PH505 Introduction to Nuclear
and Particle Physics
Recap. The Exchange Force Model
Experimental data of n-p scattering
at medium energy
d!
d!
a.u.
The cross section as a function of cm
shows two peaks. One at 00 and the
other one at 1800.
0
Scattering of

Allowed and Forbidden transitions
The emission of the electron or positron from the nucleus is hindered by
the Coulomb and angular momentum barriers
(similar to the case for the -decay)
Minimum hinderance when
angular momentum for electron/positron
(e ) 0

Hamiltonian:
2
H
V
2
H d Ed d
d a 3 S1 b 3 D1
H11 3S1 H 3S1
Hamiltonian Matrix
H22 3D1 H 3D1
H 11
H
H 21
H 12
H 22
where
H12 H21 3D1 H 3S1
In order to have a non-vanishing off diagonal matrix elements, the
potential V must have a component (Vtens

Ground and excited states of nuclei
A nucleus is a complicated structure of interacting nucleons.
An appropriate quantum mechanical Hamiltonian H can be written
down in terms of nuclear and coulomb interactions.
The Hamiltonian will have a series of eigen

PH 505 Introduction to Nuclear and Particle Physics
Prof. (Mrs.) Pragya Das
Room no. 220 (E), Physics Department
Phone no. 7566 (Ext.)
E-mail: pragya@phy.iitb.ac.in
Examinations
Mid-semester
30 marks
Quiz
10 marks
End-semester
50 marks
Class performance 1

Beta-Decay
1) -decay
A(Z, N) A(Z+1, N-1) + e- + e
n p + e- e
2) +-decay
A(Z, N) A(Z-1, N+1) + e+ + e
p n + e+ e
3) Electron-Capture
e - + A(Z, N) A(Z-1, N+1) + e
e- + p n e
Orbital electron is captured by the nucleus.
Free neutron decay:
allowed (mn > mp)

Experimental observations and Independent Particle Model
1) All even-even nuclei have ground state spin parity 0+ (without any
exception).
(i) Since each of the orbit can have (2j+1) particles of one kind, above
experimental observation says that when we

Nuclear Decay
Types of Decay
1) Nucleon-emission or a cluster of nucleon emission (-decay, for
example),
2) -decay,
3) -decay.
Decay can occur spontaneously,
Initiated by bombardment with a particle from outside, called nuclear
reactions.
Conservation

In the shell-model, we include the residual interaction as H.
The energy eigenstates will be the solution of complete Schrdinger
V ' H '
equation
(H0+V) = E -(2)
where is the wavefunction, a state which is the superposition of s.
cii -(3)
i
(This is beca

PH505 Introduction to Nuclear
and Particle Physics
Introduction
To understand the following questions:
1) What are the building blocks of the nuclei?
2) How do they move relative to each other?
3) What is the law governing the forces holding a nucleus tog

PH505 Introduction to Nuclear
and Particle Physics
Recap
Nature of Nuclear Force
Charge Independent
Very strong in Nature
Short Range
Repulsive at short distances
Spin Dependent
Velocity Dependent (will be discussed in Tut)
Non-Central(Tensor)
Sa

PH505 Introduction to Nuclear
and Particle Physics
Recap.Basic Properties of Nucleus
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
2"
Nuclear size (Nuclear Radius)
Binding Energy
Angular Momentum
Parity and Symmetry
Magnetic Dipole Moment => Structure of Nucleon
Ele

PH-505: Introduction to Particle and Nuclear Physics
Tutorial Sheet 1
1. If the energy of the - particle emitted by 231Am is 5.48 MeV, find the closest
distance that it can approach a 197Au nucleus.
2. A single charged positive ion is accelerated through

PH-505: Introduction to Particle and Nuclear Physics
Tutorial Sheet 3
1. One milligram of a radioactive material with half-life of 1600 years is kept for
2000 years. Calculate the mass, which would have decayed by this time.
2. 29328U decays to Pb through

PH-505: Introduction to Particle and Nuclear Physics
Tutorial Sheet 2
1. Discuss that the nuclear force is velocity dependent.
!
2l + 1
2. Take f (! ) = "
sin ("l ) ei"l Pl ( cos! ) . If a particle is scattered by a hard sphere
k
l =0
for which V(r) = 0,

PH505 Introduction to Nuclear
and Particle Physics
Nature of Nuclear Force
Charge Independent
Very strong in Nature
Short Range
Repulsive at short distances
Spin Dependent?
Velocity Dependent?
Central/Non-Central(Tensor)?
Saturated?
2
Scattering

Expectation value of the quadrupole operator
The electric quadrupole moment of a nuclear state is defined as the
expectation value of Q op in the substate of maximum M.
Qd JM J Q op JM J
where
Q op e(3 z 2 r 2 )
er 2 (3cos2 1)
16 2
er Y20 ( , )
5
Since