- Open Access
Reduction in Nuclear Size and Quadrupole Deformation of High-Spin Isomers of
Phys. Rev. Lett. 134, 252501 – Published 26 June, 2025
DOI: https://doi.org/10.1103/m35x-mw7z
Abstract
We employed laser spectroscopy of atomic transitions to measure the nuclear charge radii and electromagnetic properties of the high-spin isomeric states in neutron-rich indium isotopes () near the closed proton and neutron shells at and . Our data reveal a reduction in the nuclear charge radius and intrinsic quadrupole moment when protons and neutrons are fully aligned in , to form the high spin isomer. Such a reduction is not observed in , where more complex configurations can be formed by the existence of four neutron holes. These observations are not consistently described by nuclear theory.
Physics Subject Headings (PhySH)
See Also
Variations in the charge radii of indium isotopes between and 82
Article Text
Supplemental Material
References (90)
- G. D. Dracoulis, P. M. Walker, and F. G. Kondev, Review of metastable states in heavy nuclei, Rep. Prog. Phys. 79, 076301 (2016).
- P. M. Walker, High-spin isomers: Structure and applications, Nucl. Phys. A834, 22c (2010).
- P. M. Walker and Z. Podolyák, Nuclear isomers, in Handbook of Nuclear Physics, edited by I. Tanihata, H. Toki, and T. Kajino (Springer Nature, Singapore, 2020), pp. 1–37.
- A. K. Jain, B. Maheshwari, and A. Goel, Nuclear Isomers: A Primer (Springer Nature, 2021).
- P. Walker and G. Dracoulis, Energy traps in atomic nuclei, Nature (London) 399, 35 (1999).
- A. Aprahamian and Y. Sun, Long live isomer research, Nat. Phys. 1, 81 (2005).
- J. Pedersen, B. B. Back, F. M. Bernthal, S. Bjørnholm, J. Borggreen, O. Christensen, F. Folkmann, B. Herskind, T. L. Khoo, M. Neiman, F. Pühlhofer, and G. Sletten, Island of high-spin isomers near , Phys. Rev. Lett. 39, 990 (1977).
- C. Yuan, Z. Liu, F. Xu, P. M. Walker, Z. Podolyák, C. Xu, Z. Z. Ren, B. Ding, M. L. Liu, X. Y. Liu, H. S. Xu, Y. H. Zhang, X. H. Zhou, and W. Zuo, Isomerism in the “south-east” of and a predicted neutron-decaying isomer in , Phys. Lett. B 762, 237 (2016).
- P. M. Walker, Nuclear isomers: Stepping stones to the unknown, AIP Conf. Proc. 819, 16 (2006).
- Y. Gangrsky, Laser spectroscopy of high spin isomers—a review, Hyperfine Interact. 171, 203 (2006).
- C. Thibault, F. Touchard, S. Büttgenbach, R. Klapisch, M. De Saint Simon, H. Duong, P. Jacquinot, P. Juncar, S. Liberman, P. Pillet, J. Pinard, J. Vialle, A. Pesnelle, and G. Huber, Hyperfine structure and isotope shift of the D2 line of and some of their isomers, Nucl. Phys. A367, 1 (1981).
- R. Moore, A. Bruce, P. Dendooven, J. Billowes, P. Campbell, A. Ezwam, K. Flanagan, D. Forest, J. Huikari, A. Jokinen, A. Nieminen, H. Thayer, G. Tungate, S. Zemlyanoi, and J. Äystö, Character of an isomer of , Phys. Lett. B 547, 200 (2002).
- M. L. Bissell, K. T. Flanagan, M. D. Gardner, M. Avgoulea, J. Billowes, P. Campbell, B. Cheal, T. Eronen, D. H. Forest, J. Huikari, A. Jokinen, I. D. Moore, A. Nieminen, H. Penttilä, S. Rinta-Antila, B. Tordoff, G. Tungate, and J. Äystö, On the decrease in charge radii of multi-quasi particle isomers, Phys. Lett. B 645, 330 (2007).
- M. Dasgupta, P. Walker, G. Dracoulis, A. Byrne, P. Regan, T. Kibédi, G. Lane, and K. Yeung, Yrast isomers, multi-quasiparticle states and blocking in and , Phys. Lett. B 328, 16 (1994).
- N. Boos et al., Nuclear properties of the exotic high-spin isomer from collinear laser spectroscopy, Phys. Rev. Lett. 72, 2689 (1994).
- H. Liu and F. Xu, Calculations of electric quadrupole moments and charge radii for high-K isomers, Sci. China Phys. Mech. Astron. 56, 2037 (2013).
- G. Yeandle, J. Billowes, P. Campbell, E. C. A. Cochrane, P. Dendooven, D. E. Evans, J. A. R. Griffith, J. Huikari, A. Jokinen, I. D. Moore, A. Nieminen, K. Peräjärvi, G. Tungate, and J. Äystö, Nuclear moments and charge radii of the ground state and isomer, J. Phys. G 26, 839 (2000).
- G. Neyens, Nuclear magnetic and quadrupole moments for nuclear structure research on exotic nuclei, Rep. Prog. Phys. 66, 633 (2003).
- A. R. Vernon et al., Nuclear moments of indium isotopes reveal abrupt change at magic number 82, Nature (London) 607, 260 (2022).
- J. Karthein et al., Electromagnetic properties of indium isotopes illuminate the doubly magic character of , Nat. Phys. 20, 1719 (2024).
- H. Gausemel, B. Fogelberg, T. Engeland, M. Hjorth-Jensen, P. Hoff, H. Mach, K. A. Mezilev, and J. P. Omtvedt, Decay of and , Phys. Rev. C 69, 054307 (2004).
- M. Chadwick et al., ENDF/B-VII.0: Next generation evaluated nuclear data library for nuclear science and technology, Nuclear Data Sheets, (2006), Vol. 107, p. 293.
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/m35x-mw7z for experimental setup, hyperfine spectra, and theoretical methods, which includes Refs. [24–51].
- S. Goriely, S. Hilaire, M. Girod, and S. Péru, First Gogny-Hartree-Fock-Bogoliubov nuclear mass model., Phys. Rev. Lett. 102, 242501 (2009).
- K. König, S. Fritzsche, G. Hagen, J. D. Holt, A. Klose, J. Lantis, Y. Liu, K. Minamisono, T. Miyagi, W. Nazarewicz, T. Papenbrock, S. V. Pineda, R. Powel, and P.-G. Reinhard, Surprising charge-radius kink in the Sc isotopes at , Phys. Rev. Lett. 131, 102501 (2023).
- I. Dillmann, M. Hannawald, U. Köster, V. Fedoseyev, A. Wöhr, B. Pfeiffer, D. Fedorov, J. Shergur, L. Weissman, W. Walters, and K.-L. Kratz, Selective laser ionization of indium isotopes: The new r-process nuclide , Eur. Phys. J. A 13, 281 (2002).
- U. Köster, Intense radioactive-ion beams produced with the ISOL method, Eur. Phys. J. A 15, 255 (2002).
- S. Rothe, B. A. Marsh, C. Mattolat, V. N. Fedosseev, and K. Wendt, A complementary laser system for ISOLDE RILIS, J. Phys. Conf. Ser. 312, 052020 (2011).
- E. Mané et al., An ion cooler-buncher for high-sensitivity collinear laser spectroscopy at ISOLDE, Eur. Phys. J. A 42, 503 (2009).
- H. Frånberg, P. Delahaye, J. Billowes, K. Blaum, R. Catherall, F. Duval, O. Gianfrancesco, T. Giles, A. Jokinen, M. Lindroos, D. Lunney, E. Mane, and I. Podadera, Off-line commissioning of the ISOLDE cooler, Nucl. Instrum. Methods Phys. Res., Sect. B 266, 4502 (2008).
- A. Vernon, J. Billowes, C. Binnersley, M. Bissell, T. Cocolios, G. Farooq-Smith, K. Flanagan, R. Garcia Ruiz, W. Gins, R. de Groote, Á. Koszorús, K. Lynch, G. Neyens, C. Ricketts, K. Wendt, S. Wilkins, and X. Yang, Simulation of the relative atomic populations of elements following charge exchange tested with collinear resonance ionization spectroscopy of indium, Spectrochim. Acta B Atom. Spectros. 153, 61 (2019).
- V. Sonnenschein, I. D. Moore, S. Raeder, M. Reponen, H. Tomita, and K. Wendt, Characterization of a pulsed injection-locked Ti:sapphire laser and its application to high resolution resonance ionization spectroscopy of copper, Laser Phys. 27, 085701 (2017).
- M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Optical mixing, Phys. Rev. Lett. 8, 18 (1962).
- P.-G. Reinhard and W. Nazarewicz, Nuclear charge densities in spherical and deformed nuclei: Toward precise calculations of charge radii, Phys. Rev. C 103, 054310 (2021).
- J. A. Sheikh, J. Dobaczewski, P. Ring, L. M. Robledo, and C. Yannouleas, Symmetry restoration in mean-field approaches, J. Phys. G 48, 123001 (2021).
- A. Koszorús, X. F. Yang, J. Billowes, C. L. Binnersley, M. L. Bissell, T. E. Cocolios, G. J. Farooq-Smith, R. P. de Groote, K. T. Flanagan, S. Franchoo, R. F. Garcia Ruiz, S. Geldhof, W. Gins, A. Kanellakopoulos, K. M. Lynch, G. Neyens, H. H. Stroke, A. R. Vernon, K. D. A. Wendt, and S. G. Wilkins, Precision measurements of the charge radii of potassium isotopes, Phys. Rev. C 100, 034304 (2019).
- T. Miyagi, S. R. Stroberg, J. D. Holt, and N. Shimizu, Ab initio multishell valence-space Hamiltonians and the island of inversion, Phys. Rev. C 102, 034320 (2020).
- A. Ekström, G. Hagen, T. D. Morris, T. Papenbrock, and P. D. Schwartz, isobars and nuclear saturation, Phys. Rev. C 97, 024332 (2018).
- B. Hu, W. Jiang, T. Miyagi, Z. Sun, A. Ekström, C. Forssén, G. Hagen, J. D. Holt, T. Papenbrock, S. R. Stroberg, and I. Vernon, Ab initio predictions link the neutron skin of to nuclear forces, Nat. Phys. 18, 1196 (2022).
- D. Cline, Nuclear shapes studied by Coulomb excitation, Annu. Rev. Nucl. Part. Sci. 36, 683 (1986).
- J. Berger, M. Girod, and D. Gogny, Time-dependent quantum collective dynamics applied to nuclear fission, Comput. Phys. Commun. 63, 365 (1991).
- J. Dechargé and D. Gogny, Hartree-Fock-Bogolyubov calculations with the D1 effective interaction on spherical nuclei, Phys. Rev. C 21, 1568 (1980).
- J. Dobaczewski, P. Bączyk, P. Becker, M. Bender, K. Bennaceur, J. Bonnard, Y. Gao, A. Idini, M. Konieczka, M. Kortelainen, L. Próchniak, A. M. Romero, W. Satuła, Y. Shi, T. R. Werner, and L. F. Yu, Solution of universal nonrelativistic nuclear DFT equations in the cartesian deformed harmonic-oscillator basis. (IX) HFODD (v3.06h): A new version of the program, J. Phys. G 48, 102001 (2021).
- J. Dobaczewski et al. [J. Phys. G (to be published)].
- C. Gorges et al., Laser spectroscopy of neutron-rich tin isotopes: A discontinuity in charge radii across the Shell closure, Phys. Rev. Lett. 122, 192502 (2019).
- A. J. Miller, K. Minamisono, A. Klose, D. Garand, C. Kujawa, J. D. Lantis, Y. Liu, B. Maaß, P. F. Mantica, W. Nazarewicz, W. Nörtershäuser, S. V. Pineda, P. G. Reinhard, D. M. Rossi, F. Sommer, C. Sumithrarachchi, A. Teigelhöfer, and J. Watkins, Proton superfluidity and charge radii in proton-rich calcium isotopes, Nat. Phys. 15, 432 (2019).
- P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, Berlin, 1980).
- G. Andersson, S. Larsson, G. Leander, P. Möller, S. Nilsson, I. Ragnarsson, S. Åberg, R. Bengtsson, J. Dudek, B. Nerlo-Pomorska, K. Pomorski, and Z. Szymański, Nuclear shell structure at very high angular momentum, Nucl. Phys. A268, 205 (1976).
- M. Cerkaski, J. Dudek, P. Rozmej, Z. Szymanski, and S. Nilsson, Particle-hole structure of nuclear isomers at high angular momenta, Nucl. Phys. A315, 269 (1979).
- N. Schulz, S. Khazrouni, A. Chevallier, J. Chevallier, L. Kraus, I. Linck, D. C. Radford, J. Dudek, and W. Nazarewicz, High-spin states in , J. Phys. G 10, 1201 (1984).
- K. J. Pototzky, J. Erler, P.-G. Reinhard, and V. O. Nesterenko, Properties of odd nuclei and the impact of time-odd mean fields: A systematic Skyrme-Hartree-Fock analysis, Eur. Phys. J. A 46, 299 (2010).
- T. E. Cocolios et al., High-resolution laser spectroscopy with the Collinear Resonance Ionisation Spectroscopy (CRIS) experiment at CERN-ISOLDE, Nucl. Instrum. Methods Phys. Res., Sect. B 376, 284 (2016).
- M. Wang, W. Huang, F. Kondev, G. Audi, and S. Naimi, The AME 2020 atomic mass evaluation (II). Tables, graphs and references, Chin. Phys. C 45, 030003 (2021).
- F. Kondev, M. Wang, W. Huang, S. Naimi, and G. Audi, The NUBASE2020 evaluation of nuclear physics properties, Chin. Phys. C 45, 030001 (2021).
- A. Vernon et al., companion paper, Variations in the charge radii of indium isotopes between and 82, Phys. Rev. C 111, 064325 (2025).
- B. Fogelberg, H. Mach, H. Gausemel, J. P. Omtvedt, and K. A. Mezilev, New high spin isomers obtained in thermal fission, AIP Conf. Proc. 1, 191 (1998).
- J. Taprogge et al., decay of and excited states in , Phys. Rev. C 91, 054324 (2015).
- J. Genevey, J. A. Pinston, H. R. Faust, R. Orlandi, A. Scherillo, G. S. Simpson, I. S. Tsekhanovich, A. Covello, A. Gargano, and W. Urban, High-spin microsecond isomers in and , Phys. Rev. C 67, 6 (2003).
- L. V. Skripnikov, S. D. Prosnyak, A. V. Malyshev, M. Athanasakis-Kaklamanakis, A. J. Brinson, K. Minamisono, F. C. P. Cruz, J. R. Reilly, B. J. Rickey, and R. F. G. Ruiz, Isotope-shift factors with quantum electrodynamics effects for many-electron systems: A study of the nuclear charge radius of , Phys. Rev. A 110, 012807 (2024).
- A. Bohr, On the quantization of angular momenta in heavy nuclei, Phys. Rev. 81, 134 (1951).
- R. F. Garcia Ruiz, A. R. Vernon, C. L. Binnersley, B. K. Sahoo, M. Bissell, J. Billowes, T. E. Cocolios, W. Gins, R. P. De Groote, K. T. Flanagan, A. Koszorus, K. M. Lynch, G. Neyens, C. M. Ricketts, K. D. Wendt, S. G. Wilkins, and X. F. Yang, High-precision multiphoton ionization of accelerated laser-ablated species, Phys. Rev. X 8, 041005 (2018).
- C. P. Flynn and E. F. W. Seymour, Knight shift of the nuclear magnetic resonance in liquid indium, Proc. Phys. Soc. 76, 301 (1960).
- J. Eberz, U. Dinger, G. Huber, H. Lochmann, R. Menges, R. Neugart, R. Kirchner, O. Klepper, T. Kühl, D. Marx, G. Ulm, and K. Wendt, Spins, moments and mean square charge radii of determined by laser spectroscopy, Nucl. Phys. A464, 9 (1987).
- J. R. Persson, Table of hyperfine anomaly in atomic systems, At. Data Nucl. Data Tables 99, 62 (2013).
- K. Tsukiyama, S. K. Bogner, and A. Schwenk, In-medium similarity renormalization group for open-shell nuclei, Phys. Rev. C 85, 061304(R) (2012).
- S. R. Stroberg, A. Calci, H. Hergert, J. D. Holt, S. K. Bogner, R. Roth, and A. Schwenk, Nucleus-dependent valence-space approach to nuclear structure, Phys. Rev. Lett. 118, 032502 (2017).
- S. R. Stroberg, S. K. Bogner, H. Hergert, and J. D. Holt, Nonempirical interactions for the nuclear shell model: An update, Annu. Rev. Nucl. Part. Sci. 69, 307 (2019).
- N. Pillet, J.-F. Berger, and E. Caurier, Variational multiparticle-multihole configuration mixing method applied to pairing correlations in nuclei, Phys. Rev. C 78, 24305 (2008).
- C. Robin, N. Pillet, D. Peña Arteaga, and J.-F. Berger, Description of nuclear systems with a self-consistent configuration-mixing approach: Theory, algorithm, and application to the test nucleus, Phys. Rev. C 93, 024302 (2016).
- C. Robin, N. Pillet, M. Dupuis, J. Le Bloas, D. Peña Arteaga, and J.-F. Berger, Description of nuclear systems with a self-consistent configuration-mixing approach. II. Application to structure and reactions in even-even sd-shell nuclei, Phys. Rev. C 95, 044315 (2017).
- N. Pillet, C. Robin, M. Dupuis, G. Hupin, and J. F. Berger, The self-consistent multiparticle-multihole configuration mixing, Eur. Phys. J. A 53, 49 (2017).
- J. Le Bloas, N. Pillet, M. Dupuis, J. M. Daugas, L. M. Robledo, C. Robin, and V. G. Zelevinsky, First characterization of sd-shell nuclei with a multiconfiguration approach, Phys. Rev. C 89, 011306(R) (2014).
- P. L. Sassarini, J. Dobaczewski, J. Bonnard, and R. F. G. Ruiz, Nuclear DFT analysis of electromagnetic moments in odd near doubly magic nuclei, J. Phys. G 49, 11LT01 (2022).
- J. Bonnard, J. Dobaczewski, G. Danneaux, and M. Kortelainen, Nuclear DFT electromagnetic moments in heavy deformed open-shell odd nuclei, Phys. Lett. B 843, 138014 (2023).
- S. R. Stroberg, J. Henderson, G. Hackman, P. Ruotsalainen, G. Hagen, and J. D. Holt, Systematics of E2 strength in the sd shell with the valence-space in-medium similarity renormalization group, Phys. Rev. C 105, 034333 (2022).
- K. Hebeler, S. K. Bogner, R. J. Furnstahl, A. Nogga, and A. Schwenk, Improved nuclear matter calculations from chiral low-momentum interactions, Phys. Rev. C 83, 031301(R) (2011).
- J. Simonis, S. R. Stroberg, K. Hebeler, J. D. Holt, and A. Schwenk, Saturation with chiral interactions and consequences for finite nuclei, Phys. Rev. C 96, 014303 (2017).
- W. G. Jiang, A. Ekström, C. Forssén, G. Hagen, G. R. Jansen, and T. Papenbrock, Accurate bulk properties of nuclei from to infinity from potentials with isobars, Phys. Rev. C 102, 054301 (2020).
- S. R. Stroberg, J. D. Holt, A. Schwenk, and J. Simonis, Ab initio limits of atomic nuclei, Phys. Rev. Lett. 126, 022501 (2021).
- Á. Koszorús et al., Charge radii of exotic potassium isotopes challenge nuclear theory and the magic character of , Nat. Phys. 17, 439 (2021).
- P. Klüpfel, P.-G. Reinhard, T. J. Bürvenich, and J. A. Maruhn, Variations on a theme by Skyrme: A systematic study of adjustments of model parameters, Phys. Rev. C 79, 034310 (2009).
- M. Kortelainen, J. McDonnell, W. Nazarewicz, P.-G. Reinhard, J. Sarich, N. Schunck, M. V. Stoitsov, and S. M. Wild, Nuclear energy density optimization: Large deformations, Phys. Rev. C 85, 024304 (2012).
- C. Thibault, F. Touchard, S. Büttgenbach, R. Klapisch, M. de Saint Simon, H. T. Duong, P. Jacquinot, P. Juncar, S. Liberman, P. Pillet, J. Pinard, J. L. Vialle, A. Pesnelle, and G. Huber, Hyperfine structure and isotope shift of the line of and some of their isomers, Phys. Rev. C 23, 2720 (1981).
- U. Georg, W. Borchers, M. Keim, A. Klein, P. Lievens, R. Neugart, M. Neuroth, P. M. Rao, C. Schulz (t. I. Collaboration), Laser spectroscopy investigation of the nuclear moments and radii of lutetium isotopes, Eur. Phys. J. A 3, 225 (1998).
- B. Cheal, M. Gardner, M. Avgoulea, J. Billowes, M. Bissell, P. Campbell, T. Eronen, K. Flanagan, D. Forest, J. Huikari, A. Jokinen, B. Marsh, I. Moore, A. Nieminen, H. Penttilä, S. Rinta-Antila, B. Tordoff, G. Tungate, and J. Äystö, The shape transition in the neutron-rich yttrium isotopes and isomers, Phys. Lett. B 645, 133 (2007).
- K. T. Flanagan, J. Billowes, P. Campbell, B. Cheal, G. D. Dracoulis, D. H. Forest, M. D. Gardner, J. Huikari, A. Jokinen, B. A. Marsh, R. Moore, A. Nieminen, H. Penttilä, H. L. Thayer, G. Tungate, and J. Äystö, Nuclear moments, charge radii and spins of the ground and isomeric states in and , J. Phys. G 39, 125101 (2012).
- T. Miyagi, X. Cao, R. Seutin, S. Bacca, R. F. Garcia Ruiz, K. Hebeler, J. D. Holt, and A. Schwenk, Impact of two-body currents on magnetic dipole moments of nuclei, Phys. Rev. Lett. 132, 232503 (2024).
- A. Vernon, Dataset: Nuclear moments of indium isotopes reveal abrupt change at magic number 82, 10.5281/zenodo.6406949 (2022).
- J. Karthein (The CRIS Collaboration), Dataset: Electromagnetic properties of indium isotopes elucidate the doubly magic character of , 10.5281/zenodo.10138423 (2023).
- K. M. Lynch (The CRIS Collaboration), Dataset: Variations in the charge radii of indium isotopes between and 82, 10.5281/zenodo.15102530 (2025).