partícula por diversos procesos + \item Comparación con el experimento + \end{itemize} +\end{frame} + + + +\end{document} diff --git a/pres5.tex~ b/pres5.tex~ new file mode 100644 index 0000000..5c174e1 --- /dev/null +++ b/pres5.tex~ @@ -0,0 +1,627 @@ +\documentclass[12pt]{beamer} +\usetheme{Berlin} +\usepackage[utf8]{inputenc} +\usepackage[spanish]{babel} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{graphicx} +\usepackage{braket} + +\usepackage{appendixnumberbeamer} + +%\setbeamerfont{page number in head}{size=\large} +%\setbeamertemplate{footline}{Diapositiva} +\setbeamertemplate{footline}[frame number] + +\newcommand{\backupbegin}{ + \newcounter{finalframe} + \setcounter{finalframe}{\value{framenumber}} +} + +\newcommand{\backupend}{ + \setcounter{framenumber}{\value{finalframe}} +} + +\author{Física Nuclear y subnuclear } +\title{Experimentos en física de partículas y nuclear} +%\setbeamercovered{transparent} +%\setbeamertemplate{navigation symbols}{} +%\logo{} +%\institute{} +%\date{} +%\subject{} +\begin{document} + +\begin{frame} +\titlepage +\end{frame} + +%\begin{frame}{Contenido} +% \tableofcontents +%\end{frame} +\section*{Paso de partículas a través de la materia} +\begin{frame}{Partículas cargadas} + \begin{itemize} + \item Interacción coulombiana + \item Electrones o el núcleo + \item Depositando energía + \item Sufriendo dispersiones + \end{itemize} +\end{frame} + +\begin{frame}{Partículas cargadas} + + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.7\linewidth]{frenamiento.png} + \caption{Esquema del paso de partículas a través de la materia} + \label{fig:frena} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Distribución} + \begin{itemize} + \item Suceden múltiples y pequeñas dispersiones + \item Tenemos una distribución en energía y ángulo para las prtículas que salen. + \item Rango $R_0$ + \end{itemize} + Grosor + \begin{equation} + x_{\rho} = x\rho [gr/cm^2] + \end{equation} +\end{frame} + +\begin{frame}{Detenciones} + \begin{itemize} + \item Una fracción sale, otra es ``atrapada'' + \item Camino libre medio + \end{itemize} + \begin{align*} + dN =& -N(x)\mu dx \\ + N(x)=& N(0)e^{-\mu x}, + \end{align*} +\end{frame} + +\begin{frame}{Partículas cargadas pesadas} + \begin{itemize} + \item Colisiones inelásticas con los electrones (las más) + \item Colisiones elásticas con el núcleo (las menos) + \item Otros procesos posibles + \begin{itemize} + \item Radiación Cherenkov + \item Reacciones nucleares + \item Bremsstrahlung + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame}{La división} + \begin{itemize} + \item Electrones y positrones + \item El resto de leptones, hadrones y núcleos ligeros + \item Núcleos pesados + \end{itemize} +\end{frame} + +\begin{frame}{Poder de frenamiento} + Pérdidas por ionización + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.65\linewidth]{bethe.png} + \caption{Poder de frenamiento másico para anti-muones en cobre como función de $\beta \gamma = p/Mc$ Tomada de PDG: P.A. Zyla et al. (Particle Data Group), to be published in Prog. Theor. Exp. Phys. 2020, 083C01 (2020).} + \label{fig:bethe} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Bethe-Bloch} + \begin{equation*} + W_{max} = \frac{2m_e c^2 \beta^2 \gamma^2}{1 + 2\gamma\frac{m_e}{M}+\left(\frac{m_e}{M}\right)^2} + \end{equation*} + + \begin{align*} + -\frac{dE}{dx} &= (4\pi N_A r_e^2 m_e c^2) z^2 \frac{Z}{A}\frac{1}{\beta^2} \times \\ + &\left[ \frac{1}{2} ln\left(\frac{2m_e c^2 \beta^2 \gamma^2 W_{max}}{I^2}\right) - \beta^2 -\frac{\delta(\beta \gamma)}{2}\right] + \end{align*} +\end{frame} + +\begin{frame}{Valores} + \begin{itemize} + \item $N_A$, $r_e$, $m_e$ y $c$ $\rightarrow$ $K=4\pi N_A r_e^2 m_e c^2$ + \item $z$ de partícula incidente + \item $Z$ y $A$ de los núcleos del medio + \item $\beta$ y $\gamma$ de la partícula incidente + \item $I$ potencial de ionización + \end{itemize} + + +\end{frame} + +\begin{frame}{Ecuación de Bethe-Bloch compacta} + \begin{equation} + -\frac{dE}{dx} = K z^2 \frac{Z}{A}\frac{1}{\beta^2}\left[ ln\left(\frac{2m_e c^2 \beta^2 \gamma^2}{I}\right) - \beta^2 - \frac{\delta(\beta \gamma)}{2}\right] + \end{equation} + + \begin{equation*} + K= 0.3071\ MeV mol^{-1}cm^2 + \end{equation*} + + \begin{equation*} + K/A= 0.3071\ MeV gr^{-1} cm^2\ (\text{con } A=1 gr/mol) + \end{equation*} + +\end{frame} + + +\begin{frame}{Pérdida de energía total} + + \begin{equation*} + \Delta E_{perdida} = -\rho \int_0^d \frac{dE}{dx} dx + \end{equation*} + +\end{frame} + +\begin{frame}{Dispersión múltiple: ángulos pequeños} + \begin{equation} + \theta_0 = \theta_{plano}^{rms} = \frac{1}{\sqrt{2}} \theta_{espacio}^{rms} + \end{equation} + + \begin{equation} + \theta_0 = \frac{13.6 MeV}{\beta c p} z \sqrt{\frac{x}{X_0}}\left[ 1 + 0.038 ln \left( \frac{x z^2}{X_0 \beta^2} \right) \right] + \end{equation} + +\end{frame} + +\begin{frame}{Longitud de radiación} + \begin{itemize} + \item La distancia para la cual la energía del electrón se reduce en $1/e$ + \item $7/9$ del camino libre medio de fotones para producción de pares + \end{itemize} + + \begin{equation*} + X_0 = 716.4\ \frac{gr}{cm^2} \frac{A}{Z(Z+1)ln\left({\frac{287}{\sqrt{Z}}}\right)} + \end{equation*} + +\end{frame} + +\begin{frame}{Fotones} + \begin{itemize} + \item Efecto fotoeléctrico + \item Efecto Compton + \item Producciones de pares ($E>2m_e c^2$) + \end{itemize} + +\end{frame} + +\begin{frame}{Efecto fotoeléctrico} + \begin{equation*} + T_e = h\nu -I_B + \end{equation*} +\end{frame} + +\begin{frame}{Dispersión de Compton} + +\begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.7\linewidth]{compton.png} + \caption{Dispersión de Compton, el fotón es marcado por $\lambda = 1/\nu$. Imagen tomada de This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.} + \label{fig:frena} + \end{center} + \end{figure} + +\end{frame} + +\begin{frame}{Relaciones dispersión de Compton} + + \begin{equation} + h\nu'=\frac{h\nu}{1+\gamma (1-cos\theta)}, + \end{equation} + + \begin{equation*} + T_e = h\nu - h\nu'= h\nu \frac{\gamma (1-cos\theta)}{1+\gamma (1-cos\theta)} + \end{equation*} + Límite de Compton + \begin{equation} + T_{max} = h\nu \left( \frac{2\gamma}{1+2\gamma} \right) + \end{equation} + +\end{frame} + +\begin{frame}{Producción de pares} + + \begin{itemize} + \item Fotón crea un par electrón-positrón + \item Solo puede suceder dentro del medio + \item Conservación de la energía y el momento + \item Mínimo de energía de $2m_ec^2$ + \end{itemize} + +\end{frame} + +\begin{frame}{Camino libre medio para producción de pares} + \begin{equation*} + X_{pares} = \mu_{pares}^{-1} \approx \frac{9}{7} X_0 + \end{equation*} + + ?`Qué sucede con el positrón después? + +\end{frame} + +\begin{frame}{Coeficiente de absorción} + \begin{equation*} + \mu = n\sigma + \end{equation*} +\end{frame} + +\section*{Detectores} +\begin{frame}{Detectores de ionización} + \begin{itemize} + \item Funcionan en el mismo rango de Bethe-Bloch + \item Se aplica un campo eléctrico + \item Medio ionizable y químicamente estable (bajo potencial de ionización) + \item Eletrodos: ánodo y cátodo + \end{itemize} + +\end{frame} + +\begin{frame}{Detectores de ionización } + + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.6\linewidth]{regiones.jpg} + \caption{Regiones de operación de los detectores de ionización. Imagen adaptada de la original de \href{https://commons.wikimedia.org/wiki/User:Dougsim}{Doug Sim} con licencia \href{https://en.wikipedia.org/wiki/en:Creative_Commons}{Creative Commons Attribution-Share Alike 3.0 Unported}} + \label{fig:region} + \end{center} + \end{figure} + +\end{frame} + +\begin{frame}{Contadores de ionización} + \begin{itemize} + \item En la región de ionización + \item Poco sensible a los cambios de voltaje + \item Sin amplificación + \item Requiere filtros + \item Respuesta rápida + \end{itemize} +\end{frame} + +\begin{frame}{Contadores proporcionales} + \begin{itemize} + \item Región proporcional + \item Campos eléctricos intensos $\sim 10^4 V/cm$ + \item Hay amplificación $\sim 10^5$ + \end{itemize} +\end{frame} + + + +\begin{frame}{Cámaras multilámbricas} + \begin{itemize} + \item Diseñadas por George Charpak + \item Alambres de $10-50 \mu m$ separados por $2mm.$ + \item Cátodos a $1cm$ por encima y debajo + \end{itemize} +\end{frame} + +\begin{frame}{Cámara multialámbrica} + \begin{figure} + \begin{center} + \includegraphics[width=0.4\linewidth]{mwpc.png} + \caption{Líneas de campo en cámara multialámbrica. This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.} + \label{fig:frena} + \end{center} + \end{figure} + +\end{frame} + + +\begin{frame}{Detector Geiger-Muller} + \begin{itemize} + \item Funciona en el límite + \item Produce una descarga por cada partícula que produce una ionización + \end{itemize} + +\end{frame} + + +\begin{frame}{Detector Geiger-Müller} + \begin{figure} + \begin{center} + \includegraphics[width=0.5\linewidth]{geiger.jpg} + \caption{Detector Geiger-Müller. This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.} + \label{fig:frena} + \end{center} + \end{figure} + +\end{frame} + + +\begin{frame}{Detectores de centelleo} + \begin{itemize} + \item Excitaciones de los átomos del material + \item Al regresar al estado base: emiten un fotón + \item Centelladores orgánicos: antraceno, naftaleno + \item Centelladores inorgánicos: NaI, CsI dopados + \end{itemize} + +\end{frame} + +\begin{frame}{PMT} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.7\linewidth]{pmt_es.png} + \caption{Tubo fotomultiplicador. Imagen de \href{https://commons.wikimedia.org/wiki/User:Wiso}{Wiso} con licencia \href{https://creativecommons.org/licenses/by-sa/3.0/deed.en}{Creative Commons Attribution-Share Alike 3.0 Unported}} + \end{center} + \end{figure} + ?`Usos de centelladores? +\end{frame} + +\begin{frame}{Detector Cherenkov} + \begin{itemize} + \item Partículas cargadas, pero el proceso no es ionización + \item Viaja más rápido que la luz \emph{en el medio} $v>c/n$ o $\beta>1/n$. + \item $\cos\theta_c = \frac{1}{\beta n}$ + \end{itemize} +\end{frame} + +\begin{frame}{Detectores semiconductores} + \begin{itemize} + \item Semiconductores + \item Detectores de ionización + \item $200-300 \mu m$ de grosor + \end{itemize} +\end{frame} + +\begin{frame}{Calorímetro} + \begin{itemize} + \item Las partículas depositan toda su energía cinética + \item Centelladores, contadores de ionizción o proporcionles + \item Fotones: producción de pares + \item Hadrones: procesos fuertes + \item Problemáticos: neutrinos y $\pi^0$ + \end{itemize} + +\end{frame} + +\begin{frame}{Aceleradores} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.7\linewidth]{tevatron.jpg} + \caption{Foto del Tevatrón en Fermilab. Imagen de Fermilab, Reidar Hahn, del dominio público} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Partículas nuevas} + \begin{itemize} + \item De forma natural tenemos poca variedad + \item Partículas de mayor masa requiere mayor energía + \item ?`Límite?: posiblemente $\hbar c/G_g\approx 1.22\times 10^20 eV/c^2$ + \end{itemize} + +\end{frame} + +\begin{frame}{Estudios de estructura} + \begin{columns} + \begin{column}{0.48\textwidth} + \begin{equation*} + \lambda = \frac{h}{p} + \end{equation*} + + \begin{equation*} + \bar{\lambda}= \frac{\lambda}{2\pi} = \frac{\hbar}{p} + \end{equation*} + + \begin{equation*} + \bar{\lambda} \leq d + \end{equation*} + + \begin{equation*} + p \geq \frac{\hbar}{d} + \end{equation*} + + \begin{equation*} + E_{kin} = \frac{p^2}{2m_p} = \frac{\hbar^2}{2m_p d^2} + \end{equation*} + + \end{column} + \begin{column}{0.48\textwidth} + + \begin{equation*} + \frac{E_{kin}}{m_pc^2} = \frac{1}{2d^2} \left( \frac{\hbar}{m_pc} \right)^2 + \end{equation*} + + \begin{align*} + \bar{\lambda}_p =& \frac{\hbar}{m_pc} = \frac{\hbar c}{m_pc^2}\\ + &= \frac{197.3\ MeV\ fm}{938\ MeV} = 0.210\ fm. + \end{align*} + + \begin{align*} + \frac{E_{kin}}{m_pc^2} =& \frac{1}{2} \left( \frac{\bar{\lambda}_p}{d} \right)^2 = 0.02\\ + E_{kin} =& 0.02 m_pc^2 = 0.02\times 938 MeV + \end{align*} + \end{column} + \end{columns} + + +\end{frame} + +\begin{frame}{Aceleración} + \begin{itemize} + \item $E=Fd=q|E|d = qV$ + \end{itemize} + + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.5\linewidth]{catodicos.png} + \caption{Foto de un cinescopio de televisión. Imagen de JMPerez~commonswiki con licencia Creative Commons Attribution-Share Alike 3.0 Unported} + \end{center} + \end{figure} + +\end{frame} + +\begin{frame}{Conceptos útiles} + \begin{itemize} + \item \emph{Flujo}: la cantidad de partículas que cruzan un área unitaria perpendicular al eje del haz por unidad de tiempo + + \begin{equation} + \mathcal{F} = n_i v, + \end{equation} + + \begin{equation*} + dN = \mathcal{F}N\sigma d\Omega + \end{equation*} + + \item \emph{Luminosidad}: la cantidad de eventos por unidad de sección eficaz que tienen lugar en una sección de encuentro del haz por unidad de tiempo + + \begin{equation*} + \mathcal{L} = \frac{\mathcal{N}_s}{\sigma_{tot}}=\frac{N_1 N_2 f}{A}, + \end{equation*} + + \end{itemize} + +\end{frame} + +\begin{frame}{Generadores elestrostáticos} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.5\linewidth]{vandegraff.jpg} + \caption{Esquema de un generador Van de Graff. Tomado con fines educativos de Henley} + \label{fig:vandegraff} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Van de Graff} + \begin{itemize} + \item Llega a $30-40 MeV$ + \item Más energías con un Van de Graff tandem + \item Un tandem en el IFUNAM + \end{itemize} + +\end{frame} + +\begin{frame}{Acelerdores lineales} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.5\linewidth]{slac.png} + \caption{Foto del acelerador lineal de Stanford, 3 km de longitud. Imagen de Victor Blacus en dominio público} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Linac} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.6\linewidth]{linac.jpg} + \caption{Esquema de un acelerador lineal. Imagen adaptada de Chetvorno con licencia CC0} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Óptica del haz} + \begin{itemize} + \item Lentes magnéticas + \item Dipolos pueden deflectar + \item Cuadrupolos lo más parecido a una lente óptica + \end{itemize} + \begin{equation*} + \overrightarrow{F} = q\left( \overrightarrow{E} + \frac{1}{c} \overrightarrow{v}\times \overrightarrow{B} \right) + \end{equation*} +\end{frame} + +\begin{frame}{Ciclotrón} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.7\linewidth]{ciclotron.png} + \caption{Esquema de funcionamiento de un ciclotron. Imagen de Ernest O. Lawrence - U.S. Patent 1,948,384, de dominio público} + \label{fig:ciclotron} + \end{center} + \end{figure} + +\end{frame} + +\begin{frame}{Resonancia y energía} + \begin{equation*} + \frac{v}{r} = \frac{qB}{m} + \end{equation*} + + \begin{equation*} + \omega = \frac{v}{r} + \end{equation*} + + \begin{equation*} + \nu = \frac{\omega}{2\pi} = \frac{qB}{2\pi m} = \frac{1}{2\pi}\left( \frac{q}{m} \right) B + \end{equation*} + + \begin{align*} + T_{max}=& \frac{1}{2}mv_{max}^2 = \frac{1}{2} m \omega^2 R^2 \\ + =& \frac{1}{2} m \left( \frac{qB}{m} \right)^2 R^2 = \frac{(qBR)^2}{2m} + \end{align*} +\end{frame} + +\begin{frame}{Sincrotrón} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.7\linewidth]{sincrotron.jpg} + \caption{Modelo de un acelerador sincrotrón. Imagen de EPSIM 3D/JF Santarelli, Synchrotron Soleil} + \label{fig:ciclotron} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Método Monte Carlo} + \begin{itemize} + \item Tratamiento estadístico en experimentos + \item Integración numérica + \item Optimización + \end{itemize} +\end{frame} + +\begin{frame}{Áreas por Monte Carlo} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.5\linewidth]{area.png} + \caption{Ejemplo del cálculo de una área con Montecarlo. Imagen de Mysid Yoderj con licencia Creative Commons CC0 1.0 Universal Public Domain Dedication} + \label{fig:ciclotron} + \end{center} + \end{figure} +\end{frame} + +\begin{frame}{Generando a partir de distribución estadística} + \begin{itemize} + \item Valores al azar pero bajo cierta distribución + \end{itemize} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.5\linewidth]{montecarlo1.png} + \caption{Ejemplo de integración Monte Carlo. Imagen de Femizban con licencia Creative Commons Attribution-Share Alike 4.0 International} + \label{fig:ciclotron} + \end{center} + \end{figure} + +\end{frame} + +\begin{frame}{Números pseudo-aleatorios} + \begin{itemize} + \item Para acercarnos a la naturaleza necesitamos lo más aleatorio + \item Las computadoras no pueden generar números aleatorios + \item Mecanismos pseudo-aleatorios + \item Complementos verdadero-aleatorios + \end{itemize} +\end{frame} + +\begin{frame}{Paso de partículas a través de la materia} + \begin{itemize} + \item Los valores calculados por pedazos + \item Propagación de la partícula por diversos procesos + \item Comparación con el experimento + \end{itemize} +\end{frame} + + + +\end{document} diff --git a/slac.png b/slac.png new file mode 100644 index 0000000000000000000000000000000000000000..8834ea4ba2679db3eb5bf673317a9eb54abc1c5b GIT binary patch literal 1528599 zcmV*cKvTboP)Y&}$;CuY?5d=4o&O-ETqQU8 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