nuclear physics

Nuclear PhysicsAn introduction

Brief historyBinding energySemi empirical mass formula or the Liquid drop modelRadioactivityNuclear 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 stardustApplications are plenty

◦ Energy (Fission, fusion, transmutation)◦ Medicine (Radiotherapy, MRI)◦ Instrumentation (e.g. spectroscopy)◦ Devices (e.g. Smoke detector)◦ Radioactive dating

Brief history1896 Becquerel - radioactivity1897 Thomson - electron1898 Curies – radium1911 Rutherford – nucleus1932 Chadwick - neutron

Dimensions

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 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

Nuclei with longer lifetime in an excited state Isomers

AZ NE

Basic propertiesSize

◦ Most nuclei are nearly spherical, with the radius being given by

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◦ The difference is known as the binding energy

and is given by

◦ Measure relative masses by energy released in decays or reactions: X Y + Z + DE

◦ Mass difference between X and Y+Z is DE/c2.

1/31.2 fmR A

2( , ) H NBE Z M N M M A Z c

Nuclear binding energy

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 modelBethe-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 termBulk binding energy volume

Ev R3

= (r0 A1/3)3

V VE a A

Surface term

Coulomb termThe work done to bring together Z protons from infinity

2Surface area = 4 r 1/ 3 204 ( )r A 2 2/ 3

04 r A

2/ 3Surface energy Sa A

04e

Vr

For ( 1)/ 2 pairs of protonsZ Z ( 1)

2C

Z ZE V

2

0

( 1) 18 AV

Z Z er

1/ 31/ 3

( 1)C C

Z Zr A E a

A

Neutron and proton states with 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 NZ excess protons over neutrons the extra energy is [(N Z)/2]2 . relative to Z = N.

1/A

Asymmetry term

2( )Asym a

N ZE a

A

Neutrons Protons

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)

Its observed that this effect smaller for larger A

Phenomenological fit to A dependence EPair 1/A1/3

(even- ,odd- )(even- ,even- ) (odd- ,odd- )

(odd- ,even- )

BE Z NBE Z N BE Z N

BE Z N

Pairing term

1/ 3Pair pE aA

= +ve 0 -ve

3/1

2

31

23

2 )(

Aa

A

ZNa

A

ZaAaAaE pacsvBind

av=14.1 MeV ac=0.595 MeV

as=13.0 MeV aa=19.0 MeV

e=even o=odd

+ 33.5 MeV (e-e)

ap= 0 MeV (o-e or e-o)

- 33.5 MeV (o-o)

Const.

( , )Constraint for most stable isotope

Z

BE N ZN

#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); }}

-10

-5

0

5

10

15

0 50 100 150 200 250

A

BE

/A (

MeV

) Volume Surface

Coulomb AsymmetryPairing Total

0

20

40

60

80

100

120

140

160

180

200

0 50 100 150

Neutrons

Protons N=Z

beta stability

SHE – discovery in nuclear labs

The Chart of Nuclides

Present scenario

2900 nuclei till year 20003090 till August 20083000 more to be discovered

21

Classification of Decays

Neutrons

Pro

ton

s

a

b-

a-decay: • emission of Helium nucleus• ZZ-2• NN-2• AA-4

b--decay• emission of e- and n• ZZ+1• NN-1• A=const

g-decay• emission of g• Z,N,A all const

b+-decay• emission of e+ and n• ZZ-1• NN+1• A=const

b+EC

Electron Capture (EC)• absorbtion of e- and emiss

n• ZZ-1• NN+1• A=const

Spin

2

1

2

31

2

1

2

1)1(

sm

ssS

Magnetic Moment

BEBU

S

S

m

e

zzm

nzNnz

pzNpz

pN

2,energy Magnetic

toopposite is 913.1Neutron

asdirection same has 793.2Proton

J/T10051.52

magneton Nuclear 27

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?