Skip to main content

Advertisement

SpringerLink
Log in

A theoretical analysis of the electromagnetic dipole response in odd-A thorium isotopes

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

An Erratum to this article was published on 10 July 2023

This article has been updated

Abstract

We here present a theoretical analysis of electric and magnetic dipole (E1 and M1) resonances in the \(^{229-233}\)Th isotopes. In this study, the characteristic features of M1 and E1 excitations were calculated using the rotational invariant (RI-) and the translational Galilean invariant (TGI-) quasiparticle phonon nuclear models (QPNM), respectively.These models have been successfully applied to most rare-earth and actinide nuclei, with them yielding results that are consistent with the available experimental data.This study directly compares the TGI-QPNM results with experimental cross-section data (Oslo type; (\(\gamma \),abs.)), and the model was found to reproduce the structural splitting of the E1 strength into two humps in the 8–20 MeV energy region.Furthermore, the study shows that the theoretical spectra of the \(^{231,233}\)Th isotopes, whose giant dipole resonance (GDR) has not yet been measured, almost overlaps with the experimental GDR spectrum of the neighboring \(^{232}\)Th nucleus.The predicted GDR parameters, such as peak energy, cross section, and width, are consistent with the experimental results. Our analysis also yields results that are similar to the corresponding parameters reported in the Oslo data for the PDR E1 (\(\omega _{\text {pyg}} \approx 7.2 \, \text {MeV}\); \(\sigma _{\text {pyg}} \approx 10 \, \text {mb}\)) and spin-flip M1 (\(\omega _{\textit{M}1} \approx 6.67 \, \text {MeV}\); \(\sigma _{\textit{M}1} \approx 4.36 \, \text {mb}\)) resonances.

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

Similar content being viewed by others

Data availability statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All data are stored indefinitely by the authors. Data will be shared upon request.]

Change history

References

  1. B. LoBerman, S.C. Fultz, Measurements of the giant dipole resonance with monoenergetic photons. Rev. Mod. Phys. 47(3), 713 (1975)

    ADS  Google Scholar 

  2. S. Ceruti et al., Experimental study of the isovector giant dipole resonance in \(^{80}Zr\) and \(^{81}Rb\). Phys. Rev. C 95(1), 014312 (2017)

    ADS  Google Scholar 

  3. D. Mondal et al., Study of giant dipole resonance in hot rotating light mass nucleus \(^{31}P\). Phys. Lett. B 784, 423–428 (2018)

    ADS  Google Scholar 

  4. N. Kobayashi et al., Excitation and \(\gamma \)-decay coincidence measurements at the GRAF beamline for studies of pygmy and giant dipole resonances. Eur. Phys. J. A 55(12), 231 (2019)

    ADS  Google Scholar 

  5. B.S. Ishkhanov, V.N. Orlin, Semimicroscopic description of the giant dipole resonance. Phys. Part. Nuclei 38, 232–254 (2007)

    ADS  Google Scholar 

  6. G.C. Baldwin, G.S. Klaiber, Photo-fission in heavy elements. Phys. Rev. 71(1), 3 (1947)

    ADS  Google Scholar 

  7. A. Bracco, E.G. Lanza, A. Tamii, Isoscalar and isovector dipole excitations: nuclear properties from low-lying states and from the isovector giant dipole resonance. Prog. Part. Nucl. Phys. 106, 360–433 (2019)

    ADS  Google Scholar 

  8. X. Wang, L. Zhu, J. Su, Providing physics guidance in Bayesian neural networks from the input layer: the case of giant dipole resonance predictions. Phys. Rev. C 104(3), 034317 (2021)

    ADS  Google Scholar 

  9. O. Papst et al., Photo response of \(^{164}Dy\). Phys. Rev. C 102(3), 034323 (2020)

    ADS  Google Scholar 

  10. E. Grosse, A.R. Junghans, R. Massarczyk, Breaking of axial symmetry in excited heavy nuclei as identified in giant dipole resonance data. Eur. Phys. J. A 53, 1–21 (2017)

    Google Scholar 

  11. E. Lipparini, S. Stringari, Sum rules and giant resonances in nuclei. Phys. Rep. 175(3–4), 103–261 (1989)

    ADS  Google Scholar 

  12. I. Deloncle, S. Péru, M. Martini, Electromagnetic dipole and Gamow–Teller responses of even and odd \({}_{40}^{90-94} Zr\) isotopes in QRPA calculations with the D1M Gogny force. Eur. Phys. J. A 53, 1–13 (2017)

    Google Scholar 

  13. T. Hartmann et al., Microscopic nature of the pygmy dipole resonance: the stable Ca isotopes. Phys. Rev. Lett. 93(19), 192501 (2004)

    ADS  Google Scholar 

  14. C. Tao et al., Pygmy and giant dipole resonances by Coulomb excitation using a quantum molecular dynamics model. Phys. Rev. C 87(1), 014621 (2013)

    ADS  Google Scholar 

  15. T.K. Eriksen et al., Pygmy resonance and low-energy enhancement in the \(\gamma \)-ray strength functions of Pd isotopes. Phys. Rev. C 90(4), 044311 (2014)

    ADS  MathSciNet  Google Scholar 

  16. A. Repko et al., Toroidal nature of the low-energy E1 mode. Phys. Rev. C 87(2), 024305 (2013)

    ADS  Google Scholar 

  17. R. Bijker, F. Iachello, Evidence for tetrahedral symmetry in \(^{16}O\). Phys. Rev. Lett. 112(15), 152501 (2014)

    ADS  Google Scholar 

  18. M. Spieker et al., High-resolution (p, t) study of low-spin states in Pu 240: octupole excitations, \(\alpha \) clustering, and other structure features. Phys. Rev. C 97(6), 064319 (2018)

    ADS  Google Scholar 

  19. Y. Kanada-En’yo, Y. Shikata, Toroidal, compressive, and E1 properties of low-energy dipole modes in \(^{10}Be\). Phys. Rev. C 95(6), 064319 (2017)

    ADS  Google Scholar 

  20. K. Yoshida, T. Nakatsukasa, Dipole responses in Nd and Sm isotopes with shape transitions. Phys. Rev. C 83(2), 021304 (2011)

    ADS  Google Scholar 

  21. K. Yoshida, T. Nakatsukasa, Shape evolution of giant resonances in Nd and Sm isotopes. Phys. Rev. C 88(3), 034309 (2013)

    ADS  Google Scholar 

  22. E.G. Lanza, et al., Theoretical studies of Pygmy resonances. Prog.Part. Nucl. Phys. 129, 104006 (2023)

  23. R.-D. Herzberg et al., Observation of dipole transitions to a \(2^{+} \otimes 3^{-} \otimes \) particle multiplet in \(^{143}Nd\). Phys. Rev. C 51(3), 1226 (1995)

    ADS  Google Scholar 

  24. I. Bauske et al., First observation of scissors mode states in an odd-mass nucleus. Phys. Rev. Lett. 71(7), 975 (1993)

    ADS  Google Scholar 

  25. J. Margraf et al., Systematics of low-lying dipole strengths in odd and even Dy and Gd isotopes. Phys. Rev. C 52(5), 2429 (1995)

    ADS  Google Scholar 

  26. A. Nord et al., Systematic study of the fragmentation of low-lying dipole strength in odd-A rare earth nuclei investigated in nuclear resonance fluorescence experiments. Phys. Rev. C 54(5), 2287 (1996)

    ADS  MathSciNet  Google Scholar 

  27. R.-D. Herzberg et al., Observation of an octupole \(\otimes \) quasiparticle band in \(^{175}Lu\) using photon scattering experiments. Phys. Rev. C 56(5), 2484 (1997)

    ADS  MathSciNet  Google Scholar 

  28. A. Nord et al., Low-energy photon scattering experiments of \(^{151,153}Eu\), \(^{163}Dy\), and \(^{165}Ho\) and the systematics of the M1 scissors mode in odd-mass rare-earth nuclei. Phys. Rev. C 67(3), 034307 (2003)

    ADS  Google Scholar 

  29. N. Huxel et al., Complete scissors mode strength in heavy deformed odd-mass nuclei: a case study of \(^{165}Ho\) and \(^{169}Tm\). Nucl. Phys. A 645(2), 239–261 (1999)

    ADS  Google Scholar 

  30. R.D. Heil et al., Observation of orbital magnetic dipole strength in the actinide nuclei \({}^{232}Th\) and \({}^{238}U\). Nucl. Phys. A 476(1), 39–47 (1988)

    ADS  Google Scholar 

  31. J. Margraf et al., Photoexcitation of low-lying dipole transitions in \({}^{236}U\). Phys. Rev. C 42(2), 771 (1990)

    ADS  Google Scholar 

  32. A.S. Adekola et al., Discovery of low-lying \(E1\) and \(M1\) strengths in \({}^{232}Th\). Phys. Rev. C 83(3), 034615 (2011)

    ADS  Google Scholar 

  33. E. Kwan et al., Discrete deexcitations in \({}^{235}U\) below 3 MeV from nuclear resonance fluorescence. Phys. Rev. C 83(4), 041601 (2011)

    ADS  Google Scholar 

  34. B.J. Quiter et al., Nuclear resonance fluorescence in \({}^{240}Pu\). Phys. Rev. C 86(3), 034307 (2012)

    ADS  Google Scholar 

  35. C.T. Angell et al., Nuclear resonance fluorescence of \(^{237}Np\). Phys. Rev. C 82(5), 054310 (2010)

    ADS  Google Scholar 

  36. W. Bertozzi et al., Nuclear resonance fluorescence excitations near 2 MeV in \({}^{235}U\) and \({}^{239}Pu\). Phys. Rev. C 78(4), 041601 (2008)

    ADS  Google Scholar 

  37. O. Yevetska et al., Dipole strength in the \({}^{235}U\) (\(\gamma \),\(\gamma \)’) reaction up to 2.8 MeV. Phys. Rev. C 81(4), 044309 (2010)

    ADS  Google Scholar 

  38. A. Zilges et al., Strong dipole excitations around 1.8 MeV in \({}^{238}U\). Phys. Rev. C 52(2), R468 (1995)

    ADS  Google Scholar 

  39. V.O. Nesterenko et al., Microscopic analysis of lowenergy spin and orbital magnetic dipole excitations in deformed nuclei. Phys. Rev. C 103(6), 064313 (2021)

    ADS  Google Scholar 

  40. P. Vesely et al., Skyrme random-phase-approximation description of spin-flip M1 giant resonance. Phys. Rev. C 80(3), 031302 (2009)

    ADS  Google Scholar 

  41. N. Pietralla, J. Isaak, V. Werner, Photonuclear reactions: achievements and perspectives. Eur. Phys. J. A 55, 1–10 (2019)

    Google Scholar 

  42. I. Bentley et al., Instantaneous shape sampling: a model for the \(\gamma \)-absorption cross section of transitional nuclei. Phys. Rev. C 83(1), 014317 (2011)

    ADS  Google Scholar 

  43. A.P. Tonchev et al., Measurement of the \(^{241}Am\) (\(\gamma \), n) \(^{240}Am\) reaction in the giant dipole resonance region. Phys. Rev. C 82(5), 054620 (2010)

    ADS  Google Scholar 

  44. T. Kawano et al., IAEA photonuclear data library. Nucl. Data Sheets 163(2020), 109–162 (2019)

    ADS  Google Scholar 

  45. A. Voinov et al., \(\gamma \)-Ray strength function and pygmy resonance in rare earth nuclei. Phys. Rev. C 63(4), 044313 (2001)

    ADS  Google Scholar 

  46. S. Siem et al., Level densities and \(\gamma \)-strength functions in \(^{148,149}Sm\). Phys. Rev. C 65(4), 044318 (2002)

    ADS  Google Scholar 

  47. M. Guttormsen et al., Observation of large scissors resonance strength in actinides. Phys. Rev. Lett. 109(16), 162503 (2012)

    ADS  Google Scholar 

  48. T.G. Tornyi et al., Level density and \(\gamma \)-ray strength function in the odd–odd \(^{238}Np\) nucleus. Phys. Rev. C 89(4), 044323 (2014)

    ADS  Google Scholar 

  49. M. Guttormsen et al., Scissors resonance in the quasicontinuum of Th, Pa, and U isotopes. Phys. Rev. C 89(1), 014302 (2014)

    ADS  Google Scholar 

  50. F. Zeiser et al., Restricted spin-range correction in the Oslo method: the example of nuclear level density and \(\gamma \)-ray strength function from \({}^{239}Pu\) (d, p \(\gamma \)) \({}^{240}Pu\). Phys. Rev. C 100(2), 024305 (2019)

    ADS  Google Scholar 

  51. T.A. Laplace et al., Statistical properties of \({}^{243}Pu\), and \({}^{242}Pu\) (n, \(\gamma \)) cross section calculation. Phys. Rev. C 93(1), 014323 (2016)

    ADS  Google Scholar 

  52. J. Kvasil, A. Repko, V.O. Nesterenko, Elimination of spurious modes before the solution of quasiparticle random-phase-approximation equations. Eur. Phys. J. A 55(11), 213 (2019)

    ADS  Google Scholar 

  53. J. Speth et al., Generalized Skyrme randomphase approximation for nuclear resonances: Different trends for electric and magnetic modes. Phys. Rev. C 102(5), 054332 (2020)

    ADS  Google Scholar 

  54. E. Guliyev, A. Kuliev, M. Guner, Electric dipole strength distribution below the E1 giant resonance in N= 82 nuclei. Open Phys. 8(6), 961–969 (2010)

    ADS  Google Scholar 

  55. E. Tabar, H. Yakut, A.A. Kuliev, Lowenergy dipole strength in even-even \(^{152-164}Dy\) isotopes within the quasiparticle random phase approximation (QRPA) including symmetry restoring interactions. Nucl. Phys. A 979, 143–164 (2018)

    ADS  Google Scholar 

  56. E. Guliyev, A.A. Kuliev, F. Ertugral, Systematic investigation of the low-energy dipole excitations in \(^{176,178,180}Hf\) within rotational, translational and Galilean invariant quasiparticle RPA. Nucl. Phys. A 915, 78–89 (2013)

    ADS  Google Scholar 

  57. E. Guliyev, H. Quliyev, A.A. Kuliev, Pygmy dipole resonance in the well-deformed even-even \(^{152-162}Gd\). J. Phys. G Nucl. Part. Phys. 47(11), 115107 (2020)

    ADS  Google Scholar 

  58. E. Tabar, H. Yakut, A.A. Kuliev, Microscopic description of ground state magnetic moment and low-lying magnetic dipole excitations in heavy odd-mass \(^{181}Ta\) nucleus. Int. J. Mod. Phys. E 25(08), 1650053 (2016)

    ADS  Google Scholar 

  59. E. Tabar, H. Yakut, A.A. Kuliev, Magnetic dipole response of the \(^{169}Tm\) nucleus. Nucl. Phys. A 981, 130–146 (2019)

    ADS  Google Scholar 

  60. E. Tabar, H. Yakut, A.A. Kuliev, Microscopic description of low-lying M1 excitations in odd-mass actinide nuclei. Nucl. Phys. A 957, 33–50 (2017)

    ADS  Google Scholar 

  61. A.A. Kuliev et al., The low-energy dipole structure of \({}^{232}Th\), \({}^{236}U\) and \({}^{238}U\) actinide nuclei. Eur. Phys. J. A 43(3), 313–321 (2010)

    ADS  Google Scholar 

  62. H. Quliyev et al., The electric dipole response of even-even \(^{154-164}Dy\) isotopes. Phys. Scr. 97(2), 025302 (2022)

    ADS  Google Scholar 

  63. K.-G. Dietrich et al., Magnetic dipole strength distribution at high excitation energies in deformed nuclei. Phys. Lett. B 220(3), 351–355 (1989)

    ADS  Google Scholar 

  64. H. Quliyev, E. Guliyev, A.A. Kuliev, Electric dipole strength in the deformed \(^{144,146,148,150,152,154}Nd\) nuclei. Nucl. Phys. A 1014, 122239 (2021)

    Google Scholar 

  65. J. Carter et al., Damping of the isovector giant dipole resonance in \(^{40,48}Ca\). Phys. Lett. B 833, 137374 (2022)

    Google Scholar 

  66. D. Gambacurta, M. Grasso, J. Engel, Gamow–Teller strength in \(^{48}\)Ca and \(^{78}\)Ni with the charge-exchange subtracted second random-phase approximation. Phys. Rev. Lett. 125(21), 212501 (2020)

    ADS  Google Scholar 

  67. D. Gambacurta, M. Grasso, Quenching of Gamow–Teller strengths and two-particle-two-hole configurations. Phys. Rev. C 105(1), 014321 (2022)

    ADS  Google Scholar 

  68. T.H.R. Skyrme, The effective nuclear potential. Nucl. Phys. 9(4), 615–634 (1958)

    MATH  Google Scholar 

  69. D. Gogny, Simple separable expansions for calculating matrix elements of two-body local interactions with harmonic oscillator functions. Nucl. Phys. A 237(3), 399–418 (1975)

    ADS  MathSciNet  Google Scholar 

  70. A.P. Severyukhin et al., Separable Skyrme interactions and quasiparticle RPA. Phys. At. Nucl. 66, 1434–1438 (2003)

    Google Scholar 

  71. S. Péru, J.F. Berger, P.F. Bortignon, Giant resonances in exotic spherical nuclei within the RPA approach with the Gogny force. Eur. Phys. J. A Hadrons Nucl. 26, 25–32 (2005)

    ADS  Google Scholar 

  72. M. Martini et al., Large-scale deformed QRPA calculations of the gamma-ray strength function based on a Gogny force. J. Phys. Conf. Ser. 665(1), 012058 (2016)

    Google Scholar 

  73. V.G. Solov’ev, Theory of Complex Nuclei, vol. 81 (Pergamon, Oxford, 1976)

    Google Scholar 

  74. V.G. Soloviev et al., Low-lying magnetic and electric dipole transitions in odd-mass deformed nuclei: a microscopic approach. Nucl. Phys. A 613(1–2), 45–68 (1997)

    ADS  Google Scholar 

  75. E. Tabar, A. Kuliev, Microscopic investigation of the low-lying magnetic dipole transitions in the odd-mass \(^{155-169}\)Ho isotopes. Nucl. Phys. A 964, 1–17 (2017)

    ADS  Google Scholar 

  76. H. Yakut et al., Microscopic calculation of the electromagnetic dipole strength for \({}^{239,243}\text{ Pu }\) isotopes. J. Phys. G Nucl. Part. Phys. 50(1), 015104 (2022)

    ADS  Google Scholar 

  77. E. Tabar et al., Electromagnetic dipole transitions below 4 MeV in odd-neutron \(^{161,163}\)Dy. Nucl. Phys. A 1014, 122252 (2021)

    Google Scholar 

  78. H. Yakut et al., Theoretical description of pygmy and giant dipole resonances in \(^{237}\)Np. Phys. Scr. 96(12), 125315 (2021)

    ADS  Google Scholar 

  79. E. Tabar et al., Scissors mode and effects of the lowlying E1 excitations on the dipole distributions in \(^{175}\)Lu. Phys. Scr. 97(6), 065303 (2022)

    ADS  Google Scholar 

  80. E. Tabar et al., Pygmy and isovector giant dipole resonance in \(^{175}\)Lu. Eur. Phys. J. A 58(6), 101 (2022)

    ADS  Google Scholar 

  81. E. Tabar et al., Investigation of the electric dipole (E1) excitations in \(^{181}\)Ta nucleus. Eur. Phys. J. A 56(10), 271 (2020)

    ADS  Google Scholar 

  82. E. Tabar et al., Translational and Galilean invariant quasiparticle phonon nuclear model (TGI-QPNM) for electric dipole (\(E1\)) transitions in odd-mass deformed nuclei. Nucl. Phys. A 1001, 121885 (2020)

    Google Scholar 

  83. E. Tabar et al., Study of the high lying electric dipole excitations in odd-A \(^{153-159}\)Eu isotopes. Phys. Scr. 96(7), 075303 (2021)

    ADS  Google Scholar 

  84. E. Tabar et al., Systematics of electric dipole excitations for odd-mass \({}^{233-239}\text{ U }\) isotopes. Nucl. Phys. A 1008, 122138 (2021)

    Google Scholar 

  85. G.M. Gurevich et al., Giant resonance in the total photoabsorption cross section of \(\text{ Z }\approx 90\) nuclei. Nucl. Phys. A 273(2), 326–340 (1976)

    ADS  Google Scholar 

  86. J.T. Caldwell et al., Giant resonance for the actinide nuclei: photoneutron and photofission cross sections for U 235, U 236, U 238, and Th 232. Phys. Rev. C 21(4), 1215 (1980)

    ADS  Google Scholar 

  87. A.M. Khan, J.W. Knowles, Photofission of \({}^{232}\text{ Th }\), \({}^{238}\text{ U }\) and \({}^{235}\text{ U }\) near threshold using a variable energy beam of \(\gamma \)-rays. Nucl. Phys. A 179(2), 333–352 (1972)

    ADS  Google Scholar 

  88. M. Guttormsen et al., Constant-temperature level densities in the quasicontinuum of Th and U isotopes. Phys. Rev. C 88(2), 024307 (2013)

    ADS  Google Scholar 

  89. V.G. Soloviev, C. Stoyanov, A.I. Vdovin, Fragmentation of giant multipole resonances over twophonon states in spherical nuclei. Nucl. Phys. A 288(3), 376–396 (1977)

    ADS  Google Scholar 

  90. J. Meyer-ter-Vehn, Exact removal of spurious states in RPA calculations. Zeitschrift für Physik A At. Nucl. 289(3), 319–323 (1979)

    ADS  Google Scholar 

  91. S. Cwiok, J. Kvasil, B. Choriev, The RPA and restoration of translational symmetry of the Hamiltonian of a rotating nucleus. J. Phys. G Nucl. Phys. 10(7), 903 (1984)

    ADS  Google Scholar 

  92. N.I. Pyatov, D.I. Salamov, Conservation laws and collective excitations in nuclei. Nukleonika 22(1), 127–141 (1977)

    Google Scholar 

  93. J. Dudek, T. Werner, New parameters of the deformed Woods-Saxon potential for A= 110–210 nuclei. J. Phys. G Nucl. Phys. 4(10), 1543 (1978)

    ADS  Google Scholar 

  94. S. Raman, C.W. Nestor Jr., P. Tikkanen, Transition probability from the ground to the first-excited \(2^{+}\)state of even-even nuclides. At. Data Nucl. Data Tables 78(1), 1–128 (2001)

    ADS  Google Scholar 

  95. J. Suhonen, From Nucleons to Nucleus: Concepts of Microscopic Nuclear Theory (Springer Science & Business Media, Berlin, 2007)

    MATH  Google Scholar 

  96. P. Möller, J.R. Nix, Nuclear pairing models. Nucl. Phys. A 536(1), 20–60 (1992)

    ADS  Google Scholar 

  97. M.R. Bhat, Evaluated nuclear structure data file (ENSDF), in Nuclear Data for Science and Technology: Proceedings of an International Conference, held at the Forschungszentrum Jülich, Federal Republic of Germany, 13–17 May 1991 (Springer, 1992), pp. 817–821

  98. C.Z. Khuong, V.G. Soloviev, V.V. Voronov, Description of the substructure in the radiative strength function of 117Sn and 119Sn. J. Phys. G Nucl. Phys. 5(4), L79 (1979)

    Google Scholar 

  99. S.V. Akulinichev, L.A. Malov, Semi-microscopic calculation of the giant dipole resonances in deformed nuclei. J. Phys. G Nucl. Phys. 3(5), 625 (1977)

    ADS  Google Scholar 

  100. S.S. Dietrich, B.L. Berman, Atlas of photoneutron cross sections obtained with monoenergetic photons. At. Data Nucl. Data Tables 38(2), 199–338 (1988)

    ADS  Google Scholar 

  101. O. Bohigas, N.V. Giai, D. Vautherin, Selfconsistent description of the static nuclear dipole polarizability. Phys. Lett. B 102(2–3), 105–108 (1981)

    ADS  Google Scholar 

  102. A. Molinari, II. Photon induced nuclear processes. Phys. Rep. 64(5), 283–336 (1980)

    ADS  Google Scholar 

  103. J.H. Bai et al., The description of giant dipole resonance key parameters with multitask neural networks. Phys. Lett. B 815, 136147 (2021)

    Google Scholar 

  104. I. Raskinyte et al., Photonuclear data evaluation of actinides. Ric. Sci. Educ. Perm. Suppl. 126(DAPNIA–2006–147), 545–554 (2006)

    Google Scholar 

  105. L.A. Malov, V.G. Solov’ev, Quasiparticle-phonon nuclear model. Fizika Ehlementarnykh Chastits i Atomnogo Yadra 11(2), 301–341 (1980)

    Google Scholar 

  106. A. Repko et al., Pairing and deformation effects in nuclear excitation spectra. Eur. Phys. J. A 53, 1–12 (2017)

    Google Scholar 

  107. K. Heyde, P. von Neumann-Cosel, A. Richter, Magnetic dipole excitations in nuclei: elementary modes of nucleonic motion. Rev. Mod. Phys. 82(3), 2365 (2010)

    ADS  Google Scholar 

  108. P. Sarriguren, E.M. de Guerra, R. Nojarov, Spin M1 excitations in deformed nuclei from self-consistent Hartree–Fock plus random-phase approximation. Phys. Rev. C 54(2), 690 (1996)

    ADS  Google Scholar 

  109. T. Weber et al., Nuclear levels in 228 Th populated in the decay of 228 Pa (II). Eur. Phys. J. A Hadrons Nucl. 3, 25–48 (1998)

    ADS  Google Scholar 

  110. V.G. Soloviev, A.V. Sushkov, N. Yu Shirikova, Dipole \(\gamma \)-ray transition rates in 238 U. Zeitschrift für Physik A Hadrons Nucl. 358, 287–296 (1997)

    ADS  Google Scholar 

  111. E. Ruchowska et al., Nuclear structure of Th 229. Phys. Rev. C 73(4), 044326 (2006)

  112. V.G. Soloviev et al., Dipole strength distribution in doubly even deformed nuclei. J. Phys. G Nucl. Part. Phys. 25(5), 1023 (1999)

  113. E. Tabar, A theoretical study on the ground and low-energy magnetic dipole characteristics of 239Pu nucleus. Nucl. Phys. A 987, 202–221 (2019)

    ADS  Google Scholar 

Download references

Acknowledgements

This work has been supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under Project no. 118F094, and the Research Fund of Sakarya University under Project no. 2020-7-25-55. Additionally, the authors E. Kemah, MSc. and G. Hoşgör, MSc. acknowledge the support of the Council of Higher Education (CoHE) through PhD Scholarships under the 100/2000 program, as well as the support of the Scientific and Technological Research Council of Turkey (TÜBİTAK) under the 2211-A PhD Scholarship Program.

Author information

Authors and Affiliations

  1. Sakarya Üniversitesi Fen Fakültesi Fizik Bölümü, Sakarya, Türkiye

    E. Kemah, H. Yakut, E. Tabar & G. Hoşgör

  2. The National Aviation Academy of Azerbaijan, Baku, Azerbaijan

    A. A. Kuliev

Authors
  1. E. Kemah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Yakut
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Tabar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. G. Hoşgör
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. A. Kuliev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Kemah.

Additional information

Communicated by Dario Vretenar.

The original online version of this article was revised: The references in table 3 were not structured correctly. The correct order is as follows: a Gurevich et al.,1976, b Caldwell et al., 1980, c Guttormsen et al., 2014.

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

Kemah, E., Yakut, H., Tabar, E. et al. A theoretical analysis of the electromagnetic dipole response in odd-A thorium isotopes. Eur. Phys. J. A 59, 135 (2023). https://doi.org/10.1140/epja/s10050-023-01054-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/s10050-023-01054-z

Search

Navigation