Semi Empirical Mass Formula. A Review
(Sprache: Englisch)
Nuclear physics is the field of physics that studies the constituents and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation, but the research has provided application in many fields,...
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Nuclear physics is the field of physics that studies the constituents and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation, but the research has provided application in many fields, including those in nuclear medicine and magnetic resonance imaging, nuclear weapons, ion implantation in materials engineering, and radiocarbon in geology and archaeology. The field of particle physics evolved out of nuclear physics and is typically taught in close association with nuclear physics.A heavy nucleus can contain hundreds of nucleons which means that with some approximation it can be treated as a classical system, rather than a quantum-mechanical one. In the resulting liquid-drop model, the nucleus has an energy which arises partly from surface tension and partly from electrical repulsion of the protons. The liquid-drop model is able to reproduce many features of nuclei, including the general trend of binding energy with respect to mass number, as well as the phenomenon of nuclear fission.
Superimposed on this classical picture, however, are quantummechanical effects, which can be described using the nuclear shell model, developed in large part by Maria Goeppert-Mayer and J. Hans D. Jensen. Nuclei with certain numbers of neutrons and protons (the magic numbers 2, 8, 20, 28, 50, 82, 126, ...) are particularly stable, because their shells are filled.
Other more complicated models for the nucleus have also been proposed, such as the interacting boson model, in which pairs of neutrons and protons interact as bosons, analogously to Cooper pairs of electrons.
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'Text sample:Chapter: 1.4 Historical Development:
For the study to explain the properties of nuclei and their structure and internal motion, one has to require modeling, in nuclear physics. There are several conceptual or mathematical models based on simple assumption without too heavy calculation, could provide more or less satisfactory description of various characteristic of nuclear structure and nuclear property. One of them is Liquid Drop Model purposed by George Germow in 1928. In nuclear physics, the semi empirical mass formula is used to find nuclear masses, binding energy and other properties of nuclei which is based on liquid drop model and firstly formulated by C. F. V. Weizsacker and after then modified by Bethe and some other physician. It is based partially on the theory and partially on empirical measurement so this formula is called semi empirical mass formula.
The Semi Empirical Mass Formula (SEMF) plays a significant role in the development of nuclear physics and it involved five kind of energy namely, the volume, surface, coulomb, asymmetry and pairing energy corresponding five type of coefficient, although refinements have been made to the coefficients over the years, the structure of the formula remains the same today. Over the past few decades, SEMF has sometimes been extended by adding extra terms or sometimes been modified by changing the dependence of each term on A and Z slightly in an effort to predict the nuclear binding energies as accurately as possible.
In 1958 D. William et. al. modifies Weizsacker's SEMF to include effects of the diffuse nuclear surface indicated by recent electron scattering experiments. Volume and surface effects are combined by integrating over an assumed trapezoidal density function similar to that found experimentally and get good fits with experimental data. In 1962 R. Ayres et. al. gives a new SEMF for binding energy of nuclear species resembling the usual bathe Weizsacker formula. In 1965 M. Bauer et.
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al. show the suitable rearrangement for the ground state energy of a super fluid nucleus can reproduce SEMF. They also concluded that the coefficients are not constant but depend on the deformation, and being larger for deformed nuclei. In 1965 N. Zeldes et. al. revised the mass table (1961) using least squares adjustment including newer experimental data, then difference of masses were plotted as a function of N or Z and formulated a generalized shell model mass formula.
In 1966 D. William et. al. represented a semi empirical mass theory to consider the potential energy as a function of N, Z and the nuclear shape with assumption given by the liquid drop model, modified by shell correction as the resultant formula has 7 adjustable parameter in which 4 due to LDM part and 3 due to shell correction. In 1971 H.A. Mavromatis calculated the coefficients of the volume, surface and symmetry terms in the SEMF from a first-order shell-model calculation using the Sussex matrix elements. In 1976 D. William et. al. developed the droplet model and formulated new SEMF with 16 coefficients, based on the literature and simple physical arguments. Some of these coefficient determined by fitting of masses, deformation etc.
In 1980 C.Y. Tseng et. al. presented a new formula which has forms for the Coulomb-energy, symmetry-energy and pairing-energy terms different from the conventional ones. It gives good agreement with experiment for the _-stability position and calculated binding energy. In 1986 X. Fuxin presented a new binding energy formula using 1271 nuclei masses exactly measured by the least square method; determine the parameters in order to obtain the concrete form of the new formula.
In 2002 C. Samanta et. al. extended the Bethe-Wisecracker (BW) mass formula to light nuclei and some new shell closures have been identified. This modified BW mass formula explains the shapes of the bindin
In 1966 D. William et. al. represented a semi empirical mass theory to consider the potential energy as a function of N, Z and the nuclear shape with assumption given by the liquid drop model, modified by shell correction as the resultant formula has 7 adjustable parameter in which 4 due to LDM part and 3 due to shell correction. In 1971 H.A. Mavromatis calculated the coefficients of the volume, surface and symmetry terms in the SEMF from a first-order shell-model calculation using the Sussex matrix elements. In 1976 D. William et. al. developed the droplet model and formulated new SEMF with 16 coefficients, based on the literature and simple physical arguments. Some of these coefficient determined by fitting of masses, deformation etc.
In 1980 C.Y. Tseng et. al. presented a new formula which has forms for the Coulomb-energy, symmetry-energy and pairing-energy terms different from the conventional ones. It gives good agreement with experiment for the _-stability position and calculated binding energy. In 1986 X. Fuxin presented a new binding energy formula using 1271 nuclei masses exactly measured by the least square method; determine the parameters in order to obtain the concrete form of the new formula.
In 2002 C. Samanta et. al. extended the Bethe-Wisecracker (BW) mass formula to light nuclei and some new shell closures have been identified. This modified BW mass formula explains the shapes of the bindin
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Autoren-Porträt von Ankita Goyal, Bhuvneshwer Suthar
Ms Ankita was born in 1995 in Phephana (Nohar), India. She received her B.Sc. in 2013 and her M.Sc. (Physics) in 2015 from M.G.S. University, Bikaner. She already presented a paper in a national conference at MLV College, Bhilwara.
Bibliographische Angaben
- Autoren: Ankita Goyal , Bhuvneshwer Suthar
- 2016, 48 Seiten, 12 Abbildungen, Masse: 15,5 x 22 cm, Kartoniert (TB), Englisch
- Verlag: Anchor Academic Publishing
- ISBN-10: 396067001X
- ISBN-13: 9783960670018
Sprache:
Englisch
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