# Chapter18-Elementry Particles¶

## Ex1-pg770¶

In [1]:
## Exa18.1 : : Page-770 (2011)
#find The root mean square radius of charge distribution
import math
m_sqr = 0.71;        ## For proton, (GeV/c-square)^2
R_rms = math.sqrt(12.)/(math.sqrt(m_sqr)*5.1);    ## Root mean square radius, femto metre
print'%s %.2f %s'%("\nThe root mean square radius of charge distribution: ",R_rms," fermi");

## Result
## The root mean square radius of charge distribution: 0.81 fermi

The root mean square radius of charge distribution:  0.81  fermi


## Ex3-pg763¶

In [1]:
## Ex18.3 : : Page-763 (2011)
#find all reactions
import math
import numpy
p = numpy.zeros((1,2));             ## proton
pi_minus = numpy.zeros((1,2));      ##pi minus meson
pi_plus = numpy.zeros((1,2));       ## pi plus meson
n = numpy.zeros((1,2));             ## neutron
lamda_0 = numpy.zeros((1,2));       ## lamda hyperon
K_0 = numpy.zeros((1,2));           ## K zero (Kaons)
K_plus =numpy.zeros((1,2));        ## K plus (Kaons)
sigma_plus = numpy.zeros((1,2));    ## hyperon
sigma_minus = numpy.zeros((1,2))    ## hyperon
ksi_minus = numpy.zeros((1,2));     ## hyperon
## Allocate the value of Isospins (T and T3)
p[0,0] = 1/2;
p[0,1] = 1/2;
pi_minus[0,0] = 1;
pi_minus[0,1] = -1;
pi_plus[0,0] = 1;
pi_plus[0,1] = +1;
n[0,0] = 1/2;
n[0,1] = -1/2;
lambda_0=numpy.zeros((1,2));
lambda_0[0,0] = 0;
lambda_0[0,1] = 0;
K_0[0,0] = pi_minus[0,0]+p[0,0];
K_0[0,1] = pi_minus[0,1]+p[0,1] ;
K_plus[0,0] = p[0,0]+p[0,0]-lambda_0[0,0]-p[0,0];
K_plus[0,1] = p[0,1]+p[0,1]-lambda_0[0,1]-p[0,1] ;
sigma_plus[0,0] = pi_plus[0,0]+p[0,0]-K_plus[0,0];
sigma_plus[0,1] =  pi_plus[0,1]+p[0,1]-K_plus[0,1];
sigma_minus[0,0] =  pi_minus[0,0]+p[0,0]-K_plus[0,0];
sigma_minus[0,1] =  pi_minus[0,1]+p[0,1]-K_plus[0,1];
ksi_minus[0,0] = pi_plus[0,0]+n[0,0]-K_plus[0,0]-K_plus[0,0];
ksi_minus[0,1] = pi_plus[0,1]+n[0,1]-K_plus[0,1]-K_plus[0,1];
print'%s'%("\n  Reaction I \n         pi_minus + p ......> lambda_0  + K_0");
print'%s %.2f %s'%("\n The value of T for K_0 is : %3.1f ",K_0[0,0],"");
print'%s %.2f %s'%("\n The value of T3 for K_0 is : %3.1f ",K_0[0,1],"");
print("\n  Reaction II \n         pi_plus + p -> lambda_0  + K_plus");
print'%s %.2f %s'%("\n The value of T for K_plus is : %3.1f ",K_plus[0,0],"");
print'%s %.2f %s'%("\n The value of T3 for K_plus is : %3.1f ",K_plus[0,1],"");
print("\n  Reaction III \n         pi_plus + n -> lambda_0 + K_plus");
print'%s %.2f %s'%("\n The value of T for K_plus is : %3.1f ",K_plus[0,0],"");
print'%s %.2f %s'%("\n The value of T3 for K_plus is : %3.1f ",K_plus[0,1],"");
print("\n  Reaction VI \n         pi_minus + p -> sigma_minus  + K_plus");
print'%s %.2f %s'%("\n The value of T for sigma_minus is : %3.1f ",sigma_minus[0,0],"");
print'%s %.2f %s'%("\n The value of T3 for sigma_minus is : %3.1f ",sigma_minus[0,1],"");
print("\n  Reaction V \n         pi_plus + p -> sigma_plus  + K_plus");
print'%s %.2f %s'%("\n The value of T for sigma_plus is : %3.1f ",sigma_plus[0,0],"");
print'%s %.2f %s'%("\n The value of T3 for sigma_plus is : %3.1f ",sigma_plus[0,1],"");
print("\n  Reaction VI \n         pi_plus + n -> ksi_minus  + K_plus + K_plus");
print'%s %.2f %s'%("\n The value of T for Ksi_minus is : %3.1f ",ksi_minus[0,0],"");
print'%s %.2f %s'%("\n The value of T3 for Ksi_minus is : %3.1f ",ksi_minus[0,1],"");

## Result
##
##  Reaction I
##         pi_minus + p -> lambda_0  + K_0
## The value of T for K_0 is : 1.5
## The value of T3 for K_0 is : -0.5
##  Reaction II
##         pi_plus + p -> lambda_0  + K_plus
## The value of T for K_plus is : 0.5
## The value of T3 for K_plus is : 0.5
##  Reaction III
##         pi_plus + n -> lambda_0  + K_plus
## The value of T for K_plus is : 0.5
## The value of T3 for K_plus is : 0.5
##  Reaction VI
##        pi_minus + p -> sigma_minus  + K_plus
## The value of T for sigma_minus is : 1.0
## The value of T3 for sigma_minus is : -1.0
##  Reaction V
##         pi_plus + p -> sigma_plus  + K_plus
## The value of T for sigma_plus is : 1.0
## The value of T3 for sigma_plus is : 1.0
##  Reaction VI
##        pi_plus + n -> ksi_minus  + K_plus + K_plus
## The value of T for Ksi_minus is : 0.5
## The value of T3 for Ksi_minus is : -0.5
print("ans is slighlty different from book due to rounding off error")

  Reaction I
pi_minus + p ......> lambda_0  + K_0

The value of T for K_0 is : %3.1f  1.00

The value of T3 for K_0 is : %3.1f  -1.00

Reaction II
pi_plus + p -> lambda_0  + K_plus

The value of T for K_plus is : %3.1f  0.00

The value of T3 for K_plus is : %3.1f  0.00

Reaction III
pi_plus + n -> lambda_0 + K_plus

The value of T for K_plus is : %3.1f  0.00

The value of T3 for K_plus is : %3.1f  0.00

Reaction VI
pi_minus + p -> sigma_minus  + K_plus

The value of T for sigma_minus is : %3.1f  1.00

The value of T3 for sigma_minus is : %3.1f  -1.00

Reaction V
pi_plus + p -> sigma_plus  + K_plus

The value of T for sigma_plus is : %3.1f  1.00

The value of T3 for sigma_plus is : %3.1f  1.00

Reaction VI
pi_plus + n -> ksi_minus  + K_plus + K_plus

The value of T for Ksi_minus is : %3.1f  1.00

The value of T3 for Ksi_minus is : %3.1f  0.00
ans is slighlty different from book due to rounding off error


## Ex9-pg766¶

In [4]:
## Ex18.9 : : Page-766 (2011)
import math
#find The lifetime of sigma particle and The isospin of sigma particle
h_cross = 6.62e-022;      ## Redueced planck's constant, MeV sec
p_width = 0.88*35;        ## Partial width of the decay, MeV
tau = h_cross/p_width;    ## Life time of sigma, sec
T_pi = 1.;                 ## Isospin of pi plus particle
T_lambda = 0.;             ## Isospin of lambda zero particle
T_sigma  = T_pi+T_lambda; ## Isospin of sigma particle
print'%s %.2e %s'%("\nThe lifetime of sigma particle = ",tau," s")
print("The reaction is strong")
print"%s %.2f %s"%("The isospin of sigma particle is : ",T_sigma,"");

## Result
## The lifetime of sigma particle = 2.15e-023 s
## The reaction is strong
## The isospin of sigma particle is : 1

The lifetime of sigma particle =  2.15e-23  s
The reaction is strong
The isospin of sigma particle is :  1.00


## Ex10-pg767¶

In [5]:
##Exa18.10 : : Page-767 (2011)
#find The mean life for tau plus
import math
m_mew = 106.;        ## Mass of mew lepton, mega electron volts per square c
m_tau = 1784.;       ## Mass of tau lepton, mega electron volts per square c
tau_mew = 2.2e-06;    ## Mean life of mew lepton, sec
R = 16/100.;           ## Branching factor
tau_plus = R*(m_mew/m_tau)**5*tau_mew;        ## Mean life for tau plus, sec
print'%s %.2e %s'%("\nThe mean life for tau plus : ",tau_plus," sec");

## Result
## The mean life for tau plus : 2.6e-013 sec

The mean life for tau plus :  2.61e-13  sec


## Ex13-pg768¶

In [18]:
# Exa18.13 : : Page-768(2011)
#find The possible charge states
def symbol(val):
global s
if val == 2 :
s = '++';
elif val == 1:
s = '+';
elif val == 0:
s = '0';
elif val == -1:
s = '-';
return s

B = 1;         # Baryon number
S1 = 0;        # Strangeness quantum number
Q = numpy.zeros((1,4))    # Charge
I3 = 3/2.;
print ("\nThe possible charge states are");
for i in range(0,4):
Q = I3+(B+S1)/2.;
symb = symbol(Q);
print symb
I3 = I3 - 1;

print (" respectively");

# Result
# The possible charge states are ++ + 0 - respectively

The possible charge states are
++
+
0
-
respectively


## Ex15-pg768¶

In [6]:
## Exa18.15 : : Page-768 (2011)
#find The branching ratio for a resonanc
import math
I_1 = 3/2.;         ## Isospin for delta(1232)
I_2 = 1/2.;         ## Isospin for delta 0
delta_ratio = math.sqrt((2./3.)**2)/math.sqrt((1./3.)**2);        ## Branching ratio
print'%s %.2f %s'%("\nThe branching ratio for a resonance with I = 1/2 is ", delta_ratio,"");

## Result
## The branching ratio for a resonance with I = 1/2 is 2

The branching ratio for a resonance with I = 1/2 is  2.00


## Ex16-pg768¶

In [7]:
## Exa18.16 : : Page-768 (2011)
#find The cross section ratio
import math
phi = 45*math.pi/180;        ## Phase difference
Cross_sec_ratio = 1/4.*(5.+4.*math.cos(phi))/(1-math.cos(phi));        ## Cross section ratio
print'%s %.2f %s'%("\nThe cross section ratio : ", Cross_sec_ratio,"");

## Result

The cross section ratio :  6.68


## Ex18-pg770¶

In [8]:
## Exa18.18 : : Page-770 (2011)
#find The root mean square radius of charge distribution
import math
m_sqr = 0.71;        ## For proton, (GeV/c-square)^2
R_rms = math.sqrt(12.)/(math.sqrt(m_sqr)*5.1);    ## Root mean square radius, femto metre
print'%s %.2f %s'%("\nThe root mean square radius of charge distribution: ",R_rms," fermi");

## Result
## The root mean square radius of charge distribution: 0.81 fermi math

The root mean square radius of charge distribution:  0.81  fermi