Systematic evaluation of reduced electric quadruple transition probabilities B(E2), provides critical insights in studying nuclear structural properties. The B(E2) for the gamma transition 0+ to 2+, 2+ to 4+, 4+ to 6+, and finally 6+ to 8+ excited states for the even-even 106-116Pd isotopes have been computed in our present study by means of the global best fit (GBF) method. Then, the quadruple moment, Q0 and the deformation parameter, β for low-lying quadruple collective states of the Pd nuclei with the even neutron numbers, N = 60 - 70 have also been calculated. The deviation of the spherical nuclear structure of the even-even 106-116Pd has been studied using those key parameters, namely, quadruple moment and deformation parameter. Moreover, the variable moment of inertia (VMI) model was employed to elucidate collective rotational behavior of Pd isotopes. Lastly, the estimated values of the first 4+ to 2+ excited states energy ratios of these even-even 106-116Pd isotopes exhibit excellent concordance with experimental data, which manifests γ-unstable O(6) symmetrical behavior during the transitions.
References
[1]
Sorlin, O. and Porquet, M.G. (2008) Nuclear Magic Numbers: New Features Far from Stability. ProgressinParticleandNuclearPhysics, 61, 602-673. https://doi.org/10.1016/j.ppnp.2008.05.001
[2]
Watanabe, H., Lorusso, G., Nishimura, S., Xu, Z.Y., Sumikama, T., S？derstr？m, P.-., et al. (2013) Isomers in 128Pd and 126Pd: Evidence for a Robust Shell Closure at the Neutron Magic Number 82 in Exotic Palladium Isotopes. PhysicalReviewLetters, 111, Article ID: 152501. https://doi.org/10.1103/physrevlett.111.152501
[3]
Kumar, K. and Baranger, M. (1968) Nuclear Deformations in the Pairing-Plus-Quadrupole Model: (III). Static Nuclear Shapes in the Rare-Earth Region. NuclearPhysicsA, 110, 529-554. https://doi.org/10.1016/0375-9474(68)90371-0
[4]
Prados-Estévez, F.M., Peters, E.E., Chakraborty, A., Mynk, M.G., Bandyopadhyay, D., Boukharouba, N., et al. (2017) Collective quadrupole behavior in 106Pd. PhysicalReviewC, 95, Article ID: 034328. https://doi.org/10.1103/physrevc.95.034328
[5]
Islam, T., Amin, R., Alam, M.A. and Islam, J. (2020) Upward Transition Probabilities B(E2)↑ Properties Study of Even-Even 104-114Ru Nuclei. WorldJournalofNuclearScienceandTechnology, 10, 129-137. https://doi.org/10.4236/wjnst.2020.103012
[6]
Hua, H., Wu, C.Y., Cline, D., Hayes, A.B., Teng, R., Clark, R.M., et al. (2003) The Sudden Onset of the Band Crossing for the Aligned πg9/2 Orbitals: A Possible Transition of a Triaxial Shape from Prolate to Oblate? PhysicsLettersB, 562, 201-207. https://doi.org/10.1016/s0370-2693(03)00569-0
[7]
Zhang X.Q., et al. (2001) Observation of a vh 1 1/2 Pair Alignment in Neutron-Rich 118Pd. Physical Review C, 63, Article ID: 027302.
[8]
Butler-Moore, K., et al. (1999) High-Spin States in Neutron-Rich Even-Even Pd Iso-topes. Journal of Physics G: Nuclear and Particle Physics, 25, Article 2253.
[9]
Krücken, R., Asztalos, S.J., Clark, R.M., Deleplanque, M.A., Diamond, R.M., Fallon, P., et al. (2001) Spectroscopy of 112Pd Using Heavy-Ion-Induced Fission. TheEuropeanPhysicalJournalA, 10, 151-155. https://doi.org/10.1007/s100500170127
[10]
Wang, Y.B. and Rissanen, J. (2014) Collective Properties of Neutron-Rich Ru, Pd, and Cd Isotopes. HyperfineInteractions, 223, 167-174. https://doi.org/10.1007/s10751-012-0615-6
[11]
Abdullah, H.Y., Hossain, I., Ahmed, I.M., Ahmad, S.T., Kasmin, M.K., Saeed, M.A., et al. (2013) Electromagnetic Reduced Transition Properties of Even-Even 104-112Cd Isotopes. IndianJournalofPhysics, 87, 571-574. https://doi.org/10.1007/s12648-013-0257-9
[12]
Hossain, I., et al. (2015) Yrast States and B (E2) Values of Even 100-102Ru Isotopes Using Interacting Boson Model (IBM-1). Chiang Mai Journal of Science, 42, 996-1004.
[13]
Hossain, I., Saeed, M.A., Ghani, N.N.A.M.B., Sa’adeh, H., Hussein, M. and Abdullah, H.Y. (2014) Electromagnetic Reduced Transition Properties of the Ground State Band of Even-Even 102-106Pd Isotopes by Means of Interacting Boson Model-I. IndianJournalofPhysics, 88, 5-9. https://doi.org/10.1007/s12648-013-0374-5
[14]
Hossain, I., Abdullah, H.Y., Ahmad, I.M. and Saeed, M.A. (2014) B (E2) Value of Even-Even 108-112Pd Isotopes by Interacting Boson Model-1. ChinesePhysicsC, 38, Article ID: 024103. https://doi.org/10.1088/1674-1137/38/2/024103
[15]
Hasan, M.M., Tabussum, M., Roy, P.K., Tasnim, M.M., Sakib, K.N. and Islam, J. (2022) Nuclear Properties Exploration for the Even-Even Nuclei. ResearchTrendsandChallengesinPhysicalScience, 7, 52-60. https://doi.org/10.9734/bpi/rtcps/v7/15224d
[16]
Venkova, T. and Andrejtscheff, W. (1981) Transition Strengths B(E2) in the Yrast Bands of Doubly Even Nuclei. AtomicDataandNuclearDataTables, 26, 93-136. https://doi.org/10.1016/0092-640x(81)90001-2
[17]
Weidenmuller, H.A. (2004) The Ratio R4/2 of the Excitation Energies of the First 4+ and 2+ Levels and Assumes. World Scientific.
[18]
Hossain, I., Abdullah, H.Y., Ahmed, I.M. and Islam, J. (2013) Yrast State Band of Even 120-130Te Isotopes under the Framework of Interacting Boson Model-1. arXiv: 1310.2721.
[19]
Islam, J., Bhuyan, M.D.I., Rahman, O. and Rahman, M.H. (2014) B(E2) Value of 82Se, 84Kr and 86Sr Isotones for N = 48 by Using Interacting Boson Model-1. European Scientific Journal, 10, 470-474.
[20]
Mariscotti, M.A.J., Scharff-Goldhaber, G. and Buck, B. (1969) Phenomenological Analysis of Ground-State Bands in Even-Even Nuclei. PhysicalReview, 178, 1864-1886. https://doi.org/10.1103/physrev.178.1864
[21]
Johnson, A., Ryde, H. and Hjorth, S.A. (1972) Nuclear Moment of Inertia at High Rotational Frequencies. NuclearPhysicsA, 179, 753-768. https://doi.org/10.1016/0375-9474(72)90617-3
[22]
Sorensen, R.A. (1973) Nuclear Moment of Inertia at High Spin. ReviewsofModernPhysics, 45, 353-377. https://doi.org/10.1103/revmodphys.45.353
[23]
Raman, S., Nestor, C.W. and Tikkanen, P. (2001) Transition Probability from the Ground to the First-Excited 2+ State of Even-Even Nuclides. AtomicDataandNuclearDataTables, 78, 1-128. https://doi.org/10.1006/adnd.2001.0858
Rowe, D.J. (2010) Nuclear Collective Motion: models and Theory. World Scientific. https://doi.org/10.1142/9789812790668
[26]
Grodzins, L. (1962) The Uniform Behaviour of Electric Quadrupole Transition Probabilities from First 2+ States in Even-Even Nuclei. PhysicsLetters, 2, 88-91. https://doi.org/10.1016/0031-9163(62)90162-2
[27]
Raman, S., Nestor, C.W. and Bhatt, K.H. (1988) Systematics of B(E2; →) Values for Even-Even Nuclei. PhysicalReviewC, 37, 805-822. https://doi.org/10.1103/physrevc.37.805
[28]
Raman, S., Nestor, C.W., Kahane, S. and Bhatt, K.H. (1989) Predictions of B(E2; →) Values for Even-Even Nuclei. AtomicDataandNuclearDataTables, 42, 1-54. https://doi.org/10.1016/0092-640x(89)90031-4
[29]
Raman, S., Malarkey, C.H., Milner, W.T., Nestor, C.W. and Stelson, P.H. (1987) Transition Probability, B(E2)↑, from the Ground to the First-Excited 2+ State of Even-Even Nuclides. AtomicDataandNuclearDataTables, 36, 1-96. https://doi.org/10.1016/0092-640x(87)90016-7
[30]
Raman, S., Nestor, C.W., Kahane, S. and Bhatt, K.H. (1991) Low-Lying Collective Quadrupole and Octupole Strengths in Even-Even Nuclei. Physical Review C, 43, 556-581. https://doi.org/10.1103/physrevc.43.556
[31]
Roy, R. and Nigam, B. (2005) Nuclear Moments. In: Nuclear Physics Theory and Experiment (2nd Edition), New Age international (P) Limited, 271-274.
[32]
John, L. (2001) Nuclear Physics (Principles and Application). John Willey & Sons.
[33]
De Frenne, D. and Negret, A. (2008) Nuclear Data Sheets for A = 106. NuclearDataSheets, 109, 943-1102. https://doi.org/10.1016/j.nds.2008.03.002
[34]
Blachot, J. (2000) Nuclear Data Sheets for A = 108. NuclearDataSheets, 91, 135-296. https://doi.org/10.1006/ndsh.2000.0017
[35]
De Frenne, D. and Jacobs, E. (2000) Nuclear Data Sheets for A = 110. NuclearDataSheets, 89, 481-640. https://doi.org/10.1006/ndsh.2000.0004
[36]
Frenne, D.d. and Jacobs, E. (1996) Nuclear Data Sheets for A = 112. NuclearDataSheets, 79, 639-758. https://doi.org/10.1006/ndsh.1996.0015
[37]
Blachot, J. (2012) Nuclear Data Sheets for A = 114. NuclearDataSheets, 113, 515-714. https://doi.org/10.1016/j.nds.2012.02.002
[38]
Blachot, J. (2010) Nuclear Data Sheets for A = 116. NuclearDataSheets, 111, 717-895. https://doi.org/10.1016/j.nds.2010.03.002
[39]
Bharti, A. and Khosa, S.K. (1996) E2 Transition and Systematics of Even Mass Palladium Nuclei. PhysicalReviewC, 53, 2528-2531. https://doi.org/10.1103/physrevc.53.2528
[40]
Bonatsos, D., Martinou, A., Peroulis, S.K., Mertzimekis, T.J. and Minkov, N. (2024) Prolate-Oblate Shape Transitions and O(6) Symmetry in Even-Even Nuclei: A Theoretical Overview. PhysicaScripta, 99, Article ID: 062003. https://doi.org/10.1088/1402-4896/ad4186
[41]
Hossain, I., Hussein, M., Mansour, S. and Islam, J. (2014) Back-Bending Phenomena in Even-Even 110-118Te Isotopes. JournaloftheNationalScienceFoundationofSriLanka, 42, 335-339. https://doi.org/10.4038/jnsfsr.v42i4.7732
[42]
Ahmed, I.M., Abdullah, H.Y., Ahmad, S.T., Hossain, I., Kasmin, M.K., Saeed, M.A., et al. (2012) The Evolution Properties of Even-Even 100-110Pd Nuclei. InternationalJournalofModernPhysicsE, 21, Article ID: 1250101. https://doi.org/10.1142/s0218301312501017
[43]
Bonatsos, D., Martinou, A., Peroulis, S.K., Petrellis, D., Vasileiou, P., Mertzimekis, T.J., et al. (2025) Triaxial Shapes in Even-Even Nuclei: A Theoretical Overview. Atoms, 13, Article 47. https://doi.org/10.3390/atoms13060047
[44]
Devi, V. (2013) Structure and Odd-Even Staggering of Mo, Ru, and Pd Even-Even Nuclei in the Framework of IBM-1. TurkishJournalofPhysics, 37, 330-347. https://doi.org/10.3906/fiz-1301-4
[45]
Klamra, W., Bialkowski, J., Hildingsson, L., Jerrestam, D., Johnson, A., Kownacki, J., et al. (1984) Experimental Moments of Inertia in Pd and Cd Isotopes and Their Interpretation within the Extended Nilsson-Strutinsky Model. NuclearPhysicsA, 431, 367-380. https://doi.org/10.1016/0375-9474(84)90180-5
[46]
Cline, D. (1986) Nuclear Shapes Studied by Coulomb Excitation. AnnualReviewofNuclearandParticleScience, 36, 683-716. https://doi.org/10.1146/annurev.ns.36.120186.003343
