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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 18: Elementary Particles"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 18.10: Estimation_of_the_mean_life_of_tau_plus.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa18.10 : : Page-767 (2011)\n",
+"clc; clear;\n",
+"m_mew = 106; // Mass of mew lepton, mega electron volts per square c\n",
+"m_tau = 1784; // Mass of tau lepton, mega electron volts per square c\n",
+"tau_mew = 2.2e-06; // Mean life of mew lepton, sec\n",
+"R = 16/100; // Branching factor\n",
+"tau_plus = R*(m_mew/m_tau)^5*tau_mew; // Mean life for tau plus, sec\n",
+"printf('\nThe mean life for tau plus : %3.1e sec', tau_plus);\n",
+"// Result\n",
+"// The mean life for tau plus : 2.6e-013 sec "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 18.13: Possible_electric_charge_for_a_baryon_and_a_meson.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa18.13 : : Page-768(2011)\n",
+"clc; clear;\n",
+"function s = symbol(val)\n",
+" if val == 2 then\n",
+" s = '++';\n",
+" elseif val == 1 then\n",
+" s = '+';\n",
+" elseif val == 0 then\n",
+" s = '0';\n",
+" elseif val == -1 then\n",
+" s = '-';\n",
+" end\n",
+"endfunction\n",
+"B = 1; // Baryon number\n",
+"S = 0; // Strangeness quantum number\n",
+"Q = rand(1,4) // Charge\n",
+"I3 = 3/2; \n",
+"printf('\nThe possible charge states are');\n",
+"for i = 0:1:3\n",
+" Q = I3+(B+S)/2;\n",
+" sym = symbol(Q);\n",
+" printf(' %s', sym);\n",
+" I3 = I3 - 1;\n",
+"end\n",
+"printf(' respectively');\n",
+"// Result\n",
+"// The possible charge states are ++ + 0 - respectively "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 18.15: Branching_ratio_for_resonant_decay.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa18.15 : : Page-768 (2011)\n",
+"clc; clear;\n",
+"I_1 = 3/2; // Isospin for delta(1232)\n",
+"I_2 = 1/2; // Isospin for delta 0\n",
+"delta_ratio = sqrt((2/3)^2)/sqrt((1/3)^2); // Branching ratio\n",
+"printf('\nThe branching ratio for a resonance with I = 1/2 is %d', delta_ratio);\n",
+"// Result\n",
+"// The branching ratio for a resonance with I = 1/2 is 2 "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 18.16: Ratio_of_cross_section_for_reactions.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa18.16 : : Page-768 (2011)\n",
+"clc; clear;\n",
+"phi = 45*%pi/180; // Phase difference\n",
+"Cross_sec_ratio = 1/4*(5+4*cos(phi))/(1-cos(phi)); // Cross section ratio\n",
+"printf('\nThe cross section ratio : %4.2f', Cross_sec_ratio);\n",
+"// Result"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 18.18: Root_mean_square_radius_of_charge_distribution.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa18.18 : : Page-770 (2011)\n",
+"clc; clear; \n",
+"m_sqr = 0.71; // For proton, (GeV/c-square)^2\n",
+"R_rms = sqrt(12)/(sqrt(m_sqr)*5.1); // Root mean square radius, femto metre\n",
+"printf('\nThe root mean square radius of charge distribution: %4.2f fermi', R_rms);\n",
+"// Result\n",
+"// The root mean square radius of charge distribution: 0.81 fermi "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 18.1: Root_mean_square_radius_of_charge_distribution.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa18.1 : : Page-770 (2011)\n",
+"clc; clear; \n",
+"m_sqr = 0.71; // For proton, (GeV/c-square)^2\n",
+"R_rms = sqrt(12)/(sqrt(m_sqr)*5.1); // Root mean square radius, femto metre\n",
+"printf('\nThe root mean square radius of charge distribution: %4.2f fermi', R_rms);\n",
+"// Result\n",
+"// The root mean square radius of charge distribution: 0.81 fermi "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 18.3: Isospin_of_the_strange_particles.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex18.3 : : Page-763 (2011)\n",
+"clc; clear;\n",
+"p = rand(1,2); // proton\n",
+"pi_minus = rand(1,2); //pi minus meson\n",
+"pi_plus = rand(1,2); // pi plus meson\n",
+"n = rand(1,2); // neutron\n",
+"lamda_0 = rand(1,2); // lamda hyperon\n",
+"K_0 = rand(1,2); // K zero (Kaons)\n",
+"K_plus = rand(1,2); // K plus (Kaons)\n",
+"sigma_plus = rand(1,2); // hyperon \n",
+"sigma_minus = rand(1,2) // hyperon\n",
+"ksi_minus = rand(1,2); // hyperon\n",
+"// Allocate the value of Isospins (T and T3)\n",
+"p(1,1) = 1/2;\n",
+"p(1,2) = 1/2;\n",
+"pi_minus(1,1) = 1;\n",
+"pi_minus(1,2) = -1;\n",
+"pi_plus(1,1) = 1;\n",
+"pi_plus(1,2) = +1;\n",
+"n(1,1) = 1/2;\n",
+"n(1,2) = -1/2;\n",
+"lambda_0(1,1) = 0;\n",
+"lambda_0(1,2) = 0;\n",
+"K_0(1,1) = pi_minus(1,1)+p(1,1);\n",
+"K_0(1,2) = pi_minus(1,2)+p(1,2) ;\n",
+"K_plus(1,1) = p(1,1)+p(1,1)-lambda_0(1,1)-p(1,1);\n",
+"K_plus(1,2) = p(1,2)+p(1,2)-lambda_0(1,2)-p(1,2) ;\n",
+"sigma_plus(1,1) = pi_plus(1,1)+p(1,1)-K_plus(1,1);\n",
+"sigma_plus(1,2) = pi_plus(1,2)+p(1,2)-K_plus(1,2);\n",
+"sigma_minus(1,1) = pi_minus(1,1)+p(1,1)-K_plus(1,1);\n",
+"sigma_minus(1,2) = pi_minus(1,2)+p(1,2)-K_plus(1,2);\n",
+"ksi_minus(1,1) = pi_plus(1,1)+n(1,1)-K_plus(1,1)-K_plus(1,1);\n",
+"ksi_minus(1,2) = pi_plus(1,2)+n(1,2)-K_plus(1,2)-K_plus(1,2);\n",
+"printf('\n Reaction I \n pi_minus + p ......> lambda_0 + K_0');\n",
+"printf('\n The value of T for K_0 is : %3.1f ',K_0(1,1));\n",
+"printf('\n The value of T3 for K_0 is : %3.1f ',K_0(1,2));\n",
+"printf('\n Reaction II \n pi_plus + p -> lambda_0 + K_plus');\n",
+"printf('\n The value of T for K_plus is : %3.1f ',K_plus(1,1));\n",
+"printf('\n The value of T3 for K_plus is : %3.1f ',K_plus(1,2));\n",
+"printf('\n Reaction III \n pi_plus + n -> lambda_0 + K_plus');\n",
+"printf('\n The value of T for K_plus is : %3.1f ',K_plus(1,1));\n",
+"printf('\n The value of T3 for K_plus is : %3.1f ',K_plus(1,2));\n",
+"printf('\n Reaction VI \n pi_minus + p -> sigma_minus + K_plus');\n",
+"printf('\n The value of T for sigma_minus is : %3.1f ',sigma_minus(1,1));\n",
+"printf('\n The value of T3 for sigma_minus is : %3.1f ',sigma_minus(1,2));\n",
+"printf('\n Reaction V \n pi_plus + p -> sigma_plus + K_plus');\n",
+"printf('\n The value of T for sigma_plus is : %3.1f ',sigma_plus(1,1));\n",
+"printf('\n The value of T3 for sigma_plus is : %3.1f ',sigma_plus(1,2));\n",
+"printf('\n Reaction VI \n pi_plus + n -> ksi_minus + K_plus + K_plus');\n",
+"printf('\n The value of T for Ksi_minus is : %3.1f ',ksi_minus(1,1));\n",
+"printf('\n The value of T3 for Ksi_minus is : %3.1f ',ksi_minus(1,2));\n",
+"// Result\n",
+"// \n",
+"// Reaction I \n",
+"// pi_minus + p -> lambda_0 + K_0\n",
+"// The value of T for K_0 is : 1.5 \n",
+"// The value of T3 for K_0 is : -0.5 \n",
+"// Reaction II \n",
+"// pi_plus + p -> lambda_0 + K_plus\n",
+"// The value of T for K_plus is : 0.5 \n",
+"// The value of T3 for K_plus is : 0.5 \n",
+"// Reaction III \n",
+"// pi_plus + n -> lambda_0 + K_plus\n",
+"// The value of T for K_plus is : 0.5 \n",
+"// The value of T3 for K_plus is : 0.5 \n",
+"// Reaction VI \n",
+" // pi_minus + p -> sigma_minus + K_plus\n",
+"// The value of T for sigma_minus is : 1.0 \n",
+"// The value of T3 for sigma_minus is : -1.0 \n",
+"// Reaction V \n",
+"// pi_plus + p -> sigma_plus + K_plus\n",
+"// The value of T for sigma_plus is : 1.0 \n",
+"// The value of T3 for sigma_plus is : 1.0 \n",
+"// Reaction VI \n",
+" // pi_plus + n -> ksi_minus + K_plus + K_plus\n",
+"// The value of T for Ksi_minus is : 0.5 \n",
+"// The value of T3 for Ksi_minus is : -0.5 "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 18.4: Allowed_and_forbidden_reactions_under_conservation_laws.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa18.4 : : Page-764 (2011)\n",
+"clc;clear;\n",
+"p = rand(1,3); // proton\n",
+"pi_minus = rand(1,3); // pi minus meson\n",
+"pi_plus = rand(1,3); // pi plus meson\n",
+"pi_0 = rand(1,3); // pi zero meson\n",
+"n = rand(1,3); // neutron\n",
+"lambda_0 = rand(1,3); // lambda zero hyperon\n",
+"K_0 = rand(1,3); // k zero meson\n",
+"K_plus = rand(1,3); // k plus meson\n",
+"K_0_bar = rand(1,3); // anti particle of k zero\n",
+"sigma_plus = rand(1,3); // sigma hyperon\n",
+"// Now in the following steps we allocated the value of charge(Q),baryon number(B) and strangeness number (S) \n",
+"p(1,1) = 1;\n",
+"p(1,2) = 1;\n",
+"p(1,3) = 0;\n",
+"pi_minus(1,1) = -1;\n",
+"pi_minus(1,2) = 0;\n",
+"pi_minus(1,3) = 0;\n",
+"pi_plus(1,1) = 1;\n",
+"pi_plus(1,2) = 0;\n",
+"pi_plus(1,3) = 0;\n",
+"n(1,1) = 0;\n",
+"n(1,2) = 1;\n",
+"n(1,3) = 0;\n",
+"lambda_0(1,1) = 0;\n",
+"lambda_0(1,2) = 1;\n",
+"lambda_0(1,3) = -1;\n",
+"K_0(1,1) =0 ;\n",
+"K_0(1,2) = 0 ;\n",
+"K_0(1,3) = 1;\n",
+"K_plus(1,1) = 1;\n",
+"K_plus(1,2) = 0 ;\n",
+"K_plus(1,3) = 1;\n",
+"sigma_plus(1,1) = 1;\n",
+"sigma_plus(1,2) = 1;\n",
+"sigma_plus(1,3) = -1;\n",
+"K_0_bar(1,1) = 0;\n",
+"K_0_bar(1,2) = 0;\n",
+"K_0_bar(1,3) = -1;\n",
+"pi_0(1,1) = 0;\n",
+"pi_0(1,2) = 0;\n",
+"pi_0(1,3) = 0;\n",
+"j = 0;\n",
+"k = 0;\n",
+"printf('\n Reaction I \n pi_plus + n ......> lambda_0 + K_plus')\n",
+"for i = 1:3\n",
+" if pi_plus(1,i)+n(1,i) == lambda_0(1,i)+K_plus(1,i) then\n",
+" j = j+1;\n",
+" else\n",
+" printf('\n Reaction I is forbidden')\n",
+" if i == 1 then\n",
+" printf('\n Delta Q is not zero')\n",
+" elseif i == 2 then\n",
+" printf('\n Delta B is not zero')\n",
+" elseif i == 3 then\n",
+" printf('\n Delta S is not zero')\n",
+" end \n",
+" end \n",
+"end \n",
+"if j==3 then\n",
+" printf('\n Reaction I is allowed ');\n",
+" printf('\n Delta Q is zero \n Delta B is zero \n Delta S is zero')\n",
+"end \n",
+"printf('\n Reaction II \n pi_plus + n ......> K_0 + K_plus')\n",
+"j = 0;\n",
+"for i = 1:3\n",
+" if pi_plus(1,i)+n(1,i) == K_0(1,i)+K_plus(1,i) then\n",
+" j = j+1;\n",
+" else\n",
+" printf('\n Reaction II is forbidden')\n",
+" if i == 1 then\n",
+" printf('\n Delta Q is not zero')\n",
+" elseif i == 2 then\n",
+" printf('\n Delta B is not zero')\n",
+" elseif i == 3 then\n",
+" printf('\n Delta S is not zero')\n",
+" end \n",
+" end \n",
+"end \n",
+"if j==3 then\n",
+" printf('\n Reaction II is allowed ');\n",
+" printf('\n Delta Q is zero \n Delta B is zero \n Delta S is zero')\n",
+"end \n",
+"j = 0;\n",
+"printf('\n Reaction III \n pi_plus + n ......> K_0_bar + sumison_plus')\n",
+"for i = 1:3\n",
+" if pi_plus(1,i)+n(1,i) == K_0_bar(1,i)+sigma_plus(1,i) then\n",
+" j = j+1;\n",
+" else\n",
+" printf('\n Reaction III is forbidden')\n",
+" if i == 1 then\n",
+" printf('\n Delta Q is not zero')\n",
+" elseif i == 2 then\n",
+" printf('\n Delta B is not zero')\n",
+" elseif i == 3 then\n",
+" printf('\n Delta S is not zero')\n",
+" end \n",
+" end \n",
+"end \n",
+"if j==3 then\n",
+" printf('\n Reaction III is allowed ');\n",
+" printf('\n Delta Q is zero \n Delta B is zero \n Delta S is zero')\n",
+"end \n",
+"j = 0;\n",
+"printf('\n Reaction IV \n pi_plus + n ......> pi_minus + p')\n",
+"for i = 1:3\n",
+" if pi_plus(1,i)+n(1,i) == pi_minus(1,i)+p(1,i) then\n",
+" j = j+1;\n",
+" else\n",
+" printf('\n Reaction IV is forbidden')\n",
+" if i == 1 then\n",
+" printf('\n Delta Q is not zero')\n",
+" elseif i == 2 then\n",
+" printf('\n Delta B is not zero')\n",
+" elseif i == 3 then\n",
+" printf('\n Delta S is not zero')\n",
+" end \n",
+" end \n",
+"end \n",
+"if j==3 then\n",
+" printf('\n Reaction IV is allowed ');\n",
+" printf('\n Delta Q is zero \n Delta B is zero \n Delta S is zero')\n",
+"end \n",
+"j = 0;\n",
+"printf('\n Reaction V \n pi_minus + p ......> lambda_0 + K_0')\n",
+"for i = 1:3\n",
+" if pi_minus(1,i)+p(1,i) == lambda_0(1,i)+K_0(1,i) then\n",
+" j = j+1;\n",
+" else\n",
+" printf('\n Reaction V is forbidden')\n",
+" if i == 1 then\n",
+" printf('\n Delta Q is not zero')\n",
+" elseif i == 2 then\n",
+" printf('\n Delta B is not zero')\n",
+" elseif i == 3 then\n",
+" printf('\n Delta S is not zero')\n",
+" end \n",
+" end \n",
+"end \n",
+"if j==3 then\n",
+" printf('\n Reaction V is allowed ');\n",
+" printf('\n Delta Q is zero \n Delta B is zero \n Delta S is zero')\n",
+"end \n",
+"j = 0;\n",
+"printf('\n Reaction VI \n pi_plus + n ......> lambda_0 + K_plus')\n",
+"for i = 1:3\n",
+" if pi_minus(1,i)+p(1,i) == pi_0(1,i)+lambda_0(1,i) then\n",
+" j = j+1;\n",
+" else\n",
+" printf('\n Reaction VI is forbidden')\n",
+" if i == 1 then\n",
+" printf('\n Delta Q is not zero');\n",
+" elseif i == 2 then\n",
+" printf('\n Delta B is not zero')\n",
+" elseif i == 3 then\n",
+" printf('\n Delta S is not zero')\n",
+" end \n",
+" end \n",
+"end \n",
+"if j==3 then\n",
+" printf('\n Reaction VI is allowed ');\n",
+" printf('\n Delta Q is zero \n Delta B is zero \n Delta S is zero');\n",
+"end\n",
+" \n",
+"// Result\n",
+"// Reaction I \n",
+" // pi_plus + n ......> lambda_0 + K_plus\n",
+"// Reaction I is allowed \n",
+"// Delta Q is zero \n",
+"// Delta B is zero \n",
+"// Delta S is zero\n",
+"// Reaction II \n",
+" // pi_plus + n ......> K_0 + K_plus\n",
+"// Reaction II is forbidden\n",
+"// Delta B is not zero\n",
+"// Reaction II is forbidden\n",
+"// Delta S is not zero\n",
+"// Reaction III \n",
+"// pi_plus + n ......> K_0_bar + sumison_plus\n",
+"// Reaction III is forbidden\n",
+"// Delta S is not zero\n",
+"// Reaction IV \n",
+"// pi_plus + n ......> pi_minus + p\n",
+"// Reaction IV is forbidden\n",
+"// Delta Q is not zero\n",
+"// Reaction V \n",
+"// pi_minus + p ......> lambda_0 + K_0\n",
+"// Reaction V is allowed \n",
+"// Delta Q is zero \n",
+"// Delta B is zero \n",
+"// Delta S is zero\n",
+"// Reaction VI \n",
+"// pi_plus + n ......> lambda_0 + K_plus\n",
+"// Reaction VI is forbidden\n",
+"// Delta S is not zero "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 18.9: Decay_of_sigma_particle.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex18.9 : : Page-766 (2011)\n",
+"clc; clear;\n",
+"h_cross = 6.62e-022; // Redueced planck's constant, MeV sec\n",
+"p_width = 0.88*35; // Partial width of the decay, MeV \n",
+"tau = h_cross/p_width; // Life time of sigma, sec \n",
+"T_pi = 1; // Isospin of pi plus particle \n",
+"T_lambda = 0; // Isospin of lambda zero particle \n",
+"T_sigma = T_pi+T_lambda; // Isospin of sigma particle \n",
+"printf('\nThe lifetime of sigma particle = %4.2e s\nThe reaction is strong\nThe isospin of sigma particle is : %d',tau, T_sigma);\n",
+"// Result\n",
+"// The lifetime of sigma particle = 2.15e-023 s\n",
+"// The reaction is strong\n",
+"// The isospin of sigma particle is : 1 "
+ ]
+ }
+],
+"metadata": {
+ "kernelspec": {
+ "display_name": "Scilab",
+ "language": "scilab",
+ "name": "scilab"
+ },
+ "language_info": {
+ "file_extension": ".sce",
+ "help_links": [
+ {
+ "text": "MetaKernel Magics",
+ "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+ }
+ ],
+ "mimetype": "text/x-octave",
+ "name": "scilab",
+ "version": "0.7.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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