nuclear physics

Nuclear Physics
An introduction

Brief history
Binding energy
Semi empirical mass formula or the Liquid drop
model
Radioactivity
Nuclear energy & some applications

Why Study Nuclear Physics?
 To understand origin of different nuclei
◦ Big bang: H, He and Li
◦ Stars: elements up to Fe
◦ Supernova: heavy elements
 We are all made of stardust
 Applications are plenty
◦ Energy (Fission, fusion, transmutation)
◦ Medicine (Radiotherapy, MRI)
◦ Instrumentation (e.g. spectroscopy)
◦ Devices (e.g. Smoke detector)
◦ Radioactive dating

Brief history
 1896 Becquerel - radioactivity
 1897 Thomson - electron
 1898 Curies – radium
 1911 Rutherford – nucleus
 1932 Chadwick - neutron

Basics
 The number of protons inside the nucleus is designated by
Z and is known as the Atomic Number
 The number of neutrons inside the nucleus is designated
by N and is known as the Neutron Number
 The mass number, A, is the sum of the atomic number and
the neutron number A = Z + N
 The mass number is an integer and is only approximately
equal to the atomic weight of a element
 A nuclide is a single nuclear species having a specific Z
A
Z EN
and N. The notation that is used to designate the nuclides
is
 Nuclei with same Z, but differing N  Isotopes
 Nuclei with same N, but differing Z  Isotones
 Nuclei with same A  Isobars

Basic properties
 Size
◦ Most nuclei are nearly spherical, with the radius being
given by1/3 fm
R 1.2 A

 Density
◦ The nucleus has approximately constant density ~ 1017
kg/m3
 Binding energy
◦ When you measure the mass of an atom you find that it
is less than the sum of its parts
BE Z M H N M N M ( A, Z ) c2
◦ The difference is known as the binding energy and is
given by

Models of the nucleus

 No fundamental theory that can explain all observed
properties of the nucleus exists
 Several models developed to explain some of the
observed properties
 Liquid Drop Model–Nucleons are treated as
molecules in a liquid
 Shell Model–Similar to central field approximation in
atomic structure

Liquid drop model
Bethe-Wiezsacker mass formula (1935)
Assumptions
Each nucleon in interacting solely with its nearest neighbours
Equivalent to atoms in a solid or molecules in liquid which
move freely while maintaining fixed intermolecular
distance
Vibrations in solid would be too high for stability
 Nucleus ~ charged liquid drop

We may consider different effects term-wise

Volume term
Bulk binding energy volume EV aV A
Ev R3
= (r0 A1/3)3

Surface term
Surface area = 4 r 2 4 (r0 A 1/ 3 )2 4 r02 A 2/ 3

Surface energy aS A 2/ 3

Coulomb term
The work done to bring together Z protons from infinity
e
V
4 0r
For Z ( Z 1) / 2 pairs of protons
Z ( Z 1) Z ( Z 1)e2 1
EC V
2 8 0 r AV

1/ 3 Z ( Z 1)
r A EC aC
A1/ 3

Asymmetry term
 Neutron and proton states with
Neutrons Protons same spacing .

 Crosses represent initially
occupied states in ground state.

 If three protons were turned into
neutrons the extra energy required
would be 3 3 .

 In general if there are N Z
excess protons over neutrons the
extra energy is [(N Z)/2]2 .
relative to Z = N.
(N Z )2
E Asym aa
A  1/A

Pairing term
 Like Cooper pair formation, the nucleons also can pair
 Some energy is spent in binding the pairs
 BE(Nucleus with paired nucleons)
> BE(Nucleus with unpaired nucleons)
BE (even-Z , odd-N )
BE (even-Z , even-N ) BE (odd-Z , odd-N )
BE (odd-Z , even-N )

= +ve 0 -ve

 Its observed that this effect smaller for larger A
 Phenomenological fit to A dependence  EPair 1/A1/3

E Pair ap 1/ 3
A

e=even o=odd
+ 33.5 MeV (e-e)
ap= 0 MeV (o-e or e-o)
av=14.1 MeV ac=0.595 MeV - 33.5 MeV (o-o)

2 2
2
3
Z (N Z )
EBind av A as A ac 1
aa ap 1/ 3
A 3 A A
as=13.0 MeV aa=19.0 MeV

BE ( N , Z )
Constraint for most stable isotope
N Z Const.

#include<stdio.h>
#include<math.h>
#include<string.h>
FILE *fout1;
main()
{
int iA,iZ;
float A,Z,del;
float VEP,SEP,CEP,AEP,PEP,BEP;
float av=14.1,as=13.0,ac=0.595,aa=19.0,ap=33.5;
fout1=fopen("BEP.OUT","w");
fprintf(fout1," Z A VEP SEP CEP AEP PEP BEP");
for (iA=1;iA<=300;iA++)
{A=(float)(iA);
Z=0.5*A/(1.0+pow(A,2.0/3.0)*ac/(4.0*aa));
iZ=(int)(Z);
Z=(float)(iZ);
printf("n%f %f",Z,A);
VEP=av;
SEP=-as/pow(A,1.0/3.0);
CEP=-ac*Z*Z/pow(A,4.0/3.0);
AEP=-aa*pow((A-2*Z)/A,2);
if(iA%2 != 0)
del=0;
else
{ if(iZ%2 != 0)
del=-1;
else
del=1;
}
PEP=ap*del/pow(A,4.0/3.0);
BEP=VEP+SEP+CEP+AEP+PEP;

fprintf(fout1,"n%10.4f%10.4f%10.4f%10.4f%10.4f%10.4f%10.4f%10.4f",Z,A,VEP,SEP,CEP,AEP,PEP,BEP);
}
}

15

10

Volume Surface
BE/A (MeV)

5
Coulomb Asymmetry
Pairing Total
0

-5

-10
0 50 100 150 200 250

A

200

180

160

140

120
Protons

N=Z
100

80

60
beta stability

40

20

0
0 50 100 150

Neutrons

SHE – discovery in nuclear labs

Present scenario

2900 nuclei till year 2000
3090 till August 2008
3000 more to be discovered

Classification of Decays
-decay:
• emission of Helium nucleus
• ZZ-2
Protons

• NN-2
• AA-4
EC --decay
• emission of e- and
• ZZ+1
• NN-1
• A=const
+-decay
• emission of e+ and
• ZZ-1
• NN+1
Neutrons • A=const
Electron Capture (EC)
• absorbtion of e- and emiss
-decay • ZZ-1
• emission of • NN+1
• Z,N,A all const • A=const 21

Spin 1 1 3
S s( s 1)  1  
2 2 2
1
ms
2

Magnetic Moment
e 27
Nuclear magneton N 5.051 10 J/T
2m p
 
Proton pz 2.793 N pz has same direction as S
 
Neutron nz  1.913 N nz is opposite to S

Magnetic energy U m z B, E 2 z B

Nuclear Zeeman effect

Practical Applications

 Nuclear fission for energy generation.
◦ No greenhouse gasses
◦ Safety and storage of radioactive material.

 Nuclear fusion
◦ No safety issue (not a bomb)
◦ Less radioactive material but still some technical
difficulties.

 Nuclear transmutation of radioactive waste
with neutrons.
◦ Turn long lived isotopes  stable or short lived.

Medical Applications

 Radiotherapy for cancer
◦ Kill cancer cells.
◦ Used for 100 years but can be improved by better
delivery and dosimetery
◦ Heavy ion beams can give more localised energy
deposition.

 Medical Imaging
◦ MRI (Nuclear magnetic resonance)
◦ X-rays (better detectors  lower doses)
◦ Many others…

Other Applications

 Radioactive Dating
◦ C14/C12 gives ages for dead
plants/animals/people.
◦ Rb/Sr gives age of earth as 4.5 Gyr.

 Element analysis
◦ Forenesic (eg date As in hair).
◦ Biology (eg elements in blood cells)
◦ Archaeology (eg provenance via isotope
ratios).

Carbon Dating
 C14 produced by Cosmic rays (mainly
neutrons) at the top of the atmosphere.
◦ n N14  p C14
 C14 mixes in atmosphere and absorbed by
plants/trees  constant ratio C14 / C12 . Ratio
decreases when plant dies. t1/2=5700 years.
 Either
◦ Rate of C14 radioactive decays
◦ Count C14 atoms in sample by Accelerator Mass
Spectrometer.
 Which is better?
 Why won’t this work in the future?

nuclear physics

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