Skip to main content
SpringerLink
Log in

Two-proton radioactivity of the excited state within the Gamow-like and modified Gamow-like models

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

Abstract

In this study, we systematically investigated the two-proton (\(\text {2p}\)) radioactivity half-lives from the excited state of nuclei near the proton drip line within the Gamow-like model (GLM) and modified Gamow-like model (MGLM). The calculated results were highly consistent with the theoretical values obtained using the unified fission model [Chin. Phys. C \({\textbf {45}}\), 124105 (2021)], effective liquid drop model, and generalized liquid drop model [Acta Phys. Sin \({\textbf {71}}\), 062301 (2022)]. Furthermore, utilizing the GLM and MGLM, we predicted the \(\text {2p}\) radioactivity half-lives from the excited state for some nuclei that are not yet available experimentally. Simultaneously, by analyzing the calculated results from these theoretical models, it was found that the half-lives are strongly dependent on \(Q_\text {2p}\) and \(\ell \).

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. X.D. Sun, P. Guo, X.H. Li, Systematic study of \(\alpha \) decay half-lives for even-even nuclei within a two-potential approach. Phys. Rev. C 93, 034316 (2016). https://doi.org/10.1103/PhysRevC.93.034316

    Article  ADS  Google Scholar 

  2. X.D. Sun, P. Guo, X.H. Li, Systematic study of favored \(\alpha \)-decay half-lives of closed shell odd-\(A\) and doubly-odd nuclei related for the ground and isomeric states, respectively. Phys. Rev. C 94, 024338 (2016). https://doi.org/10.1103/PhysRevC.94.024338

    Article  ADS  Google Scholar 

  3. C.Z. Shi, Y.G. Ma, \(\alpha \)-clustering effect on flows of direct photons in heavy-ion collisions. Nucl. Sci. Tech. 32, 66 (2021). https://doi.org/10.1007/s41365-021-00897-9

    Article  Google Scholar 

  4. M. Ji, C. Xu, Quantum anti-zeno effect in nuclear \(\beta \) decay. Chin. Phys. Lett. 38, 032301 (2021). https://doi.org/10.1088/0256-307X/38/3/032301

    Article  ADS  Google Scholar 

  5. 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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. L.L. Zhu, B. Wang, M. Wang et al., Energy and centrality dependence of light nuclei production in relativistic heavy-ion collisions. Nucl. Sci. Tech. 33, 45 (2022). https://doi.org/10.1007/s41365-022-01028-8

    Article  Google Scholar 

  8. C. Shen, L. Yan, Recent development of hydrodynamic modeling in heavy-ion collisions. Nucl. Sci. Tech. 31, 122 (2020). https://doi.org/10.1007/s41365-020-00829-z

    Article  MathSciNet  Google Scholar 

  9. F. Zhang, J. Su, Probing neutron-proton effective mass splitting using nuclear stopping and isospin mix in heavy-ion collisions in GeV energy region. Nucl. Sci. Tech. 31, 77 (2020). https://doi.org/10.1007/s41365-020-00787-6

    Article  Google Scholar 

  10. Y.J. Wang, F.H. Guan, X.Y. Diao et al., CSHINE for studies of HBT correlation in heavy ion reactions. Nucl. Sci. Tech. 32, 4 (2021). https://doi.org/10.1007/s41365-020-00842-2

    Article  Google Scholar 

  11. P.J. Woods, C.N. Davids, Nuclei beyond the proton drip-line. Annu. Rev. Nucl. Part. Sci. 47, 541 (1977). https://doi.org/10.1146/annurev.nucl.47.1.541

    Article  ADS  Google Scholar 

  12. A.A. Sonzogni, Proton radioactivity in \(Z > 50\) nuclides. Nucl. Data. Sheets 95, 1 (2002). https://doi.org/10.1006/ndsh.2002.0001

    Article  ADS  Google Scholar 

  13. D.S. Delion, R.J. Liotta, R. Wyss, Systematics of proton emission. Phys. Rep. 424, 113 (2006). https://doi.org/10.1103/PhysRevLett.96.072501

    Article  ADS  Google Scholar 

  14. M. Pfützner, M. Karny, L.V. Grigorenko et al., Radioactive decays at limits of nuclear stability. Rev. Mod. Phys. 84, 567 (2012). https://doi.org/10.1103/RevModPhys.84.567.

    Article  ADS  Google Scholar 

  15. D. Pathak, P. Singh, H. Parshad, H. Kaur, R. Sudhir, Jain., Quest for two-proton radioactivity. Eur. Phys. J. Plus. 137, 272 (2022). https://doi.org/10.1140/epjp/s13360-022-02354-x

    Article  Google Scholar 

  16. 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. 32, 52 (2020). https://doi.org/10.1007/s41365-020-00759-w

    Article  Google Scholar 

  17. L. Zhou, S.M. Wang, D.Q. Fang et al., Recent progress in two-proton radioactivity. Nucl. Sci. Tech. 33, 105 (2022). https://doi.org/10.1007/s41365-022-01091-1

    Article  Google Scholar 

  18. B. Blank, J. Giovinazzo, M. Pfützner, First observation of two-proton radioactivity from an atomic nucleus. Compt. Rend. Phys. 4, 521 (2003). https://doi.org/10.1016/S1631-0705(03)00051-3

    Article  ADS  Google Scholar 

  19. Y. B. Zel’dovich, The existence of new isotopes of light nuclei and the equation of state of neutrons. Sov. Phys. JETP 11, 812 (1960). www.jetp.ras.ru/cgi-bin/dn/e_011_04_0812.pdf

  20. V.M. Galitsky, V.F. Cheltsov, Two-proton radioactivity theory. Nucl. Phys. 56, 86 (1964). https://doi.org/10.1016/0029-5582(64)90455-9

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. A. Kruppa, W. Nazarewicz, Gamow and \(R\)-matrix approach to proton emitting nuclei. Phys. Rev. C 69, 054311 (2004). https://doi.org/10.1103/PhysRevC.69.054311

    Article  ADS  Google Scholar 

  23. S.M. Wang, W. Nazarewicz, Puzzling Two-Proton Decay of \(^{67}\)Kr. Phys. Rev. Lett. 120, 212502 (2018). https://doi.org/10.1103/PhysRevLett.120.212502

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  28. I. Mukha, K. Sümmerer, L. Acosta et al., Observation of two-Proton Radioactivity of \(^{19}\)Mg by Tracking the Decay Products. Phys. Rev. Lett. 99, 182501 (2007). https://doi.org/10.1103/PhysRevLett.99.182501

    Article  ADS  Google Scholar 

  29. I. Mukha, E. Roeckl, L. Batist et al., Proton-proton correlations observed in two-proton radioactivity of \(^{94}\)Ag. Nature 439, 298 (2006). https://doi.org/10.1038/nature04453

    Article  ADS  Google Scholar 

  30. B. Blank, M. Chartier, S. Czajkowski et al., Discovery of doubly magic \(^{48}\)Ni. Phys. Rev. Lett. 84, 1116 (2000). https://doi.org/10.1103/PhysRevLett.84.1116

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. J. Jänecke, The emission of protons from light neutron-deficient nuclei. Nucl. Phys. 61, 326 (1965). https://doi.org/10.1016/0029-5582(65)90907-7

    Article  Google Scholar 

  34. M.D. Cable, J. Honkanen, R.F. Parry et al., Discovery of Beta-Delayed Two-Proton Radioactivity: \(^{22}\)Al. Phys. Rev. Lett 50, 404 (1983). https://doi.org/10.1103/PhysRevLett.50.404

    Article  ADS  Google Scholar 

  35. B. Blank, F. Bouns, S. Andriamonje, Spectroscopic studies of the \(\beta \)p and \(\beta \)2p decay of \(^{23}\)Si. Z. Phys. A. 357, 247 (1997). https://doi.org/10.1007/s002180050241

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  38. 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 (2007). https://doi.org/10.1016/j.nuclphysa.2007.05.004

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  41. J. del Gomez del Compo., A. Galindo-Uribarri, J.R. Beene, Decay of a resonance in by the simultaneous emission of two protons. Phys. Rev. Lett. 86, 43 (2001). https://doi.org/10.1103/PhysRevLett.86.43

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  43. M.J. Chromik, P.G. Thirolf, M. Thoennessen et al., Two-proton spectroscopy of low-lying states in \(^{17}\)Ne. Phys. Rev. C 66, 024313 (2002). https://doi.org/10.1103/PhysRevC.66.024313

    Article  ADS  Google Scholar 

  44. T. Zerguerras, B. Blank, Y. Blumenfeld et al., Study of light proton-rich nuclei by complete kinematics measurements. Eur. Phys. J. A 20, 389 (2004). https://doi.org/10.1140/epja/i2003-10176-1

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  46. D.Q. Fang, Y.G. Ma, X.Y. Sun et al., Proton-proton correlations in distinguishing the two-proton emission mechanism of \(^{23}\)Al and \(^{22}\)Mg. Phys. Rev. C 94, 044621 (2016). https://doi.org/10.1103/PhysRevC.94.044621

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  50. O.A.P. Tavares, E.L. Medeiros, A calculation model to half-life estimate of two-proton radioactive decay process. Eur. Phys. J. A 54, 65 (2018). https://doi.org/10.1140/epja/i2018-12495-4

    Article  ADS  Google Scholar 

  51. Y.Z. Wang, J.P. Cui, Y.H. Gao et al., Two-proton radioactivity of exotic nuclei beyond proton drip-line. Commun. Theor. Phys. 73, 075301 (2021). https://doi.org/10.1088/1572-9494/abfa00

    Article  ADS  Google Scholar 

  52. D.X. Zhu, H.M. Liu, Y.Y. Xu et al., Two-proton radioactivity within Coulomb and proximity potential model. Chin. Phys. C 46, 044106 (2022). https://doi.org/10.1088/1674-1137/ac45ef

    Article  ADS  Google Scholar 

  53. D.S. Delion, R.J. Liotta, R. Wyss, Simple approach to two-proton emission. Phys. Rev. C 87, 034328 (2013). https://doi.org/10.1103/PhysRevC.87.034328

    Article  ADS  Google Scholar 

  54. L.V. Grigorenko, R.C. Johnson, I. Mukha et al., Two-proton radioactivity and three-body decay: General problems and theoretical approach. Phys. Rev. C 64, 054002 (2001). https://doi.org/10.1103/PhysRevC.64.054002

    Article  ADS  Google Scholar 

  55. A. Adel, A.R. Abdulghany, Proton radioactivity and \(\alpha \)-decay of neutron-deficient nuclei. Phys. Script. 96, 125314 (2021). https://doi.org/10.1088/1402-4896/ac33f6

    Article  ADS  Google Scholar 

  56. 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 \(^{23}\)Na + \(^{40}\)Ca elastic scattering. Nucl. Sci. Tech. 32, 53 (2021). https://doi.org/10.1007/s41365-021-00889-9

    Article  Google Scholar 

  57. C. Chen, Y.J. Li, H. Zhang et al., Preparation of large-area isotopic magnesium targets for the \(^{25}\)Mg(\(p\),\(\gamma \))\(^{26}\)Al experiment at JUNA. Nucl. Sci. Tech. 31, 91 (2020). https://doi.org/10.1007/s41365-020-00800-y

    Article  Google Scholar 

  58. H.C. Manjunatha, N. Sowmya, P.S. Damodara Gupta et al., Investigation of decay modes of superheavy nuclei. Nucl. Sci. Tech. 32, 130 (2021). https://doi.org/10.1007/s41365-021-00967-y

    Article  Google Scholar 

  59. 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

    Article  ADS  Google Scholar 

  60. I. Sreeja, M. Balasubramaniam, An empirical formula for the half-lives of exotic two-proton emission. Eur. Phys. J. A 55, 33 (2019). https://doi.org/10.1140/epja/i2019-12694-5

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  62. B.J. Cole, Systematics of proton and diproton separation energies for light nuclei. Phys. Rev. C 56, 1866 (1997). https://doi.org/10.1103/PhysRevC.56.1866

    Article  ADS  Google Scholar 

  63. A. Zdeb, M. Warda, K. Pomorski, Half-lives for \(\alpha \) and cluster radioactivity within a Gamow-like model. Phys. Rev. C 87, 024308 (2013). https://doi.org/10.1103/PhysRevC.87.024308

    Article  ADS  Google Scholar 

  64. A. Zdeb, M. Warda, C.M. Petrache, K. Pomorski, Proton emission half-lives within a Gamow-like model. Eur. Phys. J. A 52, 323 (2016). https://doi.org/10.1140/epja/i2016-16323-7

    Article  ADS  Google Scholar 

  65. H.M. Liu, X. Pan, Y.T. Zou et al., Systematic study of two-proton radioactivity within a Gamow-like model. Chin. Phys. C 45, 044110 (2021). https://doi.org/10.1088/1674-1137/abe10f

    Article  ADS  Google Scholar 

  66. H.M. Liu, Y.T. Zou, X. Pan et al., Systematic study of two-proton radioactivity half-lives based on a modified Gamow-like model. Int. J. Mod. Phys. E 30, 2150074 (2021). https://doi.org/10.1142/S0218301321500749

    Article  ADS  Google Scholar 

  67. S. G. Nilsson Binding states of individual nucleons in strongly deformed nuclei, Dan. Mat .Fys. Medd 29, 16 (1955). cds.cern.ch/record/212345/files/p1.pdf

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

    Article  ADS  Google Scholar 

  69. N. Anyas-Weiss, J.C. Cornell, P.S. Fisher et al., Nuclear structure of light nuclei using the selectivity of high energy transfer reactions with heavy ions. Phys. Rep. 12, 201 (1974). https://doi.org/10.1016/0370-1573(74)90045-3

    Article  ADS  Google Scholar 

  70. 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

    Article  ADS  Google Scholar 

  71. 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

    Article  ADS  Google Scholar 

  72. A. Kankainen, V.V. Elomaa, L. Batist et al., Systematics of cluster-radioactivity-decay constants as suggested by microscopic calculations. Phys. Rev. Lett. 61, 1930 (1988). https://doi.org/10.1103/PhysRevLett.61.1930

    Article  Google Scholar 

  73. B. Durand, L. Durand, Duality for heavy-quark systems. Phys. Rev. D 23, 1092 (1981). https://doi.org/10.1103/PhysRevD.23.1092

    Article  ADS  Google Scholar 

  74. R.L. Hall, Envelope representations for screened Coulomb potentials. Phys. Rev. A 32, 14 (1985). https://doi.org/10.1103/PhysRevA.32.14

    Article  ADS  Google Scholar 

  75. R.L. Hall, R. Dutt, K. Chowdhury et al., An improved calculation for screened Coulomb potentials in Rayleigh-Schrodinger perturbation theory. J. Phys. A: Math. Gen. 18, 1379 (1985). https://doi.org/10.1088/0305-4470/18/9/020

    Article  ADS  Google Scholar 

  76. J. Lindhard, P.G. Hansen, Atomic effects in low-energy beta decay: The case of tritium. Phys. Rev. Lett. 57, 965 (1986). https://doi.org/10.1103/PhysRevLett.57.965

    Article  ADS  Google Scholar 

  77. P. Pyykkö, J. Jokisaari, Spectral density analysis of nuclear spin-spin coupling: I Hulth\(\rm \acute{e}\)n potential LCAO model for J\(\rm _{X-H}\) in hydride XH\(_4\). Chem. Phys. 10, 293 (1975). https://doi.org/10.1016/0301-0104(75)87043-1

    Article  Google Scholar 

  78. J.J. Morehead, Asymptotics of radial wave equations. J. Math. Phys. 36, 5431 (1955). https://doi.org/10.1063/1.531270

    Article  ADS  MathSciNet  MATH  Google Scholar 

  79. F.Z. Xing, J.P. Cui, Y.Z. Wang et al., Two-proton radioactivity of ground and excited states within a unified fission model. Chin. Phys. C 45, 124105 (2021). https://doi.org/10.1088/1674-1137/ac2425

    Article  ADS  Google Scholar 

  80. F.Z. Xing, J.P. Cui, Y.Z. Wang et al., Two-proton emission from excited states of proton-rich nuclei. Acta. Phys. Sin. 71, 062301 (2022). https://doi.org/10.7498/aps.71.20211839

    Article  Google Scholar 

  81. X. Zhou, M. Wang, Y.H. Zhang et al., Charge resolution in the isochronous mass spectrometry and the mass of \(^{51}\)Co. Nucl. Sci. Tech. 32, 37 (2021). https://doi.org/10.1007/s41365-021-00876-0

    Article  Google Scholar 

  82. 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 

  83. X.C. Ming, H.F. Zhang, R.R. Xu et al., Nuclear mass based on the multi-task learning neural network method. Nucl. Sci. Tech. 33, 48 (2022). https://doi.org/10.1007/s41365-022-01031-z

    Article  Google Scholar 

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

    Article  Google Scholar 

  85. H.L. Liu, D.D. Han, P. Ji et al., Reaction rate weighted multilayer nuclear reaction network. Chin. Phys. Lett. 37, 112601 (2020). https://doi.org/10.1088/0256-307X/37/11/112601

    Article  ADS  Google Scholar 

  86. H.Y. Lu, C.H. Li, B.B. Chen, State classification via a random-walk-based quantum neural network. Chin. Phys. Lett. 39, 050301 (2022). https://doi.org/10.1088/0256-307X/39/5/050301

    Article  Google Scholar 

  87. H.Y. Lu, C.H. Li, B.B. Chen et al., Network-initialized Monte Carlo based on generative neural networks. Chin. Phys. Lett. 39, 050701 (2022). https://doi.org/10.1088/0256-307X/39/5/050701

    Article  ADS  Google Scholar 

  88. H.Y. Lu, C.H. Li, B.B. Chen et al., Neural network representations of quantum many-body states. Sci. China Phys. Mech. Astron. 63, 210312 (2020). https://doi.org/10.1007/s11433-018-9407-5

    Article  Google Scholar 

  89. X.R. Ma, Z.C. Tu, S.J. Ran, Deep learning quantum states for Hamiltonian estimation. Chin. Phys. Lett. 38, 110301 (2021). https://doi.org/10.1088/0256-307X/38/11/110301

    Article  ADS  Google Scholar 

  90. A. Kankainen, V.V. Elomaa, L. Batist et al., Mass measurements and implications for the energy of the high-spin isomer in \(^{94}\)Ag. Phys. Rev. Lett. 101, 142503 (2008). https://doi.org/10.1103/PhysRevLett.101.142503

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Nuclear Science and Technology, University of South China, Hengyang, 421001, China

    De-Xing Zhu, Yang-Yang Xu & Xiao-Hua Li

  2. Institute of Modern Physics, Fudan University, Shanghai, 200433, China

    Hong-Ming Liu

  3. School of Math and Physics, University of South China, Hengyang, 421001, China

    Xi-Jun Wu

  4. College of Physics and Electronics, Central South University, Changsha, 410083, China

    Biao He

  5. National Exemplary Base for International Sci & Tech. Collaboration of Nuclear Energy and Nuclear Safety, University of South China, Hengyang, 421001, China

    Xiao-Hua Li

  6. Cooperative Innovation Center for Nuclear Fuel Cycle Technology & Equipment, University of South China, Hengyang, 421001, China

    Xiao-Hua Li

  7. Key Laboratory of Low Dimensional Quantum Structures and Quantum Control, Hunan Normal University, Changsha, 410081, China

    Xiao-Hua Li

Authors
  1. De-Xing Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yang-Yang Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hong-Ming Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xi-Jun Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Biao He
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Xiao-Hua Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by De-Xing Zhu, Yang-Yang Xu, Hong-Ming Liu, Xi-Jun Wu, Biao He and Xiao-Hua Li. The first draft of the manuscript was written by De-Xing Zhu, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Xiao-Hua Li.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 12175100 and 11975132), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of the Education Bureau of Hunan Province, China (No. 18A237), the Natural Science Foundation of Hunan Province, China (No. 2018JJ2321), the Innovation Group of Nuclear and Particle Physics in USC, the Opening Project of the Cooperative Innovation Center for Nuclear Fuel Cycle Technology and Equipment, University of South China (No. 2019KFZ10).

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

Zhu, DX., Xu, YY., Liu, HM. et al. Two-proton radioactivity of the excited state within the Gamow-like and modified Gamow-like models. NUCL SCI TECH 33, 122 (2022). https://doi.org/10.1007/s41365-022-01116-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41365-022-01116-9

Keywords

Search

Navigation