Nuclear Structure of Rare-Earth 172Er, 174Yb, 176Hf, 178W, 180Os Nuclei
Keywords:erbium-osmium, ground-state band, NEE, IBM-1, B(E2), SU(3)
Using the method with new empiric equation (NEE) and the model of interacting bosons (IBM-1), we study the ground-state band and the gamma- and beta-emission spectra of erbium (Er) and osmium (Os) elements with N = 104. The absolute B(E2) strengths for the nuclei are determined. The properties of the potential energy surface are investigated within IBM-1. The ratio Ey(I + 2)/(I) as a function of the angular momentum (I) and the characteristics of the yrast states are found. The constructed plots indicate that all nuclei of 172Er, 174Yb, 176Hf, 178W, and 180Os have a rotational SU(3) character. The staggering factors of available measured data are considered. The results of both models agree well with available experimental data for 172Er, 174Yb, 176Hf, 178W, and 180Os nuclei.
F. Iachello, A. Arim. The Interacting Boson Model (Cambridge University Press, 1987) [ISBN: 9780511895517].
F. Iachello. Analytic description of critical point nuclei in a spherical-axially deformed shape phase transition. Phys. Rev. lett. 87, 052502 (2001).
F. Iachello. Dynamic symmetries at the critical point. Phys. Rev. lett. 85, 3580 (2000).
P. Cejnar, J. Jolie, R.F. Casten. Quantum phase transitions in the shapes of atomic nuclei. Rev. Mod. Phys. 82, 2155 (2010).
R.F. Casten, E.A. McCutchan. Quantum phase transitions and structural evolution in nucle. J. Phys. G 34, R285 (2007).
P.E.A. McCutchan, N.V. Zamfir.Simple description of light W, Os, and Pt nuclei in the interacting boson model. Phys. Rev. C 71, 054306 (2005).
A. Dewald, O. M¨oller, B. Saha, et al. Test of the critical point symmetry X(5) in the mass A = 180 region. J. Phys. G. Nucl. Partic. 31, S1427 (2005).
Z. Jin-Fu, L. Li-Jun, B. Hong-Bo. Critical behaviour in nuclear structure from spherical to axially symmetric deformed shape in IBM. Chinese Phys. 16, 7 (2007).
S.F. Shen, Y.B. Chen, F.R. Xu, S.J. Zheng, B. Tang, T.D. Wen. Signature for rotational to vibrational evolution along the yrast line. Phys. Rev. C 75, 047304 (2007).
P.N. Usmanov, A.A. Okhunov, U.S. Salikhbaev, A.I. Vdovin. Analysis of electromagnetic transitions in nuclei 176,178Hf. Phys. Part. Nuclei Lett. 16, 185 (2010).
K. Nomura, T. Otsuka, N. Shimizu, L. Guo. Derivation of IBM Hamiltonian for deformed nuclei. J. Phys.: Conf. Ser. 267, 012050 (2011).
H.L. Liu, F.R. Xu, P.M. Walker, C.A. Bertulani. Deformation and its influence on K isomerism in neutron-rich Hf nuclei. Phys. Rev. C 83, 067303 (2011).
X. Hao, L.H. Zhu, X.G. Wu, et al. Evolution of the X(5) critical-point symmetry in rotating 176Os. J. Phys. G. Nucl. Partic. 38, 025102 (2011).
A.A. Raduta, P. Buganu. Application of the sextic oscillator with a centrifugal barrier and the spheroidal equation for some X(5) candidate nuclei. J. Phys. G. Nucl. Partic. 40, 025108 (2013).
E. Williams, et al. High-precision excited state lifetime measurements in rare earth nuclei using LaBr3(Ce) detectors. EPJ Web of Conferences 35, 06006 (2012).
A. Okhunov, F.I. Sharrad, A.A. Al-Sammarea, M.U. Khandaker. Correspondence between phenomenological and IBM-1 models of even isotopes of Yb. Chinese Phys. C 39, 084101 (2015).
S.N. Abood, M.A. Al-Jubbori. Nuclear structure and Eeectromagnetic transitions investigation in Er isotopes within framework of interacting boson model. textitCommun. Theor. Phys. 60, 335 (2013).
M. Abed Al-Jubbori, H.H. Kassim, F.I. Sharrad, I. Hossain. Deformation properties of the evenпїЅeven rare-earth Er-Os isotopes for N = 100. Int. J. Mod. Phys. E 27, 1850035 (2018).
M. Abed Al-Jubbori, H.H. Kassim, A.A. Abd-Aljbar, H.Y. Abdullah, I. Hossain, I.M. Ahmed, F.I. Sharrad. Nuclear structure of the evenпїЅeven rare-earth Er-Os nuclei for N = 102. Indian. J. Phys. 94, 379 (2020).
A. Arima, F. Iachello. Interacting boson model of collective nuclear states II. The rotational limit. Ann. Phys-New. York. 111, 201 (1978).
F. Iachello, K. Abrahams, K. Allart, A.E. Dieperink. Nuclear Structure. Pub (Plenum, New York and London) Ed. Abrahams K., Allaart K., and Diapering AEL (1881).
R. F. Casten, D. D. Warner. The interacting boson approximation. Rev. Mod. Phys. 60, 389 (1988).
F. Iachello. Dynamical supersymmetries in nuclei. Phys. Rev. Lett. 44, 772 (1980).
H.H. Kassim, A.A. Mohammed-Ali, M. Abed Al-Jubbori, F.I. Sharrad, A.S. Ahmed, I. Hossain. Critical point of the 152Sm, 154Gd, and 156Dy isotones isotopes. Phys. Atom. Nuclei. 82, 211 (2019).
A. Arima, F. Iachello. Interacting boson model of collective states I. The vibrational limit. Ann. Phys-New. York 281, 2 (2000).
R.F. Casten, Roma. Simplicity and complexity in nuclear structure. R. Reports in Phys. 57, 515 (2005).
E.A. McCutchan, R.F. Casten. Crossing contours in the interacting boson approximation (IBA) symmetry triangle. Phys. Rev. C 74, 057302 (2006).
M.A. Al-Jubbori, F.Sh. Radhi, A.A. Ibrahim, S.A. Abdullah Albakrid, H.H. Kassim, F.I. Sharrad. Determine the 134−140Nd isotopes identity using IBM and NEF. Nucl. Phys. A 971, 35 (2018).
P.H. Regan, et al. Signature for Vibrational to Rotational Evolution Along the Yrast Line. Phys. Rev. Lett. 90, 152502 (2003).
G. Scharff-Goldhaber, J. Weneser. System of even-even nuclei. Phys. Rev. 98, 212 (1955).
B.R. Mottelson, S.G. Nilsson. Danske Videnskab. Selskab. Mat-fys Medd.(to be published) 27, 16 (1953).
B. Singe. Nuclear Data Sheets for A = 199. Nucl. Data. Sheets. 108, 196 (2007).
E. Browne, H. Junde. Nuclear data sheets for A = 174. Nucl. Data. Sheets. 87, 15 (1999).
M.S. Basunia. Nuclear Data Sheets for A = 176. Nucl. Data. Sheets. 107, 791 (2006).
E. Achterberg, O.A. Capurro, G.V. Marti. Nuclear data sheets for A = 178. Nucl. Data. Sheets. 110, 1473 (2009).
S.C. Wu, H. Niu. Nuclear Data Sheets for A = 180. Nucl. Data. Sheets. 100, 483 (2003).
D. Bonatsos, L.D. Skouras. Successive energy ratios in medium-and heavy-mass nuclei as indicators of different kinds of collectivity. Phys. Rev. C 43, 952R (1991).
A.M. Khalaf, A.M. Ismail. Structure shape evolution in lanthanide and actinide nuclei. Prog. Phys. 2, 98 (2013).
I. Mamdouh, M. Al-Jubbori. The rotational Ѕvibrational properties of 178−188Os isotope. Indian J. Phys. 89, 1085 (2015).
M.A. Al-Jubbori, H.H. Kassim, F.I. Sharrad, I. Hossain. Nuclear structure of even 120−136Ba under the framework of IBM, IVBM and new method (SEF). Nucl. Phys. A 955, 101 (2016).
I.M. Ahmed, G.N. Flaiyh, H.H. Kassim, H.Y. Abdullah, I. Hossain, F.I. Sharrad. Microscopic description of the even-even
−148Ba isotopes using BM, IBM and IVBM. Eur. Phys. J. Plus. 132, 84 (2017).
O. Scholten. Computer code PHINT, KVI (Groningen, 1980).
D. Bonatsos. Systematics of odd-even staggering in y-bands as a test for phenomenological collective models. Phys. Lett. B 200, 1 (1988).
D. Bonatsos, et al. ΔI = 1 staggering in octupole bands of light actinides: "Beat" patterns. Phys. Rev. C 62, 024301 (2000).
I.M. Ahmed, M.A. Al-Jubbori, H.H. Kassim, H.Y. Abdullah, F.I. Sharrad. Investigation of even-even 220−230Th isotopes within the IBM, IVBM and BM Nucl. Phys. A 977, 34 (2018).
H.H. Kassim, A.A. Mohammed-Ali, F.I. Sharrad, I. Hossain, K.S. Jassim. Nuclear structure of even 178−182Hf Isotopes under the framework of interacting Boson model (IBM-1). Iran. J. Sci. Technol. A. 42, 993 (2018).
H.H. Kassim, F.I. Sharrad. Energy levels and electromagnetic transition of 190−196Pt nuclei. Int. J. Mod. Phys. E 23, 1450070 (2014).
S. Raman, C.W. Nestor, JR, P. Tikaneny. Transition probability from the ground to the first-excited 2+ state of eveneven nuclides. Atom. Data. Nucl. Data. 78, 1 (2001).
A.E.L. Dieperink, O. Scholten, F. Iachello. Classical limit of the interacting-boson model. Phys. Rev. Lett. 44, 1747 (1980).
H.H. Kassim, F.I. Sharrad. Negative parity low-spin states of even-odd 187−197Pt isotopes. Nucl. Phys. A 933, 1 (2015).
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