Course Title: Nuclear PhysicsCourse Code: EEE-202

Shekh Md Mahmudul Islam,Lecturer,Department of Electrical and Electronic Engineering(EEE), University of Dhaka.Cell:+88-01818402137Email: mahmud@du.ac.bd

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Lecture-V

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Today I will talk on

Nuclear Binding Energies and the saturation of Nuclear Forces.

Nuclear Stability

The Collective Nuclear Drop Model

Optical Model for Nuclear Reactions

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The Total Binding Energy of a nucleus is nearly proportional to the number of particles in the nucleus.

Since each of the A particles in the nucleus would interact with (A-1) and the number of interacting pairs would be A (A-1) /2.

In Heavier Nuclei, A may be neglected with in comparison with A2.

The Total Binding Energy of a nucleus would be proportional to the square of the number of particles in the nucleus.

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Nuclear Binding EnergyNuclear Forces is represented by homo-polar binding like

that of hydrogen molecule. There is strong attraction between two hydrogen atoms to form the molecules H2, but a third hydrogen atom cannot be bound strongly to a hydrogen molecule. The hydrogen molecule is said to be saturated.

Nuclear Forces must have a short range: The magnitude of coulomb energy between two proton is

simply e2/r. e2/r= 0.5 Mev.

The coulomb energy between two protons is therefore small compared with the average binding energy per particle, which is about 8 Mev

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Nuclear Binding Energy Despite its smallness, the coulomb repulsion becomes important for

heavier nuclei because of the saturation of the attractive nuclear forces. For the Coulomb force shows no saturation, and the total energy of the coulomb interaction is proportional to the number of proton pairs in the nucleus

Z(Z-1)/2. The total coulomb energy has been shown to be Total Coulomb Energy= 3/5*Z*(Z-1)* e2/R

Where R is the Nuclear radius. Since R~A1/3 and Z is roughly proportional to A; the coulomb energy is roughly proportional to A5/3 but the total binding energy is directly proportional to A, so that the relative importance of the repulsive electrostatic energy increases with increasing mass number roughly as A2/3

For Heavier Nuclei Columbic Repulsion becomes stronger than Nuclear Binding Energy that’s why it disintegrates!!!!!!For Heavier Nuclei Columbic Repulsion becomes stronger than Nuclear

Binding Energy that’s why it disintegrates!!!!!

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Nuclear Stability and Forces between Nucleons

In the Case of lighter Nuclei Z=A/2

In Heavier Nuclei the number of neutron increases more rapidly than the number of protons.

As the coulomb energy increases; the ratio of the number of neutrons to that number of proton increases gradually from 1 for the light nuclei to 1.6 for uranium; with Z=92

The two possibilities can be expressed in the form: (a) n-p = n-n=p-p (b)n-p>> n-n; n-p>>p-p; n-n==p-p

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Nuclear Stability and Forces between Nucleons

This assumption of (a) is known as the hypothesis of the charge independence of nuclear forces.

The Collective Nuclear Model The Success of the liquid-drop and nuclear shell models seem to

serious dilemma.

The liquid drop model can account for the behavior of the nucleus as whole, as in nuclear reaction and nuclear fission.

Certain Nuclei actually divide into two smaller nuclei and the division can be described in terms of deformation of drops.

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The Collective Nuclear Model

Many Phenomena seem to show that nucleons behave as individual and nearly independent particles. Hence there are two entirely different ways of regarding nuclei; with a basic contradiction between them.

Collective Nuclear Model= Liquid Drop Model + Single or independent Nuclear Model .

Quadrupole :

The simplest example of an electric quadrupole consists of alternating positive and negative charges, arranged on the corners of a square.

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The Collective Nuclear Model

The particles within the nucleus exert a centrifugal pressure on the surface of the nucleus as a result of which nucleus may be deformed into a permanently non-spherical shape; the surface may undergo oscillations(liquid drop aspect)

The nuclear distortion reacts on the particle and modifies somewhat the independent particle aspect.

The Nucleus is regarded as a Shell structure capable of performing oscillations in shape and size. The collective model can be described drop like properties as nuclear fission.

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The Collective Nuclear Model

The particles within the nucleus exert a centrifugal pressure on the surface of the nucleus as a result of which nucleus may be deformed into a permanently non-spherical shape; the surface may undergo oscillations(liquid drop aspect)

The nuclear distortion reacts on the particle and modifies somewhat the independent particle aspect.

The Nucleus is regarded as a Shell structure capable of performing oscillations in shape and size. The collective model can be described drop like properties as nuclear fission.

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The Collective Nuclear Model

The rotational collective motion is sufficiently low; it will not affect the internal structure of the nucleus. According to classical physics, the rotational energy is proportional to the square of the angular velocity

Erot= I2

Rotational energy is obtained when the angular momentum is quantized and the the result is

Erot= h2 J (J +1)

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The Optical Model for Nuclear Reaction

Compound Nucleus Theory (inability to large scale energy dependence of total neutron cross section)

The statistical Model Assumes that the compound nucleus is formed immediately when the incident neutron reaches the nuclear surfaces.

The Cross section for reaching the surface decreases monotonically decreasing function of the energy, E-1/2 for small energies and reaching the asymptotic value 2R2 for large energies.

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The Optical Model for Nuclear Reaction

Optical Model for Nuclear Reaction= Single particle model + Compound Nucleus properties.

Optical Model for Nuclear Reaction=Single Particle Model+ Compound Nucleus

------The single particle moving in an attractive potential V(r) a square well but such a potential does not permit absorption of the as required by compound nucleus concept.

-----The incident neutron absorbs in the nucleus and this absorption is Supposed to form the compound nucleus.

Compound Nucleus formation does not occur immediately nor with complete certainty.

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The Optical Model for Nuclear Reaction

The optical Model is very much successful for accounting the behavior of neutron cross section

Why it is called Optical Model?

There is analogy with physical optics in that the nucleus acts like a spherical region with a given refractive index (attractive potential well) and opacity. Its another name is cloudy crystal ball model.

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Three Models

Which Model Should be Selected ?

Each Model has its own merits and disadvantages.

The Shell or independent Particle Model

Liquid Drop Model

Collective Drop Model

The optical Model for Nuclear Reaction.

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The Nuclear AtomRutherford’s Theory of Alpha Particle Scattering

Rutherford classified radioactivity

Awarded Nobel prize in chemistry 1908 “for investigations into the disintegration of the elements and the chemistry of radioactive substances”

Together with Geiger and Marsden scattered alpha particles from atomic nuclei and produced the theory of “Rutherford Scattering”.

Postulated the existence of the neutron

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The Nuclear Atom

Rutherford’s Theory of the scattering Alpha Particle

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The Nuclear Atom

Rutherford’s Theory of the scattering Alpha Particle

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Thank You!!