Hole-Hole Collective Excitations in 106, 112, 130Sn Isotopes
Abstract
In this paper, energy-level schemes of neutron rich and reduced electric transition strengths of Tin isotopes 106Sn, 112Sn and 130Sn were studied using collective models, i.e., hole-hole Tamm-Dancoff Approximation (hh TDA) and hole-hole Random Phase Approximation (hh RPA). According to these models, the excited states of closed core A-2 systems with multipolarity J and isospin T can be described as a linear combination of hole-hole (hh) pairs. Therefore, in our approach, the low-lying states of the investigated isotopes 106Sn, 112Sn and 130Sn are obtained by acting two-hole operators on a correlated core 108Sn, 114Sn and 132Sn, respectively. The Hamiltonian is diagonalized within the model space include {1g7/2, 2d5/2, 2d3/2, 3s1/2 and 1h11/2} orbits, using the matrix elements of neutron-neutron (N-N) interaction and modified surface delta interaction (MSDI). The hh TDA and hh RPA are checked by using the resultant eigenvalues and eigenvectors to calculate the excitation energies and reduced electric transition strengths. A comparison had been made between our theoretical predictions and the recent available experimental data. Reasonable agreements were obtained from these comparisons.
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References
T. Engeland, M. Hjorth-Jensen, A. Holt, and E. Osnes, “Large Shell Model Calculations with Realistic Effective Interaction,” Physica Scripta, 1995(T56), 58 (1995). https://doi.org/10.1088/0031-8949/1995/T56/009
A. Covello, F. Andreozzi, L. Coraggio and A. Gargano, T.T.S. Kuo, and A. Porrino, “Nuclear Structure Calculations With Realistic Effective Interactions”, Progress in Particle And Nuclear Physics, 38, 165 (1997). https://doi.org/10.1016/S0146-6410(97)00023-9
R. Schubart, H. Grawe, J. Heese, H. Kluge, K. H. Maier, and M. Schramm, “Shell Model Structure at 100Sn - the Nuclides 98Ag, 103In, and 104, 105Sn”, Zeitschrift Für Physik A Hadrons And Nuclei, 352, 373-390 (1995). https://doi.org/10.1007/BF01299755
E. Dikmen, “Shell Model Description of Neutron-Deficient Sn Isotopes,” Communications in Theoretical Physics, 51(5), 899 (2009). https://doi.org/10.1088/0253-6102/51/5/28
A. Covello, L. Coraggio, A. Gargano, and N. Itaco, “Shell-model study of exotic Sn isotopes with a realistic effective interaction,” Journal of Physics: Conference Series, 267, 012019 (2011). https://doi.org/10.1088/1742-6596/267/1/012019
T. Trivedi, P.C. Srivastava, D. Negi, and I. Mehrotra, “Shell Model Description of 102−108Sn Isotopes,” International Journal of Modern Physics E, 21(4), 1250049 (2012). https://doi.org/10.1142/S0218301312500498
K.S. Jassim, “Nuclear Structure of 104,106,108Sn Isotopes Using the Nushell Computer Code,” Chinese Journal of Physics, 51(3), 441 (2013). https://cdnx.uobabylon.edu.iq/research/repository1_publication889_30_1533.pdf
K.H.H. Al-Attiah, F.A. Majeed, and T.J. Al-Kawwaz, “Calaculations of Even-Even 100-108Sn Isotopes Using Shell Model in the Vicinity of 100Sn,” Journal of Babylon University/Pure and Applied Sciences, 21(8), 2831(2013). https://iasj.net/iasj/pdf/75f920c6c56d7091
F.A. Majeed, and S.M. Obaid, “Large-Scale Shell Model Calculations of 134,136Sn, 134,136Te around doubly-magic 132Sn”, International Journal of Scientific & Technology Research, 5(4), 106(2016). https://www.ijstr.org/final-print/apr2016/Large-scale-Shell-Model-Calculations-Of-134136sn-134136te-Around-Doubly-magic-132sn.pdf
F.H. Obeed, and B.S. Abed, “Study of energy spectrum of 116Sn and 116Te nuclei by using surface delta and modified surface delta interactions”, Journal of Physics: Conference Series 1664, 012145 (2020). https://doi.org/10.1088/1742-6596/1664/1/012145
A.K. Hasan, F.H. Obeed, and A.N. Rahim, “Positive Parity Levels of 21,23Na Isotopes by Using the Nuclear Shell”, Ukrainian Journal of Physics, 65(1), 3(2020). https://doi.org/10.15407/ujpe65.1.3
S. Akkoyun, “Nuclear Shell Model Calculations for A=49 Isobars”, Turkish Journal of Science and health, 1(2), 3(2020). https://dergipark.org.tr/en/download/article-file/1178106
M.M. Jabbar, and F.H. Obeed, “Description of the energy levels and electric quadrupole transitions of the 92Nb and 92Mo nuclei using nuclear shell model”, Kuwait Journal of Science, 49(2), 1 (2022). https://doi.org/10.48129/kjs.13631
I. Kaplan, Nuclear Physics, (Addison – Wesley Pub.Com. Inc, 1963).
N.D. Cook, Models of the Atomic Nucleus, (Springer -Verlag Berlin Heidelberg Netherlands, 2006).
K.S. Krane, Introductory Nuclear Physics, (John Wiley &Sons, Inc, 1988).
P. Ring, and P. Schuck, The Nuclear Many-Body Problem, (Springer-Verlag, New York, 1980).
J. Suhonen, From Nucleons to Nucleus, (Springer-Verlag, Berlin Heidelberg, 2007).
A.H. Taqi, A.A. Rasheed, and S.H. Amin, “Particle–particle and hole–hole random phase approximation calculations for 42Ca and 38Ca nuclei,” Acta Physica Polonica B, 41(6), 1327 (2010). https://www.actaphys.uj.edu.pl/R/41/6/1327/pdf
A.H. Taqi, “Particle-Particle Tamm-Dancoff Approximation and Particle-Particle Randam Phase Approximation Calculations for 18O and 18F Nuclei,” Pramana Journal of Physics, 80(2), 355-360 (2013). https://doi.org/10.1007/s12043-012-0468-1
A.H. Taqi, “The Electroexcitation of Low-Lying, Collective, Positive Parity, T=1 States in 18O, Based on the Particle-Particle Random Phase Approximation”, Chinese Journal of Physics, 45(5), 530 (2007). https://www.airitilibrary.com/Publication/Index?DocID=05779073-200710-45-5-530-536-a&jsonString=
A.H. Taqi, “A visual Fortran 90 program for the two-particle or two-hole excitations of nuclei: The PPRPA program,” SoftwareX 5, 51-61 (2016). https://doi.org/10.1016/j.softx.2016.04.003
A.H. Taqi, and A.H. Ibrahim, “Collective Excitations of 14N and 10B Nuclei,” Kirkuk University Journal-Scientific Studies, 11(1), 202 (2016). https://doi.org/10.32894/kujss.2016.124396
A.H. Taqi, and A.H. Ibrahim, “Electron scattering of 14N based on two-hole excitations,” Chinese Journal of Physics, 54, 185 193 (2016). https://doi.org/10.1016/j.cjph.2016.04.003
P.J. Brussaard, and P.W. Glaudemans, Shell model applications in nuclear spectroscopy, (Amsterdam: North-Holland, 1977).
National Nuclear Data Center https://www.nndc.bnl.gov
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