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7 Nuclear Physics – I
Selection rules
Fermi rule : ΔI = 0, I i = 0 → I f = 0 allowed, Δπ = 0
(7.68)
GT rule : ΔI = 0, ±1, I i = 0 → I f = 0 forbidden, Δπ = 0
(7.69)
7.2 Problems
7.2.1 Kinematics of Scattering
7.1 A particle of mass M is elastically scattered from a stationary proton of
mass m. The proton is projected at an angle ϕ = 22.1
◦ while the incident
particle is scattered through an angle θ = 5.6
◦ with the incident direction.
Calculate M in atomic mass units. (This event was recorded in photographic
emulsions in the Wills Lab. Bristol).
7.2 A particle of mass M is elastically scattered through an angle θ from a target
particle of mass m initially at rest (M > m). (a) Show that the largest possible
scattering angle θ max in the Lab. System is given by sin θ max = m/M, the
corresponding angle in the CMS being cos θ
∗
max = −m/M. (b) Further show
that the maximum recoil angle for m is given by sin ϕ max = [(M −m)/2M]
1/2 .
(c) Calculate the angle θ max + ϕ max for elastic collisions between the incident
deuterons and target protons.
7.3 A deuteron of velocity u collides with another deuteron initially at rest. The
collision results in the production of a proton and a triton (
3 H), the former
moving at an angle 45
◦ with the direction of incidence. Assuming that this
re-arrangement collision may be approximated to an elastic collision (quasiscattering), calculate the speed and direction of triton in the Lab and CM
system.
7.4 An α-particle from a radioactive source collides with a stationary proton and
continues with a deflection of 10
◦ . Find the direction in which the proton
moves (α-mass = 4.004 amu; Proton mass = 1.008 amu).
[University of Durham]
7.5 When α-particles of kinetic energy 20 MeV pass through a gas, they are found
to be elastically scattered at angles up to 30
◦ but not beyond. Explain this, and
identify the gas. In what way if any, does the limiting angle vary with energy?
[University of Bristol]
7.6 A perfectly smooth sphere of mass m 1 moving with velocity v collides elastically with a similar but initially stationary sphere of mass m 2 (m 1 > m 2 )
and is deflected through an angle θ L . Describe how this collision would
appear in the center of mass frame of reference and show that the relation
7 Nuclear Physics – I
Selection rules
Fermi rule : ΔI = 0, I i = 0 → I f = 0 allowed, Δπ = 0
(7.68)
GT rule : ΔI = 0, ±1, I i = 0 → I f = 0 forbidden, Δπ = 0
(7.69)
7.2 Problems
7.2.1 Kinematics of Scattering
7.1 A particle of mass M is elastically scattered from a stationary proton of
mass m. The proton is projected at an angle ϕ = 22.1
◦ while the incident
particle is scattered through an angle θ = 5.6
◦ with the incident direction.
Calculate M in atomic mass units. (This event was recorded in photographic
emulsions in the Wills Lab. Bristol).
7.2 A particle of mass M is elastically scattered through an angle θ from a target
particle of mass m initially at rest (M > m). (a) Show that the largest possible
scattering angle θ max in the Lab. System is given by sin θ max = m/M, the
corresponding angle in the CMS being cos θ
∗
max = −m/M. (b) Further show
that the maximum recoil angle for m is given by sin ϕ max = [(M −m)/2M]
1/2 .
(c) Calculate the angle θ max + ϕ max for elastic collisions between the incident
deuterons and target protons.
7.3 A deuteron of velocity u collides with another deuteron initially at rest. The
collision results in the production of a proton and a triton (
3 H), the former
moving at an angle 45
◦ with the direction of incidence. Assuming that this
re-arrangement collision may be approximated to an elastic collision (quasiscattering), calculate the speed and direction of triton in the Lab and CM
system.
7.4 An α-particle from a radioactive source collides with a stationary proton and
continues with a deflection of 10
◦ . Find the direction in which the proton
moves (α-mass = 4.004 amu; Proton mass = 1.008 amu).
[University of Durham]
7.5 When α-particles of kinetic energy 20 MeV pass through a gas, they are found
to be elastically scattered at angles up to 30
◦ but not beyond. Explain this, and
identify the gas. In what way if any, does the limiting angle vary with energy?
[University of Bristol]
7.6 A perfectly smooth sphere of mass m 1 moving with velocity v collides elastically with a similar but initially stationary sphere of mass m 2 (m 1 > m 2 )
and is deflected through an angle θ L . Describe how this collision would
appear in the center of mass frame of reference and show that the relation