CHAPTER 1

Basic Properties of Nucleus

1 Basic properties of Nucleus

Composition of Nuclues

Nuclear Size and Density

Nuclear Charge

Atomic Mass and Atomic Mass Unit

Nuclear Angular Momentum

Nucluear Magnetic Moment

Electrical Qudrapole Moment

Parity & Symmetry

2 Classification of Nuclei

3 Mass Defect and Binding Energy

4 Packing Fraction

5 Neuclear Stability

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• LS coupling : In this coupling scheme, it is assumed that there is weak interaction between the orbital (l) and spin (s) angular momentum vectors of an individual nucleon. Instead, the orbital angular momentum vectors of all nucleons assumed to be couple to give rise the resultant angular momentum.

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• It is found that i is an integer for nuclei with even A. I = 0 if Z is even and A is even. I is a half an odd integer

(1/2, 3/2, 5/2…) for nuclei of odd A.

• If the nuclear spin is i = 0,1,2,3,…, it is called boson (i.e. integral spin particle).
• If the nuclear spin is i = 1/2, 3/2, 5/2, … , it is called fermion.

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• Similarly, the spin angular momentum vectors of all nucleons are coupled to give rise total spin angular momentum.
• The total angular momentum of a nucleus arises from the intrinsic spin angular momentum of its protons and neutrons and from the orbital angular momentum due to motion of these nucleons with the nucleus. It is given us.

J = L + S

and J takes values from ।L + S। to ।L - S।.

the magnitude of the total angular momentum I is given as

where s is called nuclear spin.

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• JJ Coupling : In this coupling, it is assumed that the coupling between orbital angular momentum vector (l) and spin angular momentum vector (s) is predominant for the same nucleon. These combine to form resultant angular momentum (j) and is given by.

J = l + s

Where j takes values from ।l + s। to ।l - s।.

• The resultant nuclear angular momentum I is the vector sum of individual j vectors of all nucleons. It is given by

I = j1 + j2 + j3 + …

• The magnitude of the total angular momentum I is give as

The total angular momentum vector I can be oriented in space with respect to a given axis in (2I+1) direction. The component of any of the orientation along the axis is mh, where m takes values from I to – I as,I,(I-1), (I-2), …… -(I-1), -I.

Nuclear Magnetic Moment

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• The nuclei have magnetic dipole moments. They arise from the intrinsic dipole moments of protons and neutrons in the nuclei, and from the current circulating in the nuclei due to motion of protons. Fig. 1.2 shows the magnetic dipole moment associated with a current loop of area A and carrying current i. From an elementary course in electricity and magnetism it is well known that the magnetic dipole moment is given as.
• The direction of the magnetic dipole moment is perpendicular to the plane of the current loop as shown in Fig. 1.2

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• In addition to magnetic moment, a nucleus also has an electrical quadruple moment. It is a measure of observed deviation of shape of nucleus from the spherical symmetry. An electrical quadrupole moment is given by.
• Q = 0 for spherical shape. If he nucleus is elongated along the direction of its spin angular momentum, it has prolate shape and Q is positive. If the nucleus is elongated perpendicular to the direction of spin angular momentum, it has oblate shape and Q is negative

Electrical Quadrupole Moment

A neuclus has and electrical qudraple moment , it a measure of observed derivation of shape of nuclues from the spherical symmetry