Skip to main content
SpringerLink
Log in

Systematic study on the proton radioactivity of spherical proton emitters

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

Abstract

In this study, based on a two-potential approach, we systematically investigated the proton radioactivity half-lives of spherical proton emitters with \(69\le Z \le 81\) from the ground and/or isomeric state, choosing the nuclear potential to be a modified Woods–Saxon potential that contains the isospin effect of the daughter nucleus. It was found that the calculated half-lives could reproduce the experimental data well. Furthermore, we extended this model to predict the half-lives of 17 proton-emitting candidates whose radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020. For comparison, the unified fission model, Coulomb potential and proximity potential model, universal decay law for proton emission, and new Geiger–Nuttall law were also used. All the predicted results are consistent with each other.

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

Data availability statement

The data that support the findings of this study are openly available in Science Data Bank at https://www.doi.org/10.57760/sciencedb.j00186.00058 and http://resolve.pid21.cn/31253.11.sciencedb.j00186.00058.

References

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

    Article  ADS  Google Scholar 

  2. J. Cerny, J. Esterl, R. Gough, R. Sextro, Confirmed proton radioactivity of \(^{53}\)Co\(^{\rm {m}}\). Phys. Lett. B 33, 284 (1970). https://doi.org/10.1016/0370-2693(70)90270-4

    Article  ADS  Google Scholar 

  3. S. Hofmann, W. Reisdorf, G. Münzenberg et al., proton radioactivity of \(^{151}\)Lu. Z. Phys. A 305, 111 (1982). https://doi.org/10.1007/BF01415018

    Article  ADS  Google Scholar 

  4. O. Klepper, T. Batsch, S. Hofmann et al., Direct and beta-delayed proton decay of very neutron-deficient rare-earth isotopes produced in the reaction \(^{58}\)Ni+\(^{92}\)Mo. Z. Phys. A 305, 125 (1982). https://doi.org/10.1007/BF01415019

    Article  ADS  Google Scholar 

  5. D.S. Delion, R.J. Liotta, R. Wyss, Systematics of proton emission. Phy. Rev. Lett. 96, 072501 (2006). https://doi.org/10.1103/PhysRevLett.96.072501

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. H.F. Zhang, Y.J. Wang, J.M. Dong et al., Concise methods for proton radioactivity. J. Phys. G-Nucl. Part. Phys. 37, 085107 (2010). https://doi.org/10.1088/0954-3899/37/8/085107

    Article  ADS  Google Scholar 

  8. J.L. Chen, X.H. Li, J.H. Cheng et al., Systematic study of proton radioactivity based on Gamow-like model with a screened electrostatic barrier. J. Phys. G-Nucl. Part. Phys. 46, 065107 (2019). https://doi.org/10.1088/1361-6471/ab1a56

    Article  ADS  Google Scholar 

  9. D.S. Delion, Universal decay rule for reduced widths. Phys. Rev. C 80, 024310 (2009). https://doi.org/10.1103/PhysRevC.80.024310

    Article  ADS  Google Scholar 

  10. M. Karny, K.P. Rykaczewski, R.K. Grzywacz et al., Shell structure beyond the proton drip line studied via proton emission from deformed \(^{141}\)Ho. Phys. Lett. B 664, 52 (2008). https://doi.org/10.1016/j.physletb.2008.04.056

    Article  ADS  Google Scholar 

  11. J.H. Cheng, J.L. Chen, J.G. Deng et al., Systematic study of proton emission half-lives within the two-potential approach with Skyrme-Hartree-Fock. Nucl. Phys. A 997, 121717 (2020). https://doi.org/10.1016/j.nuclphysa.2020.121717

    Article  Google Scholar 

  12. Z.X. Zhang, J.M. Dong, A formula for half-life of proton radioactivity. Chin. Phys. C 42, 014104 (2018). https://doi.org/10.1088/1674-1137/42/1/014104

    Article  ADS  Google Scholar 

  13. Y.Y. Xu, H.M. Liu, D.X. Zhu et al., An improved formula for the favored \(\alpha\) decay half-lives. Eur. Phys. J. A 58, 16 (2022). https://doi.org/10.1140/epja/s10050-022-00666-1

    Article  ADS  Google Scholar 

  14. Y.Y. Xu, D.X. Zhu, X. Chen et al., A unified formula for \(\alpha\) decay half-lives. Eur. Phys. J. A 58, 163 (2022). https://doi.org/10.1140/epja/s10050-022-00812-9

    Article  ADS  Google Scholar 

  15. Y.T. Zou, X. Pan, H.M. Liu et al., Systematic studies on \(\alpha\) decay half-lives of neptunium isotopes. Phys. Scr. 96, 075301 (2021). https://doi.org/10.1088/1402-4896/abf795

    Article  ADS  Google Scholar 

  16. J.G. Deng, H.F. Zhang, Analytic formula for estimating the \(\alpha\)-particle preformation factor. Phys. Rev. C 102, 044314 (2020). https://doi.org/10.1103/PhysRevC.102.044314

    Article  ADS  Google Scholar 

  17. J.G. Deng, H.F. Zhang, Correlation between \(\alpha\)-particle preformation factor and \(\alpha\) decay energy. Phys. Lett. B 816, 136247 (2021). https://doi.org/10.1016/j.physletb.2021.136247

    Article  Google Scholar 

  18. N. Wan, C. Xu, Z.Z. Ren, \(\alpha\)-decay half-life screened by electrons. Nucl. Sci. Tech. 27, 149 (2016). https://doi.org/10.1007/s41365-016-0150-2

    Article  Google Scholar 

  19. Z.Z. Ren, C. Xu, Z.J. Wang, New perspective on complex cluster radioactivity of heavy nuclei. Phys. Rev. C 70, 034304 (2004). https://doi.org/10.1103/PhysRevC.70.034304

    Article  ADS  Google Scholar 

  20. D.M. Deng, Z.Z. Ren, Systematics of \(\alpha\)-preformation factors in closed-shell regions. Nucl. Sci. Tech. 27(6), 150 (2016). https://doi.org/10.1007/s41365-016-0151-1

    Article  Google Scholar 

  21. D.N. Basu, P.R. Chowdhury, C. Samanta, Folding model analysis of proton radioactivity of spherical proton emitters. Phys. Rev. C 72, 051601 (2005). https://doi.org/10.1103/PhysRevC.72.051601

    Article  ADS  Google Scholar 

  22. D.X. Zhu, Y.Y. Xu, H.M. Liu et al., Two-proton radioactivity of the excited state within the Gamowlike and modified Gamow-like models. Nucl. Sci. Tech. 33, 122 (2022). https://doi.org/10.1007/s41365-022-01116-9

    Article  Google Scholar 

  23. D.X. Zhu, M. Li, Y.Y. Xu et al., Systematic study of two-proton radioactivity within various versions of proximity formalisms. Phys. Scr. 97, 095304 (2022). https://doi.org/10.1088/1402-4896/ac8585

    Article  ADS  Google Scholar 

  24. 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 

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

    Article  ADS  Google Scholar 

  26. 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 

  27. H.F. Zhang, Y.Z. Wang, J.M. Dong et al., Theoretical study on spherical proton emission. Sci. China Ser. G-Phys. Mech. Astron. 52, 1536–1541 (2009). https://doi.org/10.1007/s11433-009-0204-0

    Article  ADS  Google Scholar 

  28. K.P. Santhosh, I. Sukumaran, Decay of Z= 82–102 heavy nuclei via emission of one-proton and two-proton halo nuclei. Pramana J. Phys. 92, 6 (2019). https://doi.org/10.1007/s12043-018-1672-4

    Article  ADS  Google Scholar 

  29. 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 

  30. Y.Z. Wang, F.Z. Xing, Y. Xiao et al., An improved semi-empirical relationship for cluster radioactivity. Chin. Phys. C 45, 044111 (2021). https://doi.org/10.1088/1674-1137/abe112

    Article  ADS  Google Scholar 

  31. Y.J. Ren, Z.Z. Ren, New Geiger-Nuttall law of odd-Z nuclei and long-lived island beyond the stable line. Nucl. Sci. Tech 24, 050518 (2013). https://doi.org/10.13538/j.1001-8042/nst.2013.05.018

    Article  Google Scholar 

  32. M. Bhattacharya, G. Gangopadhyay, Microscopic calculation of half lives of spherical proton emitters. Phys. Lett. B 651, 263 (2007). https://doi.org/10.1016/j.physletb.2007.06.012

    Article  ADS  Google Scholar 

  33. Y.B. Qian, Z.Z. Ren, D.D. Ni et al., Half-lives of proton emitters with a deformed density-dependent model. Chin. Phys. Lett. 27, 112301 (2010). https://doi.org/10.1088/0256-307X/27/11/112301

    Article  ADS  Google Scholar 

  34. M. Balasubramaniam, N. Arunachalam, Proton and \(\alpha\)-radioactivity of spherical proton emitters. Phys. Rev. C 71, 014603 (2005). https://doi.org/10.1103/PhysRevC.71.014603

    Article  ADS  Google Scholar 

  35. J.M. Dong, H.F. Zhang, W. Zuo et al., Unified fission model for proton emission. Chin. Phys. C 34, 182 (2010). https://doi.org/10.1088/1674-1137/34/2/005

    Article  ADS  Google Scholar 

  36. A. Zdeb, M. Warda, C.M. Petrache et al., 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 

  37. K.P. Santhosh, I. Sukumaran, Description of proton radioactivity using the Coulomb and proximity potential model for deformed nuclei. Phys. Rev. C 96, 034619 (2017). https://doi.org/10.1103/PhysRevC.96.034619

    Article  ADS  Google Scholar 

  38. C.L. Guo, G.L. Zhang, Analysis of proton radioactivity of nuclei by using proximity potential with a new universal function. Eur. Phys. J. A 50, 187 (2014). https://doi.org/10.1140/epja/i2014-14187-5

    Article  ADS  Google Scholar 

  39. C.L. Guo, G.L. Zhang, X.Y. Le, Study of the universal function of nuclear proximity potential from density-dependent nucleon-nucleon interaction. Nucl. Phys. A 897, 54 (2013). https://doi.org/10.1016/j.nuclphysa.2012.10.003

    Article  ADS  Google Scholar 

  40. J.M. Dong, H.F. Zhang, G. Royer, Proton radioactivity within a generalized liquid drop model. Phys. Rev. C 79, 054330 (2009). https://doi.org/10.1103/PhysRevC.79.054330

    Article  ADS  Google Scholar 

  41. Y.Z. Wang, J.P. Cui, Y.L. Zhang et al., Competition between \(\alpha\) decay and proton radioactivity of neutron-deficient nuclei. Phys. Rev. C 95, 014302 (2017). https://doi.org/10.1103/PhysRevC.95.014302

    Article  ADS  Google Scholar 

  42. Y.Q. Xin, J.G. Deng, H.F. Zhang, Proton radioactivity within the generalized liquid drop model with various versions of proximity potentials. Commun. Theor. Phys. 73, 065301 (2021). https://doi.org/10.1088/1572-9494/abf5e6

    Article  ADS  Google Scholar 

  43. J.L. Chen, X.H. Li, X.J. Wu et al., Systematic study on proton radioactivity of spherical proton emitters within two-potential approach. Eur. Phys. J. A 57, 305 (2021). https://doi.org/10.1140/epja/s10050-021-00618-1

    Article  ADS  Google Scholar 

  44. Y.B. Qian, Z.Z. Ren, Calculations on decay rates of various proton emissions. Eur. Phys. J. A 52, 68 (2016). https://doi.org/10.1140/epja/i2016-16068-3

    Article  ADS  Google Scholar 

  45. H. Geiger, J.M. Nuttall, The ranges of the \(\alpha\) particles from various radioactive substances and a relation between range and period of transformation. Philos. Mag. 22, 613 (1911). https://doi.org/10.1080/14786441008637156

    Article  Google Scholar 

  46. C. Qi, D.S. Delion, R.J. Liotta et al., Effects of formation properties in one-proton radioactivity. Phys. Rev. C 85, 011303 (2012). https://doi.org/10.1103/PhysRevC.85.011303

    Article  ADS  Google Scholar 

  47. J.L. Chen, J.Y. Xu, J.G. Deng et al., New Geiger-Nuttall law for proton radioactivity. Eur. Phys. J. A 55, 214 (2019). https://doi.org/10.1140/epja/i2019-12927-7

    Article  ADS  Google Scholar 

  48. R. Budaca, A.I. Budaca, Deformation dependence of the screened decay law for proton emission. Nucl. Phys. A 1017, 122355 (2022). https://doi.org/10.1016/j.nuclphysa.2021.122355

    Article  Google Scholar 

  49. N. Wang, W. Scheid, Quasi-elastic scattering and fusion with a modified Woods-Saxon potential. Phys. Rev. C 78, 014607 (2008). https://doi.org/10.1103/PhysRevC.78.014607

    Article  ADS  Google Scholar 

  50. N. Wang, K. Zhao, W. Scheid et al., Fusion-fission reactions with a modified Woods-Saxon potential. Phys. Rev. C 77, 014603 (2008). https://doi.org/10.1103/PhysRevC.77.014603

    Article  ADS  Google Scholar 

  51. F. Saidi, M.R. Oudih, M. Fellah et al., Cluster decay investigation within a modified Woods-Saxon potential. Mod. Phys. Lett. A 30, 1550150 (2015). https://doi.org/10.1142/S0217732315501503

    Article  ADS  Google Scholar 

  52. M.R. Oudih, M. Ouhachi, M. Fellah et al., Investigation of alpha decay half-lives within a modified Woods-Saxon potential. Int. J. Mod. Phys. E 31, 2250009 (2022). https://doi.org/10.1142/S0218301322500094

    Article  ADS  Google Scholar 

  53. S.A. Gurvitz, G. Kalbermann, Decay width and the shift of a quasistationary state. Phys. Rev. Lett. 59, 262–265 (1987). https://doi.org/10.1103/PhysRevLett.59.262

    Article  ADS  Google Scholar 

  54. 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 

  55. 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 to ground and isomeric states. Phys. Rev. C 94, 024338 (2016). https://doi.org/10.1103/PhysRevC.94.024338

    Article  ADS  Google Scholar 

  56. F.G. Kondev, M. Wang, W.J. Huang et al., The NUBASE2020 evaluation of nuclear physics properties. Chin. Phys. C 45, 030001 (2021). https://doi.org/10.1088/1674-1137/abddae

    Article  ADS  Google Scholar 

  57. V.Y. Denisov, H. Ikezoe, \(\alpha\)-nucleus potential for \(\alpha\)-decay and sub-barrier fusion. Phys. Rev. C 72, 064613 (2005). https://doi.org/10.1103/PhysRevC.72.064613

    Article  ADS  Google Scholar 

  58. K.N. Huang, M. Aoyagi, M.H. Chen et al., Neutral-atom electron binding energies from relaxed-orbital relativistic Hartree-Fock-Slater calculations 2 \(\le\) Z \(\le\) 106. At. Data Nucl. Data Tables 18, 243 (1976). https://doi.org/10.1016/0092-640X(76)90027-9

    Article  ADS  Google Scholar 

  59. M.R. Oudih, M. Fellah, N.H. Allal, Theoretical study of proton radioactivity. Bull. Russ. Acad. Sci. Phys. 84, 1022–1026 (2020). https://doi.org/10.3103/S1062873820080237

    Article  Google Scholar 

  60. M.R. Pahlavani, S.A. Alavi, N. Tahanipour, Effect of nuclear deformation on the potential barrier and alpha-decay half-lives of superheavy nuclei. Mod. Phys. Lett. A 28, 1350065 (2013). https://doi.org/10.1142/S021773231350065X

    Article  ADS  Google Scholar 

  61. O.A.P. Tavares, E.L. Medeiros, A simple description of cluster radioactivity. Phys. Scr. 86, 015201 (2012). https://doi.org/10.1088/0031-8949/86/01/015201

    Article  ADS  Google Scholar 

  62. G. Naveya, S. I. A. Philominraj, A. Stephen, Study on alpha decay chains of \(Z\) = 122 superheavy nuclei with deformation effects and Langer modification. arXiv preprint arXiv 1810, 04421 (2018). https://doi.org/10.48550/arXiv.1810.04421

  63. J.J. Morehead, Asymptotics of radial wave equations. J. Math. Phys. 36, 5431 (1995). https://doi.org/10.1063/1.531270

    Article  ADS  MathSciNet  MATH  Google Scholar 

  64. C. Qi, F.R. Xu, R.J. Liotta, R. Wyss, Universal decay law in charged-particle emission and exotic cluster radioactivity. Phys. Rev. Lett. 103, 072501 (2009). https://doi.org/10.1103/PhysRevLett.103.072501

    Article  ADS  Google Scholar 

  65. C. Qi, F.R. Xu, R.J. Liotta et al., Microscopic mechanism of charged-particle radioactivity and generalization of the Geiger-Nuttall law. Phys. Rev. C 80, 044326 (2009). https://doi.org/10.1103/PhysRevC.80.044326

    Article  ADS  Google Scholar 

  66. J.G. Deng, X.H. Li, J.L. Chen et al., Systematic study of proton radioactivity of spherical proton emitters within various versions of proximity potential formalisms. Eur. Phys. J. A 55, 58 (2019). https://doi.org/10.1140/epja/i2019-12728-0

    Article  ADS  Google Scholar 

  67. Y.Y. Xu, X.Y. Hu, D.X. Zhu et al., Systematic study of proton radioactivity half-lives. Nucl. Sci. Tech. 34, 30 (2023). https://doi.org/10.1007/s41365-023-01178-3

    Article  Google Scholar 

  68. D.N. Poenaru, R.A. Gherghescu, W. Greiner, Single universal curve for cluster radioactivities and \(\alpha\) decay. Phys. Rev. C 83, 014601 (2011). https://doi.org/10.1103/PhysRevC.83.014601

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  70. L.J. Qi, D.M. Zhang, S. Luo et al., Systematic calculations of cluster radioactivity half-lives in trans-lead nuclei. Chin. Phys. C 47(1), 014101 (2023). https://doi.org/10.1088/1674-1137/ac94bd

    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

    Dong-Meng Zhang, Lin-Jing Qi, De-Xing Zhu, Yang-Yang Xu, Song Luo & Xiao-Hua Li

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

    Xiao-Hua Li

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

    Xiao-Hua Li

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

    Xiao-Hua Li

Authors
  1. Dong-Meng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lin-Jing Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. De-Xing Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yang-Yang Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Song Luo
    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 Lin-Jing Qi, De-Xing Zhu, Yang-Yang Xu, Song Luo and Xiao-Hua Li. The first draft of the manuscript was written by Dong-Meng Zhang, 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 in part 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 Education Bureau of Hunan Province, China (Nos. 21B0402 and 18A237), the Natural Science Foundation of Hunan Province, China (No. 2018JJ2321), the Innovation Group of Nuclear and Particle Physics in USC, the Shandong Province Natural Science Foundation, China (No. ZR2022JQ04), the Hunan Provincial Innovation Foundation for Postgraduates (No. CX20220993), and the Opening Project of Cooperative Innovation Center for Nuclear Fuel Cycle Technology and Equipment, University of South China (No. 2019KFZ10).

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) 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

Zhang, DM., Qi, LJ., Zhu, DX. et al. Systematic study on the proton radioactivity of spherical proton emitters. NUCL SCI TECH 34, 55 (2023). https://doi.org/10.1007/s41365-023-01201-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41365-023-01201-7

Keywords

Search

Navigation