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Impact of octupole deformation on the nuclear electromagnetic response

Manu Kanerva* and Markus Kortelainen†

  • *Contact author: manu.v.kanerva@jyu.fi
  • †Contact author: markus.kortelainen@jyu.fi

Phys. Rev. C 113, 044320 – Published 23 April, 2026

DOI: https://doi.org/10.1103/ddl7-y8xj

Abstract

Background: Properties of giant dipole resonances, along with other nuclear resonances, provide valuable tools for refining theoretical models as they reflect collective features of nuclear matter. Among such collective phenomena is octupole deformation, whose impact on resonance features, however, is less studied.

Purpose: Investigate the effect of reflection-symmetry-breaking octupole deformation on electric and magnetic transition strengths in atomic nuclei.

Methods: Calculations were performed using linear response theory with the iterative finite amplitude method to solve quasiparticle random phase approximation–type equations. Underlying ground-state solutions were obtained within the framework of axially symmetric Skyrme–Hartree–Fock–Bogoliubov (HFB) using three different Skyrme functionals.

Results: Electric and magnetic multipole responses were calculated for octupole-deformed even-even Rn, Ra, Th, U, Pu, and Cm isotopes. Calculations were performed on top of two distinct deformed ground-state solutions: one constrained to conserve parity, and the other allowing parity breaking. Sum rules were calculated from M1 transition strengths and compared with the expected correlations to certain ground-state properties.

Conclusions: Based on our results, the octupole deformation has only a modest effect on the transition strengths in the resonances. In turn, M1 transition strengths have a greater effect at lower energies (0–8MeV), which encourages further investigation. Isoscalar E3 transition strength was confirmed to have a significant contribution from the rotational Nambu–Goldstone mode in the parity-breaking HFB solution, and, thus, removing it was found necessary.

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References (64)

  1. P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New York, 1980).
  2. M. Bender, P.-H. Heenen, and P.-G. Reinhard, Self-consistent mean-field models for nuclear structure, Rev. Mod. Phys. 75, 121 (2003).
  3. Energy Density Functional Methods for Atomic Nuclei, edited by N. Schunck (IOP Publishing, Bristol, UK, 2019).
  4. H. Hergert, A guided tour of ab initio nuclear many-body theory, Front. Phys. 8, 379 (2020).
  5. J. A. Sheikh, J. Dobaczewski, P. Ring, L. M. Robledo, and C. Yannouleas, Symmetry restoration in mean-field approaches, J. Phys. G: Nucl. Part. Phys. 48, 123001 (2021).
  6. P. A. Butler and W. Nazarewicz, Intrinsic reflection asymmetry in atomic nuclei, Rev. Mod. Phys. 68, 349 (1996).
  7. M. Chen, T. Li, J. Dobaczewski, and W. Nazarewicz, Microscopic origin of reflection-asymmetric nuclear shapes, Phys. Rev. C 103, 034303 (2021).
  8. P. A. Butler, Pear-shaped atomic nuclei, Proc. R. Soc. A 476, 20200202 (2020).
  9. Y. Cao, S. E. Agbemava, A. V. Afanasjev, W. Nazarewicz, and E. Olsen, Landscape of pear-shaped even-even nuclei, Phys. Rev. C 102, 024311 (2020).
  10. S. E. Agbemava, A. V. Afanasjev, and P. Ring, Octupole deformation in the ground states of even-even nuclei: A global analysis within the covariant density functional theory, Phys. Rev. C 93, 044304 (2016).
  11. S. Ebata and T. Nakatsukasa, Octupole deformation in the nuclear chart based on the 3D Skyrme Hartree–Fock plus BCS model, Phys. Scr. 92, 064005 (2017).
  12. G. Grams, W. Ryssens, G. Scamps, S. Goriely, and N. Chamel, Skyrme-Hartree-Fock-Bogoliubov mass models on a 3D mesh: III. From atomic nuclei to neutron stars, Eur. Phys. J. A 59, 270 (2023).
  13. A. Bohr and B. R. Mottelson, Nuclear Structure, Vol 2, Nuclear Deformations (Advanced Book Program, W.A., Reading, Massachusetts, 1975).
  14. X. Roca-Maza and N. Paar, Nuclear equation of state from ground and collective excited state properties of nuclei, Prog. Part. Nucl. Phys. 101, 96 (2018).
  15. B. L. Berman and S. C. Fultz, Measurements of the giant dipole resonance with monoenergetic photons, Rev. Mod. Phys. 47, 713 (1975).
  16. R. R. Hilton, Talk Presented at The International Conference on Nuclear Structure (JINR, Dubna, 1976) (unpublished).
  17. T. Suzuki and D. Rowe, The splitting of giant multipole states of deformed nuclei, Nucl. Phys. A 289, 461 (1977).
  18. N. L. Iudice and F. Palumbo, New isovector collective modes in deformed nuclei, Phys. Rev. Lett. 41, 1532 (1978).
  19. D. Bohle, A. Richter, W. Steffen, A. Dieperink, N. Lo Iudice, F. Palumbo, and O. Scholten, New magnetic dipole excitation mode studied in the heavy deformed nucleus Gd156 by inelastic electron scattering, Phys. Lett. B 137, 27 (1984).
  20. K. Heyde, P. von Neumann-Cosel, and A. Richter, Magnetic dipole excitations in nuclei: Elementary modes of nucleonic motion, Rev. Mod. Phys. 82, 2365 (2010).
  21. J. J. Cowan, C. Sneden, J. E. Lawler, A. Aprahamian, M. Wiescher, K. Langanke, G. Martínez-Pinedo, and F.-K. Thielemann, Origin of the heaviest elements: The rapid neutron-capture process, Rev. Mod. Phys. 93, 015002 (2021).
  22. M. Eichler, W. Sayar, A. Arcones, and T. Rauscher, Probing the production of actinides under different r-process conditions, Astrophys. J. 879, 47 (2019).
  23. T. Nakatsukasa, K. Matsuyanagi, M. Matsuo, and K. Yabana, Time-dependent density-functional description of nuclear dynamics, Rev. Mod. Phys. 88, 045004 (2016).
  24. T. Nakatsukasa, T. Inakura, and K. Yabana, Finite amplitude method for the solution of the random-phase approximation, Phys. Rev. C 76, 024318 (2007).
  25. P. Avogadro and T. Nakatsukasa, Finite amplitude method for the quasiparticle random-phase approximation, Phys. Rev. C 84, 014314 (2011).
  26. T. Oishi, M. Kortelainen, and N. Hinohara, Finite amplitude method applied to the giant dipole resonance in heavy rare-earth nuclei, Phys. Rev. C 93, 034329 (2016).
  27. T. Li, N. Schunck, and M. Grosskopf, Multipole responses in fissioning nuclei and their uncertainties, Phys. Rev. C 110, 034317 (2024).
  28. K. Washiyama, N. Hinohara, and T. Nakatsukasa, Finite-amplitude method for collective inertia in spontaneous fission, Phys. Rev. C 103, 014306 (2021).
  29. N. Hinohara, Collective inertia of the Nambu-Goldstone mode from linear response theory, Phys. Rev. C 92, 034321 (2015).
  30. N. Hinohara and W. Nazarewicz, Pairing Nambu-Goldstone Modes within Nuclear Density Functional Theory, Phys. Rev. Lett. 116, 152502 (2016).
  31. K. Petrík and M. Kortelainen, Thouless-Valatin rotational moment of inertia from linear response theory, Phys. Rev. C 97, 034321 (2018).
  32. T. Shafer, J. Engel, C. Fröhlich, G. C. McLaughlin, M. Mumpower, and R. Surman, β decay of deformed r-process nuclei near A=80 and A=160, including odd-A and odd-odd nuclei, with the Skyrme finite-amplitude method, Phys. Rev. C 94, 055802 (2016).
  33. N. Hinohara and J. Engel, Global calculation of two-neutrino double-β decay within the finite amplitude method in nuclear density functional theory, Phys. Rev. C 105, 044314 (2022).
  34. J. Zhao, Multipole modes of excitation in tetrahedrally deformed neutron-rich Zr isotopes, Phys. Rev. C 110, L011301 (2024).
  35. J. Zamora et al., First measurement of isoscalar giant resonances in a stored-beam experiment, Phys. Lett. B 763, 16 (2016).
  36. R. Reifarth and Y. A. Litvinov, Measurements of neutron-induced reactions in inverse kinematics, Phys. Rev. ST Accel. Beams 17, 014701 (2014).
  37. R. Reifarth, K. Göbel, T. Heftrich, M. Weigand, B. Jurado, F. Käppeler, and Y. A. Litvinov, Spallation-based neutron target for direct studies of neutron-induced reactions in inverse kinematics, Phys. Rev. Accel. Beams 20, 044701 (2017).
  38. A. L. Cooper, S. Mosby, R. Reifarth, A. Couture, E. Bennett, N. Gibson, D. Gorelov, C. Keith, A. Lovell, G. Misch, and M. Mumpower, A high-intensity, low-energy heavy ion source for a neutron target proof-of-principle experiment at LANSCE, J. Phys.: Conf. Ser. 2743, 012091 (2024).
  39. M. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Axially deformed solution of the Skyrme-Hartree–Fock–Bogoliubov equations using the transformed harmonic oscillator basis (II) hfbtho v2.00d: A new version of the program, Comput. Phys. Commun. 184, 1592 (2013).
  40. M. Stoitsov, M. Kortelainen, T. Nakatsukasa, C. Losa, and W. Nazarewicz, Monopole strength function of deformed superfluid nuclei, Phys. Rev. C 84, 041305(R) (2011).
  41. M. Kortelainen, N. Hinohara, and W. Nazarewicz, Multipole modes in deformed nuclei within the finite amplitude method, Phys. Rev. C 92, 051302(R) (2015).
  42. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ddl7-y8xj for additional figures and further analyses.
  43. G. Scamps and D. Lacroix, Systematics of isovector and isoscalar giant quadrupole resonances in normal and superfluid spherical nuclei, Phys. Rev. C 88, 044310 (2013).
  44. W. Younes and D. Gogny, Microscopic calculation of Pu240 scission with a finite-range effective force, Phys. Rev. C 80, 054313 (2009).
  45. M. Kortelainen, Thouless-Valatin moment of inertia and removal of the spurious mode in the linear response theory, J. Phys.: Conf. Ser. 1643, 012142 (2020).
  46. J. Bartel, P. Quentin, M. Brack, C. Guet, and H.-B. Håkansson, Towards a better parametrisation of Skyrme-like effective forces: A critical study of the SkM force, Nucl. Phys. A 386, 79 (1982).
  47. E. Chabanat, P. Bonche, P. Haensel, J. Meyer, and R. Schaeffer, A Skyrme parametrization from subnuclear to neutron star densities Part II. Nuclei far from stabilities, Nucl. Phys. A 635, 231 (1998).
  48. M. Kortelainen, J. McDonnell, W. Nazarewicz, P.-G. Reinhard, J. Sarich, N. Schunck, M. V. Stoitsov, and S. M. Wild, Nuclear energy density optimization: Large deformations, Phys. Rev. C 85, 024304 (2012).
  49. N. Schunck, D. Duke, H. Carr, and A. Knoll, Description of induced nuclear fission with Skyrme energy functionals: Static potential energy surfaces and fission fragment properties, Phys. Rev. C 90, 054305 (2014).
  50. J. Bonnard, J. Dobaczewski, G. Danneaux, and M. Kortelainen, Nuclear DFT electromagnetic moments in heavy deformed open-shell odd nuclei, Phys. Lett. B 843, 138014 (2023).
  51. M. Bender, J. Dobaczewski, J. Engel, and W. Nazarewicz, Gamow-Teller strength and the spin-isospin coupling constants of the Skyrme energy functional, Phys. Rev. C 65, 054322 (2002).
  52. P. L. Sassarini, J. Dobaczewski, J. Bonnard, and R. F. G. Ruiz, Nuclear DFT analysis of electromagnetic moments in odd near doubly magic nuclei, J. Phys. G: Nucl. Part. Phys. 49, 11LT01 (2022).
  53. V. O. Nesterenko, W. Kleinig, J. Kvasil, P. Vesely, and P.-G. Reinhard, Giant dipole resonance in deformed nuclei: Dependence on Skyrme forces, Int. J. Mod. Phys. E 16, 624 (2007).
  54. A. Richter, Probing the nuclear magnetic dipole response with electrons, photons and hadrons, Prog. Part. Nucl. Phys. 34, 261 (1995).
  55. P. Vesely, J. Kvasil, V. O. Nesterenko, W. Kleinig, P. G. Reinhard, and V. Y. Ponomarev, Skyrme random-phase-approximation description of spin-flip M1 giant resonance, Phys. Rev. C 80, 031302(R) (2009).
  56. W. Ziegler, C. Rangacharyulu, A. Richter, and C. Spieler, Orbital magnetic dipole strength in Sm148,150,152,154 and nuclear deformation, Phys. Rev. Lett. 65, 2515 (1990).
  57. J. Dobaczewski, A. E. Stuchbery, G. Danneaux, A. Nagpal, P. L. Sassarini, and H. Wibowo, Electromagnetic moments of ground and excited states calculated in heavy odd-N open-shell nuclei, Phys. Rev. C 113, 024306 (2026).
  58. N. L. Iudice, Magnetic dipole excitations in deformed nuclei, Phys. Part. Nuclei 28, 556 (1997).
  59. D. Kurath, Strong M1 Transitions in Light Nuclei, Phys. Rev. 130, 1525 (1963).
  60. N. Lo Iudice, Collective excitations in deformed nuclei, Riv. Nuovo Cim. 23, 1 (2000).
  61. P.-G. Reinhard, Skyrme forces and giant resonances in exotic nuclei, Nucl. Phys. A 649, 305 (1999).
  62. N. Hinohara, M. Kortelainen, and W. Nazarewicz, Low-energy collective modes of deformed superfluid nuclei within the finite-amplitude method, Phys. Rev. C 87, 064309 (2013).
  63. A. Porro, G. Colò, T. Duguet, D. Gambacurta, and V. Somà, Symmetry-restored Skyrme-random-phase-approximation calculations of the monopole strength in deformed nuclei, Phys. Rev. C 109, 044315 (2024).
  64. M. Kanerva and M. Kortelainen, Transition strengths of octupole-deformed actinide nuclei, University of Jyväskylä (2026), doi: https://doi.org/10.17011/jyx/dataset/109498.

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