Course Title: Nuclear Physics Course Code: EEE-202 Lecture-V Shekh Md Mahmudul Islam, Lecturer, Department of Electrical and Electronic Engineering(EEE), University of Dhaka. Cell:+88-01818402137 Email: mahmud@du.ac.bd Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA.

Nuclear Binding Energies and the saturation of Nuclear Forces. 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 Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

In Heavier Nuclei, A may be neglected with in comparison with A2. 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. Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

Nuclear Binding Energy Nuclear 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 Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

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!!!!! Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

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 Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

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. Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

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. Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

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. Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

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. Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

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= 𝟏 𝟐 I2 Rotational energy is obtained when the angular momentum is quantized and the the result is Erot= 𝟏 𝟐𝑰 h2 J (J +1) Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

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 2R2 for large energies. Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

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. Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

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. Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

Which Model Should be Selected ? 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. Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

Rutherford’s Theory of Alpha Particle Scattering The Nuclear Atom Rutherford’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 Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

Rutherford’s Theory of the scattering Alpha Particle The Nuclear Atom Rutherford’s Theory of the scattering Alpha Particle Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

Rutherford’s Theory of the scattering Alpha Particle The Nuclear Atom Rutherford’s Theory of the scattering Alpha Particle Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA

Thank You!! Electrical and electronic ENGINEERING,UNIVERSITY OF DHAKA