Chapter 14: Particle Physics

Example 14.1, Page 522

In [1]:
import math

#Variable declaration
e = 1.6e-019;  # Energy equivalent of 1 eV, J
h = 6.62e-034;    # Planck's constant, Js
c = 3.00e+008;    # Speed of light in vacuum, m/s
h_bar = h/(2*math.pi);    # Reduced Planck's constant, Js
R_N = 1e-015;     # Range of nuclear force, m

#Calculations
# As delta_E*delta_t = h_bar/2 and delta_E = m_pion*c^2, solving for m_pion
m_pion = h_bar*c/(2*R_N*e*1e+006);    # Mass of the meson, MeV/c^2

#Result
print "The estimated mass of meson from Heisenberg uncertainty principle = %.2f MeV/c^2"%(m_pion)

The estimated mass of meson from Heisenberg uncertainty principle = 98.78 MeV/c^2

Example 14.2, Page 526

In [2]:
import math

#Variable declaration
e = 1.6e-019;  # Energy equivalent of 1 eV, J
h = 6.62e-034;    # Planck's constant, Js
c = 3.00e+008;    # For simplicity assume speed of light to be unity
h_bar = h/(2*math.pi);    # Reduced Planck's constant, Js
m_W = 80.4;    # Energy equivalent of mass of W- particle, MeV

#Calculations
R_W = h_bar*c/(2*m_W*e*1e+009);    # Range of W- particle, m
delta_t = h_bar/(2*m_W*e*1e+009);    # Time during which the energy conservation is violated, s

#Results
print "The range of W- particle = %3.1e m"%R_W
print "The time during which the energy conservation is violated = %1.0e s"%delta_t

The range of W- particle = 1.2e-18 m
The time during which the energy conservation is violated = 4e-27 s

Example 14.10, Page 548

In [3]:
import math

#Variable declaration
m_p = 0.938;    # Rest mass energy of the proton, GeV
K = 6.4;    # Kinetic energy of the proton projectile, GeV

#Calculations
E_cm = math.sqrt(2*m_p**2+2*m_p*K);    # Centre of mass energy of proton collsion with the fixed proton target, GeV
Q = 2*m_p - 4*m_p;     # Q value of the reaction, GeV
K_th = -3*Q;    # Threshold kinetic energy required to produce the antiprotons, GeV
K = 1000;    # Kinetic energy of the protons in Tevatron, GeV
E_cm_T = math.sqrt(2*m_p**2+2*m_p*K);    # Centre-of-mass energy available for the reaction for the Tevatron, GeV

#Results
print "The available energy in the center on mass = %4.2f GeV"%E_cm
print "The threshold kinetic energy required to produce the antiprotons = %3.1f GeV"%K_th
print "The centre-of-mass energy available for the reaction for the Tevatron = %d GeV"%E_cm_T

The available energy in the center on mass = 3.71 GeV
The threshold kinetic energy required to produce the antiprotons = 5.6 GeV
The centre-of-mass energy available for the reaction for the Tevatron = 43 GeV

Example 14.11, Page 550

In [4]:
import math

#Variable declaration
m_p = 0.938;    # Rest mass energy of the proton, GeV
E_cm = 14000;    # Centre of mass energy of colliding proton beams at LHC, GeV

#Calculations
# As E_cm = math.sqrt(2*m_p**2+2*m_p*K), solving for K
K = E_cm**2*1e+009/(2*m_p);    # Approx. kinetic energy of the protons needed for fixed-target experiment, eV 

#Result
print "The kinetic energy of the protons needed for fixed-target experiment = %3.1e eV"%K

The kinetic energy of the protons needed for fixed-target experiment = 1.0e+17 eV