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b/notas4.tex index b1693d2..d361bd8 100755 --- a/notas4.tex +++ b/notas4.tex @@ -25,7 +25,7 @@ En 1932 Chadwick, seguramente acompañado de un equipo más amplio de investigad \section*{Propiedades del núcleo} \subsection*{Etiquetado} -Un núcleo lo nombramos igual que al elemento que pertenece, puede se H, He, C, Fe, U, etc., con ligeras diferencias. Tenemos un núcleo $X$, además de ser identificado por el nombre, como redundancia es identificado por su $Z$. Lo que define a un núcleo justo es eso, su número atómico. Además agregamos la cantidad de nucleones que posee, nótese que $A$ no define que núcleo es, veamos porque. +Un núcleo lo nombramos igual que al elemento que pertenece, puede ser H, He, C, Fe, U, etc., con ligeras diferencias. Tenemos un núcleo $X$, además de ser identificado por el nombre, como redundancia es identificado por su $Z$. Lo que define a un núcleo justo es eso, su número atómico. Además agregamos la cantidad de nucleones que posee, nótese que $A$ no define que núcleo es, veamos porque. Tenemos nuestro núcleo ${}^AX^Z$, con $Z$ protones y $N-Z$ neutrones, de aquí podemos identificarlo como respecto a otro núecleo ${}^{A'}{X'}^{Z'}$ \begin{itemize} @@ -70,7 +70,7 @@ La energía promedio para liberar un nucleón se da por la razón \frac{B}{A} = \frac{B.E.}{A} = \frac{-\Delta M(A,Z)c^2}{A} \end{equation*} -Este valor es útil pues pensaríamos que la energía de enlace por nucleón $B/A$, si todo se comportara bien, sería una constante, mas su comportamiento nos da más características de esta energía, como se puede ver en la figura \ref{fig:binding}. Para núcleos ligeros $B/A$ oscila un poco, aumenta rápidamente y se satura, alcanzando un pico alrededor de los $9\ MeV$ por nucleón, que en el eje de las $X$ corresponde a un $A = 60$. Para $A$ mayor $B/A$ decae lentamente. $8\ MeV$ es un valor promedio para estos núcleos restantes, nos sirve para ver que esperamos obtener. +Este valor es útil pues pensaríamos que la energía de enlace por nucleón $B/A$, si todo se comportara bien, sería una constante, mas su comportamiento nos da más características de esta energía, como se puede ver en la figura \ref{fig:binding}. Para núcleos ligeros $B/A$ oscila un poco, aumenta rápidamente y se satura, alcanzando un pico alrededor de los $9\ MeV$ por nucleón, que en el eje de las $X$ corresponde a un $A = 60$. Para $A$ mayor, $B/A$ decae lentamente. $8\ MeV$ es un valor promedio para estos núcleos restantes, nos sirve para ver que esperamos obtener. \begin{figure}[ht!] @@ -167,11 +167,11 @@ Por ejemplo, para el ${}^{197}Au^{79}$, su radio sería $R\approx 1.2 (197)^{\fr Rememorando la parte de espín en partículas elementales, sabemos que los protones y neutrones tienen espín $\hbar/2$ y un momento angular (entero) asociado. La suma que ya conocemos de momento angular define el momento angular del núcleo, pero hay detalles. Por el momento la parte fenomenológica nos dice que: \begin{itemize} -\item Núcleos con número atómico par tienen espín nuclear entero -\item Núcleos con número atómico impar tienen espín nuclear semi-entero -\item Núcleos con número par de protones y número par de protones (par-par) tienen espín nuclear cero +\item Núcleos con número $A$ par tienen espín nuclear entero +\item Núcleos con número $A$ impar tienen espín nuclear semi-entero +\item Núcleos con número par de protones y número par de neutrones (par-par) tienen espín nuclear cero \item Núcleos muy grandes tienen espín nuclear muy pequeño en su estado base -\item Hace pensar qu los nucleones dentro del núcleo están fuertemente apareados +\item Hace pensar que los nucleones dentro del núcleo están fuertemente apareados \end{itemize} Por otro lado, el momento dipolar magnético para una partícula cargada está dado por @@ -196,7 +196,7 @@ Son momentos magnéticos bastante grandes y anómalos, sobre todo para el neutr \subsection*{Estabilidad de los núcleos} -Ya les he contado, ya saben un poco de su experiencia, que hay núcleos estables y otros que decaen fácilmente en otros núcleos. Si observamos lo que los experimentos y observaciones nos dicen, para $A\lesssim 40$ el número de protones y neutrones se mantiene igual (para los núcleos estables, recuerden), es decir $N=Z=A/2$, pero para núcleos más pesados $N\approx 1.7Z$, en promedio hay $1.7$ veces más neutrones que protones, casi el doble pero no llega a tanto. El exceso e neutrones evita que la inestabilidad por carga aumente. Una ionterpretación como islas puede verse en al figura \ref{fig:islas}. +Ya les he contado, ya saben un poco de su experiencia, que hay núcleos estables y otros que decaen fácilmente en otros núcleos. Si observamos lo que los experimentos y observaciones nos dicen, para $A\lesssim 40$ el número de protones y neutrones se mantiene igual (para los núcleos estables, recuerden), es decir $N=Z=A/2$, pero para núcleos más pesados $N\approx 1.7Z$, en promedio hay $1.7$ veces más neutrones que protones, casi el doble pero no llega a tanto. El exceso de neutrones evita que la inestabilidad por carga aumente. Una interpretación como islas puede verse en al figura \ref{fig:islas}. Las observaciones además nos dicen que los núcleos más estables más abundantes suelen ser par-par. @@ -230,13 +230,13 @@ Ya hablamos de los tres tipos de radiación \item $\gamma$, fotones de muy alta energía \end{itemize} -En esos primeros estudios (un poco después de Becquerel) se descubrió que para detener la radiación $\beta$ se requiere una pared de plomo, $3mm.$ para las energías de esta radiación de forma natural, una hoja de papel para partículas $\alpha$, y para los $\gamma$ se requieren varios centímetros de plomo para poder detenerlos (absorberlos). +En esos primeros estudios (un poco después de Becquerel) se descubrió que para detener la radiación $\beta$ se requiere una pared de plomo, de apenas $3mm.$ para las energías en que se encuentra esta radiación de forma natural. En cambio se requiere sólo una hoja de papel para detener partículas $\alpha$, y para los $\gamma$ se requieren varios centímetros de plomo para absorberlos. \subsection*{Fuerza nuclear} -Otro tópico que ya hemos tratado, sabemos que es de corto alcance, actúa sobre los hadrones y por ello podemos tener un núcleo formado por protón y neutrón (el deuterio, que a pesar de no ser estable sí existe por un momento). +La fuerza nuclear es un tópico que ya se ha tratado en el curso. Sabemos que es de corto alcance, actúa sobre los hadrones y por ello podemos tener un núcleo formado por protón y neutrón (el deuterio, que a pesar de no ser estable sí existe por un momento). Pero sabemos que hay dos tipos ¿porqué referirse como si fuera una sola? Ya veremos porque. -El hecho de que la energía de enlace por núcleon tienda a una constante es muestra del corto alcance de esta fuerza, se satura. Esta fuerza a su vez de ser atractiva tiene un núcleo repulsivo (lo que evita que colapse el núcleo), por ello podemos pensar esta fuerza como un pozo de potencial (como el de la figura \ref{fig:pozo}). Por ser un pozo de potencial de inmediato sabemos que hay estados ligados cuantizados y que de ahí deriva un modelo que se parcerá mucho al modelo de nivles atómicos, pero de eso ya hablaremos en la próxima sección. +El hecho de que la energía de enlace por nucleon tienda a una constante es muestra del corto alcance de la fuerza nuclear, se satura. Además de ser atractiva tiene un núcleo repulsivo (lo que evita que colapse el núcleo), por ello podemos pensar esta fuerza como un pozo de potencial (como el de la figura \ref{fig:pozo}). Por ser un pozo de potencial de inmediato sabemos que hay estados ligados cuantizados y que de ahí deriva un modelo que se parecerá mucho al modelo de nivles atómicos, pero de eso ya hablaremos en la próxima sección. \begin{figure}[ht!] \begin{center} diff --git a/pres_nuc0.pdf b/pres_nuc0.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a9f75a0e8a57e902c46eb7ba05e3962319214d42 GIT binary patch literal 613861 zcmd421z23m(l$D{y9Cz(g1ZxfySuwHxC9G?;O;I-&=A}mf;$9v2r{_41o$U=?{m)n zzH`2N|9hYRKF{s7hE=P&t9o@!b#?W-1{xI!DQ0#SZe*GtGkpul>^vM4Y!psrcF00P z$gB#Mj@Irr6zm*4Y!rVKWL7C#kh`TT1*;Uu)ZJ3T(%i|y5?NRn+0EV6($oRjYw6ff z-f4vgv*Wb#r^{^>YM7G|3YVno>z@PV$6cyNzz?L~(La8E=@6F#*2nSLS8mOGxBf2g zGDtY?cj*E&d`%;aNb{`owLGoYRF0pH7!kkNpWKD9}V{iV&s9i1)&ezm%+o%L`(b zcek%xCZQ&645iWj*v6D^7-yF7L!nwJlTqu%ANA)hM{SqPRQmTcX~3Q(GOZ=-jPTjV z=p!qO1aK-}5d*uLGL$p^ed3ic7Hd{3L+SKP)KqEWHa!|p@XGKL7Bfz;-}dnEL!iiOVqe zu$}6YlbP&&GM#op!nVeRuE>(rir5@y%$@5#wJZ`b_ zx517rlQFP;9P?@=)!{9o#pMX_v6WN-A?37_LzJkt0BXo 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