1. Noether, E. Invariante Variationsprobleme. Nachr. Ges. Wiss. Göttingen Math.-Phys. Kl. 1918, 235–257 (1918).

2. Elliott, J. & Dawber, P. Symmetry in Physics: Principles and Simple Applications (Oxford Univ. Press, 1984).

3. Dirac, P. A. M. The quantum theory of the electron. Proc. R. Soc. Lond. A 117, 610–624 (1928).

4. Heisenberg, W. On the structure of atomic nuclei. Z. Phys. 77, 1–11 (1932).

5. Wigner, E. On the consequences of the symmetry of the nuclear Hamiltonian on the spectroscopy of nuclei. Phys. Rev. 51, 106–119 (1937).

6. Wilkinson, D. H. Isospin in Nuclear Physics (North Holland Pub. Co., 1970).

7. Warner, D., Bentley, M. & Van Isacker, P. The role of isospin symmetry in collective nuclear structure. Nat. Phys. 2, 311–318 (2006).

8. Schatz, H. et al. rp-process nucleosynthesis at extreme temperature and density conditions. Phys. Rep. 294, 167–263 (1998).

9. Grindlay, J. et al. Discovery of intense X-ray bursts from the globular cluster NGC 6624. Astrophys. J. 205, L127–L130 (1976).

10. Woosley, S. E. & Taam, R. E. γ-ray bursts from thermonuclear explosions on neutron stars. Nature 263, 101–103 (1976).

11. Suzuki, H. et al. Discovery of 72Rb: a nuclear sandbank beyond the proton drip line. Phys. Rev. Lett. 119, 192503 (2017).

12. Rogers, A. M. et al. 69Kr β-delayed proton emission: a Trojan horse for studying states in proton-unbound 69Br. Phys. Rev. C 84, 051306 (2011).

13. Del Santo, M. et al. β-delayed proton emission of 69Kr and the 68Se rp-process waiting point. Phys. Lett. B 738, 453–456 (2014).

14. Schmidt, K. H. A new test for random events of an exponential distribution. Eur. Phys. J. A 8, 141–145 (2000).

15. Batchelder, J. C. et al. Beta-delayed proton decay of 73Sr. Phys. Rev. C 48, 2593–2597 (1993).

16. Wang, M. et al. The AME2016 atomic mass evaluation: (II). Tables, graphs and references. Chinese Phys. C 41, 030003 (2017).

17. Singh, B., Rodriguez, J., Wong, S. & Tuli, J. Review of logft values in β decay. Nucl. Data Sheets 84, 487–563 (1998).

18. Hagberg, E. et al. Tests of isospin mixing corrections in superallowed 0+ → 0+ β decays. Phys. Rev. Lett. 73, 396–399 (1994).

19. Konieczka, M., Baczyk, P. & Satuła, W. β-decay study within multireference density functional theory and beyond. Phys. Rev. C 93, 042501 (2016).

20. Bączyk, P. et al. Isospin-symmetry breaking in masses of N ≃ Z nuclei. Phys. Lett. B 778, 178–183 (2018).

21. Michel, N., Nazarewicz, W., Płoszajczak, M. & Vertse, T. Shell model in the complex energy plane. J. Phys. G 36, 013101 (2009).

22. Murray, G., White, W., Willmott, J. & Entwistle, R. The decay of 73Br. Nucl. Phys. A 142, 21–34 (1970).

23. Wörmann, B. et al. Rotational bands in 73Br: the disappearance of shape coexistence in 72Se. Z. Phys. A 322, 171–172 (1985).

24. Heese, J. et al. Spectroscopy of high spin states in 73Br. Phys. Rev. C 36, 2409–2421 (1987).

25. Heese, J. et al. Conversion electron and yrast state measurements in 73Br. Phys. Rev. C 41, 1553–1561 (1990).

26. Griffiths, A. G. et al. Magnetic moments and shape coexistence in the light Br isotopes. Phys. Rev. C 46, 2228–2240 (1992).

27. Wang, S. M., Michel, N., Nazarewicz, W. & Xu, F. R. Structure and decays of nuclear three-body systems: the Gamow coupled-channel method in Jacobi coordinates. Phys. Rev. C 96, 044307 (2017).

28. Wang, S. M. & Nazarewicz, W. Puzzling two-proton decay of 67Kr. Phys. Rev. Lett. 120, 212502 (2018).

29. Berggren, T. On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes. Nucl. Phys. A 109, 265–287 (1968).

30. Bouchez, E. et al. New shape isomer in the self-conjugate nucleus 72Kr. Phys. Rev. Lett. 90, 082502 (2003).

31. Gade, A. et al. Quadrupole deformation of the self-conjugate nucleus 72Kr. Phys. Rev. Lett. 95, 022502 (2005).

32. Iwasaki, H. et al. Evolution of collectivity in 72Kr: evidence for rapid shape transition. Phys. Rev. Lett. 112, 142502 (2014).

33. Rykaczewski, K. et al. Proton emitters 140Ho and 141Ho: probing the structure of unbound Nilsson orbitals. Phys. Rev. C 60, 011301 (1999).

34. Sonzogni, A. A. et al. Fine structure in the decay of the highly deformed proton emitter 131Eu. Phys. Rev. Lett. 83, 1116–1118 (1999).

35. Kruppa, A. T., Barmore, B., Nazarewicz, W. & Vertse, T. Fine structure in the decay of deformed proton emitters: nonadiabatic approach. Phys. Rev. Lett. 84, 4549–4552 (2000).

36. Karny, M. et al. Shell structure beyond the proton drip line studied via proton emission from deformed 141Ho. Phys. Lett. B 664, 52–56 (2008).

37. Miller, G. A., Opper, A. K. & Stephenson, E. J. Charge symmetry breaking and QCD. Annu. Rev. Nucl. Part. Sci. 56, 253–292 (2006).

38. Borsanyi, S. et al. Ab initio calculation of the neutron–proton mass difference. Science 347, 1452–1455 (2015).

39. Alvarez, L. W. & Bloch, F. A quantitative determination of the neutron moment in absolute nuclear magnetons. Phys. Rev. 57, 111–122 (1940).

40. Wiringa, R. B., Stoks, V. G. J. & Schiavilla, R. Accurate nucleon–nucleon potential with charge-independence breaking. Phys. Rev. C 51, 38–51 (1995).

41. Thomas, R. G. On the determination of reduced widths from the one-level dispersion formula. Phys. Rev. 81, 148–149 (1951).

42. Ehrman, J. B. On the displacement of corresponding energy levels of 13C and 13N. Phys. Rev. 81, 412–416 (1951).

43. Thomas, R. G. An analysis of the energy levels of the mirror nuclei, 13C and 13N. Phys. Rev. 88, 1109–1125 (1952).

44. Morrissey, D., Sherrill, B., Steiner, M., Stolz, A. & Wiedenhoever, I. Commissioning the A1900 projectile fragment separator. Nucl. Instrum. Methods Phys. Res. B 204, 90–96 (2003).

45. Bazin, D. et al. Radio Frequency Fragment Separator at NSCL. Nucl. Instrum. Methods Phys. Res. A 606, 314–319 (2009).

46. Prisciandaro, J., Morton, A. & Mantica, P. Beta counting system for fast fragmentation beams. Nucl. Instrum. Methods Phys. Res. A 505, 140–143 (2003).

47. Mueller, W. et al. Thirty-two-fold segmented germanium detectors to identify γ-rays from intermediate-energy exotic beams. Nucl. Instrum. Methods Phys. Res. A 466, 492–498 (2001).

48. Prokop, C. et al. Digital data acquisition system implementation at the National Superconducting Cyclotron Laboratory. Nucl. Instrum. Methods Phys. Res. A 741, 163–168 (2014).

49. Kibédi, T., Burrows, T. W., Trzhaskovskaya, M. B., Davidson, P. M. & Nestor, C. W. Jr. Evaluation of theoretical conversion coefficients using BrIcc. Nucl. Instrum. Methods Phys. Res. A 589, 202–229 (2008).

50. Condon, E. U. & Odishaw, H. Handbook of Physics (McGraw-Hill, 1958).

51. Hagberg, E. et al. The decay of a new nuclide: 71B. Nucl. Phys. A 383, 109–118 (1982).

52. Meisel, Z. et al. β-particle energy-summing correction for β-delayed proton emission measurements. Nucl. Instrum. Methods Phys. Res. A 844, 45–52 (2017).

53. Huang, W. J. & Audi, G. Corrections of alpha- and proton-decay energies in implantation experiments. EPJ Web Conf. 146, 10007 (2017).

54. International Network of Nuclear Structure and Decay Data Evaluators. Evaluated nuclear structure data file (ENSDF) National Nuclear Data Center (Brookhaven National Laboratory, 2020); https://www.nndc.bnl.gov/ensdf/.

55. Cwiok, S., Nazarewicz, W., Dudek, J., Skalski, J. & Werner, T. Single-particle energies, wave functions, quadrupole moments and g-factors in an axially deformed Woods−Saxon potential with applications to the two-centre-type nuclear problems. Comput. Phys. Commun. 46, 379–399 (1987).

56. Nazarewicz, W., Dudek, J., Bengtsson, R., Bengtsson, T. & Ragnarsson, I. Microscopic study of the high-spin behaviour in selected A ≃ 80 nuclei. Nucl. Phys. A 435, 397–447 (1985).

57. Thompson, I. J. et al. Pauli blocking in three-body models of halo nuclei. Phys. Rev. C 61, 024318 (2000).