Computing the Mean Value of Quark Energy Binding Nucleons in the Nuclides

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1 R.Javahery ssociate Professor, University of Tehran, Faculty of Sciences bstract The purpose of this article is to determine the total quark binding energy which is consumed for binding the nucleons in the nuclide based on the Bethe-Weizacker formula (also called semiempirical mass formula) inspired by the liquid-drop model we will explain the nuclear structural from in the framework of the total energy Consumed by the quark which causes binding energy between all nucleons in the nuclide. Ke ywords: nuclear mass; liquid drop model; coulomb repulsion; quark binding energy. Introduction The focal point in this paper and the pervious papers is that binding energy between nucleons in the nuclide caused by the quark. t the present time, it is accepted universally that quarks are physical entinies. The evidence of quark come from different experiments, the Particle that causes the strong interaction between quarks called gluon. Its mass is zero, its sping is s=1 and its electric charge is zero. The quark inside the nucleons because of very strong attraction between them can not get out

2 of the nucleons. In other words they are confined in the nuclide. However, for two nucleons that are close (about m). their quarks attract one another strongly, which causes partial overlap of in their volumes. The quarks are still in the common volume of these nucleons. attraction between them. This is the reason why the nucleons inside the nuclide bind together stornly. Therefore, nuclear force originates from the quark reaction and the nucleons bond in the nuclide. The distribution of the nucleons inside the nuclide should be symmetrical and for nuclide with a spin of zero, preferably spherical. We tried to make the distribution of nucleons in the nuclide as spherical as possible. Each nucleon inside the nuclide binds with the neighboring nucleons. The nucleons in the central part possess six binding. The nucleons that are in the surface of the nuclide have three or a minimum of two binding between them. 2

3 Quark binding energy s mentioned in the previous paper, to study the quark action, two important quantities are needed, first, the total binding energy consumed by the quarks bond the nucleons in the nuclide, this quantity is shown by (QBE). Second, the total number of quarks binding the nucleons is shown by, NOB. In this research, some minor changes in equation of Weizsaker have been applied as follow: If Z and N are both even, z(z 1) ( 2z) (QBE) = B.E δ = and if both Z and N are odd then δ [Ref. 1] δ =, and if once of them (Z and N) is odd the other is even, δ = 0, For each nuclide the value of (QBE) is given for each nuclide. The above equation, which has been some what altered by the author, originates from weizsacker's formula. The second point to be found is the number of quarks bindings between nucleons in each nuclide. the nucleons in each plat layer are binding to the neighboring nucleons in the same plat layer. The total number of this kind binding is shown by n(i), and, besides that the nucleon in the two neighboring plat layers are bond together. For example, in the central part of nuclide, each nucleon in layer 'b' is bonded by neighboring nucleons in layer 'a' and the same thing happens to nucleons in layer 'c',and layer 'c' which are bonded by layers 'b' and 'd'. The sum of the bindings of these nucleons in the nuclide is shown by m(i, j). Thus, the total number of nucleons bound in the nuclide is: NQB = n(i) + m(i, j) For more details refer to the previous articles. Given (QBE) and NQB, the value (QBE) R = is NQB calculated, which is the average value of quarks binding energy causing between nucleons in (QBE) nuclide per numbers of its nucleons bonding R =, and R are more precervalbe and NQB meaningful than B.E To save space, nucleons are presented by dots rather than spheres. Dotted diagrams can be easily converted to spherical diagrams, which can help counting n(i) and m(i, j). therefore, NQB = n(i) + m(i, j). Finally, we can calculate the value of (QBE) R = NQB The following is a sample diagram showing how dotted diagrams can be converted to spherical diagrams

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22 CONCLUSION 1. On the left side of Weizsaker Formula in the introduction, nuclear binding energy (B.E) is given. This quantity can be calculated easily. On the right side of the equation the first term [a b - a s 1/3 ] is the total binding energy that quarks consume in the nuclide which will be shown by (QBE). In Weizsaker equation by placing B.E on the right hand and (QBE) on the left hand, For coefficients see in introduction, we will have the flowing equations: 2 Z(Z 1) ( 2Z) (QBE) = BE + a c + asym + δ [Ref.1] 1 3 For more information see [Ref.2 and 3] 2- Weizsaker equation can not be used for light nuclides since for them in Coulomb term Z(Z 1) [0.711 ], The volume of nuclides is not proportional to the mass number () Now we will explain another quantity: The total number of nucleons bonded by quarks in the nuclide is shown by NQB. (QBE) The mount of energy for each bonding can be calculated by. for 105 nuclide which NQB we have studied, the value of (QBE) R = is between 2.7 and 2.9 MeV Per bonding. (not for the NQB light nuclides) 4- In this article for the first time instead of showing nucleons in the nuclides as circles, They are shown as point. Therefore we are able to consider more nuclides (105) in this papers. B.E 5- Comparing the variation curve of (QBE) NQB B.E versus, with Versus : for a nuclide only depends of its nucleons mass. There for the Curve is smooth. But only for magic number of nuclides the values of (QBE) NQB B.E are greater than neighboring nuclides. The variation of versus, the quarks in the nucleons have several effect, such as terms of B.E, Coulomb energy, Symmetry energy and also different effects, for nuclide if Z and N are both even or both odd and one is even and other odd. It could be concluded that (QBE) NQB is more meaningful and perceivable than B.E. 22

23 Reference [1] G. Segre, "Nuclei and particets", Benjamin Press, p , 1964P. [2] Marmier, E. Sheldon, "P hysics of nuclei and particle", cademic P ress, p.32-37, 1969 [3] Rohlf, Jame Wiliam, "Liguid drop model of nucleus", Modern Physics, Wiley P ress, sec.11.3, [4] R. Javahery, " new explanation of quark causing binding energy between nucleons in the nuclide I ", The General Scince Journal, ISSN : (GSI), No E, 2008 [5] R.Javahery, " new explanation of quark cousing binding energy between nucleons in the nuclide II", the General Scince journal, ISSN: (GSI) No E, [6] R.Javahery, " new explanation of quark causing binding energy between nucleons in the nuclide III", The General Scince Journal, ISSN : (GSI), No E, [7] R.Javahery, " new explanation of quark causing binding energy between nucleons in the nuclide IV", The General Science journal, ISSN : (GSI), No E,