عنوان البحث(Papers / Research Title)
Largescale shell model calculation of neutron rich evenEven 5466Fe isotopes
الناشر \ المحرر \ الكاتب (Author / Editor / Publisher)
فؤاد عطية مجيد
Citation Information
فؤاد,عطية,مجيد ,Largescale shell model calculation of neutron rich evenEven 5466Fe isotopes , Time 28/07/2014 21:27:15 : كلية التربية للعلوم الصرفة
وصف الابستركت (Abstract)
Shell model calcuations for Fe isotopes using Nushellx@msu
الوصف الكامل (Full Abstract)
Largescale shell model calculation of neutron rich evenEven 5466Fe isotopes
Fouad A. Majeed, and Abeer J. Ejam
Department of Physics, College of Education for Pure Sciences, University of Babylon, Babylon, Iraq.
Abstract: Shell model calculations were performed to study the energy levels and the reduced transition probabilities B(E2;0g.s?2) for eveneven 5466Fe neutron rich isotopes by using the shell model code Nushellx@MSU for windows by employing the effective interactions GXPF1, GXPF1A, KB3G and FPD6. The core is taken at 48Ca for all nuclei under study and the results of our theoretical calculations for both energy levels and reduced transition probabilities B(E2;0g.s?2) are compared with the most recent available experimental data. A good agreement were obtained for all isotopes under study for energy levels and unable to reproduce the experimental data for the reduced transition probabilities using constant effective charges which proves the limitation of fullfp calculations.
Introduction The neutron rich nuclei in the fpshell region are at the focus of attention of the nuclear physics community at present. Unstable nuclei in this region exhibit many new phenomenon such as appearance of new magic numbers and disappearance of wellestablished ones, softening of core at N=28, interplay of collective and single particle properties (Srivastava and Mehrotra, 2009). The 2+ energy in these nuclei, and sometimes the 4+ energy as well, could be well reproduced by shellmodel calculations in which an fpmodel space is employed. However, in the level sequences above the 4+ states, structural changes have been observed in these systems that may require an inclusion of highj orbitals in order to discuss these changes (Yang Sun et al., 2009). It is a common feature of systems of interacting fermions to form a shell structure. In atomic nuclei the spinorbit interaction lowers the energy of the orbitals with the highest angular momentum into the next lower oscillator shell with opposite parity, leading to the wellknown sequence of magic numbers. While the shell structure and the resulting energy gaps between the orbitals explain many general properties of nuclei across the nuclear chart, it has become evident that the shell structure and magic numbers change for nuclei with large neutron excess. As protons and neutrons in such exotic nuclei occupy different orbitals compared to their stable counterparts, the effective singleparticle energies are shifted. (Ljungvall et al., 2010). Full fp shell model study of A=48 nuclei were performed by Caurier and Zuker (Caurier and Zuker, 1994) by modifying KuoBrown (KB) (Kuo and Brown, 1968) to KB1 and KB3. The isobaric chains A=50, A=51 and A=52 studied by Poves et al. (Poves, et al. 2001) using KB3 and FPD6 (Richter et al., 1994) and their new released version KB3G. Shell model study for full fpshell model were performed by (Majeed and Auda, 2006) to study the levels schemes and transition rates B(E2,) for eveneven 4856Ti isotopes by employing FPD6 and GXPF1 effective interactions. Shell model calculations using Oxbash for windows (Brown, et al., 2004) by employing the residual effective interactions were performed to study the levels schemes and reduced transition probabilities for 46Ti, 46Cr and 46V for the isovector T=1 positive parity states by (Majeed, 2008). F. I. Sharrad (Sharrad, 2013) calculated the binding energies, energy levels and the reduced transition probabilities of neutronrich 6066Fe isotopes by using Nushellx.
The aim of the present work is to study the reduced transition probabilities and level schemes of eveneven 54 66Fe isotopes using the shell model Nushellx for windows by employing the effective residual interactions fitted for the fpshell region codenamed FPD6, GXPF1,GXPF1A and KB3G. Shell model calculations The calculation were carried out in the HO model space for nuclei eveneven 5466Fe near the closed core 48Ca by using Nushellx@MSU code for windows without any restriction imposed on the model space with four effective interactions codenamed GXPF1,GXPF1A, KB3G and FPD6 interactions. The calculation of excitation energy levels and reduced transition probabilities were compared with the most recent available experimental data and the best agreement achieved using FPD6 effective interaction. Within the framework of the shell model, an auxiliary onebody potential U is introduced in order to break up the Hamiltonian for a system of A nucleons as the sum of a onebody term H0, which describes the independent motion of the nucleons, and a residual interaction H1:
Once H0 has been introduced, it is possible to define a reduced model space in terms of afinite subset of HO’s eigenvectors. In this space, an effective Hamiltonian Heff may be constructed and the diagonalization of the manybody Hamiltonian equation (1) in an infinite Hilbert space is then reduced to the solution of an eigenvalue problem in a finite space (Itaco, et al., 2011). The reduced transition probability for electric multipole radiation is given by (Greiner and Maruhn, 1996)
Results and Discussion The test of success of largescale shell model calculations is the predication of the first 2+ level and the transition rates B E2; 0g.s + ? 21 + using the optimized effective interactions for the description of fpshell nuclei (Majeed and Auda, 2006) For all isotopes under investigation the core are taken at 48Ca and the valence nucleons distributed over 1f7/2, 2p3/2, 1f5/2 and 2p1/2 orbits. Energy levels Figure 1 presents the comparison between our theoretical calculations for the energy levels using the residual effective interactions FPD6, GXPF1, GXPF1A and KB3G with the experimental data taken from Ref. (ENSDF, 2014). Good agreement were obtained for all interactions employed in the present work and the best results achieved by employing FPD6 effective interaction.
Transition probabilities Since the transition rates represent a sensitive test for the most modern effective interactions that have been developed to describe fpshell nuclei. The transition strengths calculated in this work performed using the harmonic oscillator potential HO for each inband transition by assuming pure E2 transition. The effective charges were taken to be e?=1.25e for proton and e?=0.8e for neutron. Figure 9 presents the comparison between the calculated reduced transition probabilities for all isotopes using FPD6 effective interaction with the experimental data. From the figure it is shown that there is agreement only for the isotopes 54Fe and 56Fe and the calculations starts to deviate severely for the rest of the isotopes due to increase of the number of valence neutrons which effect the structure evolution of these isotopes and effect the theoretical prediction of these isotopes.
Conclusions The present study demonstrated that the best effective interactions that might be used to describe nuclei lies in the fpshell region is FPD6 and GXPF1A. The use of constant effective charges for the proton and neutron are not always the best choice to describe the dynamic properties of the nuclei such as the reduced transition probabilities B(E2), especially when the neutron number increase that effect the structure evolution of the nuclei with neutron rich access. This work can be extended to study more neutron rich chain of isotopes to have better understanding of these effective interactions and the possible ways to modify them to be more agreeable with the experimental data. Acknowledgments The authors would like to acknowledge the financial support from the college education for pure sciences, University of Babylon. References Brown, B. A. (2004). “OXBASH for Windows”, MSUNSCL report number 1289: 132 Brown, B. A., Rae W. D. M. (2007). Nushellx@MSU. MSUNSCL report 524:129 E. Caurier, E., Zuker, A. P., Poves, A., Mart?nezPinedo, M. (1994). Full pf shell model study of A=48 nuclei. Phys. Rev. C 50: 225236. ENSDF, National Nuclear Data Center (2014). Evaluated nuclear structure data file Greiner W., Maruhn, J. A. (1996). Nuclear Models, SpringerVerlag, Berlin Heidelberg: 7598. Itaco, N., Coraggio, L., Covello, A., Gargano, A. (2011). Microscopic approach to the shell model: study of nuclei northeast of 48Ca. J. Phys.: Conf. Ser. 336: 0120080120018. Ljungvall J., Gorgen, A., Obertelli, A., Korten, W., Clement, E., de France, G., Burger, A., Delaroche, J.P., Dewald, A., Gadea, A., Gaudefroy, L., Girod, M., Hackstein, M., Libert, J., Mengoni, D., Nowacki, F., Pissulla, T., Poves, A., Recchia, F., Rejmund, M., Rother, W., Sahin, E., Schmitt, C. , Shrivastava, A., Sieja, K., ValienteDobon, J. J., Zell, K. O., Zielinska, M. (2010). Phys. Rev. C 81: 061301 061305. Majeed F. A. (2008). Level excitation and transition probabilities of some nuclei in the lower fpshell. Rom. Journ. Phys., Vol. 53, Nos. 7–8: 809815. Majeed, F. A., Auda A. A. (2006). Full fpshell study of eveneven 4856Ti isotopes. Brazil. Journ. of Phys., Vol. 36, no. 1B: 229231. NNDC, National Nuclear Data Center. (2014 Poves, A., Sanchez Solano, J., Caurier, E., Nowacki, F. (2001). Shell model study of the isobaric chains A=50, A=51 and A=52. Nucl. Phys. A 694:157198. Richter W. A., van der Merwe, M.G., Julies, R.E., B.A. Brown, B. A. (1994). Tests and predictions of new effective interactions in the 0f1p shell. Nucl. Phys. A 577: 585604. Sharrad, F. I. (2013). Binding Energy and Energy Level with B(E2;0?2) of NeutronRich 6066Fe Isotopes using NuShellX. Research & Reviews: J. of Phys. Vol. 2, No. 2:14. Srivastava, P. C., I. Mehrotra, I. (2009). Largescale shell model calculations for even–even 62–66Fe isotopes. Phys. G: Nucl. Part. Phys. 36:105 113. Steppenbeck, D., Janssens, R. V. F., Freeman, S. J., Carpenter, M. P., Chowdhury, P., Deacon, A. N., Honma, M., Jin, H., Lauritsen, T., Lister, C. J., Meng, J., Peng J., D. Seweryniak, D., Smith, J. F., Sun, Y., Tabor, S. L. , Varley, B. J. , Yang, Y.C., Zhang, S. Q.Zhao, P. W., Zhu S. (2012). Magnetic rotation and quasicollective structures in 58Fe: Influence of the ?g9/2 orbital. Phys. Rev. C 85: 044316044339. Sun, Y.,Yang, Y. C., Liu, H. L., Kaneko, K., Hasegawa, M., Mizusaki T. (2009). Projected shell model description for highspin states in neutronrich Fe isotopes. Phys. Rev. C 80:054306 054317. T. T. S. Kuo, T. T. S., Brown, G. E. (1968). Reaction matrix elements for the 0f1p shell nuclei. Nucl. Phys. A 114: 241279.
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