Abstract
The projected shell model (PSM) was employed to study the signature inversion of \({}^{160}\hbox {Tm}\) and \({}^{161}\hbox {Tm}\) isotopes. The Hamiltonian of these isotopes were constructed and solved to obtain the energy levels and the \(\gamma \)-ray transition energies. The rotational bands of the odd–odd \({}^{160}\hbox {Tm}\) and odd–even \({}^{161}\hbox {Tm}\) isotopes of thulium nucleus were constructed based on the \(\pi h\frac{11}{2} \otimes \upsilon i\frac{13}{2}\) Nilsson configuration to calculate the kinetic and dynamic moments of inertia, \(\gamma \)-ray transition energy (\(\Delta {I}=1\)) and the staggering parameter (S(I)). Yrast band with two signatures for both isotopes have been extracted and compared with the experimental data. The anomalous splitting and signature inversion occurred due to the quadruple deformation in both isotopes. Analysis of level staggering and signature inversion show that signature inversion for the \({}^{160}\hbox {Tm}\) isotope occurs at low spin region, while for the \({}^{161}\hbox {Tm}\) isotope, it occured in the intermediate spin region. As expected, zig-zag behaviour and phase transition, as well as signature of energy splitting are clearly indicated in figures showing variation of S(I) and \(\Delta E\) with spin. This behaviour is more visible for the odd–even \({}^{161}\hbox {Tm}\) isotope than for the odd–odd \({}^{160}\hbox {Tm}\) isotope. Good agreement between the calculated results and experimental data confirms the success of the PSM model.
Similar content being viewed by others
References
S G Nilsson, Dan. Mat. Fys. Medd. 29(16), 1 (1955)
Inger-Lena Lamm, Nucl. Phys. A 125, 504 (1969)
K Hara and S Iwasaki, Nucl. Phys. A 332, 61 (1979)
K Hara and S Iwasaki, Nucl. Phys. A 348, 200 (1980)
K Hara and S Iwasaki, Nucl. Phys. A 430, 175 (1984)
K Hara and Y Sun, Int. J. Mod. Phys. E 4(4), 637 (1991)
K Hara and Y Sun, Nucl. Phys. A 529(3), 445 (1991)
R Devi, B D Sehgal, S K Khosa and J A Sheikh, Phys. Rev. C 72, 064304-1 (2005)
B Slathia, R Devi and S K Khosa, Nucl. Phys. A 943, 39 (2015)
Y Sun and K Hara, Comput. Phys. Commun. 104, 245 (1997)
K Hara and Y Sun, Nucl. Phys. A 537, 77 (1992)
B Slathia, R Devi and S K Khosa, Ind. J. Phys. 90, 1165 (2016)
H Drost, W Weiss and G Weyer, Nucl. Phys. A 172, 348 (1971)
U Birkental et al, Nucl. Phys. A 555, 643 (1993)
R Devi, B D Sehgal and S K Khosa, Pramana – J. Phys. 67(3), 467 (2006)
M Mahmoud, Turk. J. Phys. 33, 333 (2009)
A Ibanez-Sandova, M E Ortiz and V Velazquez, Phys. Rev. C 83, 034308-1 (2011)
A Mita, Ashok Kumar Jain, Alpana Goel and Balraj Singh, Pramana – J. Phys. 53(3), 463 (1999)
J Y Zeng, S X Liu, Y A Lei and L Yu, Phys. Rev. C 63, 024305-1 (2001)
Ali Khalaf, Madiha Okasha and Essam Ragheb, Aust. J. Basic Appl. Sci. 10(16), 192 (2016)
M Shahriarie, S Mohammadi and Z Firouzi, J. Kor. Phys. Soc. 75, L1 (2019)
S Iwasaki and K Hara, Prog. Theor. Phys. 68(5), 1782 (1982)
Y -X Liu et al, Nucl. Phys. A 858, 11 (2011)
L M Chen and R S Guo, Chin. J. Phys. 47, 788 (2009)
P Möller, A J Sierk, T Ichikawa and H Sagawa, At. Data Nucl. Data Tables 109–110, 1 (2016)
B Slathia, R Devi and S K Khosa, Ind. J. Phys. 90, 1165 (2016)
N Yoshida, H Sagawa and J Otsuka, Nucl. Phys. A 567, 17 (1994)
A Goel and A K Jain, Pramana – J. Phys. 46, 51 (1996)
K Lagergren et al, Phys. Rev. C 72, 057303-1 (2005)
C Teal et al, Phys. Rev. C 78, 017305-1 ( 2008)
Sun Liang et al, Chin. Phys. Lett. 25, 1996 (2008)
J A Sheikh, G H Bhat, Y Su, G B Vakil and R Palit, Phys. Rev. C 77, 034313-1 (2008)
R Bengtsson, H Frisk and F R May, Nucl. Phys. A 415, 189 (1984)
P Verma et al, Nucl. Phys. A 918, 1 (2013)
K Hara, Nucl. Phys. A 557, 449c (1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pahlavani, M.R., Teymoori, M. Description of energy spectrum and signature inversion for \({}^{160}\hbox {Tm}\) and \({}^{161}\hbox {Tm}\) isotopes using the projected shell model. Pramana - J Phys 97, 67 (2023). https://doi.org/10.1007/s12043-023-02545-w
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12043-023-02545-w