British Journal of Science 166 February 2012, Vol. 3 (2)
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1 British Journal of Science 166 Calculation of Energy Levels of 205 Hg by using Nuclear Shell Model and (OXBASH) Program Khalid Hussain Hattif al Attiah Babylon University, College of Science, Department of Physics Abstract We deal with the energy levels of 205 Hg by applying the nuclear shell model and (oxbash) program, to calculate ( TBME ) the effective interaction ( khhe ) is used, it has been found that the energy levels are identical with the practical results available for the first band, and it is expected that them would be identical energy levels and identical spin in the second,third, fourth, and fifth band. 1. Introduction It is expected that there is about 6000 nucleus in the nuclear table cited between the 1 Drip lines of the protons and the neutrons. Till now, only 600 are really discovered, 198 of them are stable inactive and their ages is close to half age of the earth [ Al_Khalili and Roceckl 200 ]. The fact that most of the famous nuclei are unstable help proving a great deal of in formation about the nucleus through nuclear fission. The progress in the nuclear characteristics represented by the number of protons and neutrons is the most important aspects in the nuclear physics [ Klimkiewicz 2007 ]. The 205 Hg is rich of neutrons n=125, however the information about it is very less because defecate product this nuclear [ Jungclaus 2007 ] [ Dillmann 200 ]. 2. Theoretical part The practical calculations about th e nuclear shell model proves the theoretical expectation, and allows to calculate the energy levels, nuclear density, nuclear component structure. The Hamionin which governs the neutrons dynamics on the part of the nuclear shell model is represented by the following formula [ Honma 2002 ] : H Eiai Vijkl ai a jaia j ( 1 ) i ijkl Where Ei : stands for the energy of the single ( SPE ) particle of the orbit i its value can be found from the closed shell side of the mass number A= closed core + 1, ni, stand for the busy space in orbit i. V ijkl : is known as the two body matrix element ( TBME ) of the interaction between nucleon of the orbits ( i, j, k, l ), and it can be calculated by A= closed core +2 a j + a i + : reactive effects ( to generate a couple of phermons ). a j a i : decline effects ( to decline acouple phermons ). The element matrixes for duboul Particals ( TBME) can be write as follow British Journals ISSN 20775
2 British Journal of Science 167 V T J, J J (2J 2 1) JJV JJ J (2J 1) JT And the calculation is achieved by employing the affective interactions. The calculate the shell model by using ( oxbash ) program, is it proposed that the levels which are rich of protons and neutrons, i.e ( closed shell ) are the magic number that stand for the inert core, and the nucleons in the next shell are the magic number that stand for valence nucleons [ kranel 1988 ] the orbital between two magic number represent the valence shell named the main shell such as ( 1h 9/2, 2h 7/2, 2f 5/2, p /2,p 1/2, 1i 1/2 ) the main shell between two magic number ( 126 ) and ( 82 ) is called single particle space ( sps ) according to the effective interaction. [Honma,200]. Calculation and discussion The nuclear shell model ia applied to calculate the energy levels of 205 Hg which is multi _single nuclear, whose mass number A= 205, P= 80, and N=125, and it is positioned in the shell ( khh ), according to the shell model the closed shell occurs, at the magic number P= 50, N=82. the valence nucleons, of P=0, and N=5, their summation is 75 particles out of the closed shell in the folloing shell : P= 1g 7/2, 2d 5/2, 2d /2, s 1/2, 1h 11/2 N= 1h 9/2, 2f 5/2,p /2, p 1/2, 1i 1/2 To make calculation on 205 Hg, the closed shell at 208 is selected whose P=82, N= 126, and where it is possible to use the number of gaps instead of the valence particles, i.e the number of nucleons is a gaps instead of 75 particles to close the shell at the magic number P= 82, N= 126 In the shell area ( 1H 11/2 ), there is two proton gaps and one neutron gap in shell ( 1I 1/2 ). The (oxbash ) program is used to calculate the energy levels and the band.the obtained values are compared th those of the international standards as it is shown in fig (1) and (2) [ Grory and Kuol 1975 ]. It can be noticed fig (1), (2) that the energy levels on earth land obtained on the level 1/2, are identical with the practical valuesw 1/2, by the same token, the practical and theoretical values in the first band are all identical ( 9/2 1, 7/2 1, /2 1, 5/2 1 ) we also get new values that do not have been compared to the practical values as the later are not available, these value are ( 1/2 +, 11/2, /2 +, 5/2 1 +, 11/2 1 +, 9/2 1 + ) in the first band. Identical energy levels and spin are also expected in the other bands levels [ British Journals ISSN 20775
3 Energy Levels (kev) British Journal of Science / / / / / / /2 1 / /2 + 7/ / / /2 1 7/2 1 /2 1 5/ /2 2 5/ / / /2 2 Fig ( 1 ) Shows the energy levels compared with theoretically calculated to isotopes ( 205 Hg ) with practical results /2 5/ /2 2 5/2 / / / British Journals ISSN Exp[ 1/2 1 P.W. 0
4 Energy Levels (kev) British Journal of Science / / /2 + / / /2 + 5/2 + 11/2 7/2 + 9/2 + 11/2 + 9/2 7/2 5/2 1/2 / /2 5/2 + 7/2 + 9/2 9/2 + 7/2 /2 1/2 5/ / /2 5 9/2 7/ / / /2 5 1/2 5 / British Journals ISSN
5 British Journal of Science 170. Conclusions The application of the nuclear shell model using the ( Oxbash ) nuclied 205 Hg and the expline of following below. 1 Been confirmed theoretical values of energies ( 0, 77, 85, 177, 189 ) are well defined angular momentum and replicate ( 9/2 1, 7/2 1, /2 1, 5/2 1, 1/2 ) with practical values. 2 Been identified similar levels of momentum and energy have not been identified in practice ( 1/2+, 11/2, /2+, 5/21+, 7/21+, 11/21+, 9/21+ ). The effectiveness of file effective interaction in the calculations of neutronrich regions of the nuclear shell. 5. Reference A.Jungclaus et al., Phys.Rev. Lett. 99, (2007 ). A.Klimkiewicz et al., Phys. Rev. C76, ( 2007). C.Normand et al., J.Radional.Nucl.Chem.282,95 (2005 ). Dillmann et al., Phys, Rev.Lett.91, (200 ). J. Lichtenstadt., J.Alester, M.A.Moinester, S.Kowalsli, Phys. Lett., B121,6,77 (198 ) K.S.Krane introductory Nuclear Physics ( J.wiley & Sons, Hoboken, NJ, 1988 ). M. Honma, T. Otsuka, B.A.Brown, T. Mizusaki,Phys.Rev.C 65,06101(2002). M. Honma, T.Otsuka, B.A.Brown, T. Mizusaki,Phys.Rev. C 69, 05 (200). Mc.Grory and Kuo, NPA27,28(1975 ). P.G.Reinhard,J. Friedrich and N.Voegler, Z, Phys. A 16, 207 (198 ). R.B.Mooy and P.W.M.Glaudemans, Nucl.Phys.,A 8,61, ( 1985 ). T.W.Donnelly and J.D.Wa;eaka, Nucl.Phys., A 201, 81 c, (197 ). The Euroschool Lectures on Physics with Exotic Beams, edited by J.Al_Khalili and E. Roeckl ( Springer, Berlin Heidelberg. 200 ), Vol British Journals ISSN 20775
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