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Impact of finite-range tensor terms in the Gogny force on the \(\beta \)-decay of magic nuclei

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Abstract

Effects of finite-range tensor force on \(\beta \)-decay of magic and semimagic nuclei of \(^{34}\)Si, \(^{68,78}\)Ni, and \(^{132}\)Sn have been investigated using the self-consistent Hartree–Fock plus random-phase approximation model. The tensor force shifts the low-lying Gamow–Teller states downward and systematically improves the calculations of Q and \(\log {ft}\) values. Consequently, it systematically reduces the deviations between the theoretical and experimental data and significantly improves the calculation of \(\beta \)-decay half-lives. This effect is similar to that of zero-range tensor force.

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References

  1. E.M. Burbidge, G.R. Burbidge, W.A. Fowler et al., Synthesis of the elements in stars. Rev. Mod. Phys. 29, 547 (1957). https://doi.org/10.1103/RevModPhys.29.547

    Article  ADS  Google Scholar 

  2. J.J. Cowan, F.-K. Thielemann, J.W. Truran, The R-process and nucleochronology. Phys. Rep. 208, 267 (1991). https://doi.org/10.1016/0370-1573(91)90070-3

    Article  ADS  Google Scholar 

  3. 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 

  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. K. Takahashi, M. Yamada, Gross theory of nuclear \(\beta \)-decay. Prog. Theor. Phys. 41, 1470 (1969). https://doi.org/10.1143/PTP.41.1470

    Article  Google Scholar 

  6. T. Tachibana, M. Yamada, Y. Yoshida, Improvement of the gross theory of \(\beta \)-decay. II: one-particle strength function. Prog. Theor. Phys. 84, 641 (1990). https://doi.org/10.1143/ptp/84.4.641

    Article  Google Scholar 

  7. K. Langanke, G. Martínez-Pinedo, Shell-model calculations of stellar weak interaction rates: II. Weak rates for nuclei in the mass range \(A=45-61\) in supernovae environments. Nucl. Phys. A 673, 481 (2000). https://doi.org/10.1016/S0375-9474(00)00131-7

    Article  Google Scholar 

  8. G. Martínez-Pinedo, K. Langanke, Shell-model half-lives for \(N=82\) nuclei and their implications for the \(r\) process. Phys. Rev. Lett. 83, 4502 (1999). https://doi.org/10.1103/PhysRevLett.83.4502

    Article  Google Scholar 

  9. J.J. Cuenca-García, G. Martínez-Pinedo, K. Langanke et al., Shell model half-lives for \(r\)-process \(N=82\) nuclei. Eur. Phys. J. A 34, 99 (2007). https://doi.org/10.1140/epja/i2007-10477-3

    Article  Google Scholar 

  10. T. Suzuki, T. Yoshida, T. Kajino et al., \(\beta \) decays of isotones with neutron magic number of \(N=126\) and \(r\)-process nucleosynthesis. Phys. Rev. C 85, 015802 (2012). https://doi.org/10.1103/PhysRevC.85.015802

    Article  Google Scholar 

  11. Q. Zhi, E. Caurier, J.J. Cuenca-García et al., Shell-model half-lives including first-forbidden contributions for \(r\)-process waiting-point nuclei. Phys. Rev. C 87, 025803 (2013). https://doi.org/10.1103/PhysRevC.87.025803

    Article  Google Scholar 

  12. J. Krumlinde, P. Möller, Calculation of Gamow–Teller \(\beta \)-strength functions in the rubidium region in the RPA approximation with Nilsson-model wave functions. Nucl. Phys. A 417, 419 (1984). https://doi.org/10.1016/0375-9474(84)90406-8

    Article  Google Scholar 

  13. P. Möller, J. Randrup, New developments in the calculation of \(\beta \)-strength functions. Nucl. Phys. A 514, 1 (1990). https://doi.org/10.1016/0375-9474(90)90330-O

    Article  Google Scholar 

  14. I.N. Borzov, S. Goriely, J.M. Pearson, Microscopic calculations of \(\beta \)-decay characteristics near the \(A=130\)r-process peak. Nucl. Phys. A 621, 307 (1997). https://doi.org/10.1016/S0375-9474(97)00260-1

    Article  Google Scholar 

  15. D.L. Fang, B.A. Brown, T. Suzuki, Investigating \(\beta \)-decay properties of spherical nuclei along the possible \(r\)-process path. Phys. Rev. C 88, 034304 (2013). https://doi.org/10.1103/PhysRevC.88.034304

    Article  Google Scholar 

  16. D.D. Ni, Z.Z. Ren, \(\beta \)-decay rates of neutron-rich Zr and Mo isotopes in the deformed quasiparticle random-phase approximation with realistic interactions. Phys. Rev. C 89, 064320 (2014). https://doi.org/10.1103/PhysRevC.89.064320

    Article  ADS  Google Scholar 

  17. D.D. Ni, Z.Z. Ren, \(\beta ^+\)/EC decay rates of deformed neutron-deficient nuclei in the deformed QRPA with realistic interactions. Phys. Lett. B 744, 22 (2015). https://doi.org/10.1016/j.physletb.2015.03.025

    Article  MATH  ADS  Google Scholar 

  18. T. Nik\(\check{s}\)ić, T. Marketin, D. Vretenar et al., \(\beta \)-decay rates of \(r\)-process nuclei in the relativistic quasiparticle random phase approximation. Phys. Rev. C 71, 014308 (2005). https://doi.org/10.1103/PhysRevC.71.014308

  19. T. Marketin, D. Vretenar, P. Ring, Calculation of \(\beta \)-decay rates in a relativistic model with momentum-dependent self-energies. Phys. Rev. C 75, 024304 (2007). https://doi.org/10.1103/PhysRevC.75.024304

    Article  Google Scholar 

  20. Z.M. Niu, Y.F. Niu, H.Z. Liang et al., \(\beta \)-decay half-lives of neutron-rich nuclei and matter flow in the \(r\)-process. Phys. Lett. B 723, 172 (2013). https://doi.org/10.1016/j.physletb.2013.04.048

    Article  Google Scholar 

  21. J. Engel, M. Bender, J. Dobaczewski et al., \(\beta \) decay rates of \(r\)-process waiting-point nuclei in a self-consistent approach. Phys. Rev. C 60, 014302 (1999). https://doi.org/10.1103/PhysRevC.60.014302

    Article  Google Scholar 

  22. F. Minato, C.L. Bai, Impact of tensor force on \(\beta \) decay of magic and semimagic nuclei. Phys. Rev. Lett. 110, 122501 (2013). https://doi.org/10.1103/PhysRevLett.110.122501

    Article  Google Scholar 

  23. M.T. Mustonen, J. Engel, Global description of \(\beta \)-decay in even-even nuclei with the axially-deformed Skyrme finite-amplitude method. Phys. Rev. C 93, 014304 (2016). https://doi.org/10.1103/PhysRevC.93.014304

    Article  Google Scholar 

  24. M. Martini, S. Peru, S. Goriely, Gamow–Teller strength in deformed nuclei within the self-consistent charge-exchange quasiparticle random-phase approximation with the Gogny force. Phys. Rev. C 89, 044306 (2014). https://doi.org/10.1103/PhysRevC.89.044306

    Article  ADS  Google Scholar 

  25. T. Otsuka, R. Fujimoto, Y. Utsuno et al., Magic numbers in exotic nuclei and spin–isospin properties of the NN interaction. Phys. Rev. Lett. 87, 082502 (2001). https://doi.org/10.1103/PhysRevLett.87.082502

    Article  ADS  Google Scholar 

  26. T. Otsuka, T. Suzuki, R. Fujimoto et al., Evolution of nuclear shells due to the tensor force. Phys. Rev. Lett. 95, 232502 (2005). https://doi.org/10.1103/PhysRevLett.95.232502

    Article  ADS  Google Scholar 

  27. T. Otsuka, T. Matsuo, D. Abe, Mean field with tensor force and shell structure of exotic nuclei. Phys. Rev. Lett. 97, 162501 (2006). https://doi.org/10.1103/PhysRevLett.97.162501

    Article  ADS  Google Scholar 

  28. B.A. Brown, T. Duguet, T. Otsuka et al., Tensor interaction contributions to single-particle energies. Phys. Rev. C 74, 061303(R) (2006). https://doi.org/10.1103/PhysRevC.74.061303

    Article  ADS  Google Scholar 

  29. M. Grasso, Z.Y. Ma, E. Khan et al., Evolution of the proton \(sd\) states in neutron-rich Ca isotopes. Phys. Rev. C 76, 044319 (2007). https://doi.org/10.1103/PhysRevC.76.044319

    Article  Google Scholar 

  30. G. Colò, H. Sagawa, S. Fracasso et al., Spin–orbit splitting and the tensor component of the Skyrme interaction. Phys. Lett. B 646, 227 (2007). https://doi.org/10.1016/j.physletb.2007.01.033

    Article  ADS  Google Scholar 

  31. D.M. Brink, F.L. Stancu, Evolution of nuclear shells with the Skyrme density dependent interaction. Phys. Rev. C 75, 064311 (2007). https://doi.org/10.1103/PhysRevC.75.064311

    Article  ADS  Google Scholar 

  32. T. Lesinski, M. Bender, K. Bennaceur et al., Tensor part of the Skyrme energy density functional: spherical nuclei. Phys. Rev. C 76, 014312 (2007). https://doi.org/10.1103/PhysRevC.76.014312

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  34. E.B. Suckling, P.D. Stevenson, The effect of the tensor force on the predicted stability of superheavy nuclei. Europhys. Lett. 90, 12001 (2010). https://doi.org/10.1209/0295-5075/90/12001

    Article  ADS  Google Scholar 

  35. X.-R. Zhou, H. Sagawa, Effect of tensor interaction on heavy and superheavy nuclei. Mod. Phys. Lett. A 25, 1809 (2010). https://doi.org/10.1142/S0217732310000381

    Article  ADS  Google Scholar 

  36. L.-G. Cao, G. Colò, H. Sagawa et al., Effects of the tensor force on the multipole response in finite nuclei. Phys. Rev. C 80, 064304 (2009). https://doi.org/10.1103/PhysRevC.80.064304

    Article  ADS  Google Scholar 

  37. D. Davesne, M. Martini, K. Bennaceur et al., Nuclear response for the Skyrme effective interaction with zero-range tensor terms. Phys. Rev. C 80, 024314 (2009). https://doi.org/10.1103/PhysRevC.80.024314

    Article  ADS  Google Scholar 

  38. L.-G. Cao, H. Sagawa, G. Colò, Effects of tensor correlations on low-lying collective states in finite nuclei. Phys. Rev. C 83, 034324 (2011). https://doi.org/10.1103/PhysRevC.83.034324

    Article  ADS  Google Scholar 

  39. C.L. Bai, H. Sagawa, H.Q. Zhang et al., Effect of tensor correlations on Gamow–Teller states in \(^{90}\)Zr and \(^{208}\)Pb. Phys. Lett. B 675, 28 (2009). https://doi.org/10.1016/j.physletb.2009.03.077

    Article  Google Scholar 

  40. C.L. Bai, H.Q. Zhang, X.Z. Zhang et al., Quenching of Gamow–Teller strength due to tensor correlations in \(^{90}\)Zr and \(^{208}\)Pb. Phys. Rev. C 79, 041301(R) (2009). https://doi.org/10.1103/PhysRevC.79.041301

    Article  Google Scholar 

  41. C.L. Bai, H.Q. Zhang, X.Z. Zhang et al., Effect of the tensor force on charge-exchange spin-dependent multipole excitations. Chin. Phys. Lett. 27, 102101 (2010). https://doi.org/10.1088/0256-307X/27/10/102101

    Article  ADS  Google Scholar 

  42. C.L. Bai, H.Q. Zhang, H. Sagawa et al., Effect of the tensor force on the charge exchange spin-dipole excitations of \(^{208}\)Pb. Phys. Rev. Lett. 105, 072501 (2010). https://doi.org/10.1103/PhysRevLett.105.072501

    Article  Google Scholar 

  43. C.L. Bai, H.Q. Zhang, H. Sagawa et al., Spin–isospin excitations as quantitative constraints for the tensor force. Phys. Rev. C 83, 054316 (2011). https://doi.org/10.1103/PhysRevC.83.054316

    Article  ADS  Google Scholar 

  44. L.J. Jiang, S. Yang, B.Y. Sun et al., Nuclear tensor interaction in a covariant energy density functional. Phys. Rev. C 91, 034326 (2015). https://doi.org/10.1103/PhysRevC.91.034326

    Article  ADS  Google Scholar 

  45. Z.-H. Wang, Q. Zhao, H.Z. Liang et al., Quantitative analysis of tensor effects in the relativistic Hartree–Fock theory. Phys. Rev. C 98, 034313 (2018). https://doi.org/10.1103/PhysRevC.98.034313

    Article  ADS  Google Scholar 

  46. J. Geng, J. Xiang, B.Y. Sun et al., Relativistic Hartree–Fock model for axially deformed nuclei. Phys. Rev. C 101, 064302 (2020). https://doi.org/10.1103/PhysRevC.101.064302

    Article  ADS  Google Scholar 

  47. T. Marketin, E. Litvinova, D. Vretenar et al., Fragmentation of spin-dipole strength in \(^{90}\)Zr and \(^{208}\)Pb. Phys. Lett. B 706, 477 (2012). https://doi.org/10.1016/j.physletb.2011.11.050

    Article  Google Scholar 

  48. H.Z. Liang, N.V. Giai, J. Meng, Spin–isospin resonances: a self-consistent covariant description. Phys. Rev. Lett. 101, 122502 (2008). https://doi.org/10.1103/PhysRevLett.101.12250

    Article  ADS  Google Scholar 

  49. Z.H. Wang, T. Naito, H.Z. Liang et al., Self-consistent random-phase approximation based on the relativistic Hartree–Fock theory: role of \(\rho \)-tensor coupling. Phys. Rev. C 101, 064306 (2020). https://doi.org/10.1103/PhysRevC.101.064306

    Article  Google Scholar 

  50. M. Anguiano, M. Grasso, G. Cò, V. De Donno et al., Tensor and tensor-isospin terms in the effective Gogny interaction. Phys. Rev. C 86, 054302 (2012). https://doi.org/10.1103/PhysRevC.86.054302

    Article  ADS  Google Scholar 

  51. M. Grasso, M. Anguiano, Tensor parameters in Skyrme and Gogny effective interactions: trends from a ground-state-focused study. Phys. Rev. C 88, 054328 (2013). https://doi.org/10.1103/PhysRevC.88.054328

    Article  ADS  Google Scholar 

  52. G. Cò, M. Anguiano, V. De Donno et al., Matter distribution and spin–orbit force in spherical nuclei. Phys. Rev. C 97, 034313 (2018). https://doi.org/10.1103/PhysRevC.97.034313

    Article  ADS  Google Scholar 

  53. M. Anguiano, G. Cò, V. De Donno, A.M. Lallena, Tensor effective interaction in self-consistent random-phase approximation calculations. Phys. Rev. C 83, 064306 (2011). https://doi.org/10.1103/PhysRevC.83.064306

    Article  ADS  Google Scholar 

  54. V. De Donno, G. Cò, M. Anguiano, A.M. Lallena, Charge-exchange excitations with finite-range interactions including tensor terms. Phys. Rev. C 90, 024326 (2014). https://doi.org/10.1103/PhysRevC.90.024326

    Article  ADS  Google Scholar 

  55. I.N. Borzov, S. Goriely, Weak interaction rates of neutron-rich nuclei and the r-process nucleosynthesis. Phys. Rev. C 62, 035501 (2000). https://doi.org/10.1103/PhysRevC.62.035501

    Article  ADS  Google Scholar 

  56. C. Gaarde, in Proceedings of the Niels Bohr Centennial Conference, edited by R. Broglia, G. Hagemann, and B. Herskind (North-Holland, Amsterdam, 1985), p. 449

  57. E. Caurier, G. Martínez-Pinedo, F. Nowacki et al., The shell model as a unified view of nuclear structure. Rev. Mod. Phys. 77, 427 (2005). https://doi.org/10.1103/RevModPhys.77.427

    Article  ADS  Google Scholar 

  58. M. Kleban, B. Nerlo-Pomorska, J.F. Berger et al., Global properties of spherical nuclei obtained from Hartree–Fock–Bogoliubov calculations with the Gogny force. Phys. Rev. C 65, 024309 (2002). https://doi.org/10.1103/PhysRevC.65.024309

    Article  ADS  Google Scholar 

  59. J. Decharge, M. Girod, D. Gogny, Self consistent calculations and quadrupole moments of even Sm isotopes. Phys. Lett. B 55, 361 (1975). https://doi.org/10.1016/0370-2693(75)90359-7

    Article  ADS  Google Scholar 

  60. D. Gogny, in Nuclear Self-Consistent Fields, edited by G. Ripka, M. Porneuf (North-Holland, Amsterdam, 1975)

  61. N. Onishi, J.W. Negele, Two-body and three-body effective interactions in nuclei. Nucl. Phys. A 301, 336 (1978). https://doi.org/10.1016/0375-9474(78)90266-X

    Article  ADS  Google Scholar 

  62. J.F. Berger, M. Girod, D. Gogny, Microscopic analysis of collective dynamics in low energy fission. Nucl. Phys. A 428, 23 (1984). https://doi.org/10.1016/0375-9474(84)90240-9

    Article  ADS  Google Scholar 

  63. S. Goriely, S. Hilaire, M. Girod et al., First Gogny–Hartree–Fock–Bogoliubov nuclear mass model. Phys. Rev. Lett. 102, 242501 (2009). https://doi.org/10.1103/PhysRevLett.102.242501

    Article  ADS  Google Scholar 

  64. M. Anguiano, A.M. Lallena, G. Cò, V. De Donno et al., Gogny interactions with tensor terms. Eur. Phys. J. A 52, 183 (2016). https://doi.org/10.1140/epja/i2016-16183-1

    Article  ADS  Google Scholar 

  65. P.D. Cottle, K.W. Kemper, Single-neutron energies near \(N=28\) and the absence of the \(N=34\) subshell closure in the Ti isotopes. Phys. Rev. C 78, 037304 (2008). https://doi.org/10.1103/PhysRevC.78.037304

    Article  Google Scholar 

  66. G. Audi, F.G. Kondev, M. Wang et al., The NUBASE2016 evaluation of nuclear properties. Chin. Phys. C 41, 030001 (2017). https://doi.org/10.1088/1674-1137/41/3/030001

    Article  ADS  Google Scholar 

  67. National Nuclear Data Center, ”NuDat 2.8 Database”

  68. S. Goriely, N. Chamel, J.M. Pearson, Further explorations of Skyrme–Hartree–Fock–Bogoliubov mass formulas. XIII. The 2012 atomic mass evaluation and the symmetry coefficient. Phys. Rev. C 88, 024308 (2013). https://doi.org/10.1103/PhysRevC.88.024308

    Article  ADS  Google Scholar 

  69. S. Goriely, N. Chamel, J.M. Pearson, Further explorations of Skyrme–Hartree–Fock–Bogoliubov mass formulas. XVI. Inclusion of self-energy effects in pairing. Phys. Rev. C 93, 034337 (2016). https://doi.org/10.1103/PhysRevC.93.034337

    Article  ADS  Google Scholar 

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All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Da-Zhuang Chen, Dong-Liang Fang, and Chun-Lin Bai. The first draft of the manuscript was written by Da-Zhuang Chen, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Chun-Lin Bai.

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This work was supported by the National Natural Science Foundation of China (Nos. 11575120 and 11822504) and the Science Specialty Program of Sichuan University (No. 2020SCUNL210).

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Chen, DZ., Fang, DL. & Bai, CL. Impact of finite-range tensor terms in the Gogny force on the \(\beta \)-decay of magic nuclei. NUCL SCI TECH 32, 74 (2021). https://doi.org/10.1007/s41365-021-00908-9

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