arXiv : Manifestation of the Berry phase in the atomic nucleus $^{213}$Pb

Valiente-Dobón, J.J.; Goasduff, A.; Camera, F.; Weick, H.; Van Isacker, P.; Gadea, A.; Napoli, D.R.; Sahin, E.; Corsi, A.; Doncel, M.; Algora, A.; Bruce, A.M.; de Angelis, G.; Cortés, M.L.; Gerl, J.; Sharma, A.; Regan, P.H.; Leoni, S.; Gregor, E.; Grebosz, J.; Strmen, P.; Sitar, B.; Ur, C.A.; Mengoni, D.; Lunardi, S.; Pfützner, M.; Walker, P.M.; Lenzi, S.M.; Bazzacco, D.; Goel, N.; Nociforo, C.; Szarka, I.; Rudolph, D.; Schaffner, H.; Naqvi, F.; Kurz, N.; Prochazka, A.; Wieland, O.; Podolyák, Zs.; Benzoni, G.; Habermann, T.; Geissel, H.; Siwal, D.; Klupp, S.; Wollersheim, H.J.; Benlliure, J.; Gottardo, A.; Morales, A.I.; Bracco, A.; Pietri, S.; Recchia, F.; Menegazzo, R.; Engert, T.; Casarejos, E.; Górska, M.; Kojouharov, I.; Domingo-Pardo, C.; Crespi, F.C.L.; Mandal, S.; Million, B.; Boutachkov, P.

doi:10.1016/j.physletb.2021.136183

Article
Report number	arXiv:2010.14859
Title	Manifestation of the Berry phase in the atomic nucleus $^{213}$Pb
Author(s)	Valiente-Dobón, J.J. (INFN, Legnaro) ; Gottardo, A. (INFN, Legnaro) ; Benzoni, G. (INFN, Milan) ; Gadea, A. (Valencia U., IFIC) ; Lunardi, S. (Padua U. ; INFN, Padua) ; Algora, A. (Valencia U., IFIC) ; de Angelis, G. (INFN, Legnaro) ; Bazzacco, D. (INFN, Padua) ; Benlliure, J. (Santiago de Compostela U., IGFAE) ; Boutachkov, P. (Darmstadt, GSI) ; Bracco, A. (INFN, Milan ; Milan U.) ; Bruce, A.M. (Brighton U.) ; Camera, F. (INFN, Milan ; Milan U.) ; Casarejos, E. (Vigo U.) ; Cortés, M.L. (Darmstadt, GSI) ; Crespi, F.C.L. (INFN, Milan) ; Corsi, A. (INFN, Milan ; Milan U.) ; Domingo-Pardo, C. (Darmstadt, GSI) ; Doncel, M. (U. Salamanca (main)) ; Engert, T. (Darmstadt, GSI) ; Geissel, H. (Darmstadt, GSI) ; Gerl, J. (Darmstadt, GSI) ; Goasduff, A. (INFN, Legnaro) ; Goel, N. (Darmstadt, GSI) ; Górska, M. (Darmstadt, GSI) ; Grebosz, J. (Cracow, INP) ; Gregor, E. (Darmstadt, GSI) ; Habermann, T. (Darmstadt, GSI) ; Klupp, S. (Munich, Tech. U.) ; Kojouharov, I. (Darmstadt, GSI) ; Kurz, N. (Darmstadt, GSI) ; Lenzi, S.M. (Padua U. ; INFN, Padua) ; Leoni, S. (INFN, Milan ; Milan U.) ; Mandal, S. (Delhi U.) ; Menegazzo, R. (INFN, Padua) ; Mengoni, D. (INFN, Padua) ; Million, B. (INFN, Milan) ; Morales, A.I. (INFN, Milan) ; Napoli, D.R. (INFN, Legnaro) ; Naqvi, F. (Darmstadt, GSI ; Cologne U.) ; Nociforo, C. (Darmstadt, GSI) ; Pfützner, M. (Warsaw U.) ; Pietri, S. (Darmstadt, GSI) ; Podolyák, Zs. (Surrey U.) ; Prochazka, A. (Darmstadt, GSI) ; Recchia, F. (INFN, Padua) ; Regan, P.H. (Surrey U.) ; Rudolph, D. (Lund U.) ; Sahin, E. (INFN, Legnaro) ; Schaffner, H. (Darmstadt, GSI) ; Sharma, A. (Darmstadt, GSI) ; Sitar, B. (Comenius U.) ; Siwal, D. (Delhi U.) ; Strmen, P. (Comenius U.) ; Szarka, I. (Comenius U.) ; Ur, C.A. (INFN, Padua) ; Walker, P.M. (Surrey U. ; CERN) ; Weick, H. (Darmstadt, GSI) ; Wieland, O. (INFN, Milan) ; Wollersheim, H.J. (Darmstadt, GSI) ; Van Isacker, P. (GANIL)
Publication	2021-05-10
Imprint	2020-10-28
Number of pages	7
In:	Phys. Lett. B 816 (2021) 136183
DOI	10.1016/j.physletb.2021.136183 (publication)
Subject category	nucl-th ; Nuclear Physics - Theory ; nucl-ex ; Nuclear Physics - Experiment
Abstract	The neutron-rich $^{213}$Pb isotope was produced in the fragmentation of a primary 1 GeV $A$ $^{238}$U beam, separated in FRS in mass and atomic number, and then implanted for isomer decay $\gamma$-ray spectroscopy with the RISING setup at GSI. A newly observed isomer and its measured decay properties indicate that states in $^{213}$Pb are characterized by the seniority quantum number that counts the nucleons not in pairs coupled to angular momentum $J=0$. The conservation of seniority is a consequence of the Berry phase associated with particle-hole conjugation, which becomes gauge invariant and therefore observable in semi-magic nuclei where nucleons half-fill the valence shell. The $\gamma$-ray spectroscopic observables in $^{213}$Pb are thus found to be driven by two mechanisms, particle-hole conjugation and seniority conservation, which are intertwined through the Berry phase.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2021-2024 The Authors (License: CC-BY-4.0)

$(a) Gamma-ray spectrum showing the six $\gamma$-ray transitions assigned to the decay of the isomeric state in $^{213}$Pb. The spectrum is obtained by selecting the time window $\Delta t = 0.12$--$1.70~\mu$s after the implantation (referred to as delayed coincidence). The inset shows the time distribution and exponential fit for the sum of the transitions, yielding a half-life of $t_{1/2}=0.26(2)~\mu$s. \mbox{(b)--(g)} Prompt $\gamma$-$\gamma$ coincidence spectra ($\Delta~t~\leq~100$~ns) between the six observed transitions following the isomer decay.$ $(a) Level scheme of $^{213}$Pb following the decay of the $21/2^+$ 0.26(2)~$\mu$s isomer deduced from the present data. The widths of the arrows are proportional to the relative $\gamma$-ray intensities but for display purposes the width of the 71~keV transition is reduced by a factor of three. The white part of the arrow is the internal conversion percentage of the transitions. Also shown is a schematic picture of the structure of the different states with seniority $\upsilon=1$ (black), $\upsilon=3$ (red), and $\upsilon=5$ (blue). The pairs of nucleons coupled to angular momentum $J=0$ are shown in yellow. (b) Theoretical predictions of a simple shell-model approach with five neutrons in $1g_{9/2}$ (sm-g) and of a large-scale shell-model calculation with the Kuo-Herling interaction (sm-kh), as described in the text.$ $Complete energy spectrum of five nucleons in the $1g_{9/2}$ shell. The spectrum applies to $^{213}$Pb and is calculated with two-body matrix elements derived by interpolation between $^{210}$Pb and $^{216}$Pb (sm-g). States can be of seniority $\upsilon=1$ (black), 3 (red), or 5 (blue), having two, one, or no pairs of nucleons coupled to angular momentum $J=0$ (yellow), respectively. All states conserve seniority, except for the two $9/2^+$ states with $\upsilon\approx1$ and $\upsilon\approx5$ shown on the left-hand side.$ Show more plots

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