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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. Así se pueden medir distintas energías dependiendo de en cuantas capas ya no aparece la partícula. +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. Así se pueden medir distintas energías dependiendo de en cuantas capas ya no aparece la partícula. Es de destacar que este detector altera la naturaleza de las partículas, es decir, la intención es reducir la energía hasta que se detengan, decaigan o se recombinen, por lo que el haz no puede ser posteriormente utilizado. Un centellador también puede ser un calorímetro, se puede asociar la cantidad de luz emitida y asociarlo a la energía de la partícula, de nueva cuenta enfatizando que la partícula debe perder toda su energía cinética. Varias capas, o lo suficientemente gruesas, de cámaras proporcionales o contadores de ionización sirven de la misma manera, además de entregar información por medio de las ionizaciones. @@ -655,7 +655,14 @@ No sólo partículas cargadas pueden depositar su energía en un calorímetro, l Para hadrones el caso también puede ser distinto, si es cargado y no muy enérgetico deposita su energía por ionizaciones, no es un caso nuevo. Pero si lleva mucha energía o es neutro sus interacciones son con el núcleo por interacción fuerte, estas interacciones provocan que los hadrones más pesados vayan produciendo hadrones ligeros que depositarán toda su energía en el medio. -Las únicas partículas que nos darán problemas en un calorímetro serán los neutrino, por un lado para neutrino no sirve este detector, debido a su masa tan pequeña y su carga neutra, pero además si algún hadrón tiene una interacción en la que libere un neutrino se perderá esa información de la energía, tendremos una medida errónea. Por otro lado los piones neutros directos o derivados decaen en un par de fotones, aquí hubo un cambio de procesos, pasamos seguramente de una interacción fuerte a una electromagnética, la última actúa de forma local y de nueva cuenta tenemos pérdida de información. +Las únicas partículas que nos darán problemas en un calorímetro serán los neutrinos. Por un lado, para neutrino no sirve este detector debido a su masa tan pequeña y su carga neutra, pero además si algún hadrón tiene una interacción en la que libere un neutrino se perderá esa información de la energía, tendremos una medida errónea. Por otro lado los piones neutros directos o derivados decaen en un par de fotones, aquí hubo un cambio de procesos, pasamos seguramente de una interacción fuerte a una electromagnética, la última actúa de forma local y de nueva cuenta tenemos pérdida de información. + +Las ventajas de usar calorímetros para la medida de energía para partículas cargadas, y como se ha visto para algunas neutras incluso: + +\begin{enumerate} +\item El proceso de absorción es estadístico, dictado por una distribución de Poisson, la precisión relativa en la medida de energía es $\Delta E /E \approx E^{1/2}$ para energías altas\footnote{Los espectrómetros de alta energía tenían una precisión relativa alrededor de $E^2$.}. +\item La señal de respuesta tiene una resolución temporal $\sim 10-100 ns$, que es bastante rápida. +\end{enumerate} \section{Aceleradores} @@ -666,7 +673,7 @@ Hay dos principales usos para los aceleradores de partículas \item El estudio de la estructura de núcleos y partículas \end{itemize} -La primera tarea se debe a que de forma natural, sea por rayos cósmicos o decaimientos, tenemos muy poca variedad de partículas elementales, para generar partículas cada vez más pesadas se necesitan energías cada vez mayores. ¿Cuál es el límite de la masa que se puede producir? No lo sabemos pero se piensa que el límite es la masa de Plank ($\hbar c/G_g\approx 1.22\times 10^20 eV/c^2$), pero ¡imagínense la cantidad de energía necesaria para producir esa partícula! +La primera tarea se debe a que de forma natural, sea por rayos cósmicos o decaimientos, tenemos muy poca variedad de partículas elementales, para generar partículas cada vez más pesadas se necesitan energías cada vez mayores. ¿Cuál es el límite de la masa que se puede producir? No lo sabemos pero se piensa que el límite es la masa de Plank ($\hbar c/G_g\approx 1.22\times 10^{20} eV/c^2$), pero ¡imagínense la cantidad de energía necesaria para producir esa partícula! Para el estudio de la estructura veamos qué energías son necesarias, recordemos la longitud de onda de de Broglie @@ -735,7 +742,7 @@ Unos conceptos útiles para esta sección: \mathcal{F} = n_i v, \end{equation} -\noindent donde $n_i$ es la densidad de partículas (por unidad de volumen ¿la recuerdan?). Tomemos que pasa una partícula como caso ideal, entonces $n_i=1/V$, ponemos detectores pequeños para detectar las dispersiones, ese detector encierra una parte diferencial del ángulo sólido ($d\Omega$), la dispersión depende del flujo, de la cantidad inicial de partículas, del ángulo sólido encerrado por el detector, entonces la cantidad de partículas detectadas son: +\noindent donde $n_i$ es la densidad de partículas (por unidad de volumen ¿la recuerdan?). Tomemos que pasa una partícula como caso ideal, entonces $n_i=1/V$, ponemos detectores pequeños para detectar las dispersiones, ese detector encierra una parte diferencial del ángulo sólido ($d\Omega$), la dispersión depende del flujo, de la cantidad de centros dispersores, del ángulo sólido encerrado por el detector, entonces la cantidad de partículas detectadas son: \begin{equation*} dN = \mathcal{F}N\sigma d\Omega @@ -746,6 +753,12 @@ Imaginen que no saben qué es $\sigma$, sería una constante de proporcionalidad \begin{equation*} \sigma(\theta)d\Omega = d\sigma(\theta) \Rightarrow \sigma (\theta) = \frac{d\sigma (\theta)}{d\Omega} \end{equation*} + +El número total de partículas dispersadas por unidad de tiempo se obtiene integrando sobre todo el ángulo sólido + +\begin{equation*} + N_S = FN\sigma_{tot} +\end{equation*} \emph{Luminosidad}: la cantidad de eventos por unidad de sección eficaz que tienen lugar en una sección transversal del haz por unidad de tiempo @@ -843,13 +856,13 @@ Este aclerador ya no funciona para poder acelerar a velociodades relativistas, l \subsection{Sincrotón} -Seguimos con el mismo principio de funcionamiento del linac, pero acomodado en un círculo, en lugar e un campo magnético que bañe a toda la circunferencia ahora ponemos campos magnéticos pequeños en los segmentos de aceleración que como el linac van alternando voltaje para acelerar la partícula, pero ahora el campo magnético actúa en cada segmento. +Seguimos con el mismo principio de funcionamiento del linac, pero acomodado en un círculo, en lugar de un campo magnético que bañe a toda la circunferencia ahora ponemos campos magnéticos pequeños en los segmentos de aceleración que como el linac van alternando voltaje para acelerar la partícula, pero ahora el campo magnético actúa en cada segmento. \begin{figure}[ht!] \begin{center} \includegraphics[width=0.7\linewidth]{sincrotron.jpg} \caption{Modelo de un acelerador sincrotrón. 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