Description of even-even Ti isotopes within IBM-1 model

Yıl 2021, Cilt: 42 Sayı: 1, 177 - 183, 29.03.2021

Yeşim Şahin Mahmut Boyukata

https://doi.org/10.17776/csj.856118

Cited By: 1

Öz

In this work, the some collective properties of even-even Ti isotopes in the A50 mass region were studied by using the interacting boson model-1 (IBM-1). This study includes calculations of the energy levels and the electromagnetic transition rates of 44-48Ti and 52-60Ti isotopes. The neutron number 50Ti isotope is 28, the magic number, and this isotope was excluded from the IBM-1 calculations. First, the energy ratios were analyzed by comparing the typical values of U(5), SU(3), O(6) dynamical symmetries and E(5), X(5) critical point symmetries. Later model Hamiltonian was constructed according to the behavior of given isotopes. The low lying energy levels of each Ti isotopes were calculated by using the fitted parameters of Hamiltonian. B(E2) values were also calculated by using the corresponding electromagnetic transition operator in the IBM-1. The calculation results were compared with experimental data and they are in good agreement with each other. Finally, R_(4/2)=E(4_1^+)/E(2_1^+), R_(0/2)=E(0_2^+)/E(2_1^+) energy ratios and B(E2:4_1^+→2_1^+)/B(E2:2_1^+→0_1^+), B(E2:0_2^+→2_1^+)/B(E2:2_1^+→0_1^+) ratios were analized to see the behavior of given isotopes. According to obtained results, Ti isotopes show E(5) behavior along the transition path from spherical to deformed -unstable region. Overall analysis indicates that these isotopes can be good example for the quantum shape phase studies along the isotopic chain.

Anahtar Kelimeler

Energy Levels, B(E2)values, Dynamical Symmetries, Critical Point Symmetries, Interacting Boson Model

Kaynakça

• [1] Heyde K., Basic Ideas and Concepts in Nuclear Physics: An Introductory Approach. Third Edition, Bristol and Philadelphia: Institute of Physics Publishers; chap. 9 (2004).
• [2] Iachello F., Arima, A., The Interacting Boson Model. Cambridge University Press; chap. 1 (1987).
• [3] Bai H.-B., Li X.-W., Shape phase transition in neutron-rich even-even light nuclei with Z = 20-28, Chin. Phys. C 35 (2011) 925-929.
• [4] Coraggio L., Covello A., Gargano A., Itaco N., Kuo T.T.S., Fully microscopic shell-model calculations with realistic effective Hamiltonians, J. Phys.: Conf. Ser. 312 (2011) 092021.
• [5] Caprio M.A., Luo F.Q., Cai K., Constantinou Ch., Hellemans V., Generalized seniority with realistic interactions in open-shell nuclei, J.Phys. (London) G 39 (2012) 105108.
• [6] Bayram T., An investigation on shape evolution of Ti isotopes with Hartree-Fock-Bogoliubov theory, Mod. Phys. Lett. A 27, 28 (2012) 1250162.
• [7] Kaneko K., Mizusaki T., Sun Y., Tazaki S., Toward a unified realistic shell-model Hamiltonian with the monopole-based universal force, Phys. Rev. C 89 (2014) 011302.
• [8] Robinson S.J.Q., Hoang T., Zamick L., Escuderos A., Sharon Y.Y., Shell model calculations of B(E2) values, static quadrupole moments, and g factors for a number of N=Z nuclei, Phys. Rev. C 89 (2014) 014316.
• [9] Ma Y.Z., Coraggio L., De Angelis L., Fukui T., Gargano A., Itaco N., Xu F.R., Contribution of chiral three-body forces to the monopole component of the effective shell-model Hamiltonian, Phys. Rev. C 100 (2019) 034324.
• [10] Ullah A., Riaz M., Nabi J.U., Böyükata M., Çakmak N., Effect of deformation on gamowteller strength and electron capture cross-section for isotopes of chromium. Bitlis Eren Univ. J. Sci. Technol., 10 (2020) 25-29.
• [11] Nabi J.-U., Böyükata M., Ullah A., Riaz M., Nuclear structure properties of even-even chromium isotopes and the effect of deformation on calculated electron capture cross sections, Nucl. Phys. A 1002 (2020) 121985.
• [12] Çakır Oruç G., Böyükata M., Investigation of nuclear properties of even-even Fe isotopes within the IBM-1 model, Bitlis Eren Univ. J. Sci., 10 (2021) 82-90.
• [13] National Nuclear Data Center (NNDC), https:nndc.bnl.gov. Retrieved December 15, 2020.
• [14] Casten R. F., Shape phase transitions and critical-point phenomena in atomic nuclei. Nature Physics 2, (2006) 811–820.
• [15] Iachello F., Analytic description of critical point nuclei in a spherical-axially deformed shape phase transition. Phys. Rev. Lett. 87 (2001) 052502.
• [16] Iachello F., Dynamic symmetries at the critical point. Phys. Rev. Lett. 85 (2000) 3580–3583.
• [17] Arias J.M., E2 transitions and quadrupole moments in the E(5) symmetry, Phys. Rev. C 63 (2001) 034308.
• [18] Casten R.F., Warner D.D., The interacting boson approximation, Rev. Mod. Phys. 60 (1988) 389-469.
• [19] Scholten O., The program package PHINT and PBEM (1979).