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Multiple valence-space and core-excited band terminations in Ho and Er isotopes

E. S. Paul ^1,*, J. Simpson ^2,†, M. A. Riley ^3,‡, J. S. Baron³, P. J. T. Hampson¹, X. Wang ^3,§, A. Aguilar ^3,∥, D. E. Appelbe ², A. D. Ayangeakaa ^4,5 et al.

A. J. Boston¹, H. C. Boston ¹, D. B. Campbell^3,∥, M. P. Carpenter⁶, C. J. Chiara ^6,7,¶, R. M. Clark^8,**, M. Cromaz⁸, I. G. Darby ^9,††, A. O. Evans ¹, P. Fallon ⁸, U. Garg ¹⁰, A. Görgen^8,‡‡, D. J. Hartley ¹¹, C. R. Hoffman ⁶, R. V. F. Janssens ^4,5, D. T. Joss ^2,§§, D. S. Judson ¹, F. G. Kondev ⁶, K. Lagergren ³, T. Lauritsen ⁶, I. Y. Lee ⁸, J. T. Matta ^10,∥∥, S. L. Miller³, M. Mustafa¹, P. J. Nolan ¹, J. Ollier ², M. Petri ^8,¶¶, A. Pipidis ³, D. C. Radford ¹², J. M. Rees ¹, J. P. Revill^1,***, L. L. Riedinger ⁹, J. F. Sharpey-Schafer ¹³, C. M. Sullivan ¹, C. Teal ³, J. Thomson¹, P. J. Twin¹, C. Unsworth ^1,†††, D. Ward^8,**, S. Zhu^6,**, J. Gellanki ^14,‡‡‡, and I. Ragnarsson ¹⁴

¹Department of Physics, University of Liverpool, Liverpool L69 7ZE, United Kingdom
²STFC Daresbury Laboratory, Daresbury, Warrington WA4 4AD, United Kingdom
³Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
⁴Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599, USA
⁵Triangle Universities Nuclear Laboratory, Duke University, Durham, North Carolina 27708, USA
⁶Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
⁷Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA
⁸Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁹Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
¹⁰Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
¹¹Department of Physics, U.S. Naval Academy, Annapolis, Maryland 21402, USA
¹²Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA
¹³Department of Physics, University of Zululand, P/B X1001, KwaDlangezwa, 3886, South Africa
¹⁴Division of Mathematical Physics, LTH, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden

^*Contact author: esp@ns.ph.liv.ac.uk
^†Contact author: john.simpson@stfc.ac.uk
^‡Contact author: mriley@admin.fsu.edu
^§Present address: Department of Physics, California Polytechnic State University, San Luis Obispo, California 93407, USA.
^∥Present address: Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, California 94550-9234, USA.
^¶Present address: U.S. Army Combat Capabilities Development Command Army Research Laboratory, Adelphi, Maryland 20783, USA.
^**Deceased.
^††Present address: United Kingdom National Nuclear Laboratory, Birchwood Park, Warrington, WA3 6AE, United Kingdom.
^‡‡Present address: Department of Physics, University of Oslo, N-0316 Oslo, Norway.
^§§Present address: Department of Physics, University of Liverpool, Liverpool L69 7ZE, United Kingdom.
^∥∥Present address: Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA.
^¶¶Present address: School of Physics, Engineering and Technology, University of York, Heslington, York YO10 5DD, United Kingdom.
^***Present address: Applied Nuclear Physics Ltd, 41A Main Street, Cockermouth CA13 9JS, United Kingdom.
^†††Present address: STFC Daresbury Laboratory, Daresbury, Warrington WA4 4AD, United Kingdom.
^‡‡‡Present Address: Department of Physics and Electronics, Hansraj College, University of Delhi 110007, India.

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Phys. Rev. C 113, 064322 – Published 30 June, 2026

DOI: https://doi.org/10.1103/393p-ghvk

Abstract

High-spin structures of holmium ( $Z = 67$ ) and erbium ( $Z = 68$ ) isotopes are presented near mass 160, a region where collective and single-particle modes of excitation compete in the generation of angular momentum at the highest experimentally attainable spins in atomic nuclei. The level schemes of the ${}^{156, 157, 158}{Ho}$ isotopes have been significantly extended, reaching spins in the $40 ℏ$ to $55 ℏ$ range, through multiple experiments utilizing the Gammasphere spectrometer. In particular, several new noncollective band-terminating states are reported for these nuclei. The nature of these states, including both valence-space terminations and core-excited oblateconfigurations, is discussed in terms of proton particle-hole (p-h) excitations across the semimagic $Z = 64$ shell closure. Cranked-Nilsson–Strutinsky (CNS) calculations have been used to interpret the nature of these noncollective states. The corresponding terminating states in ${}^{154 - 159}{Er}$ are also included, providing a systematic description of band termination in this mass region. In addition, three weak rotational structures have been assigned to ${}^{157}{Ho}$ at the highest spins. These collective bands are proposed to be based on a triaxial strongly deformed nuclear shape, involving neutron p-h excitations across the $N = 82$ shell gap.

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References (60)

M. A. Riley, J. Simpson, and E. S. Paul, High resolution gamma-ray spectroscopy and the fascinating angular momentum realm of the atomic nucleus, Phys. Scr. 91, 123002 (2016).
J. Simpson, M. A. Riley, A. Pipidis, E. S. Paul, X. Wang, P. J. Nolan, J. F. Sharpey-Schafer, A. Aguilar, D. E. Appelbe, A. D. Ayangeakaa, et al., Evolution of structure and shapes in ${}^{158}{Er}$ to ultrahigh spin, Phys. Rev. C 107, 054305 (2023).
I. Ragnarsson, A. Kardan, B. G. Carlsson, E. S. Paul, C. M. Petrache, M. A. Riley, J. F. Sharpey-Schafer, and J. Simpson, Band terminations and maximum spin values with up to 18 aligned particles (and holes) in the $Z, N = 50$ to 82 shells, Phys. Rev. C 110, 034313 (2024).
E. S. Paul, S. V. Rigby, M. A. Riley, J. Simpson, D. E. Appelbe, D. B. Campbell, P. T. W. Choy, R. M. Clark, M. Cromaz, A. O. Evans, et al., Loss of collectivity in the transitional ${}^{156}{Er}$ nucleus at high spin, Phys. Rev. C 79044324 (2009).
S. J. Gale, J. Simpson, M. A. Riley, J. F. Sharpey-Schafer, E. S. Paul, M. A. Bentley, A. M. Bruce, R. Chapman, R. M. Clark, S. Clarke, et al., Band termination spectroscopy in ${}^{157}{Er}$ J. Phys. G: Nucl. Part. Phys. 21, 193 (1995).
M. Mustafa, J. Ollier, J. Simpson, M. A. Riley, E. S. Paul, X. Wang, A. Aguilar, M. P. Carpenter, I. G. Darby, D. J. Hartley, et al., Diverse collective excitations in ${}^{159}{Er}$ up to high spin, Phys. Rev. C 84, 054320 (2011).
J. M. Rees, E. S. Paul, J. Simpson, M. A. Riley, A. D. Ayangeakaa, M. P. Carpenter, C. J. Chiara, U. Garg, P. Hampson, D. J. Hartley, et al., High-spin terminating states in the $N = 88 {}^{155}{Ho}$ and ${}^{156}{Er}$ isotones, Phys. Rev. C 91, 054301 (2015).
D. C. Radford, H. R. Andrews, G. C. Ball, D. Horn, D. Ward, F. Banville, S. Flibotte, S. Monaro, S. Pilotte, P. Taras, et al., Multiple band structure and band termination in ${}^{157}{Ho}$ towards complete high-spin spectroscopy, Nucl. Phys. A 545, 665 (1992).
A. O. Evans, E. S. Paul, J. Simpson, M. A. Riley, D. E. Appelbe, D. B. Campbell, P. T. W. Choy, R. M. Clark, M. Cromaz, P. Fallon, et al., High-spin structure beyond band termination in ${}^{157}{Er}$ , Phys. Rev. Lett. 92, 252502 (2004).
A. O. Evans, E. S. Paul, J. Simpson, M. A. Riley, D. E. Appelbe, D. B. Campbell, P. T. W. Choy, R. M. Clark, M. Cromaz, P. Fallon, et al., High-spin structure in ${}^{157}{Er}$ up to and above band termination, Phys. Rev. C 73, 064303 (2006).
E. S. Paul, P. J. Twin, A. O. Evans, A. Pipidis, M. A. Riley, J. Simpson, D. E. Appelbe, D. B. Campbell, P. T. W. Choy, R. M. Clark, et al., Return of collective rotation in ${}^{157}{Er}$ and ${}^{158}{Er}$ at ultrahigh spin, Phys. Rev. Lett. 98, 012501 (2007).
X. Wang, M. A. Riley, J. Simpson, E. S. Paul, J. Ollier, R. V. F. Janssens, A. D. Ayangeakaa, H. C. Boston, M. P. Carpenter, C. J. Chiara, et al., Quadrupole moments of collective structures up to spin $\sim 65 ℏ$ in ${}^{157}{Er}$ and ${}^{158}{Er}$ : A challenge for understanding triaxiality in nuclei, Phys. Lett. B 702, 127 (2011).
I.-Y. Lee, The GAMMASPHERE, Nucl. Phys. A 520, c641 (1990).
R. Janssens and F. Stephens, New physics opportunities at Gammasphere, Nucl. Phys. News 6, 9 (1996).
D. C. Radford, ESCL8R and LEVIT8R: Software for interactive graphical analysis of HPGe coincidence data sets, Nucl. Instrum. Methods Phys. Res., Sect. A 361, 297 (1995).
D. C. Radford, M. Cromaz, and C. J. Beyer, in AIP Conference Proceedings (AIP, Gatlinburg, 1999).
D. C. Radford, Background subtraction from in-beam HPGe coincidence data sets, Nucl. Instrum. Methods Phys. Res., Sect. A 361, 306 (1995).
B. Crowell, M. P. Carpenter, R. G. Henry, R. V. F. Janssens, T. L. Khoo, T. Lauritsen, and D. Nisius, Background subtraction for high-fold gamma-ray coincidence data, Nucl. Instrum. Methods Phys. Res., Sect. A 355, 575 (1995).
K. S. Krane, R. M. Steffen, and R. M. Wheeler, Directional correlations of gamma radiations emitted from nuclear states oriented by nuclear reactions or cryogenic methods, At. Data Nucl. Data Tables 11, 351 (1973).
L. P. Ekström and A. Nordlund, Gamma-gamma correlations with detector arrays, Nucl. Instrum. Methods Phys. Res., Sect. A 313, 421 (1992).
P. J. T. Hampson, High-spin spectroscopic studies of ${}^{156}{Ho}$ : shape changes and band termination, Ph.D. thesis, The University of Liverpool, 2014.
D. M. Cullen, C.-H. Yu, D. Cline, M. Simon, D. C. Radford, M. A. Riley, and J. Simpson, High-spin states and the first signs of band termination in ${}^{156}{Ho}$ , Phys. Rev. C 57, 2170 (1998).
R. Neugart, E. Arnold, W. Borchers, W. Neu, G. Ulm, and K. Wendt, in AIP Conference Proceedings (AIP, 1987), Vol. 164, pp. 126–135.
C. Reich, Nuclear Data Sheets for $A = 156$ , Nucl. Data Sheets 113, 2537 (2012).
J. S. Baron, Exotic nuclear deformation and the evolution of nuclear structure with angular momentum and excitation energy in ${}^{157}{Ho}, {}^{166}{Er}$ , and ${}^{169, 170}{Yb}$ , Ph.D. thesis, Florida State University, 2018, https://repository.lib.fsu.edu/islandora/object/fsu.
J. Gascon, C. H. Yu, G. B. Hagemann, M. C. Carpenter, J. M. Espino, Y. Iwata, T. Komatsubara, J. Nyberg, S. Ogaza, G. Sletten, et al., Configuration-dependent transition rates in ${}^{157}{Ho}$ , Nucl. Phys. A 513, 344 (1990).
X. Wang, M. A. Riley, J. Simpson, E. S. Paul, R. V. F. Janssens, A. D. Ayangeakaa, H. C. Boston, M. P. Carpenter, C. J. Chiara, U. Garg, et al., Collective structures up to spin $\sim 65 ℏ$ in the $N = 90$ isotones ${}^{158}{Er}$ and ${}^{157}{Ho}$ , J. Phys.: Conf. Ser. 381, 012065 (2012).
N. Nica, Nuclear data sheets for $a$ = 158, Nucl. Data Sheets 141, 1 (2017).
J. Lu, Y. Liu, X. Wu, Y. Ma, G. Zhao, H. Sun, J. Huo, S. Wen, G. Li, and C. Yang, High-spin states in doubly odd ${}^{158}{Ho}$ , Phys. Rev. C 59, 3461 (1999).
Y. Liu, Y. Ma, H. Yang, and S. Zhou, Systematic features of signature inversion of ${(h_{11 / 2})}_{p} {(i_{13 / 2})}_{n}$ bands in doubly odd nuclei around $A \sim 160$ , Phys. Rev. C 52, 2514 (1995).
C. H. Yu, D. M. Cullen, D. Cline, M. Simon, D. C. Radford, I. Y. Lee, and A. O. Macchiavelli, Gammasphere Physics-Proceedings Of The Workshop, edited by M. A. Deleplanque, O. Augusto, Macchiavelli, and I. Y. Lee (World Scientific, 1996), pp. 254–265.
L. Fortunato, Solutions of the Bohr Hamiltonian, a compendium, Eur. Phys. J. A 26, 1 (2005).
G. Andersson, S. Larsson, G. Leander, P. Möller, S. Nilsson, I. Ragnarsson, S. Åberg, R. Bengtsson, J. Dudek, B. Nerlo-Pomorska, et al., Nuclear shell structure at very high angular momentum, Nucl. Phys. A 268, 205 (1976).
A. Afanasjev, D. Fossan, G. Lane, and I. Ragnarsson, Termination of rotational bands: Disappearance of quantum many-body collectivity, Phys. Rep. 322, 1 (1999).
B. G. Carlsson and I. Ragnarsson, Calculating the nuclear mass in the very high angular momentum regime, Phys. Rev. C 74, 011302(R) (2006).
T. Bengtsson and I. Ragnarsson, Rotational bands and particle-hole excitations at very high spin, Nucl. Phys. A 436, 14 (1985).
S. G. Nilsson and I. Ragnarsson, Shapes and Shells in Nuclear Structure (Cambridge University Press, 1995).
C. Schück, M. A. Deleplanque, R. M. Diamond, F. S. Stephens, and J. Dudek, High-spin states in ${}^{154}{Er}$ and parallel proton- and neutron-core breaking, Nucl. Phys. A 496, 385 (1989).
N. Nica, G. Duchêne, V. E. Iacob, J. Dudek, F. A. Beck, T. Byrski, D. Curien, G. de France, B. Haas, B. Kharraja, et al., High-spin states in ${}^{155}{Er}$ , Phys. Rev. C 64, 034313 (2001).
R. Bengtsson and S. Frauendorf, Quasiparticle spectra near the yrast line, Nucl. Phys. A 327, 139 (1979).
S. M. Harris, Higher order corrections to the cranking model, Phys. Rev. 138, B509 (1965).
J. Simpson, D. V. Elenkov, P. D. Forsyth, D. Howe, B. M. Nyako, M. A. Riley, J. F. Sharpey-Schafer, B. Herskind, A. Holm, and P. O. Tjom, The strong interaction strength of the first proton alignment in ${}^{157}{Ho}$ , J. Phys. G: Nucl. Phys. 12, L67 (1986).
M. A. Riley, J. Simpson, J. F. Sharpey-Schafer, J. R. Cresswell, H. W. Cranmer-Gordon, P. D. Forsyth, D. Howe, A. H. Nelson, P. J. Nolan, P. J. Smith, et al., Near yrast discrete line gamma-ray spectroscopy in ${}^{156}{Dy}$ up to spin $40 ℏ$ , Nucl. Phys. A 486, 456 (1988).
W. C. Ma, R. V. F. Janssens, T. L. Khoo, I. Ragnarsson, M. A. Riley, M. P. Carpenter, J. R. Terry, J. P. Zhang, I. Ahmad, P. Bhattacharyya, et al., Competition between terminating and collective structures above spin $40 ℏ$ in ${}^{154}{Dy}$ , Phys. Rev. C 65, 034312 (2002).
J. Simpson, M. A. Riley, S. J. Gale, J. F. Sharpey-Schafer, M. A. Bentley, A. M. Bruce, R. Chapman, R. M. Clark, S. Clarke, J. Copnell, et al., Single particle excitations and properties of multiple band terminations near spin $50 ℏ$ in ${}^{158}{Er}$ , Phys. Lett. B 327, 187 (1994).
J. Ollier, J. Simpson, M. A. Riley, E. S. Paul, X. Wang, A. Aguilar, M. P. Carpenter, I. G. Darby, D. J. Hartley, R. V. F. Janssens, et al., Structure changes in ${}^{160}{Er}$ from low to ultrahigh spin, Phys. Rev. C 83, 044309 (2011).
I. Ragnarsson, Z. Xing, T. Bengtsson, and M. A. Riley, Properties of terminating bands in nuclei, Phys. Scr. 34, 651 (1986).
J. Simpson, M. A. Riley, J. R. Cresswell, P. D. Forsyth, D. Howe, B. M. Nyakó, J. F. Sharpey-Schafer, J. Bacelar, J. D. Garrett, G. B. Hagemann, et al., Observation of a prolate-to-oblate shape change near spin $40 ℏ$ in ${}^{158}{Er}$ , Phys. Rev. Lett. 53, 648 (1984).
F. G. Kondev, M. A. Riley, J. Simpson, R. V. F. Janssens, A. V. Afanasjev, I. Ragnarsson, T. B. Brown, D. J. Hartley, M. P. Carpenter, P. Fallon, et al., Exploring the $I = 50 − 60 ℏ$ domain: Collective and terminating structures in ${}^{156}{Dy}, {}^{159}{Er}$ and ${}^{160}{Er}$ , J. Phys. G 25, 897 (1999).
T. Bengtsson and I. Ragnarsson, Shape changes, band crossings and band terminations in the very high spin region of $A = 150 − 160$ nuclei, Phys. Scr. T5, 165 (1983).
J. Dudek and W. Nazarewicz, Shape evolution in the transitional gadolinium, dysprosium, erbium, and ytterbium nuclei, Phys. Rev. C 31, 298 (1985).
J. P. Revill, E. S. Paul, X. Wang, M. A. Riley, J. Simpson, R. V. F. Janssens, J. Ollier, A. J. Boston, M. P. Carpenter, C. J. Chiara, et al., Quadrupole moments of coexisting collective shapes at high spin in ${}^{154}{Er}$ , Phys. Rev. C 88, 031304(R) (2013).
Y. Shi, J. Dobaczewski, S. Frauendorf, W. Nazarewicz, J. C. Pei, F. R. Xu, and N. Nikolov, Self-consistent tilted-axis-cranking study of triaxial strongly deformed bands in ${}^{158}{Er}$ at ultrahigh spin, Phys. Rev. Lett. 108, 092501 (2012).
Y. Shi, C. L. Zhang, J. Dobaczewski, and W. Nazarewicz, Kerman-Onishi conditions in self-consistent tilted-axis-cranking mean-field calculations, Phys. Rev. C 88, 034311 (2013).
A. Kardan, I. Ragnarsson, H. Miri-Hakimabad, and L. Rafat-Motevali, Interpretation of the large-deformation high-spin bands in select $A = 158 − 168$ nuclei, Phys. Rev. C 86, 014309 (2012).
A. V. Afanasjev, Y. Shi, and W. Nazarewicz, Description of ${}^{158}{Er}$ at ultrahigh spin in nuclear density functional theory, Phys. Rev. C 86, 031304(R) (2012).
C. Teal, K. Lagergren, A. Aguilar, D. J. Hartley, M. A. Riley, J. Simpson, M. P. Carpenter, U. Garg, R. V. F. Janssens, D. T. Joss, et al., Triaxial strongly deformed bands in ${}^{160, 161}{Tm}$ , Phys. Rev. C 78, 017305 (2008).
I. Ragnarsson, How deformed are the TSD bands in odd Lu isotopes? Phys. Scr. 92, 124004 (2017).
I. Y. Lee, M. A. Deleplanque, and K. Vetter, Developments in large gamma-ray detector arrays, Rep. Prog. Phys. 66, 1095 (2003).
W. Korten, A. Atac, D. Beaumel, P. Bednarczyk, M. A. Bentley, G. Benzoni, A. Boston, A. Bracco, J. Cederkäll, B. Cederwall, et al., Physics opportunities with the advanced gamma tracking array: AGATA, Eur. Phys. J. A 56, 137 (2020).

Phys. Rev. C 113, 064322– Published 30 June, 2026

Vol. 113, Iss. 6 — June 2026

Received 9 December 2025
Accepted 15 May 2026

DOI: https://doi.org/10.1103/393p-ghvk

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Multiple valence-space and core-excited band terminations in Ho and Er isotopes

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