502
9 Particle Physics – I
9.102 What is the length L of the longest drift tube in a linac which operating at a
frequency of f = 25 MHz is capable of accelerating
12 C ions to a maximum
energy of E = 80 MeV?
9.2.15 Colliders
9.103 Two beams of particles consisting of n bunches with N 1 and N 2 particles
in each circulate in a collider and make head-on-collisions. A, the crosssectional area of the beam and f is the frequency with which the particles
circulate, obtain an expression for the luminosity L.
9.104 In an electron-positron collider the particles circulate in short cylindrical
bunches of radius 1.2 mm. The number of particles per bunch is 6 × 10
11 and
the bunches collide at a frequency of 2 MHz. The cross-section for μ
+
μ
−
creation at 8 GeV total energy is, 1.4 × 10
−33 cm
2 ; how many μ
+
μ
− pairs
are created per second?
9.105 (a) Show that in a head-on-collision of a beam of relativistic particles of
energy E 1 with one of energy E 2 , the square of the energy in the CMS is 4
E 1 E 2 and that for a crossing angle θ between the beam this is reduced by
a factor (1+cos θ)/2, (neglect the masses of beam particles in comparison
with the energy)
(b) Show that the available kinetic energy in the head-on-collision with two
25 GeV protons is equal to that in the collision of a 1,300 GeV proton with
a fixed hydrogen target. (Courtesy D.H. Perkins, Cambridge University
Press)
9.106 Head-on collisions are observed between protons each moving with velocity
(relative to the fixed observer) corresponding to 10
10 eV. If one of the protons
were to be at rest relative to the observer, what would the energy of the other
need to be so as to produce the same collision energy as before. The rest
energy of the proton is 10
9 eV.
[University of Manchester 1958]
9.107 It is required to cause protons to collide with an energy measured in their
centre of mass frame, of 4 M 0 c
2 in excess of their rest energy 2 M 0 c
2 . This
can be achieved by firing protons at one another with two accelerators each of
which imparts a kinetic energy of 2 M 0 c
2 . Alternatively, protons can be fired
from an accelerator at protons at rest. How much energy must this single
machine be capable of imparting to a proton? What is the significance of this
result for experiments in high energy nuclear physics?
[University of New Castle 1966]
9.108 The HERA accelerator in Hamburg provided head-on collisions between
30 GeV electrons and 820 GeV protons. Calculate the centre of mass energy
that was produced in each collision.
[Manchester 2008]
9 Particle Physics – I
9.102 What is the length L of the longest drift tube in a linac which operating at a
frequency of f = 25 MHz is capable of accelerating
12 C ions to a maximum
energy of E = 80 MeV?
9.2.15 Colliders
9.103 Two beams of particles consisting of n bunches with N 1 and N 2 particles
in each circulate in a collider and make head-on-collisions. A, the crosssectional area of the beam and f is the frequency with which the particles
circulate, obtain an expression for the luminosity L.
9.104 In an electron-positron collider the particles circulate in short cylindrical
bunches of radius 1.2 mm. The number of particles per bunch is 6 × 10
11 and
the bunches collide at a frequency of 2 MHz. The cross-section for μ
+
μ
−
creation at 8 GeV total energy is, 1.4 × 10
−33 cm
2 ; how many μ
+
μ
− pairs
are created per second?
9.105 (a) Show that in a head-on-collision of a beam of relativistic particles of
energy E 1 with one of energy E 2 , the square of the energy in the CMS is 4
E 1 E 2 and that for a crossing angle θ between the beam this is reduced by
a factor (1+cos θ)/2, (neglect the masses of beam particles in comparison
with the energy)
(b) Show that the available kinetic energy in the head-on-collision with two
25 GeV protons is equal to that in the collision of a 1,300 GeV proton with
a fixed hydrogen target. (Courtesy D.H. Perkins, Cambridge University
Press)
9.106 Head-on collisions are observed between protons each moving with velocity
(relative to the fixed observer) corresponding to 10
10 eV. If one of the protons
were to be at rest relative to the observer, what would the energy of the other
need to be so as to produce the same collision energy as before. The rest
energy of the proton is 10
9 eV.
[University of Manchester 1958]
9.107 It is required to cause protons to collide with an energy measured in their
centre of mass frame, of 4 M 0 c
2 in excess of their rest energy 2 M 0 c
2 . This
can be achieved by firing protons at one another with two accelerators each of
which imparts a kinetic energy of 2 M 0 c
2 . Alternatively, protons can be fired
from an accelerator at protons at rest. How much energy must this single
machine be capable of imparting to a proton? What is the significance of this
result for experiments in high energy nuclear physics?
[University of New Castle 1966]
9.108 The HERA accelerator in Hamburg provided head-on collisions between
30 GeV electrons and 820 GeV protons. Calculate the centre of mass energy
that was produced in each collision.
[Manchester 2008]