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Viaja más rápido que la luz \emph{en el medio} $v>c/n$ o $\beta>1/n$. + \item $\cos\theta_c = \frac{1}{\beta n}$ + \item $213$ fotones/cm + \item Ring-image Cherenkov + \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} + \begin{itemize} + \item Semiconductores: electrones de valencia a electrones de conducción + \item Detectores de ionización pero electrón-hoyo en lugar de electrón-ión + \item De germanio o silicio + \item Para producir un par: $3-4eV$. Ionización 10 veces más, centelleo 100 veces más. + \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} + \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} + \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} + \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{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*} + 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*} + \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} + \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{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*} + \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} + \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} diff --git a/tarea3.pdf b/tarea3.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2d8339040905ced0376c3a2bae5582ea57d94dce GIT binary patch literal 51025 zcma&NQ;aZ7@a{RbZQHhO+qP}nwr$(CZSx)5Gy9#*{8e0R6dH%3)s-s+X6Uu#q0x50l98_VY9SGldhVxniH<<|? zYdCDS4z!twte@uA9u|Cf6wl$KXD9w6fppOUc{OEqu&QJ#)nXMw#f~Nm%jWd;H79!3 z&X-GgQxwEK?l3BqwS{sdmDqMl3UeN6Q&E@HqEi++sqx7=Aw5cUB<8@$b(Doyq-B6l zjFapZBjw{sq2FO(bJU}hDU9u(i9a`lFojl{(`sPGU=D7L{|x6jwG*O{nF3dQ^QGhV 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detectores de ionización, un pequeño asomo a los detectores de Cherenkov, detectores de silicio y calorímetros. +Iniciamos el estudio de detectores teniendo como antecedente la fórmula de Bethe-Bloch, veremos para empezar los detectores de ionización, un pequeño asomo a los detectores de Cherenkov, detectores de silicio y calorímetros. \subsection{Detectores de ionización} @@ -573,10 +573,16 @@ Subiendo más el voltaje se intensifica la producción de ionizaciones debido a \subsubsection*{Contadores de ionizaciónn} También conocidas como cámaras de ionización, funcionan en la región de ionización: son poco sensibles a los cambios de voltajes, no generan amplificación por lo que requieren filtros para limpiar el ruido eléctrico asociado. Pero si la partícula que genera las ionizaciones es muy energética producen una señal aceptable y además toma muy poco tiempo para que el detector vuelva a estar listo para su operación\footnote{Existe un tiempo de relajación, que es el tiempo que le toma al gas volver a un estado neutro, ya sin iones y electrones viajando a cátodos y ánodos, listos para reiniciar el proceso de ionización.}. Por las mismas razones son útiles en medios con altas razones de interacción, altos niveles de radiación. + +Podemos tener dos tipos sencillos, una versión con placas planas y otra con cilíndros que son ánodo y cátodo: + +\begin{equation} + E=\frac{V}{d} \text{ placas planas, } E = \frac{V}{rln(\frac{r_c}{r_a})} +\end{equation} \subsubsection*{Contadores proporcionales} -Los contadores proporcionales gaseosos como su nombre lo indica trabajan en la región proporcional, con campos eléctricos intensos ($\sim 10^4 V/cm$) y amplificaciones alrededor de $10^5$ electrones por ionización. Suelen ser arreglos cilíndricos con un alambre central como ánodo y una carcasa cilíndrica como cátodo, cerca del eje axial, donde se ubica el ánodo, suceden la mayor parte de las multiplicaciones. Funcionan incluso para partículas poco ionizantes, la desventaja: es muy sensible a los cambios de voltaje, por lo que se complica el conteo total e ionizaciones. +Los contadores proporcionales gaseosos como su nombre lo indica trabajan en la región proporcional, con campos eléctricos intensos ($\sim 10^4 V/cm$) y amplificaciones alrededor de $10^5$ electrones por ionización. Suelen ser arreglos cilíndricos con un alambre central como ánodo y una carcasa cilíndrica como cátodo. Cerca del eje axial, donde se ubica el ánodo, suceden la mayor parte de las multiplicaciones, la avalancha que se produce aquí sule llamarse \emph{avalancha de Townsend}. Funcionan incluso para partículas poco ionizantes, la desventaja: es muy sensible a los cambios de voltaje, por lo que se complica el conteo total e ionizaciones. \begin{figure}[ht!] \begin{center} @@ -586,7 +592,13 @@ Los contadores proporcionales gaseosos como su nombre lo indica trabajan en la r \end{center} \end{figure} -Un caso particular son las cámaras multialámbricas, diseñadas por George Charpak usan el mismo principio pero lo repiten varias veces, un arreglo de alambres (de $10-50\mu m$ de diámetro) es dispuesto con una separación de $2mm.$, estos son los ánodos, un centímetro por encima y debajo de este arreglo se ponen dos placas metálicas que funcionan como cátodos. El arreglo se encierra en una caja aislante eléctrica y que no deje escapar el gas, y se llena con el gas a ionizarse. Por el arreglo de ánodos estas cámaras se usan para determinar las posiciones de las partículas, con dos de ellas se puede determinar la posición en 2 dimensiones, con 6 cámaras multialámbricas se puede determinar la posición en tres dimensiones. Las líneas de campo se muestran en la figura \ref{fig:mwpc}. +Un caso particular son las cámaras multialámbricas, diseñadas por George Charpak en 1968 usan el mismo principio pero lo repiten varias veces, un arreglo de alambres (de $10-50\mu m$ de diámetro) es dispuesto con una separación de $2mm.$, estos son los ánodos, un centímetro por encima y debajo de este arreglo se ponen dos placas metálicas que funcionan como cátodos. El arreglo se encierra en una caja aislante eléctrica y que no deje escapar el gas, y se llena con el gas a ionizarse. Por el arreglo de ánodos estas cámaras se usan para determinar las posiciones de las partículas, con dos de ellas se puede determinar la posición en 2 dimensiones, con 6 cámaras multialámbricas se puede determinar la posición en tres dimensiones. Las líneas de campo se muestran en la figura \ref{fig:mwpc}. Puede tener resoluciones espaciales de $50-200\mu m$ y resoluciones de tiempo típicas de $2ns$. + +Las sucesoras de las cámaras multialámbricas son las cámaras de deriva. En este caso hace uso de medidas de tiempo, el que pasa entre que la partícula cargada ingresa al detector y se recibe la señal eléctrica debida a la ionización, se agregan alambres adicionales para tratar de tener un voltaje constante en cada celda de la dirección transversa a la trayectoria de la partícula. Desde que la partícula entra el proceso es que ioniza el medio, los electrones producidos sufren una deriva hasta llegar al ánodo donde son recolectados. Con una medición precisa del tiempo, menos a los $2ns$, estas cámaras pueden dar una resolución espacial y temporal del paso de las partículas. Existen diversas configuraciones, planas, radiales o cilíndricas, de acuerdo al experimento. Un ejemplo de la versión cilíndrica es la cámara jet de \emph{DESY} en Hamburgo, usada para el estudio de colisiones electrón positrón. + +Englobando todas estas características están las cámaras de proyección temporal (\emph{Time Projection Chambers}, TPC), montado sobre un barril cilíndrico que rodea al tubo por el que viaja el haz en un acelerador, al final de ambos lados de la cámara hay una capa de contadores proporcionales, el campo eléctrico corre del centro hacia afuera, hacia las capas de contadores, junto a un campo magnético en dirección antiparalela (y paralela para la otra capa). Ahora la deriva de los electrones será en trayectoria helicoidales, asegurando una mejor resolución temporal. + +Ahora las cámaras proporcionales son sustituidas por \emph{microstrip gas chambers}, donde los alambres son cambiados por tiras de metal conductor sobre una base de circuito impreso, esto los hace más robustos. \subsubsection*{Contador Geiger-Müller} @@ -596,11 +608,11 @@ Funcionando ya en el límite máximo de voltajes, toda ionización produce una d El principio de funcionamiento de los detectores de centelleo es de igual forma los procesos de ionización, la pérdida de energía sigue el mismo perfil que da la ecuación de Bethe-Bloch, solo que en este caso el centellador cuenta con un proceso extra que nos indica que un partícula pasó. -La partícula ioniza los átomos del material, los electrones a su ver pueden generar excitaciones en los átomos circundantes, los estados excitados viven por un tiempo muy corto y decaen liberando energía a través de un fotón, esos fotones generan la luz de centelleo. Por lo regular de frecuencias cercanas al ultravioleta y de baja intensidad son difíciles de ver a simple vista, pero se utilizan tubos fotomultiplicadores en conjunto. +La partícula ioniza los átomos del material, los electrones a su ver pueden generar excitaciones en los átomos circundantes, los estados excitados viven por un tiempo muy corto y decaen liberando energía a través de un fotón, esos fotones generan la luz de centelleo. Por lo regular con frecuencias cercanas al ultravioleta y de baja intensidad son difíciles de ver a simple vista, pero se utilizan tubos fotomultiplicadores en conjunto. -Hay dos tipos de centelladores dependiendo del material que los forma: orgánicos o plásticos e inorgánicos o cristalinos. Cada tipo tiene sus característucas, siendo los plásticos los de mayor respuesta lumínica, el antraceno y naftaleno son unos de los materiales de los que pueden estar construidos. Es importante que el material del centellador sea transparente a su propia radiación, esto evita que la luz se atenúe y pueda recolectarse en el tubo fotomultiplicador la mayor cantidad. Tienen un tiempo de decaimiento corto ($\approx 10^-8 seg.$) +Hay dos tipos de centelladores dependiendo del material que los forma: orgánicos o plásticos e inorgánicos o cristalinos. Cada tipo tiene sus característucas, siendo los plásticos los de mayor respuesta lumínica, el antraceno y naftaleno son unos de los materiales de los que pueden estar construidos. Es importante que el material del centellador sea transparente a su propia radiación, esto evita que la luz se vaya atenuando y pueda recolectarse en el tubo fotomultiplicador la mayor cantidad. Tienen un tiempo de decaimiento corto ($\approx 10^-8 seg.$) -Los inorgánicos pueden ser de NaI, CsI entre otros materiales, dopados para facilitar la excitación. Tieenen un tiempo de decaimiento más lento ($\approx 10^-6 seg$) +Los inorgánicos pueden ser de NaI, CsI entre otros materiales, dopados para facilitar la excitación. Tieenen un tiempo de decaimiento más lento ($\approx 10^-6 seg$). Por lo regular emiten $10^4$ fotones/cm. \begin{figure}[ht!] @@ -621,17 +633,19 @@ Una partícula viajando en el vacío a velocidad constante no emite radiación a De manera análoga a las ondas de sonido en el caso del rompimiento de la barrera del sonido, la luz de Cherenkov se emite en un cono, cuyo ángulo plano está caracterizado por la ecuación\ref{cos:chen}. -Por esta característica de la relación del ángulo con la $\beta$ de la partícula y la $n$ del material permite que los detectores de Cherenkov pueden diferenciar entre masas de partículas que viajan a altas velocidades. Imaginemos que tenemos protones, kaones y piones con momentos de $1 GeV/c$, respectivamente tendrán $\beta$'s aproximadas de $0.73$, $0.89$ y $0.99$ (están acomodadas de la más pesada a la más ligera). Para empezar a ver luz de Cherenkov de estas partículas se requieren medios con distinto índice de refracción, para protones $n>1.37$, para kaones $n>1.12$ y piones con $n>1.01$. +Por esta característica de la relación del ángulo con la $\beta$ de la partícula y la $n$ del material permite que los detectores de Cherenkov pueden diferenciar entre masas de partículas que viajan a altas velocidades. Imaginemos que tenemos protones, kaones y piones con momentos de $1 GeV/c$, respectivamente tendrán $\beta$'s aproximadas de $0.73$, $0.89$ y $0.99$ (están acomodadas de la más pesada a la más ligera). Para empezar a ver luz de Cherenkov de estas partículas se requieren medios con distinto índice de refracción, para protones $n>1.37$, para kaones $n>1.12$ y piones con $n>1.01$. En agua emiten alrededor de $213$ fotones/cm. + + \subsection*{Detectores semiconductores} -¿Recuerdan sus clases de electrónica? En ellas, o quizá si llevaron una materia de estado sólido, y como tema extra en física atómica habrán visto semiconductores, hechos de germanio o silicio son tratados particularmente para tener una barrera que debe romperse aplicando un voltaje, hasta que se alcanza ese voltaje es que pueden conducir la corriente. Esto se parece mucho a un detector de ionización como los que vimos primero, un alto voltaje produce que haya descarga, a bajos voltajes ni las ionizaciones producen una corriente y a voltajes medios depende de la ionización. +¿Recuerdan sus clases de electrónica? En ellas, o quizá si llevaron una materia de estado sólido, y como tema extra en física atómica habrán visto semiconductores, hechos de germanio o silicio son tratados particularmente para tener una barrera que debe romperse aplicando un voltaje, hasta que se alcanza ese voltaje es que pueden conducir la corriente. Esto se parece mucho a un detector de ionización como los que vimos primero, un alto voltaje produce que haya descarga, a bajos voltajes ni las ionizaciones producen una corriente y a voltajes medios depende de la ionización. Sólo se requieren de $3-4eV$ para liberar un par electrón-hueco, en una cámara de ionización se necesitan alrededor de $30eV$ para tener un par electrón ión, y en un centellador $\approx 300eV$ para genera luz de centelleo. De igual manera las ionizaciones pueden provocar conducción en las uniones semiconductoras, no se utiliza un diodo o transistor, si no uniones especialmente hechas para este fin. Así de manera compacta podemos tener cámaras de ionización, el grosor de las placas puede ser de apenas $200-300\mu m$. Teniendo varios de estos detectores, en placas de apenas $5cm\times 5cm$, podemos sustituir las cámaras multialámbricas en la tarea de determinar posiciones y trayectorias. \subsection*{Calorímetros} -Un calorímetro es un detector que mide la energía de las partículas, no es que mida la temperatura de las partículas pero como bien saben en calor es energía, todo arreglo experimental que mida energía de las partículas es denomindo un calorímetro. +Un calorímetro es un detector que mide la energía de las partículas, no es que mida la temperatura de las partículas pero como bien saben en calor es energía, todo arreglo experimental que mida energía de las partículas es denominado un calorímetro. El material o arreglo de materiales que conforman al calorímetro absorbe toda la energía cinética de la partícula, si es un solo bloque de material por las características de la ionización en el medio es posible saber en que rangos de energía están las partículas que ya no salieron. Puede hacerse por secciones, contar la cantidad de partículas que salen tras un cierto grosor de material, contar cuantas atraviesan el siguiente y así consecutivamente. 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