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"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter18-Elementry Particles"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1-pg770"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Exa18.1 : : Page-770 (2011)\n",
"#find The root mean square radius of charge distribution\n",
"import math \n",
"m_sqr = 0.71; ## For proton, (GeV/c-square)^2\n",
"R_rms = math.sqrt(12.)/(math.sqrt(m_sqr)*5.1); ## Root mean square radius, femto metre\n",
"print'%s %.2f %s'%(\"\\nThe root mean square radius of charge distribution: \",R_rms,\" fermi\");\n",
"\n",
"## Result\n",
"## The root mean square radius of charge distribution: 0.81 fermi "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The root mean square radius of charge distribution: 0.81 fermi\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3-pg763"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Ex18.3 : : Page-763 (2011)\n",
"#find all reactions\n",
"import math\n",
"import numpy\n",
"p = numpy.zeros((1,2)); ## proton\n",
"pi_minus = numpy.zeros((1,2)); ##pi minus meson\n",
"pi_plus = numpy.zeros((1,2)); ## pi plus meson\n",
"n = numpy.zeros((1,2)); ## neutron\n",
"lamda_0 = numpy.zeros((1,2)); ## lamda hyperon\n",
"K_0 = numpy.zeros((1,2)); ## K zero (Kaons)\n",
"K_plus =numpy.zeros((1,2)); ## K plus (Kaons)\n",
"sigma_plus = numpy.zeros((1,2)); ## hyperon \n",
"sigma_minus = numpy.zeros((1,2)) ## hyperon\n",
"ksi_minus = numpy.zeros((1,2)); ## hyperon\n",
"## Allocate the value of Isospins (T and T3)\n",
"p[0,0] = 1/2;\n",
"p[0,1] = 1/2;\n",
"pi_minus[0,0] = 1;\n",
"pi_minus[0,1] = -1;\n",
"pi_plus[0,0] = 1;\n",
"pi_plus[0,1] = +1;\n",
"n[0,0] = 1/2;\n",
"n[0,1] = -1/2;\n",
"lambda_0=numpy.zeros((1,2));\n",
"lambda_0[0,0] = 0;\n",
"lambda_0[0,1] = 0;\n",
"K_0[0,0] = pi_minus[0,0]+p[0,0];\n",
"K_0[0,1] = pi_minus[0,1]+p[0,1] ;\n",
"K_plus[0,0] = p[0,0]+p[0,0]-lambda_0[0,0]-p[0,0];\n",
"K_plus[0,1] = p[0,1]+p[0,1]-lambda_0[0,1]-p[0,1] ;\n",
"sigma_plus[0,0] = pi_plus[0,0]+p[0,0]-K_plus[0,0];\n",
"sigma_plus[0,1] = pi_plus[0,1]+p[0,1]-K_plus[0,1];\n",
"sigma_minus[0,0] = pi_minus[0,0]+p[0,0]-K_plus[0,0];\n",
"sigma_minus[0,1] = pi_minus[0,1]+p[0,1]-K_plus[0,1];\n",
"ksi_minus[0,0] = pi_plus[0,0]+n[0,0]-K_plus[0,0]-K_plus[0,0];\n",
"ksi_minus[0,1] = pi_plus[0,1]+n[0,1]-K_plus[0,1]-K_plus[0,1];\n",
"print'%s'%(\"\\n Reaction I \\n pi_minus + p ......> lambda_0 + K_0\");\n",
"print'%s %.2f %s'%(\"\\n The value of T for K_0 is : %3.1f \",K_0[0,0],\"\");\n",
"print'%s %.2f %s'%(\"\\n The value of T3 for K_0 is : %3.1f \",K_0[0,1],\"\");\n",
"print(\"\\n Reaction II \\n pi_plus + p -> lambda_0 + K_plus\");\n",
"print'%s %.2f %s'%(\"\\n The value of T for K_plus is : %3.1f \",K_plus[0,0],\"\");\n",
"print'%s %.2f %s'%(\"\\n The value of T3 for K_plus is : %3.1f \",K_plus[0,1],\"\");\n",
"print(\"\\n Reaction III \\n pi_plus + n -> lambda_0 + K_plus\");\n",
"print'%s %.2f %s'%(\"\\n The value of T for K_plus is : %3.1f \",K_plus[0,0],\"\");\n",
"print'%s %.2f %s'%(\"\\n The value of T3 for K_plus is : %3.1f \",K_plus[0,1],\"\");\n",
"print(\"\\n Reaction VI \\n pi_minus + p -> sigma_minus + K_plus\");\n",
"print'%s %.2f %s'%(\"\\n The value of T for sigma_minus is : %3.1f \",sigma_minus[0,0],\"\");\n",
"print'%s %.2f %s'%(\"\\n The value of T3 for sigma_minus is : %3.1f \",sigma_minus[0,1],\"\");\n",
"print(\"\\n Reaction V \\n pi_plus + p -> sigma_plus + K_plus\");\n",
"print'%s %.2f %s'%(\"\\n The value of T for sigma_plus is : %3.1f \",sigma_plus[0,0],\"\");\n",
"print'%s %.2f %s'%(\"\\n The value of T3 for sigma_plus is : %3.1f \",sigma_plus[0,1],\"\");\n",
"print(\"\\n Reaction VI \\n pi_plus + n -> ksi_minus + K_plus + K_plus\");\n",
"print'%s %.2f %s'%(\"\\n The value of T for Ksi_minus is : %3.1f \",ksi_minus[0,0],\"\");\n",
"print'%s %.2f %s'%(\"\\n The value of T3 for Ksi_minus is : %3.1f \",ksi_minus[0,1],\"\");\n",
"\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 \n",
"print(\"ans is slighlty different from book due to rounding off error\")\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Reaction I \n",
" pi_minus + p ......> lambda_0 + K_0\n",
"\n",
" The value of T for K_0 is : %3.1f 1.00 \n",
"\n",
" The value of T3 for K_0 is : %3.1f -1.00 \n",
"\n",
" Reaction II \n",
" pi_plus + p -> lambda_0 + K_plus\n",
"\n",
" The value of T for K_plus is : %3.1f 0.00 \n",
"\n",
" The value of T3 for K_plus is : %3.1f 0.00 \n",
"\n",
" Reaction III \n",
" pi_plus + n -> lambda_0 + K_plus\n",
"\n",
" The value of T for K_plus is : %3.1f 0.00 \n",
"\n",
" The value of T3 for K_plus is : %3.1f 0.00 \n",
"\n",
" Reaction VI \n",
" pi_minus + p -> sigma_minus + K_plus\n",
"\n",
" The value of T for sigma_minus is : %3.1f 1.00 \n",
"\n",
" The value of T3 for sigma_minus is : %3.1f -1.00 \n",
"\n",
" Reaction V \n",
" pi_plus + p -> sigma_plus + K_plus\n",
"\n",
" The value of T for sigma_plus is : %3.1f 1.00 \n",
"\n",
" The value of T3 for sigma_plus is : %3.1f 1.00 \n",
"\n",
" Reaction VI \n",
" pi_plus + n -> ksi_minus + K_plus + K_plus\n",
"\n",
" The value of T for Ksi_minus is : %3.1f 1.00 \n",
"\n",
" The value of T3 for Ksi_minus is : %3.1f 0.00 \n",
"ans is slighlty different from book due to rounding off error\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9-pg766"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Ex18.9 : : Page-766 (2011)\n",
"import math\n",
"#find The lifetime of sigma particle and The isospin of sigma particle \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",
"print'%s %.2e %s'%(\"\\nThe lifetime of sigma particle = \",tau,\" s\")\n",
"print(\"The reaction is strong\")\n",
"print\"%s %.2f %s\"%(\"The isospin of sigma particle is : \",T_sigma,\"\");\n",
"\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 "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The lifetime of sigma particle = 2.15e-23 s\n",
"The reaction is strong\n",
"The isospin of sigma particle is : 1.00 \n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10-pg767"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##Exa18.10 : : Page-767 (2011)\n",
"#find The mean life for tau plus\n",
"import math\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",
"print'%s %.2e %s'%(\"\\nThe mean life for tau plus : \",tau_plus,\" sec\");\n",
"\n",
"## Result\n",
"## The mean life for tau plus : 2.6e-013 sec "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The mean life for tau plus : 2.61e-13 sec\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex13-pg768"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Exa18.13 : : Page-768(2011)\n",
"#find The possible charge states \n",
"def symbol(val):\n",
" global s\n",
" if val == 2 :\n",
" s = '++';\n",
" elif val == 1:\n",
" s = '+';\n",
" elif val == 0:\n",
" s = '0';\n",
" elif val == -1:\n",
" s = '-';\n",
" return s\n",
"\n",
"B = 1; # Baryon number\n",
"S1 = 0; # Strangeness quantum number\n",
"Q = numpy.zeros((1,4)) # Charge\n",
"I3 = 3/2.; \n",
"print (\"\\nThe possible charge states are\");\n",
"for i in range(0,4): \n",
" Q = I3+(B+S1)/2.;\n",
" symb = symbol(Q);\n",
" print symb\n",
" I3 = I3 - 1;\n",
"\n",
"print (\" respectively\");\n",
"\n",
"# Result\n",
"# The possible charge states are ++ + 0 - respectively "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The possible charge states are\n",
"++\n",
"+\n",
"0\n",
"-\n",
" respectively\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex15-pg768"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Exa18.15 : : Page-768 (2011)\n",
"#find The branching ratio for a resonanc\n",
"import math\n",
"I_1 = 3/2.; ## Isospin for delta(1232)\n",
"I_2 = 1/2.; ## Isospin for delta 0\n",
"delta_ratio = math.sqrt((2./3.)**2)/math.sqrt((1./3.)**2); ## Branching ratio\n",
"print'%s %.2f %s'%(\"\\nThe branching ratio for a resonance with I = 1/2 is \", delta_ratio,\"\");\n",
"\n",
"## Result\n",
"## The branching ratio for a resonance with I = 1/2 is 2 "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The branching ratio for a resonance with I = 1/2 is 2.00 \n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex16-pg768"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Exa18.16 : : Page-768 (2011)\n",
"#find The cross section ratio\n",
"import math\n",
"phi = 45*math.pi/180; ## Phase difference\n",
"Cross_sec_ratio = 1/4.*(5.+4.*math.cos(phi))/(1-math.cos(phi)); ## Cross section ratio\n",
"print'%s %.2f %s'%(\"\\nThe cross section ratio : \", Cross_sec_ratio,\"\");\n",
"\n",
"## Result\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The cross section ratio : 6.68 \n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex18-pg770"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Exa18.18 : : Page-770 (2011)\n",
"#find The root mean square radius of charge distribution\n",
"import math \n",
"m_sqr = 0.71; ## For proton, (GeV/c-square)^2\n",
"R_rms = math.sqrt(12.)/(math.sqrt(m_sqr)*5.1); ## Root mean square radius, femto metre\n",
"print'%s %.2f %s'%(\"\\nThe root mean square radius of charge distribution: \",R_rms,\" fermi\");\n",
"\n",
"## Result\n",
"## The root mean square radius of charge distribution: 0.81 fermi math"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The root mean square radius of charge distribution: 0.81 fermi\n"
]
}
],
"prompt_number": 8
}
],
"metadata": {}
}
]
}