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SUMMARY:The shape of the nucleus and its implications
DTSTART;VALUE=DATE-TIME:20251120T084500Z
DTEND;VALUE=DATE-TIME:20251120T090000Z
DTSTAMP;VALUE=DATE-TIME:20260420T154229Z
UID:indico-contribution-28993@indico.ific.uv.es
DESCRIPTION:Speakers: Dorian Frycz (University of Barcelona)\nThe complex 
 nature of the nucleon-nucleon interaction allows for spherical\, oblate an
 d prolate deformations to appear at similar energies within the same nucle
 us. This phenomenon\, known as shape coexistence\, is widespread across th
 e nuclear chart and it provides a crucial role in understanding nuclear st
 ructure [1]. \n\nIn our study we complement shell-model calculations [2] w
 ith beyond-mean-field Hartree-Fock-Bogoliubov techniques [3] to shed light
  on the rich coexistence of differently deformed structures. We infer shap
 e coexistence from multiple observables such as: quadrupole moments\, $E2$
  transitions\, collective wavefunctions\, and shape invariants. The combin
 ation of all these hints allows us to understand the complexities of shape
  coexistence and the notion of nuclear shape itself. \n\nParticularly\, th
 e shape invariants provide a model-independent framework to quantify the d
 eformation parameters and their fluctuations [4]\, which are significant i
 n most nuclei. We analyze how nuclear shapes evolve across the band using 
 an extended sum-rule method to compute the shape invariants for $J\\neq0$ 
 states. This method sheds light on long-standing questions\, such as wheth
 er doubly-magic nuclei are truly spherical\, whether rigid triaxial nuclei
  exist\, and how axially symmetric prolate and oblate nuclei really are.\n
 \n\nFor instance\, $^{28}$Si presents a competition between the oblate gro
 und state and the excited prolate rotational band ($6.5$ MeV)\, with a pos
 sible superdeformed structure at higher energies ($\\sim10$-$20$ MeV). We 
 find that $sdpf$ excitations are needed to correctly describe $^{28}$Si an
 d that superdeformed shapes appear at 18-20 MeV [5]. \n\nThe doubly-magic 
 nucleus $^{40}$Ca also presents shape coexistence between the spherical gr
 ound state\, the normal deformed rotational band ($3.4$ MeV) and the super
 deformed rotational band ($5.2$ MeV) [6].  We analyze the fluctuations of 
 the deformation parameters associated to these states.  \n\nAdditionally\,
  we study the impact of differences in shapes of the initial and final nuc
 lei for double-beta decay [7]\, including triaxiality. We find that larger
  deformation differences between the initial and final states lead to smal
 ler nuclear matrix elements.\n\n[1] P. E. Garrett\, M. Zielińska\, and E.
  Clément\, Prog. Part. Nucl. Phys. 124\, 103931 (2022). \n\n[2] E. Caurie
 r and F. Nowacki\, Acta Phys. Pol. B 30\, 705 (1999).\n\n[3] B. Bally\, A.
  Sánchez-Fernández\, and T. R. Rodríguez\, Eur. Phys. J. A 57\, 69 (202
 1).  \n\n[4] A. Poves\, F. Nowacki\, Y. Alhassid\, Phys. Rev. C 101\, 0543
 07 (2020) \n\n[5] D. Frycz\, J. Menéndez\, A. Rios\, B. Bally\, T. R. Rod
 ríguez\, and A. M. Romero\, Phys. Rev. C 110\, 054326 (2024)   \n\n[6] E.
  Caurier\, J. Menéndez\, F. Nowacki\, and A. Poves\, Phys. Rev. C 75\, 05
 4317 (2007).\n\n[7] T. R. Rodríguez\, G. Martínez-Pinedo\, Phys. Rev. Le
 tt. 105\, 252503 (2010).\n\nhttps://indico.ific.uv.es/event/8035/contribut
 ions/28993/
LOCATION:
URL:https://indico.ific.uv.es/event/8035/contributions/28993/
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