Nothing Special   »   [go: up one dir, main page]

Skip to main content
Log in

Recent progress in two-proton radioactivity

  • Published:
Nuclear Science and Techniques Aims and scope Submit manuscript

Abstract

During the last few decades, rare isotope beam facilities have provided unique data for studying the properties of nuclides located far from the beta-stability line. Such nuclei are often accompanied by exotic structures and radioactive modes, which represent the forefront of nuclear research. Among them, two-proton (2p) radioactivity is a rare decay mode found in a few highly proton-rich isotopes. The 2p decay lifetimes and properties of emitted protons hold invaluable information regarding the nuclear structures in the presence of a low-lying proton continuum; as such, they have attracted considerable research attention. In this review, we present some of the recent experimental and theoretical progress regarding the 2p decay, including technical innovations for measuring nucleon–nucleon correlations and developments in the models that connect their structural aspects with their decay properties. This impressive progress should play a significant role in elucidating the mechanism of these exotic decays, probing the corresponding components inside nuclei, and providing deep insights into the open quantum nature of dripline systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

References

  1. L.N. Cooper, R.L. Mills, A.M. Sessler, Possible superfluidity of a system of strongly interacting fermions. Phys. Rev. 114, 1377–1382 (1959). https://doi.org/10.1103/PhysRev.114.1377

    ADS  MathSciNet  Google Scholar 

  2. A.J. Leggett, Nobel lecture: superfluid \(^{3}\rm He\): the early days as seen by a theorist. Rev. Mod. Phys. 76, 999–1011 (2004). https://doi.org/10.1103/RevModPhys.76.999

    ADS  Google Scholar 

  3. D.M. Brink, R.A. Broglia, Nuclear superfluidity: pairing in finite systems (Nuclear physics and cosmology) (Cambridge University Press, New York, Cambridge Monographs on Particle Physics, 2005)

  4. R.A. Broglia, V. Zelevinsky, Fifty years of nuclear BCS: pairing in finite systems (World Scientific Publishing, Singapore, 2013)

    Google Scholar 

  5. D.J. Dean, M. Hjorth-Jensen, Pairing in nuclear systems: from neutron stars to finite nuclei. Rev. Mod. Phys. 75, 607–656 (2003). https://doi.org/10.1103/RevModPhys.75.607

    ADS  Google Scholar 

  6. J. Erler, N. Birge, M. Kortelainen et al., The limits of the nuclear landscape. Nature 486, 509–512 (2012). https://doi.org/10.1038/nature11188

    ADS  Google Scholar 

  7. L. Neufcourt, Y.C. Cao, S.A. Giuliani et al., Quantified limits of the nuclear landscape. Phys. Rev. C 101, 044307 (2020). https://doi.org/10.1103/PhysRevC.101.044307

    ADS  Google Scholar 

  8. J. Dobaczewski, W. Nazarewicz, Theoretical aspects of science with radioactive nuclear beams. Phil. Trans. R. Soc. Lond. A 356, 2007 (1998). https://doi.org/10.1098/rsta.1998.0261

    ADS  Google Scholar 

  9. Scientific opportunities with a rare-isotope facility in the United States. Report of the NAS/NRC rare isotope science assessment committee (The National Academies Press, 2007)

  10. J. Dobaczewski, N. Michel, W. Nazarewicz et al., Shell structure of exotic nuclei. Prog. Part. Nucl. Phys. 59, 432 (2007). https://doi.org/10.1098/rsta.1998.0261

    ADS  Google Scholar 

  11. C. Forssén, G. Hagen, M. Hjorth-Jensen et al., Living on the edge of stability, the limits of the nuclear landscape. Phys. Scripta 2013, 014022 (2013). https://doi.org/10.1088/0031-8949/2013/T152/014022

    Google Scholar 

  12. A.B. Balantekin, J. Carlson, D.J. Dean et al., Nuclear theory and science of the Facility for Rare Isotope Beams. Mod. Phys. Lett. A 29, 1430010 (2014). https://doi.org/10.1142/S0217732314300109

    ADS  Google Scholar 

  13. The 2015 long range plan in nuclear science: reaching for the horizon (NSAC Long Range Plan Report, 2015)

  14. D.Q. Fang, Y.G. Ma, Progress of experimental studies on two-proton emission. Chin. Sci. Bull. 65, 4018 (2020). https://doi.org/10.1360/TB-2020-0423

    Google Scholar 

  15. V.I. Goldansky, On neutron-deficient isotopes of light nuclei and the phenomena of proton and two-proton radioactivity. Nucl. Phys. 19, 482–495 (1960). https://doi.org/10.1016/0029-5582(60)90258-3

    Google Scholar 

  16. M. Pfützner, Two-proton radioactivity: the status and perspectives. Nucl. Phys. A 738, 101–107 (2004). https://doi.org/10.1016/j.nuclphysa.2004.04.017

    ADS  Google Scholar 

  17. B. Blank, M. Płoszajczak, Two-proton radioactivity. Rep. Prog. Phys. 71, 046301 (2008). https://doi.org/10.1088/0034-4885/71/4/046301

    ADS  Google Scholar 

  18. M. Pfützner, M. Karny, L.V. Grigorenko, K. Riisager, Radioactive decays at limits of nuclear stability. Rev. Mod. Phys. 84, 567–619 (2012). https://doi.org/10.1103/RevModPhys.84.567

    ADS  Google Scholar 

  19. M. Pfützner, Particle radioactivity of exotic nuclei. Phys. Scripta 2013, 014014 (2013). https://doi.org/10.1088/0031-8949/2013/T152/014014

    Google Scholar 

  20. J. Giovinazzo, P. Ascher, L. Audirac et al., Two-proton radioactivity: 10 years of experimental progresses. J. Phys. Conf. Ser 436, 012057 (2013). https://doi.org/10.1088/1742-6596/436/1/012057

    Google Scholar 

  21. E. Olsen, M. Pfützner, N. Birge et al., Erratum: Landscape of two-proton radioactivity Phys. Rev. Lett. 111, 139903 (2013). https://doi.org/10.1103/PhysRevLett.111.139903

    ADS  Google Scholar 

  22. E. Olsen, M. Pfützner, N. Birge et al., Landscape of two-proton radioactivity. Phys. Rev. Lett. 110, 222501 (2013). https://doi.org/10.1103/PhysRevLett.110.222501

    ADS  Google Scholar 

  23. D.F. Geesaman, R.L. Mcgrath, P.M.S. Lesser et al., Particle decay of \(^{6}\rm Be\). Phys. Rev. C 15, 1835–1838 (1977). https://doi.org/10.1103/PhysRevC.15.1835

    ADS  Google Scholar 

  24. O.V. Bochkarev, L.V. Chulkov, A.A. Korsheninniicov et al., Democratic decay of \(^{6}\rm Be\) states. Nucl. Phys. A 505, 215–240 (1989). https://doi.org/10.1016/0375-9474(89)90371-0

    ADS  Google Scholar 

  25. G.J. KeKelis, M.S. Zisman, D.K. Scott et al., Masses of the unbound nuclei \(^{16}\rm Ne {, ^{15}\rm F}\), and \(^{12}\rm O\). Phys. Rev. C 17, 1929–1938 (1978). https://doi.org/10.1103/PhysRevC.17.1929

    ADS  Google Scholar 

  26. R.A. Kryger, A. Azhari, M. Hellström et al., Two-proton emission from the ground state of \(^{12}\rm O\). Phys. Rev. Lett. 74, 860–863 (1995). https://doi.org/10.1103/PhysRevLett.74.860

    ADS  Google Scholar 

  27. J. Giovinazzo, B. Blank, M. Chartier et al., Two-proton radioactivity of 45Fe. Phys. Rev. Lett. 89, 102501 (2002). https://doi.org/10.1103/PhysRevLett.89.102501

    ADS  Google Scholar 

  28. M. Pfützner, E. Badura, C. Bingham et al., First evidence for the two-proton decay of \(^{45}\rm Fe\). Eur. Phys. J. A 14, 279–285 (2002). https://doi.org/10.1140/epja/i2002-10033-9

    ADS  Google Scholar 

  29. F. Catara, A. Insolia, E. Maglione, A. Vitturi, Relation between pairing correlations and two-particle space correlations. Phys. Rev. C 29, 1091–1094 (1984). https://doi.org/10.1103/PhysRevC.29.1091

    ADS  Google Scholar 

  30. N. Pillet, N. Sandulescu, P. Schuck, Generic strong coupling behavior of \(\rm Cooper\) pairs on the surface of superfluid nuclei. Phys. Rev. C 76, 024310 (2007). https://doi.org/10.1103/PhysRevC.76.024310

    ADS  Google Scholar 

  31. K. Hagino, H. Sagawa, Pairing correlations in nuclei on the neutron-drip line. Phys. Rev. C 72, 044321 (2005). https://doi.org/10.1103/PhysRevC.72.044321

    ADS  Google Scholar 

  32. K. Hagino, H. Sagawa, J. Carbonell et al., Coexistence of BCS- and BEC-like pair structures in halo nuclei. Phys. Rev. Lett. 99, 022506 (2007). https://doi.org/10.1103/PhysRevLett.99.022506

    ADS  Google Scholar 

  33. K. Hagino, H. Sagawa, Correlated two-neutron emission in the decay of the unbound nucleus \({}^{26}\rm O\). Phys. Rev. C 89, 014331 (2014). https://doi.org/10.1103/PhysRevC.89.014331

    ADS  Google Scholar 

  34. M. Matsuo, Spatial structure of Cooper pairs in nuclei, in Fifty years of nuclear BCS. ed. by R.A. Broglia, V. Zelevinsky (World Scientific Publishing, Singapore, 2012), pp.61–72

    Google Scholar 

  35. K. Fossez, J. Rotureau, N. Michel et al., Continuum effects in neutron-drip-line oxygen isotopes. Phys. Rev. C 96, 024308 (2017). https://doi.org/10.1103/PhysRevC.96.024308

    ADS  Google Scholar 

  36. J.L. Fisker, F.K. Thielemann, M. Wiescher, The nuclear reaction waiting points: \(^{22}{{\rm Mg}},^{26}{{\rm Si}}\),\(^{30}{{\rm S, and}}^{34}{{\rm Ar}}\) and bolometrically double-peaked type I X-ray bursts. Astrophys. J. 608, L61–L64 (2004)

    ADS  Google Scholar 

  37. D. Seweryniak, P.J. Woods, M.P. Carpenter et al., Level structure of \(^{22}\text{ Mg }\) implications for the \(^{21}\text{ Be }(p,\gamma )^{22}\text{ Mg }\) astrophysical reaction rate and for the \(^{22}\text{ Mg }\) mass. Phys. Rev. Lett. 94, 032501 (2005). https://doi.org/10.1103/PhysRevLett.94.032501

    ADS  Google Scholar 

  38. J. Giovinazzo, B. Blank, C. Borcea et al., First direct observation of two protons in the decay of \(^{45}\rm Fe\) with a time-projection chamber. Phys. Rev. Lett. 99, 102501 (2007). https://doi.org/10.1103/PhysRevLett.99.102501

    ADS  Google Scholar 

  39. W. Nazarewicz, J. Dobaczewski, T.R. Werner et al., Structure of proton drip-line nuclei around doubly magic \(^{48}\rm Ni\). Phys. Rev. C 53, 740–751 (1996). https://doi.org/10.1103/PhysRevC.53.740

    ADS  Google Scholar 

  40. W.E. Ormand, Mapping the proton drip line up to \(A=70\). Phys. Rev. C 55, 2407–2417 (1997). https://doi.org/10.1103/PhysRevC.55.2407

    ADS  Google Scholar 

  41. F.C. Barker, 12O ground-state decay by 2He emission. Phys. Rev. C 63, 047303 (2001). https://doi.org/10.1103/PhysRevC.63.047303

    ADS  Google Scholar 

  42. B.A. Brown, F.C. Barker, Di-proton decay of \({}^{45}\text{Fe}\). Phys. Rev. C 67, 041304 (2003). https://doi.org/10.1103/PhysRevC.67.041304

    ADS  Google Scholar 

  43. M. Gonçalves, N. Teruya, O.A.P. Tavares et al., Two-proton emission half-lives in the effective liquid drop model. Phys. Lett. B 774, 14–19 (2017). https://doi.org/10.1016/j.physletb.2017.09.032

    ADS  Google Scholar 

  44. J.P. Cui, Y.H. Gao, Y.Z. Wang et al., Two-proton radioactivity within a generalized liquid drop model. Phys. Rev. C 101, 014301 (2020). https://doi.org/10.1103/PhysRevC.101.014301

    ADS  Google Scholar 

  45. J.P. Cui, Y.H. Gao, Y.Z. Wang et al., Erratum: two-proton radioactivity within a generalized liquid drop model, Phys. Rev. C 104, 029902 (2021). https://doi.org/10.1103/PhysRevC.104.029902

  46. L. Neufcourt, Y.C. Cao, S. Giuliani et al., Beyond the proton drip line: Bayesian analysis of proton-emitting nuclei. Phys. Rev. C 101, 014319 (2020). https://doi.org/10.1103/PhysRevC.101.014319

    ADS  Google Scholar 

  47. H.M. Liu, Y.T. Zou, X. Pan et al., New Geiger-Nuttall law for two-proton radioactivity. Chin. Phys. C 45, 024108 (2021). https://doi.org/10.1088/1674-1137/abd01e

    ADS  Google Scholar 

  48. D.S. Delion, S.A. Ghinescu, Two-proton emission systematics. Phys. Rev. C 105, L031301 (2022). https://doi.org/10.1103/PhysRevC.105.L031301

    ADS  Google Scholar 

  49. T. Goigoux, P. Ascher, B. Blank et al., Two-proton radioactivity of \(^{67}\rm Kr\). Phys. Rev. Lett. 117, 162501 (2016). https://doi.org/10.1103/PhysRevLett.117.162501

    ADS  Google Scholar 

  50. T.B. Webb, S.M. Wang, K.W. Brown et al., First observation of unbound \(^{11}\text{ O }\), the mirror of the halo nucleus \(^{11}\text{ Li }\). Phys. Rev. Lett. 122, 122501 (2019). https://doi.org/10.1103/PhysRevLett.122.122501

    ADS  Google Scholar 

  51. S.M. Wang, W. Nazarewicz, R.J. Charity et al., Structure and decay of the extremely proton-rich nuclei \(^{11,12}\rm O\). Phys. Rev. C 99, 054302 (2019). https://doi.org/10.1103/PhysRevC.99.054302

    ADS  Google Scholar 

  52. V.I. Goldansky, 2-proton radioactivity. Nucl. Phys 27, 648–664 (1961). https://doi.org/10.1016/0029-5582(61)90309-1

    Google Scholar 

  53. R. Barton, R.E. Bell, W.R. Frisken et al., Observation of delayed proton radioactivity. Can. J. Phys 41, 2007–2025 (1963). https://doi.org/10.1139/p63-201

    ADS  Google Scholar 

  54. K.P. Jackson, C.U. Cardinal, H.C. Evans et al., \(^{53}\rm Co ^{m}\): a proton-unstable isomer. Phys. Lett. B 33, 281–283 (1970). https://doi.org/10.1016/0370-2693(70)90269-8

    ADS  Google Scholar 

  55. S. Hofmann, W. Reisdorf, G. Munzenberg et al., Proton radioactivity of \(^{151}\rm Lu\). Z. Phys. A-Hadrons. Nuclei 305, 111–123 (1982). https://doi.org/10.1007/BF01415018

    ADS  Google Scholar 

  56. B.A. Brown, Diproton decay of nuclei on the proton drip line. Phys. Rev. C 43, R1513–R1517 (1991). https://doi.org/10.1103/PhysRevC.43.R1513

    ADS  Google Scholar 

  57. B.A. Brown, Erratum: diproton decay of nuclei on the proton drip line. Phys. Rev. C 44, 924–924 (1991). https://doi.org/10.1103/PhysRevC.44.924

    ADS  Google Scholar 

  58. B.J. Cole, Stability of proton-rich nuclei in the upper sd shell and lower pf shell. Phys. Rev. C 54, 1240–1248 (1996). https://doi.org/10.1103/PhysRevC.54.1240

    ADS  Google Scholar 

  59. W.E. Ormand, Properties of proton drip-line nuclei at the sd-fp-shell interface. Phys. Rev. C 53, 214–221 (1996). https://doi.org/10.1103/PhysRevC.53.214

    ADS  Google Scholar 

  60. V.I. Goldansky, Emission of \({\beta }^{+}\)-delayed pairs of proton and doubly \({\beta }^{+}\)-delayed protons and particles. JETP. Lett. 39, 554–556 (1980)

    ADS  Google Scholar 

  61. M.D. Cable, J. Honkanen, R.F. Parry et al., Discovery of beta-delayed two-proton radioactivity: \(^{22}\rm Al\). Phys. Rev. Lett 50, 404–406 (1983). https://doi.org/10.1103/PhysRevLett.50.404

    ADS  Google Scholar 

  62. B. Blank, F. Boue, S. Andriamonje et al., Spectroscopic studies of the \(\beta p\) and \(\beta\)2\(p\) decay of \(^{23}\rm Si\). Z. Phys. A-Hadrons. Nuclei 357, 247–254 (1997). https://doi.org/10.1007/s002180050241

    ADS  Google Scholar 

  63. J. Honkanen, M.D. Cable, R.F. Parry et al., Beta-delayed two-proton decay of \(^{26}\rm P\). Phys. Lett. B 133, 146–148 (1983). https://doi.org/10.1016/0370-2693(83)90547-6

    ADS  Google Scholar 

  64. V. Borrel, J.C. Jacmart, F. Pougheon et al., \(^{31}{{\rm Ar}}{~{\rm and}~ ^{27}{{\rm S}}}\): beta-delayed two-proton emission and mass excess. Nucl. Phys. A 531, 353–369 (1991). https://doi.org/10.1016/0375-9474(91)90616-E

    ADS  Google Scholar 

  65. J.E. Reiff, M.A.C. Hotchkis, D.M. Moltz et al., A fast in-beam recoil catcher wheel and the observation of beta-delayed two-proton emission from \(^{31}\rm Ar\). Nucl. Instrum Methods. Phys. Res. Sect A 276, 228–232 (1989). https://doi.org/10.1016/0168-9002(89)90637-2

    ADS  Google Scholar 

  66. J. Äystö, D.M. Moltz, X.J. Xu et al., Observation of the first \({T}_{z}=-\frac{5}{2}\) nuclide, \(^{35}\rm Ca\), via its \(\beta\)-delayed two-proton emission. Phys. Rev. Lett. 55, 1384–1387 (1985). https://doi.org/10.1103/PhysRevLett.55.1384

    ADS  Google Scholar 

  67. D.M. Moltz, J.C. Batchelder, T.F. Lang et al., Beta-delayed two-proton decay of \(^{39}\rm Ti\). Z. Phys. A-Hadrons. Nuclei 342, 273–276 (1992). https://doi.org/10.1007/BF01291509

    ADS  Google Scholar 

  68. V. Borrel, R. Anne, D. Bazin et al., The decay modes of proton drip-line nuclei with a between 42 and 47. Z. Phys. A-Hadrons. Nuclei 344, 135–144 (1992). https://doi.org/10.1007/BF01291696

    ADS  Google Scholar 

  69. C. Dossat, N. Adimi, F. Aksouh et al., The decay of proton-rich nuclei in the mass \(A =36-56\) region. Nucl. Phys. A 792, 18–86 (2007). https://doi.org/10.1016/j.nuclphysa.2007.05.004

    ADS  Google Scholar 

  70. L. Audirac, P. Ascher, B. Blank et al., Direct and \(\beta\)-delayed multi-proton emission from atomic nuclei with a time projection chamber: the cases of \(^{43}{{\rm Cr}}{, ^{45}{{\rm Fe}}}\), and \(^{51}{{\rm Ni}}\). Eur. Phys. J. A 48, 179 (2012). https://doi.org/10.1140/epja/i2012-12179-1

    ADS  Google Scholar 

  71. M. Pomorski, M. Pfützner, W. Dominik et al., Proton spectroscopy of \(^{48}{{\rm Ni}}{,^{46}{{\rm Fe}}}\), and \(^{44}{{\rm Cr}}\). Phys. Rev. C 90, 014311 (2014). https://doi.org/10.1103/PhysRevC.90.014311

    ADS  Google Scholar 

  72. C.R. Bain, P.J. Woods, R. Coszach et al., Two proton emission induced via a resonance reaction. Phys. Lett. B 373, 35–39 (1996). https://doi.org/10.1016/0370-2693(96)00109-8

    ADS  Google Scholar 

  73. M.J. Chromik, B.A. Brown, M. Fauerbach et al., Excitation and decay of the first excited state of \(^{17}\rm Ne\). Phys. Rev. C 55, 1676–1679 (1997). https://doi.org/10.1103/PhysRevC.55.1676

    ADS  Google Scholar 

  74. J. Gómez del Campo, A. Galindo-Uribarri, J.R. Beene et al., Decay of a resonance in \(^{18}\rm Ne\) by the simultaneous emission of two protons. Phys. Rev. Lett. 86, 43–46 (2001). https://doi.org/10.1103/PhysRevLett.86.43

    ADS  Google Scholar 

  75. G. Raciti, G. Cardella, M. De Napoli, et al., Experimental evidence of \(^{2}{{\rm He}}{~{\rm decay~from}~ ^{18}{{\rm Ne}}}\) excited states. Phys. Rev. Lett. 100, 192503 (2008). https://doi.org/10.1103/PhysRevLett.100.192503

    ADS  Google Scholar 

  76. Y.T. Wang, D.Q. Fang, K. Wang et al., Observation of \(^{2}{{\rm He}}{~{\rm emission~from~the~proton-rich~nucleus~} ^{22}{{\rm Al}}}\)-delayed 2He emission. Phys. Lett. B 784, 12–15 (2018). https://doi.org/10.1016/j.physletb.2018.07.034

  77. X.X. Xu, C.J. Lin, L.J. Sun et al., Observation of \(\beta\)-delayed two-proton emission in the decay of \(^{22}\rm Si\). Phys. Lett. B 766, 312–316 (2017). https://doi.org/10.1016/j.physletb.2017.01.028

    ADS  Google Scholar 

  78. K. Wang, D.Q. Fang, Y.T. Wang et al., Spectroscopic study of \(\beta\)-delayed particle emission from proton-rich nucleus \(^{23}\rm Si\). Int. J. Mod. Phys. E 27, 1850014 (2018). https://doi.org/10.1142/S0218301318500143

    ADS  Google Scholar 

  79. Y.G. Ma, D.Q. Fang, X.Y. Sun et al., Different mechanism of two-proton emission from proton-rich nuclei \(^{23}{{\rm Al}}{ ~{\rm and~} ^{22}{{\rm Mg}}}\). Phys. Lett. B 743, 306–309 (2015). https://doi.org/10.1016/j.physletb.2015.02.066

    ADS  Google Scholar 

  80. D.Q. Fang, Y.G. Ma, X.Y. Sun et al., Proton-proton correlations in distinguishing the two-proton emission mechanism of \(^{23}{{\rm Al}}{~{\rm and~} ^{22}{{\rm Mg}}}\). Phys. Rev. C 96, 044621 (2016). https://doi.org/10.1103/PhysRevC.96.044621

    ADS  Google Scholar 

  81. X.X. Xu, C.J. Lin, H.M. Jia et al., Correlations of two protons emitted from excited states of \(^{28}{{\rm S}}{~{\rm and~} ^{27}{{\rm P}}}\). Phys. Lett. B 727, 126–129 (2013). https://doi.org/10.1016/j.physletb.2013.10.029

    ADS  Google Scholar 

  82. C.J. Lin, X.X. Xu, H.M. Jia et al., Experimental study of two-proton correlated emission from \(^{29}\rm S\) excited states. Phys. Rev. C. 80, 014310 (2009). https://doi.org/10.1103/PhysRevC.80.014310

    ADS  Google Scholar 

  83. X.X. Xu, C.J. Lin, H.M. Jia et al., Investigation of two-proton emission from excited states of the odd-\(Z\) nucleus \(^{28}{{\rm P}}\) by complete-kinematics measurements. Phys. Rev. C. 81, 054317 (2010). https://doi.org/10.1103/PhysRevC.81.054317

    ADS  Google Scholar 

  84. G.Z. Shi, J.J. Liu, Z.Y. Lin et al., \(\beta\)-delayed two-proton decay of \(^{27}\rm S\) at the proton-drip line. Phys. Rev. C 103, L061301 (2021). https://doi.org/10.1103/PhysRevC.103.L061301

    ADS  Google Scholar 

  85. C.G. Wu, H.Y. Wu, J.G. Li et al., RIBLL Collaboration, \(\beta\)-decay spectroscopy of the proton drip-line nucleus \(^{22}\rm Al\). Phys. Rev. C 104, 044311 (2021). https://doi.org/10.1103/PhysRevC104.044311

    ADS  Google Scholar 

  86. I. Mukha, K. Suemmerer, L. Acosta et al., Spectroscopy of proton-unbound nuclei by tracking their decay products in-flight: one- and two-proton decays of \(^{15}{{\rm Fe}}{, ^{16}{{\rm Ne}}}\) and \(^{19}{{\rm Na}}\). Phys. Rev. C 82, 054315 (2010). https://doi.org/10.1103/PhysRevC.82.054315

    ADS  Google Scholar 

  87. I. Mukha, K. Sümmerer, L. Acosta et al., Observation of two-proton radioactivity of \(^{19}\rm Mg\) by tracking the decay products. Phys. Rev. Lett. 99, 182501 (2007). https://doi.org/10.1103/PhysRevLett.99.182501

    ADS  Google Scholar 

  88. T.B. Webb, R.J. Charity, J.M. Elson et al., Invariant-mass spectrum of \(^{11}\rm O\). Phys. Rev. C 101, 044317 (2020). https://doi.org/10.1103/PhysRevC.101.044317

    ADS  Google Scholar 

  89. V.I. Goldansky, Neutron-excessive nuclei and two-proton radioactivity. Phys. Lett. B 212, 11–17 (1988). https://doi.org/10.1016/0370-2693(88)91226-9

    ADS  Google Scholar 

  90. B. Blank, A. Bey, G. Canchel et al., First observation of \(^{54}\rm Zn\) and its decay by two-proton emission. Phys. Rev. Lett. 94, 232501 (2005). https://doi.org/10.1103/PhysRevLett.94.232501

    ADS  Google Scholar 

  91. C. Dossat, A. Bey, B. Blank et al., Two-proton radioactivity studies with \(^{45}{{\rm Fe}}{~{\rm and~} ^{48}{{\rm Ni}}}\). Phys. Rev. C 72, 054315 (2005). https://doi.org/10.1103/PhysRevC.72.054315

    ADS  Google Scholar 

  92. M. Pomorski, M. Pfützner, W. Dominik et al., First observation of two-proton radioactivity in \(^{48}\rm Ni\). Phys. Rev. C 83, 061303 (2011). https://doi.org/10.1103/PhysRevC.83.061303

    ADS  Google Scholar 

  93. K. Miernik, W. Dominik, Z. Janas et al., Two-proton radioactivity of \(^{45}\rm Fe\). Eur. Phys. J. A 42, 431–439 (2009). https://doi.org/10.1140/epja/i2009-10781-x

    ADS  Google Scholar 

  94. P. Ascher, L. Audirac, N. Adimi et al., Direct observation of two protons in the decay of \(^{54}\rm Zn\). Phys. Rev. Lett. 107, 102502 (2011). https://doi.org/10.1103/PhysRevLett.107.102502

    ADS  Google Scholar 

  95. Evaluated Nuclear Structure Data File (ENSDF), http://www.nndc.bnl.gov/ensdf/

  96. F. Wamers, J. Marganiec, F. Aksouh et al., First observation of the unbound nucleus \(^{15}\rm Ne\). Phys. Rev. Lett. 112, 132502 (2014). https://doi.org/10.1103/PhysRevLett.112.132502

    ADS  Google Scholar 

  97. Y. Jin, C.Y. Niu, K.W. Brown et al., First observation of the four-proton unbound nucleus \(^{18}\rm Mg\). Phys. Rev. Lett. 127, 262502 (2021). https://doi.org/10.1103/PhysRevLett.127.262502

    ADS  Google Scholar 

  98. I.A. Egorova, R.J. Charity, L.V. Grigorenko et al., Democratic decay of \(^{6}\rm Be\) exposed by correlations. Phys. Rev. Lett. 109, 202502 (2012). https://doi.org/10.1103/PhysRevLett.109.202502

    ADS  Google Scholar 

  99. R.J. Charity, J.M. Elson, J. Manfredi et al., \(2p\)-\(2p\) decay of 8C and isospin-allowed \(2p\) decay of the isobaric-analog state in 8B. Phys. Rev. C 82, 041304 (2010). https://doi.org/10.1103/PhysRevC.82.041304

    ADS  Google Scholar 

  100. T.B. Webb, R.J. Charity, J.M. Elson et al., Particle decays of levels in \(^{11,12}{{\rm N}}{{~\rm and~} ^{12}{{\rm O}}}\) investigated with the invariant-mass method. Phys. Rev. C 100, 024306 (2019). https://doi.org/10.1103/PhysRevC.100.024306

    ADS  Google Scholar 

  101. I. Mukha, L. Grigorenko, K. Sümmerer et al., Proton-proton correlations observed in two-proton decay of \(^{19}{{\rm Mg}}{{~\rm and~} ^{16}{{\rm Ne}}}\). Phys. Rev. C 77, 061303 (2008). https://doi.org/10.1103/PhysRevC.77.061303

    ADS  Google Scholar 

  102. K.W. Brown, R.J. Charity, L.G. Sobotka et al., Observation of long-range three-body \({{\rm Coulomb}}\) effects in the decay of \(^{16}{{\rm Ne}}\). Phys. Rev. Lett. 113, 232501 (2014). https://doi.org/10.1103/PhysRevLett.113.232501

    ADS  Google Scholar 

  103. K.W. Brown, R.J. Charity, L.G. Sobotka et al., Interplay between sequential and prompt two-proton decay from the first excited state of \(^{16}\rm Ne\). Phys. Rev. C 92, 034329 (2015). https://doi.org/10.1103/PhysRevC.92.034329

    ADS  Google Scholar 

  104. P. Voss, T. Baumann, D. Bazin et al., \(^{19}\rm Mg\) two-proton decay lifetime. Phys. Rev. C 90, 014301 (2014). https://doi.org/10.1103/PhysRevC.90.014301

    ADS  Google Scholar 

  105. K.W. Brown, R.J. Charity, J.M. Elson et al., Proton-decaying states in light nuclei and the first observation of \(^{17}\rm Na\). Phys. Rev. C 95, 044326 (2017). https://doi.org/10.1103/PhysRevC.95.044326

    ADS  Google Scholar 

  106. X.-D. Xu, I. Mukha, L.V. Grigorenko et al., Spectroscopy of excited states of unbound nuclei \(^{30}{{\rm Ar}}{{\rm ~and~} ^{29}{{\rm Cl}}}\). Phys. Rev. C 97, 034305 (2018). https://doi.org/10.1103/PhysRevC.97.034305

    ADS  Google Scholar 

  107. I. Mukha, L.V. Grigorenko, X. Xu et al., Observation and spectroscopy of new proton-unbound isotopes \(^{30}{{\rm Ar}}{{~\rm and~} ^{29}{{\rm Cl}}}\): an interplay of prompt two-proton and sequential decay. Phys. Rev. Lett. 115, 202501 (2015). https://doi.org/10.1103/PhysRevLett.115.202501

    ADS  Google Scholar 

  108. H.-L. Wang, Z. Wang, C.-S. Gao et al., Design and tests of the prototype beam monitor of the CSR external-target experiment. Nucl. Sci. Tech. 33, 36 (2022). https://doi.org/10.1007/s41365-022-01021-1

    Article  Google Scholar 

  109. S.-W. Bai, X.-F. Yang, S.-J. Wang et al., Commissioning of a high-resolution collinear laser spectroscopy apparatus with a laser ablation ion source. Nucl. Sci. Tech. 33, 9 (2022). https://doi.org/10.1007/s41365-022-00992-5

    Google Scholar 

  110. W. Nan, B. Guo, C.-J. Lin et al., First proof-of-principle experiment with the post-accelerated isotope separator on-line beam at brif: measurement of the angular distribution of 23Na + 40Ca elastic scattering. Nucl. Sci. Tech. 32, 53 (2021). https://doi.org/10.1007/s41365-021-00889-9

    Article  Google Scholar 

  111. C.-W. Ma, H.-L. Wei, X.-Q. Liu et al., Nuclear fragments in projectile fragmentation reactions. Prog. Part. Nucl. Phys. 121, 103911 (2021). https://doi.org/10.1016/j.ppnp.2021.103911

    Google Scholar 

  112. C.-W. Ma, X.-B. Wei, X.-X. Chen et al., Precise machine learning models for fragment production in projectile fragmentation reactions using Bayesian neural networks. Chin. Phys. C 46, 074104 (2022). https://doi.org/10.1088/1674-1137/ac5efb

    ADS  Google Scholar 

  113. T.J.M. Symons, Y.P. Viyogi, G.D. Westfall et al., Observation of new neutron-rich isotopes by fragmentation of 205-mev/nucleon 40Ar ions. Phys. Rev. Lett. 42, 40–43 (1979). https://doi.org/10.1103/PhysRevLett.42.40

    ADS  Google Scholar 

  114. O. Kofoed-Hansen, K. Nielsen, Short-lived krypton isotopes and their daughter substances. Phys. Rev. X 82, 96–97 (1951). https://doi.org/10.1103/PhysRev.82.96.2

    ADS  Google Scholar 

  115. Y.T. Wang, D.Q. Fang, X.X. Xu et al., Implantation-decay method to study the \(\beta\)-delayed charged particle decay. Nucl. Sci. Tech. 29, 98 (2018). https://doi.org/10.1007/s41365-018-0438-5

    Google Scholar 

  116. L.J. Sun, X.X. Xu, C.J. Lin et al., A detection system for charged-particle decay studies with a continuous-implantation method. Nucl. Instrum. Methods Phys. Res. Sect. A 804, 1–7 (2015). https://doi.org/10.1016/j.nima.2015.09.039

    ADS  Google Scholar 

  117. J.Y. Xu, Q.T. Li, Y.L. Ye et al., Performance of a small AT-TPC prototype. Nucl. Sci. Tech. 29, 97 (2018). https://doi.org/10.1007/s41365-018-0437-6

    Google Scholar 

  118. M. Pomorski, K. Miernik, W. Dominik et al., \(\beta\)-delayed proton emission branches in \(^{43}\rm Cr\). Phys. Rev. C 83, 014306 (2011). https://doi.org/10.1103/PhysRevC.83.014306

    ADS  Google Scholar 

  119. F.F. Duan, Y.Y. Yang, B.T. Hu et al., Silicon detector array for radioactive beam experiments at HIRFL-RIBLL. Nucl. Sci. Tech 29, 165 (2018). https://doi.org/10.1007/s41365-018-0499-5

    Google Scholar 

  120. J.H. Liu, Z. Ge, Q. Wang et al., Electrostatic-lenses position-sensitive TOF MCP detector for beam diagnostics and new scheme for mass measurements at HIAF. Nucl. Sci. Tech. 30, 152 (2019). https://doi.org/10.1007/s41365-019-0676-1

    Google Scholar 

  121. R. Grzywacz, Applications of digital pulse processing in nuclear spectroscopy. Nucl. Instrum. Methods Phys. Res. Sect. B 204, 649–659 (2003). https://doi.org/10.1016/S0168-583X(02)02146-8

    ADS  Google Scholar 

  122. L.V. Grigorenko, T.D. Wiser, K. Miernik et al., Complete correlation studies of two-proton decays: 6Be and 45Fe. Phys. Lett. B 677, 30–35 (2009). https://doi.org/10.1016/j.physletb.2009.04.085

    ADS  Google Scholar 

  123. L.V. Grigorenko, T.D. Wiser, K. Mercurio et al., Three-body decay of \(^{6}\rm Be\). Phys. Rev. C 80, 034602 (2009). https://doi.org/10.1103/PhysRevC.80.034602

    ADS  Google Scholar 

  124. T. Oishi, K. Hagino, H. Sagawa, Role of diproton correlation in two-proton-emission decay of the \(^{6}\rm Be\) nucleus. Phys. Rev. C 90, 034303 (2014). https://doi.org/10.1103/PhysRevC.90.034303

    ADS  Google Scholar 

  125. S.M. Wang, W. Nazarewicz, Fermion pair dynamics in open quantum systems. Phys. Rev. Lett. 126, 142501 (2021). https://doi.org/10.1103/PhysRevLett.126.142501

    ADS  Google Scholar 

  126. L.V. Grigorenko, I.G. Mukha, I.J. Thompson et al., Two-proton widths of \(^{12}{{\rm O}}{, ^{16}{{\rm Ne}}}\), and three-body mechanism of thomas-ehrman shift. Phys. Rev. Lett. 88, 042502 (2002). https://doi.org/10.1103/PhysRevLett.88.042502

    ADS  Google Scholar 

  127. T.B. Webb, S.M. Wang, K.W. Brown et al., First observation of unbound \(^{11}{{\rm O}}{,~{\rm the~mirror~of~the~halo~nucleus~} ^{11}{{\rm Li}}}\). Phys. Rev. Lett. 122, 122501 (2019). https://doi.org/10.1103/PhysRevLett.122.122501

    ADS  Google Scholar 

  128. S. M. Wang, W. Nazarewicz, Nucleon-nucleon correlations in the extreme oxygen isotopes. J. Phys. G: Nucl. Part. Phys. (2022). https://doi.org/10.1088/1361-6471/ac888f

  129. R. Jahn, R.L. Mcgrath, D.M. Moltz et al., Angular correlations in the beta-delayed two-proton decay of \(^{22}\rm Al\). Phys. Rev. C 31, 1576–1578 (1985). https://doi.org/10.1103/PhysRevC.31.1576

    ADS  Google Scholar 

  130. R.H. Brown, R.Q. Twiss, A test of a new type of stellar interferometer on sirius. Nature 178, 1046–1048 (1956). https://doi.org/10.1038/1781046a0

    ADS  Google Scholar 

  131. S.E. Koonin, Proton pictures of high-energy nuclear collisions. Phys. Lett. B 70, 43–47 (1977). https://doi.org/10.1016/0370-2693(77)90340-9

    ADS  Google Scholar 

  132. L. Zhou, D.Q. Fang, Effect of source size and emission time on the p-p momentum correlation function in the two-proton emission process. Nucl. Sci. Tech. 31, 52 (2020). https://doi.org/10.1007/s41365-020-00759-w

    Google Scholar 

  133. A. Spyrou, Z. Kohley, T. Baumann et al., First observation of ground state dineutron decay: \(^{16}\rm Be\). Phys. Rev. Lett. 108, 102501 (2012). https://doi.org/10.1103/PhysRevLett.108.102501

    ADS  Google Scholar 

  134. A. Revel, F.M. Marqués, O. Sorlin et al., \({\rm R\rm ^{3}\rm B}\) Collaboration, Strong neutron pairing in \(\text{ core }+4n\) nuclei. Phys. Rev. Lett. 120, 152504 (2018). https://doi.org/10.1103/PhysRevLett.120.152504

  135. B. Blank, M.J.G. Borge, Nuclear structure at the proton drip line: advances with nuclear decay studies. Prog. Part. Nucl. Phys. 60, 403–483 (2008). https://doi.org/10.1016/j.ppnp.2007.12.001

    ADS  Google Scholar 

  136. Z.-P. Gao, Y.-J. Wang, H.-L. Lü et al., Machine learning the nuclear mass. Nucl. Sci. Tech. 32, 109 (2021). https://doi.org/10.1007/s41365-021-00956-1

    Article  Google Scholar 

  137. D. Benzaid, S. Bentridi, A. Kerraci et al., Bethe-weizsäcker semi-empirical mass formula parameters 2019 update based on AME2016. Nucl. Sci. Tech. 31, 9 (2020). https://doi.org/10.1007/s41365-019-0718-8

    Article  Google Scholar 

  138. B.A. Brown, R.R.C. Clement, H. Schatz et al., Proton drip-line calculations and the \(\rm rp\) process. Phys. Rev. C 65, 045802 (2002). https://doi.org/10.1103/PhysRevC.65.045802

    ADS  Google Scholar 

  139. W. Di, C.-L. Bai, H. Sagawa et al., Contributions of optimized tensor interactions on the binding energies of nuclei. Nucl. Sci. Tech. 31, 14 (2020). https://doi.org/10.1007/s41365-020-0727-7

    Article  Google Scholar 

  140. M. Thoennessen, The discovery of isotopes (Springer, Cham, 2016)

    MATH  Google Scholar 

  141. G. Audi, A.H. Wapstra, C. Thibault, The AME2003 atomic mass evaluation: (II). Tables, graphs and references. Nucl. Phys. A 729, 337–676 (2003). https://doi.org/10.1016/j.nuclphysa.2003.11.003

    ADS  Google Scholar 

  142. M. Wang, G. Audi, F.G. Kondev et al., The AME2016 atomic mass evaluation (II). Tables, graphs and references. Chin. Phys. C 41, 030003 (2017). https://doi.org/10.1088/1674-1137/41/3/030003

    ADS  Google Scholar 

  143. J.A. Hoeting, D. Madigan, A.E. Raftery, C.T. Volinsky, Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I George, and a rejoinder by the authors. Stat. Sci. 14, 382–417 (1999)

    MATH  Google Scholar 

  144. L. Wasserman, Bayesian model selection and model averaging. J. Math. Psychol. 44, 92–107 (2000). https://doi.org/10.1006/jmps.1999.1278

    MathSciNet  MATH  Google Scholar 

  145. J.M. Bernardo, A.F.M. Smith, Bayesian Theory (Wiley, New York, 1994)

    MATH  Google Scholar 

  146. A. I. Baz’, Ya. B. Zel’dovich, and A. M. Perelomov, Scattering, reactions and decay in nonrelativistic quantum mechanics (Israel Program for Scientific Translation, Jerusalem, 1969)

  147. P. Papka, R. Álvarez-Rodríguez, F. Nemulodi et al., Decay of \(^{6}{{\rm Be}}{{\rm ~populated~in~the~} ^{6}{{\rm Li}}}\)(\(^{3}{{\rm He}}{,^{3}{{\rm H}}}\)) charge-exchange reaction. Phys. Rev. C 81, 054308 (2010). https://doi.org/10.1103/PhysRevC.81.054308

    ADS  Google Scholar 

  148. K. Miernik, W. Dominik, Z. Janas et al., Two-proton correlations in the decay of \(^{45}\rm Fe\). Phys. Rev. Lett. 99, 192501 (2007). https://doi.org/10.1103/PhysRevLett.99.192501

    ADS  Google Scholar 

  149. K. Bennaceur, F. Nowacki, J. Okołowicz et al., Analysis of the \(^{16}\)O(p,\(\gamma\))\(^{17}\)F capture reaction using the shell model embedded in the continuum. Nucl. Phys. A 671, 203–232 (2000). https://doi.org/10.1016/S0375-9474(99)00851-9

    ADS  Google Scholar 

  150. J. Okołowicz, M. Płoszajczak, I. Rotter, Dynamics of quantum systems embedded in a continuum. Phys. Rep. 374, 271–383 (2003). https://doi.org/10.1016/S0370-1573(02)00366-6

    ADS  MathSciNet  MATH  Google Scholar 

  151. J. Rotureau, J. Okołowicz, M. Płoszajczak, Microscopic theory of the two-proton radioactivity. Phys. Rev. Lett. 95, 042503 (2005). https://doi.org/10.1103/PhysRevLett.95.042503

    ADS  Google Scholar 

  152. J. Rotureau, J. Okołowicz, M. Płoszajczak, Theory of the two-proton radioactivity in the continuum shell model. Nucl. Phys. A 767, 13–57 (2006). https://doi.org/10.1016/j.nuclphysa.2005.12.005

    ADS  Google Scholar 

  153. B.A. Brown, B. Blank, J. Giovinazzo, Hybrid model for two-proton radioactivity. Phys. Rev. C 100, 054332 (2019). https://doi.org/10.1103/PhysRevC.100.054332

    ADS  Google Scholar 

  154. L.V. Grigorenko, M.V. Zhukov, Two-proton radioactivity and three-body decay. II. Exploratory studies of lifetimes and correlations. Phys. Rev. C 68, 054005 (2003). https://doi.org/10.1103/PhysRevC.68.054005

    ADS  Google Scholar 

  155. L.V. Grigorenko, T.A. Golubkova, J.S. Vaagen et al., Decay mechanism and lifetime of \(^{67}\rm Kr\). Phys. Rev. C 95, 021601 (2017). https://doi.org/10.1103/PhysRevC.95.021601

    ADS  Google Scholar 

  156. E. Braaten, H.W. Hammer, Universality in few-body systems with large scattering length. Phys. Rep. 428, 259–390 (2006). https://doi.org/10.1016/j.physrep.2006.03.001

    ADS  MathSciNet  Google Scholar 

  157. D. Baye, P. Descouvemont, N.K. Timofeyuk, Matter densities of B-8 and Li-8 in a microscopic cluster model and the proton-halo problem of B-8. Nucl. Phys. A 577, 624–640 (1994)

    ADS  Google Scholar 

  158. K. Hagino, H. Sagawa, Decay dynamics of the unbound \({}^{25}{{\rm O}}{~{\rm and~} {}^{26}{{\rm O}}}\) nuclei. Phys. Rev. C 93, 034330 (2016). https://doi.org/10.1103/PhysRevC.93.034330

    ADS  Google Scholar 

  159. K. Hagino, S. Sagawa, Are there good probes for di-neutron correlation in light neutron-rich nuclei? Few-Body Syst. 57, 185 (2016). https://doi.org/10.1007/s00601-015-1027-3

    ADS  Google Scholar 

  160. Y. Suzuki, K. Ikeda, Cluster-orbital shell model and its application to the \(\rm He\) isotopes. Phys. Rev. C 38, 410–413 (1988). https://doi.org/10.1103/PhysRevC.38.410

    ADS  Google Scholar 

  161. N. Michel, W. Nazarewicz, M. Płoszajczak et al., Gamow shell model description of neutron-rich nuclei. Phys. Rev. Lett. 89, 042502 (2002). https://doi.org/10.1103/PhysRevLett.89.042502

    ADS  Google Scholar 

  162. S.M. Wang, N. Michel, W. Nazarewicz et al., Structure and decays of nuclear three-body systems: the Gamow coupled-channel method in \(\rm Jacobi\) coordinates. Phys. Rev. C 96, 044307 (2017). https://doi.org/10.1103/PhysRevC.96.044307

    ADS  Google Scholar 

  163. T. Berggren, On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes. Nucl. Phys. A 109, 265–287 (1968). https://doi.org/10.1016/0375-9474(68)90593-9

    ADS  Google Scholar 

  164. G. Papadimitriou, A.T. Kruppa, N. Michel et al., Charge radii and neutron correlations in helium halo nuclei. Phys. Rev. C 84, 051304 (2011). https://doi.org/10.1103/PhysRevC.84.051304

    ADS  Google Scholar 

  165. T. Oishi, M. Kortelainen, A. Pastore, Dependence of two-proton radioactivity on nuclear pairing models. Phys. Rev. C 96, 044327 (2017). https://doi.org/10.1103/PhysRevC.96.044327

    ADS  Google Scholar 

  166. O. Hen, G.A. Miller, E. Piasetzky et al., Nucleon-nucleon correlations, short-lived excitations, and the quarks within. Rev. Mod. Phys. 89, 045002 (2017). https://doi.org/10.1103/RevModPhys.89.045002

    ADS  Google Scholar 

  167. K.M. Watson, The effect of final state interactions on reaction cross sections. Phys. Rev. 88, 1163 (1952). https://doi.org/10.1103/PhysRev.88.1163

    ADS  MATH  Google Scholar 

  168. A.B. Migdal, Theory of nuclear reactions with formation of slow particles. Sov. Phys. JETP 1, 2 (1955)

    MATH  Google Scholar 

  169. R.J.N. Phillips, Comparison of p-p and n-n final state interactions. Nucl. Phys. 53, 650–656 (1964). https://doi.org/10.1016/0029-5582(64)90643-1

    Google Scholar 

  170. S.M. Wang, W. Nazarewicz, Puzzling two-proton decay of \(^{67}\rm Kr\). Phys. Rev. Lett. 120, 212502 (2018). https://doi.org/10.1103/PhysRevC.120.212502

    ADS  Google Scholar 

  171. K. Hagino, N. Rowley, A.T. Kruppa, A program for coupled-channel calculations with all order couplings for heavy-ion fusion reactions. Comput. Phys. Commun. 123, 143–152 (1999). https://doi.org/10.1016/S0010-4655(99)00243-X

    ADS  MATH  Google Scholar 

  172. K. Hagino, Role of dynamical particle-vibration coupling in reconciliation of the \({d}_{3/2}\) puzzle for spherical proton emitters. Phys. Rev. C 64, 041304 (2001). https://doi.org/10.1103/PhysRevC.64.041304

    ADS  Google Scholar 

  173. B. Barmore, A.T. Kruppa, W. Nazarewicz et al., Theoretical description of deformed proton emitters: nonadiabatic coupled-channel method. Phys. Rev. C 62, 054315 (2000). https://doi.org/10.1103/PhysRevC.62.054315

    ADS  Google Scholar 

  174. A.T. Kruppa, W. Nazarewicz, Gamow and \(R\)-matrix approach to proton emitting nuclei. Phys. Rev. C 69, 054311 (2004). https://doi.org/10.1103/PhysRevC.69.034314

    ADS  Google Scholar 

  175. N. Michel, W. Nazarewicz, M. Płoszajczak et al., Shell model in the complex energy plane. J. Phys. G 36, 013101 (2009)

    ADS  Google Scholar 

  176. A.T. Kruppa, B. Barmore, W. Nazarewicz et al., Fine structure in the decay of deformed proton emitters: Nonadiabatic approach. Phys. Rev. Lett. 84, 4549–4552 (2000). https://doi.org/10.1103/PhysRevLett.84.4549

    ADS  Google Scholar 

  177. H. Esbensen, C.N. Davids, Coupled-channels treatment of deformed proton emitters. Phys. Rev. C 63, 014315 (2000). https://doi.org/10.1103/PhysRevC.63.014315

    ADS  Google Scholar 

  178. C.N. Davids, H. Esbensen, Particle-vibration coupling in proton decay of near-spherical nuclei. Phys. Rev. C 64, 034317 (2001). https://doi.org/10.1103/PhysRevC.64.034317

    ADS  Google Scholar 

  179. C.N. Davids, H. Esbensen, Decay rate of triaxially deformed proton emitters. Phys. Rev. C 69, 034314 (2004). https://doi.org/10.1103/PhysRevC.69.034314

    ADS  Google Scholar 

  180. G. Fiorin, E. Maglione, L.S. Ferreira, Theoretical description of deformed proton emitters: nonadiabatic quasiparticle method. Phys. Rev. C 67, 054302 (2003). https://doi.org/10.1103/PhysRevC.67.054302

    ADS  Google Scholar 

  181. P. Arumugam, E. Maglione, L.S. Ferreira, Nonadiabatic quasiparticle description of triaxially deformed proton emitters. Phys. Rev. C 76, 044311 (2007). https://doi.org/10.1103/PhysRevC.76.044311

    ADS  Google Scholar 

  182. W. Nazarewicz, J. Dudek, R. Bengtsson et al., Microscopic study of the high-spin behaviour in selected A≃80 nuclei. Nucl. Phys. A 435, 397–447 (1985). https://doi.org/10.1016/0375-9474(85)90471-3

    ADS  Google Scholar 

  183. M. Yamagami, K. Matsuyanagi, M. Matsuo, Symmetry-unrestricted Skyrme-Hartree-Fock-Bogoliubov calculations for exotic shapes in N=Z nuclei from 64Ge to84Mo. Nucl. Phys. A 693, 579–602 (2001). https://doi.org/10.1016/S0375-9474(01)00918-6

    ADS  Google Scholar 

  184. K. Kaneko, M. Hasegawa, T. Mizusaki, Shape transition and oblate-prolate coexistence in \(N=Z\)\(fpg\)-shell nuclei. Phys. Rev. C 70, 051301 (2004). https://doi.org/10.1103/PhysRevC.70.051301

    ADS  Google Scholar 

  185. A. Volya, Computational approaches to many-body dynamics of unstable nuclear systems, (2014), note in Proceedings of the International Conference ‘Nuclear Theory in the Supercomputing Era’, Khabarovsk, Russia. arXiv:1412.6335 [nucl-th]

  186. M. Peshkin, A. Volya, V. Zelevinsky, Non-exponential and oscillatory decays in quantum mechanics. Europhys. Lett. 107, 40001 (2014). https://doi.org/10.1209/0295-5075/107/40001

    ADS  Google Scholar 

  187. M. Bender, R. Bernard, G. Bertsch et al., Future of nuclear fission theory. J. Phys. G 47, 113002 (2020). https://doi.org/10.1088/1361-6471/abab4f

    Google Scholar 

  188. C.A. Bertulani, M.S. Hussein, G. Verde, Blurred femtoscopy in two-proton decay. Phys. Lett. B 666, 86–90 (2008). https://doi.org/10.1016/j.physletb.2008.06.062

    ADS  Google Scholar 

  189. R.M. Id Betan, R. de la Madrid, The \({{\rm Gamow}}{{\rm -state~description~of~the~decay~energy~spectrum~of~neutron-unbound~} ^{25}{{\rm O}}}\). Nucl. Phys. A 970, 398–410 (2018). https://doi.org/10.1016/j.nuclphysa.2018.01.003

    ADS  Google Scholar 

  190. D.R. Thompson, M. Lemere, Y.C. Tang, Systematic investigation of scattering problems with the resonating-group method. Nucl. Phys. A 286, 53–66 (1977). https://doi.org/10.1016/0375-9474(77)90007-0

    ADS  Google Scholar 

  191. F.C. Barker, \({R}\)-matrix formulas for three-body decay widths. Phys. Rev. C 68, 054602 (2003). https://doi.org/10.1103/PhysRevC.68.054602

    ADS  Google Scholar 

  192. Z.Q. Zhang, Y.G. Ma, Measurements of momentum correlation and interaction parameters between antiprotons. Nucl. Sci. Tech. 27, 152 (2016). https://doi.org/10.1007/s41365-016-0147-x

    Google Scholar 

  193. B.S. Huang, Y.G. Ma, Two-proton momentum correlation from photodisintegration of \(\alpha\)-clustering light nuclei in the quasideuteron region. Phys. Rev. C 101, 034615 (2020). https://doi.org/10.1103/PhysRevC.101.034615

    ADS  Google Scholar 

  194. L. Shen, B.S. Huang, Y.G. Ma, Short-range correlations in the extended quantum molecular dynamics model. Phys. Rev. C 105, 014603 (2022). https://doi.org/10.1103/PhysRevC.105.014603

    ADS  Google Scholar 

  195. D. Kostyleva, I. Mukha, L. Acosta et al., Towards the limits of existence of nuclear structure: observation and first spectroscopy of the isotope \(^{31}\rm K\) by measuring its three-proton decay. Phys. Rev. Lett. 123, 092502 (2019). https://doi.org/10.1103/PhysRevLett.123.092502

    ADS  Google Scholar 

  196. D. H. Wilkinson (Ed), Isospin in nuclear physics (North Holland Pub. Co., 1970)

  197. D.D. Warner, M.A. Bentley, P. Van Isacker, The role of isospin symmetry in collective nuclear structure. Nat. Phys. 2, 311–318 (2006). https://doi.org/10.1038/nphys291

    Google Scholar 

  198. Z. Kohley, T. Baumann, G. Christian et al., Three-body correlations in the ground-state decay of \(^{26}\rm O\). Phys. Rev. C 91, 034323 (2015). https://doi.org/10.1103/PhysRevC.91.034323

    ADS  Google Scholar 

  199. Y. Kondo, T. Nakamura, R. Tanaka et al., Nucleus \(^{26}\rm O\): a barely unbound system beyond the drip line. Phys. Rev. Lett. 116, 102503 (2016). https://doi.org/10.1103/PhysRevLett.116.102503

    ADS  Google Scholar 

  200. L.V. Grigorenko, I.G. Mukha, M.V. Zhukov, Lifetime and fragment correlations for the two-neutron decay of \(^{26}\rm O\) ground state. Phys. Rev. Lett. 111, 042501 (2013). https://doi.org/10.1103/PhysRevLett.111.042501

    ADS  Google Scholar 

  201. A. Adahchour, P. Descouvemont, Three-body continuum of \(^{26}\rm O\). Phys. Rev. C 96, 054319 (2017). https://doi.org/10.1103/PhysRevC.96.054319

    ADS  Google Scholar 

  202. J. Casal, Two-nucleon emitters within a pseudostate method: the case of \(^{6}{{\rm Be}}{~{\rm and}~ ^{16}{{\rm Be}}}\). Phys. Rev. C 97, 034613 (2018). https://doi.org/10.1103/PhysRevC.97.034613

    ADS  Google Scholar 

  203. L.V. Grigorenko, J.S. Vaagen, M.V. Zhukov, Exploring the manifestation and nature of a dineutron in two-neutron emission using a dynamical dineutron model. Phys. Rev. C 97, 034605 (2018). https://doi.org/10.1103/PhysRevC.97.034605

    ADS  Google Scholar 

  204. J.G. Li, N. Michel, W. Zuo et al., Unbound spectra of neutron-rich oxygen isotopes predicted by the Gamow shell model. Phys. Rev. C 103, 034305 (2021). https://doi.org/10.1103/PhysRevC.103.034305

    ADS  Google Scholar 

  205. L.V. Grigorenko, I.G. Mukha, C. Scheidenberger et al., Two-neutron radioactivity and four-nucleon emission from exotic nuclei. Phys. Rev. C 84, 021303 (2011). https://doi.org/10.1103/PhysRevC.84.021303

    ADS  Google Scholar 

  206. B. Alex Brown, The nuclear shell model towards the drip lines. arXiv:2204.06088 (2022)

  207. M. Duer, T. Aumann, R. Gernhäuser et al., Observation of a correlated free four-neutron system. Nature 606, 678 (2022). https://doi.org/10.1038/s41586-022-04827-6

    ADS  Google Scholar 

  208. G.L. Sobotka, M. Piarulli, Observation of a correlated free four-neutron system. Nature 606, 656 (2022). https://doi.org/10.1038/d41586-022-01634-x

    ADS  Google Scholar 

  209. K. Kisamori, S. Shimoura, H. Miya et al., Candidate resonant tetraneutron state populated by the \(^{4}{{\rm He}}{(^{8}{{\rm He}}},^{8}{{\rm Be}})\) reaction. Phys. Rev. Lett. 116, 052501 (2016). https://doi.org/10.1103/PhysRevLett.116.052501

    ADS  Google Scholar 

  210. S.C. Pieper, Can modern nuclear hamiltonians tolerate a bound tetraneutron? Phys. Rev. Lett. 90, 252501 (2003). https://doi.org/10.1103/PhysRevLett.90.252501

    ADS  Google Scholar 

  211. K. Fossez, J. Rotureau, N. Michel et al., Can tetraneutron be a narrow resonance? Phys. Rev. Lett. 119, 032501 (2017). https://doi.org/10.1103/PhysRevLett.119.032501

    ADS  Google Scholar 

  212. A. Deltuva, Tetraneutron: rigorous continuum calculation. Phys. Lett. B 782, 238–241 (2018). https://doi.org/10.1016/j.physletb.2018.05.041

    ADS  Google Scholar 

  213. J.G. Li, N. Michel, B.S. Hu et al., Ab initio no-core Gamow shell-model calculations of multineutron systems. Phys. Rev. C 100, 054313 (2019). https://doi.org/10.1103/PhysRevC.100.054313

    ADS  Google Scholar 

  214. M.D. Higgins, C.H. Greene, A. Kievsky et al., Nonresonant density of states enhancement at low energies for three or four neutrons. Phys. Rev. Lett. 125, 052501 (2020). https://doi.org/10.1103/PhysRevLett.125.052501

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by all authors. The first draft of the manuscript was written by Long Zhou and Si-Min Wang, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Si-Min Wang.

Additional information

This work is partially supported by the National Natural Science Foundation of China (Nos. 12147101, 11925502, 11935001, 11961141003, 11890714), the National Key R&D Program of China (No. 2018YFA0404404), the Strategic Priority Research Program of Chinese Academy of Sciences (No. XDB34030000), and the Shanghai Development Foundation for Science and Technology (No. 19ZR1403100).

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, L., Wang, SM., Fang, DQ. et al. Recent progress in two-proton radioactivity. NUCL SCI TECH 33, 105 (2022). https://doi.org/10.1007/s41365-022-01091-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41365-022-01091-1

Keywords

Navigation