- Open Access
Direct mass measurement of and and mid-shell trend of the one-proton separation energies for nuclei
Phys. Rev. C 114, 034311 – Published 8 September, 2026
DOI: https://doi.org/10.1103/lsp5-qntn
Abstract
Neutron-deficient nuclei in the region were produced by fragmentation of a relativistic beam at the GSI Helmholtz Centre for Heavy Ion Research (GSI), separated in the fragment separator FRS, slowed down, and thermalized, and high-precision mass measurements were performed employing the multiple-reflection time-of-flight mass spectrometer (MR-TOF-MS) of the FRS Ion Catcher. The masses of , and were determined. The mass of was measured for the first time. For , the measured mass excess deviates by more than ten standard deviations (361 keV) from the previous measurement. A possible misidentification of the measured nuclei, including , with contaminants was excluded using a newly developed identification technique for MR-TOF-MS measurements. For the other nuclides, the measured masses agree well with previous measurements. The impact of the new masses on the one-proton separation energy () of the nuclei with constant total isospin projection () in the island of inversion around is investigated, and signatures of the deformed shell gap at are found. A comparison of the experimental values with the predictions of several mass models shows a general agreement of the trends.
Physics Subject Headings (PhySH)
Article Text
References (79)
- O. Sorlin and M.-G. Porquet, Nuclear magic numbers: New features far from stability, Prog. Part. Nucl. Phys. 61, 602 (2008).
- T. Otsuka, A. Gade, O. Sorlin, T. Suzuki, and Y. Utsuno, Evolution of shell structure in exotic nuclei, Rev. Mod. Phys. 92, 015002 (2020).
- F. Nowacki, A. Poves, E. Caurier, and B. Bounthong, Shape coexistence in as the portal to the fifth island of inversion, Phys. Rev. Lett. 117, 272501 (2016).
- J. Ha, F. Recchia, S. M. Lenzi, H. Iwasaki, D. D. Dao, F. Nowacki, A. Revel, P. Aguilera, G. de Angelis, J. Ash, D. Bazin, M. A. Bentley, S. Biswas, S. Carollo, M. L. Cortes, R. Elder, R. Escudeiro, P. Farris, A. Gade, T. Ginter, et al., Abrupt structural transition in exotic molybdenum isotopes unveils an isospin-symmetric island of inversion, Nat. Commun. 16, 10631 (2025).
- W. P. Alford, R. E. Anderson, P. A. Batay-Csorba, D. A. Lind, H. H. Wieman, and C. D. Zafiratos, Structure of from the (, n) reaction, Nucl. Phys. A 293, 83 (1977).
- J. H. Hamilton, A. V. Ramayya, C. F. Maguire, R. B. Piercey, R. Bengtsson, P. Moller, J. R. Nix, J. ye Zhuang, R. L. Robinson, and S. Frauendorf, Effects of reinforcing shell gaps in the competition between spherical and highly deformed shapes, J. Phys. G: Nucl. Phys. 10, L87 (1984).
- A. Lemasson, H. Iwasaki, C. Morse, D. Bazin, T. Baugher, J. S. Berryman, A. Dewald, C. Fransen, A. Gade, S. McDaniel, A. Nichols, A. Ratkiewicz, S. Stroberg, P. Voss, R. Wadsworth, D. Weisshaar, K. Wimmer, and R. Winkler, Observation of mutually enhanced collectivity in self-conjugate , Phys. Rev. C 85, 041303(R) (2012).
- R. D. O. Llewellyn, M. A. Bentley, R. Wadsworth, H. Iwasaki, J. Dobaczewski, G. de Angelis, J. Ash, D. Bazin, P. C. Bender, B. Cederwall, B. P. Crider, M. Doncel, R. Elder, B. Elman, A. Gade, M. Grinder, T. Haylett, D. G. Jenkins, I. Y. Lee, B. Longfellow, et al., Establishing the maximum collectivity in highly deformed nuclei, Phys. Rev. Lett. 124, 152501 (2020).
- J. H. Hamilton, P. G. Hansen, and E. F. Zganjar, Advances in studies of nuclei far from stability, Rep. Prog. Phys. 48, 631 (1985).
- S. M. Fischer, T. Anderson, P. Kerns, G. Mesoloras, D. Svelnys, C. J. Lister, D. P. Balamuth, P. A. Hausladen, and D. G. Sarantites, Shape coexistence in and the question of the ground-state spin of , Phys. Rev. C 72, 024321 (2005).
- K. Kaneko, N. Shimizu, T. Mizusaki, and Y. Sun, Triple enhancement of quasi-SU(3) quadrupole collectivity in strontium-zirconium isotopes, Phys. Lett. B 817, 136286 (2021).
- M. Górska, Trends in the structure of nuclei near , Physics 4, 364 (2022).
- A. J. Nichols, R. Wadsworth, H. Iwasaki, K. Kaneko, A. Lemasson, G. de Angelis, V. M. Bader, T. Baugher, D. Bazin, M. A. Bentley, J. S. Berryman, T. Braunroth, P. J. Davies, A. Dewald, C. Fransen, A. Gade, M. Hackstein, J. Henderson, D. G. Jenkins, D. Miller, et al., Collectivity in A 70 nuclei studied via lifetime measurements in and , Phys. Lett. B 733, 52 (2014).
- K. Wimmer, W. Korten, P. Doornenbal, T. Arici, P. Aguilera, A. Algora, T. Ando, H. Baba, B. Blank, A. Boso, S. Chen, A. Corsi, P. Davies, G. de Angelis, G. de France, J.-P. Delaroche, D. T. Doherty, J. Gerl, R. Gernhäuser, M. Girod, et al., Shape changes in the mirror nuclei and , Phys. Rev. Lett. 126, 072501 (2021).
- A. Vitéz-Sveiczer, A. Algora, A. I. Morales, B. Rubio, G. G. Kiss, P. Sarriguren, P. Van Isacker, G. de Angelis, F. Recchia, S. Nishimura, J. Agramunt, V. Guadilla, A. Montaner-Pizá, S. E. A. Orrigo, A. Horváth, D. Napoli, S. Lenzi, A. Boso, V. Phong, J. Wu, et al., The -decay of into : Restoration of the pseudo-SU(4) symmetry, Phys. Lett. B 830, 137123 (2022).
- S. M. Lenzi, A. Poves, and A. O. Macchiavelli, Shell model analysis of the values in the triplet , and , Phys. Rev. C 104, L031306 (2021).
- P. Van Isacker, D. D. Warner, and D. S. Brenner, Test of Wigner's spin-isospin symmetry from double binding energy differences, Phys. Rev. Lett. 74, 4607 (1995).
- M. Wang, Y. H. Zhang, X. Zhou, X. H. Zhou, H. S. Xu, M. L. Liu, J. G. Li, Y. F. Niu, W. J. Huang, Q. Yuan, S. Zhang, F. R. Xu, Y. A. Litvinov, K. Blaum, Z. Meisel, R. F. Casten, R. B. Cakirli, R. J. Chen, H. Y. Deng, C. Y. Fu, et al., Mass measurement of upper -shell and nuclei and the importance of three-nucleon force along the line, Phys. Rev. Lett. 130, 192501 (2023).
- Y. P. Wang, Y. K. Wang, F. F. Xu, P. W. Zhao, and J. Meng, Abnormal bifurcation of the double binding energy differences and proton-neutron pairing: Nuclei close to line from Ni to Rb, Phys. Rev. Lett. 132, 232501 (2024).
- W. Nazarewicz, J. Dudek, R. Bengtsson, T. Bengtsson, and I. Ragnarsson, Microscopic study of the high-spin behaviour in selected A 80 nuclei, Nucl. Phys. A 435, 397 (1985).
- A. Petrovici, K. W. Schmid, and A. Faessler, Shape coexistence and shape transition in nuclei from krypton to molybdenum, Nucl. Phys. A 605, 290 (1996).
- P.-G. Reinhard, D. J. Dean, W. Nazarewicz, J. Dobaczewski, J. A. Maruhn, and M. R. Strayer, Shape coexistence and the effective nucleon-nucleon interaction, Phys. Rev. C 60, 014316 (1999).
- L. Gaudefroy, A. Obertelli, S. Péru, N. Pillet, S. Hilaire, J. P. Delaroche, M. Girod, and J. Libert, Collective structure of the isotones, Phys. Rev. C 80, 064313 (2009).
- T. R. Rodríguez and J. L. Egido, Multiple shape coexistence in the nucleus , Phys. Lett. B 705, 255 (2011).
- B. S. Hu, Z. H. Sun, G. Hagen, and T. Papenbrock, Ab initio computations of strongly deformed nuclei near , Phys. Rev. C 110, L011302 (2024).
- M. Sharma, M. Rajput, S. Singh, A. Bharti, G. H. Bhat, and J. A. Sheikh, Shape evolution of even-even strontium isotopes near shell closure, Eur. Phys. J. A 61, 113 (2025).
- A. Hamaker, E. Leistenschneider, R. Jain, G. Bollen, S. A. Giuliani, K. Lund, W. Nazarewicz, L. Neufcourt, C. R. Nicoloff, D. Puentes, R. Ringle, C. S. Sumithrarachchi, and I. T. Yandow, Precision mass measurement of lightweight self-conjugate nucleus , Nat. Phys. 17, 1408 (2021).
- T. Yamaguchi, H. Koura, Y. Litvinov, and M. Wang, Masses of exotic nuclei, Prog. Part. Nucl. Phys. 120, 103882 (2021).
- R. Kanungo, Shell closures in the and = 40–60 region for neutron and proton-rich nuclei, Phys. Lett. B 649, 31 (2007).
- W. R. Plaß, T. Dickel, S. Purushothaman, P. Dendooven, H. Geissel, J. Ebert, E. Haettner, C. Jesch, M. Ranjan, M. P. Reiter, H. Weick, F. Amjad, S. Ayet San Andrés, M. Diwisch, A. Estrade, F. Farinon, F. Greiner, N. Kalantar-Nayestanaki, R. Knöbel, J. Kurcewicz, et al., The FRS Ion Catcher - A facility for high-precision experiments with stopped projectile and fission fragments, Nucl. Instrum. Methods Phys. Res., Sect. B 317, 457 (2013).
- W. R. Plaß, T. Dickel, I. Mardor, S. Pietri, H. Geissel, C. Scheidenberger, D. L. Amanbayev, S. Ayet San Andrés, J. Äystö, D. Balabanski, S. Beck, J. Bergmann, V. Charviakova, P. Constantin, T. Eronen, T. Grahn, F. Greiner, E. Haettner, C. Hornung, J.-P. Hucka, et al., The science case of the FRS Ion Catcher for FAIR Phase-0, Hyperfine Interact. 240, 73 (2019).
- H. Geissel, P. Armbruster, K. Behr, A. Brünle, K. Burkard, M. Chen, H. Folger, B. Franczak, H. Keller, O. Klepper, B. Langenbeck, F. Nickel, E. Pfeng, M. Pfützner, E. Roeckl, K. Rykaczewski, I. Schall, D. Schardt, C. Scheidenberger, K.-H. Schmidt, et al., The GSI projectile fragment separator (FRS): A versatile magnetic system for relativistic heavy ions, Nucl. Instrum. Methods Phys. Res., Sect. B 70, 286 (1992).
- J. Stadlmann, L. Bozyk, P. Forck, D. Ondreka, R. Singh, and P. Spiller, SIS18 operation and recent development, in Proceedings of IPAC'23, 14th International Particle Accelerator Conference (JACoW, Geneva, 2023), pp. 1683–1686.
- E. Haettner, B. Franczak, H. Geissel, T. Dickel, S. Pietri, W. Plaß, A. Prochazka, S. Purushothaman, C. Scheidenberger, Y. Tanaka, S. Terashima, H. Weick, J. Winfield, and M. Yavor, New high-resolution and high-transmission modes of the FRS for FAIR phase-0 experiments, Nucl. Instrum. Methods Phys. Res., Sect. B 463, 455 (2020).
- G. Kripkó-Koncz, W. R. Plaß, I. Dedes, D. D. Dao, T. Dickel, C. Hornung, D. Amanbayev, S. A. S. Andrés, S. Beck, J. Bergmann, A. Blazhev, J. Dudek, H. Geissel, E. Haettner, N. Kalantar-Nayestanaki, et al. (for the Super-FRS Experiment Collaboration), Direct mass measurement of and implications for the isomer structures in : Tracing the two-proton decay branch, Phys. Rev. Res. 7, L042022 (2025).
- M. Ranjan, S. Purushothaman, T. Dickel, H. Geissel, W. R. Plaß, D. Schäfer, C. Scheidenberger, J. V. de Walle, H. Weick, and P. Dendooven, New stopping cell capabilities: RF carpet performance at high gas density and cryogenic operation, Europhys. Lett. 96, 52001 (2011).
- S. Purushothaman, M. P. Reiter, E. Haettner, P. Dendooven, T. Dickel, H. Geissel, J. Ebert, C. Jesch, W. R. Plaß, M. Ranjan, H. Weick, F. Amjad, S. Ayet San Andrés, M. Diwisch, A. Estrade, F. Farinon, F. Greiner, N. Kalantar-Nayestanaki, R. Knöbel, J. Kurcewicz, et al., First experimental results of a cryogenic stopping cell with short-lived, heavy uranium fragments produced at 1000 MeV/u, Europhys. Lett. 104, 42001 (2013).
- M. Ranjan, P. Dendooven, S. Purushothaman, T. Dickel, M. Reiter, S. Ayet San Andrés, E. Haettner, I. Moore, N. Kalantar-Nayestanaki, H. Geissel, W. Plaß, D. Schäfer, C. Scheidenberger, F. Schreuder, H. Timersma, J. Van de Walle, and H. Weick, Design, construction and cooling system performance of a prototype cryogenic stopping cell for the Super-FRS at FAIR, Nucl. Instrum. Methods Phys. Res., Sect. A 770, 87 (2015).
- W. R. Plaß, T. Dickel, U. Czok, H. Geissel, M. Petrick, K. Reinheimer, C. Scheidenberger, and M. Yavor, Isobar separation by time-of-flight mass spectrometry for low-energy radioactive ion beam facilities, Nucl. Instrum. Methods Phys. Res., Sect. B 266, 4560 (2008).
- W. R. Plaß, T. Dickel, and C. Scheidenberger, Multiple-reflection time-of-flight mass spectrometry, Int. J. Mass Spectrom. 349-350, 134 (2013).
- T. Dickel, W. R. Plaß, A. Becker, U. Czok, H. Geissel, E. Haettner, C. Jesch, W. Kinsel, M. Petrick, C. Scheidenberger, A. Simon, and M. I. Yavor, A high-performance multiple-reflection time-of-flight mass spectrometer and isobar separator for the research with exotic nuclei, Nucl. Instrum. Methods Phys. Res., Sect. A 777, 172 (2015).
- G. Kripkó-Koncz, Investigation of ground and isomeric states of exotic nuclei using advances in multiple-reflection time-of-flight mass spectrometry: Unraveling riddles surrounding the proton-emitting isomer(s) in , Ph.D. thesis, Justus-Liebig-Universität Gießen, 2025, https://doi.org/10.22029/jlupub-20182.
- W. Xian, M. Rosenbusch, V. H. Phong, M. Wada, P. Schury, D. Hou, A. Takamine, S. Chen, T. Niwase, Y. Hirayama, H. Ishiyama, S. Iimura, Y. Ito, T. M. Kojima, S. Kimura, J. Liu, J. Lee, S. Michimasa, H. Miyatake, J. Y. Moon, et al., Atomic mass measurements of neutron-rich nuclides on the path to with a -TOF-equipped MRTOF device, Front. Phys. 13, 1644477 (2025).
- S. Ayet San Andrés, C. Hornung, J. Ebert, W. R. Plaß, T. Dickel, H. Geissel, C. Scheidenberger, J. Bergmann, F. Greiner, E. Haettner, C. Jesch, W. Lippert, I. Mardor, I. Miskun, Z. Patyk, S. Pietri, A. Pihktelev, S. Purushothaman, M. P. Reiter, A.-K. Rink, et al., High-resolution, accurate multiple-reflection time-of-flight mass spectrometry for short-lived, exotic nuclei of a few events in their ground and low-lying isomeric states, Phys. Rev. C 99, 064313 (2019).
- M. Wang, W. J. Huang, F. G. Kondev, G. Audi, and S. Naimi, The AME 2020 atomic mass evaluation (II). Tables, graphs and references, Chin. Phys. C 45, 030003 (2021).
- S. Purushothaman, S. Ayet San Andrés, J. Bergmann, T. Dickel, J. Ebert, H. Geissel, C. Hornung, W. R. Plaß, C. Rappold, C. Scheidenberger, Y. K. Tanaka, and M. I. Yavor, Hyper-EMG: A new probability distribution function composed of exponentially modified Gaussian distributions to analyze asymmetric peak shapes in high-resolution time-of-flight mass spectrometry, Int. J. Mass Spectrom. 421, 245 (2017).
- A. Spătaru, G. Kripkó-Koncz, T. Dickel, C. Hornung, W. R. Plaß, P. Constantin, D. Amanbayev, S. Ayet San Andrés, D. L. Balabanski, S. Beck, J. Bergmann, H. Geissel, N. Kalantar-Nayestanaki, J. Kehat, I. Mardor, et al., Broadband mass measurements with the FRS Ion Catcher facility at GSI and theory developments investigating the shape-phase transition near , Phys. Rev. C 111, 054307 (2025).
- B. Cai, C. Yuan, G. Zhang, Y. Zhang, M. Liu, Y. Xing, X. Xu, J. Li, and M. Wang, Isomeric structure in the region: Possible competition between decay and proton emission in the isomeric unbound nucleus , Phys. Rev. C 109, L051302 (2024).
- Y. M. Xing, C. X. Yuan, M. Wang, Y. H. Zhang, X. H. Zhou, Y. A. Litvinov, K. Blaum, H. S. Xu, T. Bao, R. J. Chen, C. Y. Fu, B. S. Gao, W. W. Ge, J. J. He, W. J. Huang, T. Liao, J. G. Li, H. F. Li, S. Litvinov, S. Naimi, et al., Isochronous mass measurements of neutron-deficient nuclei from projectile fragmentation, Phys. Rev. C 107, 014304 (2023).
- N. Mărginean, C. Rusu, D. Bucurescu, C. Rossi Alvarez, C. A. Ur, D. Bazzacco, S. Lunardi, P. Pavan, G. d. Angelis, M. Axiotis, E. Farnea, A. Gadea, M. Ionescu-Bujor, A. Iordăchescu, W. Krolas, T. Kröll, S. M. Lenzi, T. Martinez, R. Menegazzo, D. R. Napoli, et al., Identification of excited states and shell model description of the nucleus , Phys. Rev. C 72, 014302 (2005).
- J. Park, R. Krücken, D. Lubos, R. Gernhäuser, M. Lewitowicz, S. Nishimura, D. S. Ahn, H. Baba, B. Blank, A. Blazhev, P. Boutachkov, F. Browne, I. Čeliković, G. de France, P. Doornenbal, T. Faestermann, Y. Fang, N. Fukuda, J. Giovinazzo, N. Goel, et al., New and comprehensive - and -decay spectroscopy results in the vicinity of , Phys. Rev. C 99, 034313 (2019).
- F. G. Kondev, M. Wang, W. J. Huang, S. Naimi, and G. Audi, The NUBASE2020 evaluation of nuclear physics properties, Chin. Phys. C 45, 030001 (2021).
- S. Garg, B. Maheshwari, B. Singh, Y. Sun, A. Goel, and A. K. Jain, Atlas of nuclear isomers—Second edition, At. Data Nucl. Data Tables 150, 101546 (2023).
- A. Mollaebrahimi, C. Hornung, T. Dickel, D. Amanbayev, G. Kripko-Koncz, W. R. Plaß, S. Ayet San Andrés, S. Beck, A. Blazhev, J. Bergmann, H. Geissel, M. Górska, H. Grawe, F. Greiner, E. Haettner, N. Kalantar-Nayestanaki, I. Miskun, F. Nowacki, C. Scheidenberger, S. Bagchi, et al., Studying Gamow-Teller transitions and the assignment of isomeric and ground states at , Phys. Lett. B 839, 137833 (2023).
- D. Amanbayev, Mass measurements at the N=Z and N=126 limits at the FRS Ion Catcher and development of the cryogenic stopping cell for the Super-FRS, Ph.D. thesis, Justus-Liebig-Universität Gießen, 2023, https://doi.org/10.22029/jlupub-18567.
- C. Hornung, D. Amanbayev, I. Dedes, G. Kripko-Koncz, I. Miskun, N. Shimizu, S. Ayet San Andrés, J. Bergmann, T. Dickel, J. Dudek, J. Ebert, H. Geissel, M. Górska, H. Grawe, F. Greiner, E. Haettner, T. Otsuka, W. R. Plaß, S. Purushothaman, A.-K. Rink, et al., Isomer studies in the vicinity of the doubly-magic nucleus : Observation of a new low-lying isomeric state in , Phys. Lett. B 802, 135200 (2020).
- M. Vilén, A. Kankainen, P. Baczyk, L. Canete, J. Dobaczewski, T. Eronen, S. Geldhof, A. Jokinen, M. Konieczka, J. Kostensalo, I. D. Moore, D. A. Nesterenko, H. Penttilä, I. Pohjalainen, M. Reponen, S. Rinta-Antila, A. de Roubin, W. Satuła, and J. Suhonen, High-precision mass measurements and production of neutron-deficient isotopes using heavy-ion beams at IGISOL, Phys. Rev. C 100, 054333 (2019).
- W. S. Porter, B. Ashrafkhani, J. Bergmann, C. Brown, T. Brunner, J. D. Cardona, D. Curien, I. Dedes, T. Dickel, J. Dudek, E. Dunling, G. Gwinner, Z. Hockenbery, J. D. Holt, C. Hornung, et al., Mapping the island of inversion: Precision mass measurements of neutron-rich Fe isotopes, Phys. Rev. C 105, L041301 (2022).
- M. Stryjczyk, A. Jaries, A. Kankainen, and T. Eronen, Comment on “Spin-trap isomers in deformed, odd-odd nuclei in the light rare-earth region near ”, Phys. Rev. C 111, 049801 (2025).
- S. Kimura, M. Wada, H. Haba, Y. Hirayama, H. Ishiyama, Y. Ito, T. Niwase, M. Rosenbusch, P. Schury, H. Ueno, Y. X. Watanabe, and Y. Yamanouchi, New ground state in removes two-neutron-separation-energy anomaly in lanthanum isotopes, Phys. Rev. Lett. 136, 232501 (2026).
- O. B. Tarasov and D. Bazin, : Radioactive beam production with in-flight separators, Nucl. Instrum. Methods Phys. Res., Sect. B 266, 4657 (2008).
- R. T. Birge, The calculation of errors by the method of least squares, Phys. Rev. 40, 207 (1932).
- S. Kimura, M. Wada, C. Y. Fu, N. Fukuda, Y. Hirayama, D. S. Hou, S. Iimura, H. Ishiyama, Y. Ito, S. Kubono, K. Kusaka, S. Michimasa, H. Miyatake, S. Nishimura, T. Niwase, V. Phong, M. Rosenbusch, H. Schatz, P. Schury, Y. Shimizu, et al., Precision mass measurements around rule out ZrNb cycle formation in the rapid proton-capture process at type I x-ray bursts, Phys. Rev. Lett. 135, 152701 (2025).
- Z. Ge, M. Reponen, T. Eronen, B. Hu, M. Kortelainen, A. Kankainen, I. Moore, D. Nesterenko, C. Yuan, O. Beliuskina, L. Cañete, R. de Groote, C. Delafosse, T. Dickel, A. de Roubin, S. Geldhof, W. Gins, J. D. Holt, M. Hukkanen, A. Jaries, et al., High-precision mass measurements of neutron deficient silver isotopes probe the robustness of the shell closure, Phys. Rev. Lett. 133, 132503 (2024).
- M. Mougeot, D. Atanasov, J. Karthein, R. N. Wolf, P. Ascher, K. Blaum, K. Chrysalidis, G. Hagen, J. D. Holt, W. J. Huang, G. R. Jansen, I. Kulikov, Y. A. Litvinov, D. Lunney, V. Manea, T. Miyagi, T. Papenbrock, L. Schweikhard, A. Schwenk, T. Steinsberger, et al., Mass measurements of challenge ab initio nuclear theory of the nuclide , Nat. Phys. 17, 1099 (2021).
- C. M. Ireland, F. M. Maier, G. Bollen, S. E. Campbell, X. Chen, H. Erington, N. D. Gamage, M. J. Gutiérrez, C. Izzo, E. Leistenschneider, E. M. Lykiardopoulou, R. Orford, W. S. Porter, D. Puentes, M. Redshaw, R. Ringle, S. Rogers, S. Schwarz, L. Stackable, C. S. Sumithrarachchi, et al., High-precision mass measurement of restores smoothness of the mass surface, Phys. Rev. C 111, 014314 (2025).
- C. M. Ireland, G. Bollen, S. E. Campbell, X. Chen, H. Erington, N. D. Gamage, K. Godbey, A. M. Houff, C. Izzo, B. Knight, S. Lalit, E. Leistenschneider, E. M. Lykiardopoulou, F. M. Maier, W. Nazarewicz, R. Orford, W. S. Porter, C. Quick, A. Ravlić, M. Redshaw, et al., Mass of and Bayesian extrapolations to the proton drip line, Phys. Rev. C 113, L021302 (2026).
- W. Satuła, D. Dean, J. Gary, S. Mizutori, and W. Nazarewicz, On the origin of the Wigner energy, Phys. Lett. B 407, 103 (1997).
- P. Möller, A. J. Sierk, T. Ichikawa, and H. Sagawa, Nuclear ground-state masses and deformations: FRDM (2012), At. Data Nucl. Data Tables 109-110, 1 (2016).
- G. Grams, N. N. Shchechilin, A. Sánchez-Fernández, W. Ryssens, N. Chamel, and S. Goriely, Skyrme–Hartree–Fock–Bogoliubov mass models on a 3D mesh: IV. Improved description of the isospin dependence of pairing, Eur. Phys. J. A 61, 35 (2025).
- J. Duflo and A. P. Zuker, Microscopic mass formulas, Phys. Rev. C 52, R23 (1995).
- S. Goriely, N. Chamel, and J. M. Pearson, Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XII. Stiffness and stability of neutron-star matter, Phys. Rev. C 82, 035804 (2010).
- 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).
- P. Möller and J. Rayford Nix, Atomic masses and nuclear ground-state deformations calculated with a new macroscopic-microscopic model, At. Data Nucl. Data Tables 26, 165 (1981).
- G. Scamps, S. Goriely, E. Olsen, M. Bender, and W. Ryssens, Skyrme-Hartree-Fock-Bogoliubov mass models on a 3D mesh: Effect of triaxial shape, Eur. Phys. J. A 57, 333 (2021).
- W. Ryssens, G. Scamps, S. Goriely, and M. Bender, Skyrme–Hartree–Fock–Bogoliubov mass models on a 3D mesh: II. Time-reversal symmetry breaking, Eur. Phys. J. A 58, 246 (2022).
- Y. Y. Zong, C. Ma, M. Q. Lin, and Y. M. Zhao, Mass relations of mirror nuclei for both bound and unbound systems, Phys. Rev. C 105, 034321 (2022).
- A. Parikh, J. José, G. Sala, and C. Iliadis, Nucleosynthesis in type I X-ray bursts, Prog. Part. Nucl. Phys. 69, 225 (2013).
- H. Schatz and W.-J. Ong, Dependence of X-ray burst models on nuclear masses, Astrophys. J. 844, 139 (2017).