Particle-Particle Collective Excitations of Sn isotopes

Ali H. Taqi; Fahema  A. Saber

doi:10.14500/aro.11153

Ali H. Taqi Department of Physics, College of Science, Kirkuk University, Kirkuk, Iraq https://orcid.org/0000-0001-5007-4858
Fahema A. Saber Department of Physics, College of Science, Kirkuk University, Kirkuk, Iraq

Keywords: Collective excitations, Energy-level schemes, Particle-particle Random Phase Approximation, Particle-particle Tamm-Dancoff Approximation

Abstract

In this paper, energy-level schemes and reduced electric transition strengths of neutron-rich Tin isotopes ^{102, 110, 116, 120, 122}Sn (Z=50) are studied using collective models, that is, particle-particle Tamm-Dancoff Approximation and particle-particle Random Phase Approximation. 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 particle-particle pairs. In our investigation, the low-lying states of the investigated isotopes ^{102, 110, 116, 120, 122}Sn are described by acting two-particle operators on a correlated core ¹⁰⁰Sn, ¹⁰⁸Sn, ¹¹⁴Sn, ¹¹⁸Sn, and ¹²⁰Sn, respectively. The Hamiltonian is diagonalized within the model space include {1g_7/2, 2d_5/2, 2d_3/2, 3s_1/2and 1h_11/2} orbits, using the matrix elements of neutron-neutron interaction and modified surface delta interaction. The calculated values are checked by using the resultant eigenvalues and eigenvectors to calculate the excitation energies and reduced electric transition strengths. Our calculated results are compared to the available experimental data, and these comparisons led to reasonable agreements. Effective charges are also used to account for the core polarization effect.

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Author Biographies

Ali H. Taqi, Department of Physics, College of Science, Kirkuk University, Kirkuk, Iraq

Ali H. Taqi is a Professor at the Department of Physics, College of Science, Kirkuk University. He got the B.Sc. degree in Physics, the M.Sc. degree in Microwaves and Antennas and the Ph.D. degree in Nuclear Physics. His research interests are in Theoretical and Experimental Nuclear Physics. Dr. Ali is a member of a number of committees in the Kirkuk University and Iraqi Ministry of Higher Education and Scientific Research.

Fahema A. Saber, Department of Physics, College of Science, Kirkuk University, Kirkuk, Iraq

Fahema A. Saber is an M.Sc. Student at the Department of Physics, College of Science, Kirkuk University. She got the B.Sc. degree in Physics. Her research interests are in Theoretical Nuclear Physics.iversity. She got the B.Sc. degree in Physics. Her research interests are in Theoretical Nuclear Physics.

References

Al-Attiah, K.H.H., Majeed, F.A., and Al-Kawwaz, T.J., 2013. Calculations of even-even 100-108Sn isotopes using shell model in the vicinity of 100Sn. Journal of Babylon University/Pure and Applied Sciences, 21(8), pp.2831-2836.

Bhatt, K.H., Nestor C.W. Jr., and Raman, S., 1992. Do nucleons in abnormal-parity states contribute to deformation. Physical Review C, Nuclear Physics, 46(1), pp.164-180. DOI: https://doi.org/10.1103/PhysRevC.46.164

Brussaard, P.J., and Glaudemans, P.W.M., 1977. Shell Model Applications in Nuclear Spectroscopy. North-Holland Publishing Company, Amsterdam.

Covello, A., Andreozzi, F., Coraggio, L., Gargano, A., Kuo, T.T.S., and Porrino, A., 1997. Nuclear structure calculations with realistic effective interactions. Progress in Particle and Nuclear Physics, 38, pp.165-172. DOI: https://doi.org/10.1016/S0146-6410(97)00023-9

Covello, A., Coraggio, L., Gargano, A., and Itaco, N., 2011. Shell-model study of exotic Sn isotopes with a realistic effective interaction. Journal of Physics Conference Series, 267, p.012019. DOI: https://doi.org/10.1088/1742-6596/267/1/012019

Dikmen, E., 2009. Shell model description of neutron-deficient Sn isotopes. Communications in Theoretical Physics, 51(5), p.899. DOI: https://doi.org/10.1088/0253-6102/51/5/28

Elliott, J.P., and Lane, A.M., 1954, Evidence for two-body spin-orbit forces in nuclei. Physical Review, 96(4), p.1160. DOI: https://doi.org/10.1103/PhysRev.96.1160

Engeland, T., Hjorth-Jensen, M., Holt, A., and Osnes, E., 1995. Large shell model calculations with realistic effective interaction. Physica Scripta, 1995(T56), p.58. DOI: https://doi.org/10.1088/0031-8949/1995/T56/009

Hasan, A.K., Obeed, F.H., and Rahim, A.N., 2020. Positive parity levels of 21,23Na isotopes by using the nuclear shell model. Ukrainian Journal of Physics, 65(1), p.3. DOI: https://doi.org/10.15407/ujpe65.1.3

Haxel, O., Jensen, J.H.D., and Suess H.E., 1949. On the magic numbers in nuclear structure. Physical Review, 75(11), p.1766. DOI: https://doi.org/10.1103/PhysRev.75.1766.2

Heyde, K.L.G., 1994. The Nuclear Shell Model. Springer-Verlag, Berlin, Heidelderg. DOI: https://doi.org/10.1007/978-3-642-79052-2

Jassim, K.S., 2013. Nuclear structure of 104,106,108Sn isotopes using the nushell computer code. Chinese Journal of Physics, 51(3), p.441.

Majeed, F.A., and Obaid, S.M., 2016. Large-scale shell model calculations of 134,136Sn, 134,136Te around doubly-magic 132Sn. International Journal of Scientific and Technology Research, 5(4), p.106.

Mayer, M.G., 1949. On closed shells in nuclei. Physical Review, 75(12), p.1969.National Nuclear Data Center. Available from: https://www.nndc.bnl.gov [Last accessed on 2023 Feb 01]. DOI: https://doi.org/10.1103/PhysRev.75.1969

Nichols, A.J., 2014. Gamma-ray Spectroscopy and Lifetime Measurements of Nuclei in the A=70, N =Z Region, PhD Thesis. University of York, United Kingdom.

Obeed, F.H., and Abed, B.S., 2020. Study of energy spectrum of 116Sn and 116Te nuclei by using surface delta and modified surface delta interactions. Journal of Physics Conference Series, 1664, p.012145. DOI: https://doi.org/10.1088/1742-6596/1664/1/012145

Ring, P., and Schuck, P., 1980. The Nuclear Many-body Problem. 1st ed., Springer-Verlag, New York. Rowe, D.J., 1970. Nuclear Collective Motion: Models and Theory. Butler and Tanner Ltd., London.

Schubart, R., Grawe, H., Heese, J., Kluge, H., Maier, K.H., and Schramm, M., 1995. Shell model structure at 100Sn-the nuclides 98Ag, 103In, and 104, 105Sn. Zeitschrift Für Physik a Hadrons and Nuclei, 352, pp.373-390. DOI: https://doi.org/10.1007/BF01299755

Sorkin, O., 2014. Shell evolutions and nuclear forces. EPJ Web of Conferences, 66, p.01016. DOI: https://doi.org/10.1051/epjconf/20146601016

Tajima, N., and Suzuki, N., 2001. Prolate dominance of nuclear shape caused by a strong interference between the effects of spin-orbit and l2 terms of the Nilsson potential. Physical Review C, 64, p.037301. DOI: https://doi.org/10.1103/PhysRevC.64.037301

Taqi, A.H., 2007. 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), p.530.

Taqi, A.H., 2013. Particle-particle Tamm-Dancoff approximation and particle-particle randam phase approximation calculations for 18O and 18F nuclei. Pramana Journal of Physics, 80(2), pp.355-360. DOI: https://doi.org/10.1007/s12043-012-0468-1

Taqi, A.H., 2016. A visual Fortran 90 program for the two-particle or two-hole excitations of nuclei: The PPRPA program. SoftwareX, 5, pp.51-61. DOI: https://doi.org/10.1016/j.softx.2016.04.003

Taqi, A.H., Rasheed, A.A., and Amin, S.H., 2010. Particle-particle and hole-hole random phase approximation calculations for 42Ca and 38Ca nuclei. Acta Physica Polonica B, 41(6), p.1327.

Trivedi, T., Srivastava, P.C., Negi, D., and Mehrotra, I., 2012. Shell model description of 102-108Sn isotopes. International Journal of Modern Physics E, 21(4), p.1250049. DOI: https://doi.org/10.1142/S0218301312500498