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\(\alpha \) + core structure described with an additional interaction in the nuclear matter saturation region

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Abstract

In a phenomenological approach, the \(\alpha \) + core structure is investigated in the \(^{20}\)Ne, \(^{44}\)Ti, \(^{94}\)Mo, \(^{104}\)Te, and \(^{212}\)Po nuclei through the local potential model using a double-folding nuclear potential with effective nucleon-nucleon interaction of M3Y + \(c_{\textrm{sat}}\delta (s)\) type, where the term \(c_{\textrm{sat}}\delta (s)\) acts only between the saturation regions of \(\alpha \)-cluster and core. Properties such as energy levels, \(\alpha \)-widths, B(E2) transition rates, and half-lives are calculated, and good level of agreement with experimental data is obtained in general. It is shown the inclusion of the term \(c_{\textrm{sat}}\delta (s)\) is determinant for a better description of the experimental energy levels compared to the ground state bands produced with the simple M3Y interaction. The properties calculated for \(^{104}\)Te reinforce the superallowed \(\alpha \)-decay feature for this nucleus, as indicated in previous studies.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: As a theoretical physics publication, there is no experimental data to be shared.]

Notes

  1. Details on the values of \(\lambda \), \(c_{\textrm{sat}}\), and R adopted for \(^{104}\)Te are discussed in Sect. 3.

  2. The \(^{94}\)Mo experimental negative parity band presents levels from (5)\(^{-}\) (\(E_x = 2.611\) MeV) to (\(17^{-}\)) (\(E_x = 7.782\) MeV) connected by \(\gamma \)-transitions [33]; however, the excited state (5)\(^{-}\) undergoes a \(\gamma \)-transition to the \(4^{+}\) state (\(E_x = 1.574\) MeV) of the \(G = 16\) g.s. band. As the excited state (5)\(^{-}\) does not undergo a transition of \(J \rightarrow J - 2\) type, the \(G = 17\) band is assumed to be incomplete and the calculation of the corresponding theoretical band is made from \(J^{\pi } = 5^{-}\).

  3. Ref. [37] presents other shell-model calculations for the \(^{104}\)Te g.s. band, such as the SD-pair approximation, the SDGIK-pair approximation and the shell-model calculation with isospin symmetry (SM2); however, such calculations produce results similar to the SM1 calculation shown in Fig. 6.

  4. The recent experimental works of von Tresckow et al. [2] and Karayonchev et al. [46] present the measures \(B(E2;6^{+}_{1} \rightarrow 4^{+}_{1}) = 8.7(15)\) W.u. and \(9.0(+9 \; -7)\) W.u. for \(^{212}\)Po, respectively, which favors the theoretical predictions of Refs. [7, 9, 12]. However, the 2020 \(^{212}\)Po experimental data compilation [34, 50] presents the value \(B(E2;6^{+}_{1} \rightarrow 4^{+}_{1}) = 13.2(+49 \; -29)\) W.u. shown in Table 6.

References

  1. M. Freer, H. Horiuchi, Y. Kanada-Enyo, D. Lee, U.-G. Meißner, Rev. Mod. Phys. 90, 035004 (2018)

    Article  ADS  Google Scholar 

  2. M. von Tresckow, M. Rudigier, T.M. Shneidman, T. Kröll, M. Boromiza, C. Clisu et al., Phys. Lett. B 821, 136624 (2021)

    Article  Google Scholar 

  3. Y.-Z. Wang, S. Zhang, Y.-G. Ma, Phys. Lett. B 831, 137198 (2022)

    Article  Google Scholar 

  4. S. Bailey, T. Kokalova, M. Freer, C. Wheldon, R. Smith, J. Walshe, N. Soić, L. Prepolec, V. Tokić, F.M. Marqués, L. Achouri, F. Delaunay, M. Parlog, Q. Deshayes, B. Fernández-Dominguez, B. Jacquot, Eur. Phys. J. A 57, 108 (2021)

    Article  ADS  Google Scholar 

  5. P. Dasgupta, G.-L. Ma, R. Chatterjee, L. Yan, S. Zhang, Y.-G. Ma, Eur. Phys. J. A 57, 134 (2021)

    Article  ADS  Google Scholar 

  6. B. Buck, A.C. Merchant, S.M. Perez, Phys. Rev. C 51, 559 (1995)

    Article  ADS  Google Scholar 

  7. S.M. Wang, J.C. Pei, F.R. Xu, Phys. Rev. C 87, 014311 (2013)

    Article  ADS  Google Scholar 

  8. M.A. Souza, H. Miyake, T. Borello-Lewin, C.A. da Rocha, C. Frajuca, Phys. Lett. B 793, 8 (2019)

    Article  ADS  Google Scholar 

  9. D. Ni, Z. Ren, Phys. Rev. C 83, 014310 (2011)

    Article  ADS  Google Scholar 

  10. M.A. Souza, H. Miyake, Phys. Rev. C 104, 064301 (2021)

    Article  ADS  Google Scholar 

  11. T.T. Ibrahim, A.C. Merchant, S.M. Perez, B. Buck, Phys. Rev. C 99, 064332 (2019)

    Article  ADS  Google Scholar 

  12. D. Bai, Z. Ren, Phys. Rev. C 103, 044316 (2021)

    Article  ADS  Google Scholar 

  13. M.A. Souza, H. Miyake, Phys. Rev. C 91, 034320 (2015)

    Article  ADS  Google Scholar 

  14. P. Mohr, Open Nucl. Part. Phys. J. 1, 1 (2008)

    Article  ADS  Google Scholar 

  15. A.M. Kobos, B.A. Brown, R. Lindsay, G.R. Satchler, Nucl. Phys. A 425, 205 (1984)

    Article  ADS  Google Scholar 

  16. S. Ohkubo, Phys. Rev. Lett. 74, 2176 (1995)

    Article  ADS  Google Scholar 

  17. P. Mohr, G.G. Kiss, Z. Fülöp, D. Galaviz, G. Gyürky, E. Somorjai, At. Data Nucl. Data Tables 99, 651 (2013)

    Article  ADS  Google Scholar 

  18. P. Mohr, Eur. Phys. J. A 53, 209 (2017)

    Article  ADS  Google Scholar 

  19. U. Atzrott, P. Mohr, H. Abele, C. Hillenmayer, G. Staudt, Phys. Rev. C 53, 1336 (1996)

    Article  ADS  Google Scholar 

  20. M.A. Souza, H. Miyake, Eur. Phys. J. A 53, 146 (2017)

    Article  ADS  Google Scholar 

  21. J. Jia, Y. Qian, Z. Ren, Phys. Rev. C 104, L031301 (2021)

    Article  ADS  Google Scholar 

  22. D.T. Khoa, G.R. Satchler, W. von Oertzen, Phys. Rev. C 56, 954 (1997)

  23. Y. Sakuragi, Prog. Theor. Exp. Phys. 2016, 06A106 (2016)

    Article  Google Scholar 

  24. V.B. Soubbotin, W. von Oertzen, X. Viñas, K.A. Gridnev, H.G. Bohlen, Phys. Rev. C 64, 014601 (2001)

    Article  ADS  Google Scholar 

  25. G.R. Satchler, W.G. Love, Phys. Rep. 55, 183 (1979)

    Article  ADS  Google Scholar 

  26. F. Hoyler, P. Mohr, G. Staudt, Phys. Rev. C 50, 2631 (1994)

    Article  ADS  Google Scholar 

  27. A.M. Kobos, B.A. Brown, P.E. Hodgson, G.R. Satchler, A. Budzanowski, Nucl. Phys. A 384, 65 (1982)

    Article  ADS  Google Scholar 

  28. R.F. Frosch, J.S. McCarthy, R.E. Rand, M.R. Yearian, Phys. Rev. 160, 874 (1967)

    Article  ADS  Google Scholar 

  29. Nuclei Charge Density Archive, and references therein. http://discovery.phys.virginia.edu/research/groups/ncd/index.html

  30. K. Wildermuth, Y.C. Tang, A Unified Theory of the Nucleus (Academic Press, New York, 1977)

    Book  Google Scholar 

  31. B. Buck, A.C. Merchant, S.M. Perez, J. Phys. G Nucl. Part. Phys. 17, 1223 (1991)

    Article  ADS  Google Scholar 

  32. B. Buck, A.C. Merchant, S.M. Perez, Phys. Rev. C 45, 2247 (1992)

    Article  ADS  Google Scholar 

  33. Y.H. Zhang, M. Hasegawa, W.T. Guo, M.L. Liu, X.H. Zhou, G. de Angelis, T.M. Axiotis, A. Gadea, N. Marginean, Martinez, D.R. Napoli, C. Rusu, Z. Podolyak, C. Ur, D. Bazzacco, F. Brandolini, S. Lunardi, S.M. Lenzi, R. Menegazzo, R. Schwengner, A. Gargano, W. von Oertzen, S. Tazaki, Phys. Rev. C 79, 044316 (2009)

    Article  ADS  Google Scholar 

  34. ENSDF: Evaluated Nuclear Structure Data File, and references therein. https://www.nndc.bnl.gov/ensdf

  35. P. Mohr, Eur. Phys. J. A 31, 23 (2007)

    Article  ADS  Google Scholar 

  36. D. Bai, Z. Ren, Eur. Phys. J. A 54, 220 (2018)

    Article  ADS  Google Scholar 

  37. H. Jiang, C. Qi, Y. Lei, R. Liotta, R. Wyss, Y.M. Zhao, Phys. Rev. C 88, 044332 (2013)

    Article  ADS  Google Scholar 

  38. S.A. Gurvitz, G. Kalbermann, Phys. Rev. Lett. 59, 262 (1987)

    Article  ADS  Google Scholar 

  39. Y. Qian, Z. Ren, D. Ni, J. Phys. G Nucl. Part. Phys. 38, 015102 (2011)

    Article  ADS  Google Scholar 

  40. Y. Qian, Z. Ren, D. Ni, Phys. Rev. C 83, 044317 (2011)

    Article  ADS  Google Scholar 

  41. K. Auranen, D. Seweryniak, M. Albers, A.D. Ayangeakaa, S. Bottoni, M.P. Carpenter et al., Phys. Rev. Lett. 121, 182501 (2018)

    Article  ADS  Google Scholar 

  42. B. Buck, J.C. Johnston, A.C. Merchant, S.M. Perez, Phys. Rev. C 52, 1840 (1995)

    Article  ADS  Google Scholar 

  43. D.R. Tilley, C.M. Cheves, J.H. Kelley, S. Raman, H.R. Weller, Nucl. Phys. A 636, 249 (1998)

    Article  ADS  Google Scholar 

  44. XUNDL: Experimental Unevaluated Nuclear Data List Search and Retrieval, and references therein. https://www.nndc.bnl.gov/xundl

  45. T. Kibédi, T.W. Burrows, M.B. Trzhaskovskaya, P.M. Davidson, C.W. Nestor Jr., Nucl. Instr. Methods Phys. Res. A 589, 202 (2008). http://bricc.anu.edu.au

  46. V. Karayonchev, G. Rainovski, J. Jolie, A. Blazhev, A. Dewald, A. Esmaylzadeh, C. Fransen, P. John, L. Knafla, D. Kocheva, K. Schomacker, V. Werner, H. Naïdja, Phys. Rev. C 106, 064305 (2022)

    Article  ADS  Google Scholar 

  47. F. Michel, S. Ohkubo, G. Reidemeister, Prog. Theor. Phys. Suppl. 132, 7 (1998)

    Article  ADS  Google Scholar 

  48. K. Arnswald, T. Braunroth, M. Seidlitz, L. Coraggio, P. Reiter, B. Birkenbach et al., Phys. Lett. B 772, 599 (2017)

    Article  ADS  Google Scholar 

  49. K. Arnswald, P. Reiter, A. Blazhev, T. Braunroth, A. Dewald, M. Droste, C. Fransen, A. Goldkuhle, R. Hetzenegger, R. Hirsch, E. Hoemann, L. Kaya, L. Lewandowski, C. Müller-Gatermann, P. Petkov, D. Rosiak, M. Seidlitz, B. Siebeck, A. Vogt, D. Werner, K. Wolf, K.-O. Zell, Phys. Rev. C 102, 054302 (2020)

    Article  ADS  Google Scholar 

  50. K. Auranen, E.A. McCutchan, Nucl. Data Sheets 168, 117 (2020)

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Acknowledgements

The authors thank the HPC resources provided by Information Technology Superintendence (HPC-STI) of University of São Paulo. Support from Instituto Nacional de Ciência e Tecnologia – Física Nuclear e Aplicações (INCT-FNA) is acknowledged.

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  1. Instituto de Física, Universidade de São Paulo, Cidade Universitária, Rua do Matão, 1371, São Paulo, SP, CEP 05508-090, Brazil

    M. A. Souza & H. Miyake

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Correspondence to M. A. Souza.

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Communicated by Chong Qi.

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Souza, M.A., Miyake, H. \(\alpha \) + core structure described with an additional interaction in the nuclear matter saturation region. Eur. Phys. J. A 59, 74 (2023). https://doi.org/10.1140/epja/s10050-023-00990-0

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