{"id":161,"date":"2018-11-09T05:20:31","date_gmt":"2018-11-09T05:20:31","guid":{"rendered":"http:\/\/phyp04.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=161"},"modified":"2019-04-29T09:29:09","modified_gmt":"2019-04-29T09:29:09","slug":"nuclear-models-1","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp04\/chapter\/nuclear-models-1\/","title":{"rendered":"Nuclear Models-1"},"content":{"raw":"
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\r\n\r\n\u00a0 \u00a0 1.<\/strong>\u00a0Nuclear Models<\/strong>\r\n\r\n \r\n\r\n \r\n

In order to understand the various observed properties of the nucleus of an atom it is important to have an adequate knowledge about the nature of the inter-nucleon interaction. In the nucleus three different kinds of force takes part (electromagnetic, weak, and strong forces), and there exist a very strong short range force between the nucleons. The combination of all the three forces makes the nuclear force quite complicated, yet to be fully understood, however, the exact mathematical form of this interaction is still not known.<\/p>\r\n \r\n

So far none of the proposed theories gives us a full understanding of the nature of the inter-nucleon interaction. Even if the exact nature of the interaction were known, it would have been extremely difficult to develop a satisfactory theory of the structure of the nucleus made up of a large number of neutron and protons, since it quite impossible to solve the Schr\u00f6dinger equation exactly for such a many body system. As the total wave function of the nucleus becomes too complicated to be useful for most such a many body system and it helps only in light nuclei. Various methods have been proposed to solve the problem with different degree of approximation. However, the problem is still far from being solved completely.<\/p>\r\n \r\n

For this reason the analysis of the nuclear structure is more complex than the analysis of many electron-atoms. Because of these difficulties in developing a satisfactory theory and explaining of the nuclear structure, different nuclear modes have been proposed for the nucleus which are of great help, each with different level of success, in gaining some insight into nuclear structure. The nuclear models are the way of describing the observed nuclear properties using basic principles of science and that gives a physical insight into a wide range of its properties.<\/p>\r\n \r\n

A successful model not only explains the existing data but also has the power to make predications; the model should also be able to explain experimental results successfully. Different approaches and different analogy gives different nuclear models.<\/p>\r\n \r\n\r\n1.1 Classification of Nuclear Models<\/strong>\r\n\r\n \r\n

Nuclear models are classified into two main groups. First group is the independent particle model (or individual particle model), in which there is little or no interaction take place between the individual particles that constitute nuclei, and each nucleons occupy discrete energy states. The Semi-classical Fermi gas model and quantum mechanical Shell model fall into this group. Second group is the Collective model with no individual particle states, in this model individual protons and neutrons are mutually coupled to each other. The semi-classical Liquid drop model and quantum mechanical rotational and vibrational model fall into group.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n\r\n2.<\/strong>\u00a0Liquid Drop Model<\/strong>\r\n\r\n \r\n

The liquid drop model gives good account of bulk properties of nuclei. It was first proposed by the George Gamow in 1928, later expanded by N. Bohr and F. Kalckar in 1935 and was later applied by C.F. von Weizsacker and H.A. Bethe to develop a semi-empirical formula for the binding energy of the nucleus. It is based on the observation that the all nuclei have nearly same density.<\/p>\r\n \r\n

In the liquid drop model nucleus is treats as a drop of incompressible nuclear liquid. As in the case of nucleus, nuclear properties like density and binding energy per nucleon is nearly constant for most of nuclei, it is same as in case of liquids where latent heat of vaporization is nearly proportional to the number of molecules within the liquid. This fact shows a close analogy of the nucleus with a liquid drop. Thus we conclude that the inter-nuclear force within the nucleus reach to a saturation value, so that each nucleon can interact only with its nearest neighbors as in case of liquids where each individual molecule within a liquid drop exerts an attractive force upon in its molecules in its immediate neighbourhood.<\/span><\/p>\r\n \r\n

2.1 Basic Assumptions<\/strong><\/p>\r\n \r\n

While treating nucleus as a drop of liquid some assumptions were made which are given as follows:<\/span><\/p>\r\n\r\n