382 7 Nuclear Physics – I
Selection rules
Fermi rule:ΔI= 0 , Ii= 0 →If=0 allowed,Δπ= 0 (7.68)
GT rule:ΔI= 0 ,± 1 ,Ii= 0 →If=0 forbidden,Δπ= 0 (7.69)7.2 Problems..................................................
7.2.1 KinematicsofScattering............................
7.1 A particle of massM is elastically scattered from a stationary proton of
mass m. The proton is projected at an angleφ= 22. 1 ◦while the incident
particle is scattered through an angleθ = 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 massMis elastically scattered through an angleθfrom a target
particle of massminitially at rest (M>m). (a) Show that the largest possible
scattering angleθmaxin the Lab. System is given by sinθmax =m/M,the
corresponding angle in the CMS being cosθmax∗ =−m/M. (b) Further show
that the maximum recoil angle for m is given by sinφmax=[(M−m)/ 2 M]^1 /^2.
(c) Calculate the angleθmax+φmaxfor elastic collisions between the incident
deuterons and target protons.7.3 A deuteron of velocityucollides 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 (quasi-
scattering), calculate the speed and direction of triton in the Lab and CM
system.7.4 Anα-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 Whenα-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 massm 1 moving with velocityvcollides elas-
tically with a similar but initially stationary sphere of massm 2 (m 1 >m 2 )
and is deflected through an angleθL. Describe how this collision would
appear in the center of mass frame of reference and show that the relation