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The SSNET 2022 Conference hosted by IJCLab in Orsay, France, was held at the auditorium Pierre Lehmann (building 200 - IJCLab) from May 30 to June 3, 2022.
The conference was organized in a hybrid mode, with 73 participants physically present in Orsay among the 209 registered participants. 45% of the talks have been performed remotely using the Zoom interface.
As in the previous -and successful!- editions, the conference aims at strengthening the international collaboration between the nuclear structure physicists from France, Europe and other laboratories all around the world. It allows fruitful discussions on recent experimental and theoretical aspects of nuclear structure related to the manifestation and description of the various shapes and geometrical symmetries of the nucleus as well as other symmetries and symmetry breaking.
Organizing committee: Costel Petrache (Chair), Alain Astier, Isabelle Deloncle, Amel Korichi, Radomira Lozeva, Jerzy Dudek (co-chair)
Conference secretary: Émilie Bonnardel, Valérie Brouillard
In two experiments at Argonne National Laboratory’s ATLAS facility, utilising both the Fragment Mass Analyzer (FMA) and Argonne Gas-Filled Analyzer (AGFA) we have revisited two long-standing puzzles in the decay of $^{185}$Bi, which is the heaviest known proton-emitting nucleus. Combining the results from the two complementary experiments has established the existence of an isomeric state in $^{185}$Bi and shown that the proton- and alpha-decaying ground state is extremely short. These results, which will be discussed in this seminar, lead to a proton-decay spectroscopic factor which is close to unity and represents the only known example of a ground-state proton decay to a daughter nucleus ($^{184}$Pb) with a major shell closure. The implications for nuclear structure in this important region of the chart will be discussed as will implications for future work studying proton-emitting nuclei - which continue to yield surprising and fascinating results.
The possibility of existence in atomic nuclei of the so called “Jacobi shape transitions”, the rapid shape changes at certain narrow angular momentum range from an oblate to a very elongated prolate shape (analogous to those predicted by Jacobi for rotating stellar objects), was postulated by theorists already in the early 1960’s [1,2]. In the 90’s, the Seattle group, and soon after the NBI Copenhagen group, studying the GDR gamma decay from hot rotating 45Sc [3] and 46Ti [4], nuclei observed signals interpreted as the first manifestations of the nuclear Jacobi shape transition.
However, the direct evidence for the existence of the Jacobi shape transition in 46Ti nucleus came from the experiment performed in Strasbourg [5], where two arrays of gamma-ray detectors, scintillator array HECTOR and the germanium array EUROBALL, were coupled. Moreover, the interpretation of the results has become possible only because of the development of a theoretical approach referred to as Lublin-Strasbourg Drop (LSD) [6], which appeared simple to use by experimentalists.
Bent Herskind was pivotal to this achievement not only by taking part in the experiment and discussing the results, by also by his strong contribution to the development of the two detector arrays used, and also to the development of the links with the LSD model.
In the talk I will present the history of the quest for nuclear Jacobi shape transitions and the impact of Bent. In addition, I will present the currents status of understanding of the phenomenon of nuclear Jacobi shape transitions, the status of the instrumentation (especially, construction of the new scintillator array PARIS [7]) and some outlook of the coming perspectives such as the search for the Poincare shape transitions [8].
References:
[1] R. Beringer, W.K. Knox, Phys. Rev. 121 (1961) 1195
[2] S. Cohen, F. Plasil, W.J. Swiatecki, Ann. Phys. (N.Y.) 82 (1974) 557
[3] M. Kicińska-Habior et al., Phys.Lett. B308 (1993) 225
[4] A. Maj et al., Nucl.Phys. A687, 192c (2001)
[5] A. Maj et al., Eur.Phys.J. A 20, 165 (2004)
[6] K. Pomorski, J. Dudek, Phys. Rev. C67 (2003) 044316
[7] F. Camera, A. Maj, PARIS White Book, http://rifj.ifj.edu.pl/handle/item/333
[8] A. Maj et al., Int.J.Mod.Phys. E19, 532 (2010)
The physics of warm rotation at high spin in the many-body atomic nucleus will be briefly reviewed with the attempt of providing a historical perspective. This fascinating research topic, investigated in past decades by various research groups in Europe and the US, was greatly inspired by the seminal work carried out at the NBI, with Bent Herskind being the central figure. Bent had unique vision for experimental techniques and analysis methods. He contributed to the birth of Compton-suppressed Ge arrays, and his pioneering multi-dimensional γ-coincidence approaches and statistical data treatment were instrumental in investigating the properties of rotational motion at high excitation energy and chaotic phenomena, also associated with nuclear superdeformation. Perspectives in nuclear structure investigations inspired by Bent legacy will be also briefly discussed.
Two of the most admirable traits of Bent Herskind were his intense curiosity and his lively imagination which were particularly evident when applied to the search for new physics and the development of new analysis techniques. In this presentation I will give an overview on the research carried out at the Niels Bohr Institute into extreme nuclear deformations (superdeformation, hyperdeformation, Jacobi shapes, etc.) and present some of the important discoveries made by Bent and his collaborators. Finally, I will present some of my own personal thoughts on what promising directions could be explored in the future to continue this important work.
Despite significant and steady advances in the synthesis of the heaviest elements, reaching the predicted superheavy island of stability is still a distant objective, because of the ever-decreasing cross sections. Nevertheless, nuclear spectroscopy, mass measurements, and laser spectroscopy of the heaviest nuclei have shown their effectiveness by providing information on the quantum nature of extreme mass nuclei. In this context, deformed midshell nuclei near N=152, Z=100, are of great relevance: a large diversity of orbitals are accessible, some of which being involved in the structure of heavier spherical nuclei, i.e., placed just above and below the predicted superheavy spherical shell gaps.
In a series of experiments performed at the University of Jyväskylä, we have studied different facets of the odd-Z $^{249}$Md and $^{251}$Md isotopes. $^{251}$Md was studied using combined gamma ray and conversion-electron in-beam spectroscopy [1]. Besides the previously known K=1/2$^-$ rotational band [2], a new band has been observed. Using the gamma and electron intensities that depend on the gyromagnetic factor, the ground-state configuration could be inferred. We will also present a new method that allows to derive the gyromagnetic factor using the gamma-ray intensity profile. A comparison of $^{251}$Md with the $^{255}$Lr nucleus [3] revealed unexpected similarities between transition energies. Skyrme-Hartree-Fock-Bogoliubov calculations were performed to investigate the origin of these similarities.
If time permits, we will discuss new isomers observed in $^{249,251}$Md using decay spectroscopy, interpreted as high-K 3qp configurations [4]. These data were compared to new theoretical calculations using two scenarios: via blocking nuclear states located in proximity to the Fermi surface or/and using the quasiparticle Bardeen–Cooper–Schrieffer method.
[1] R. Briselet, Ch. Theisen , B. Sulignano et al., Phys. Rev. C 102 (2020) 014307.
[2] A. Chatillon, C. Theisen et al., Phys. Rev. Lett. 98 (2007) 132503.
[3] S. Ketelhut, P. T. Greenlees et al., Phys. Rev. Lett. 102 (2009) 212501.
[4] T. Goigoux, Ch. Theisen, B. Sulignano et al., Eur. Phys. J. A 57 (2021) 57.
The deformation of atomic nuclei is one of the important features significantly influencing the properties of the heaviest isotopes far above uranium. It is a decisive factor for their single-particle level structure, with an essential impact on the decay properties and, afterwards, the stability of heaviest nuclei with an odd number of protons or neutrons. Nuclear deformation is also crucial for the existence of phenomena like K isomers. Although there are available theoretical predictions for low-lying single-particle states of isotopes above fermium (see for example [1–3]), experimental data are scarce in this region. For many of these isotopes, even the ground-state or ﬁrst excited states remain unassigned.
The use of sensitive α- and γ-decay studies combined with conversion-electron (CE) spectroscopy allowed detailed experimental studies of many isotopes in the region of heaviest nuclei (A > 250). This approach was applied in an extensive program aimed at nuclear structure studies of isotopes above fermium using α-CE, α-γ and CE-γ spectroscopy at the velocity filter SHIP of GSI Darmstadt.
This seminar will summarize some recent results obtained for the examples of recent studies – mainly isomeric states in $^{255}$Rf [4,5] and $^{247}$Md [6]. In addition, open problems for the single-particle level systematics of odd-Z isotopes will be discussed, as well.
[1] S. Ćwiok et al., Nucl. Phys. A 573, 356 (1994).
[2] A. Parkhomenko and A. Sobiczewski, Acta Phys. Pol. B35, 2447 (2004).
[3] A. Parkhomenko and A. Sobiczewski, Acta Phys. Pol. B36, 3115 (2005).
[4] S. Antalic et al., Eur. Phys. J. A 51, 41 (2015).
[5] P. Mošať et al., Phys. Rev. C 101, 034310 (2020).
[6] F.P. Heßberger et al., Eur. Phys. J A 58, 11 (2022)
By selecting the lowest lying of more than 2000 excitations we found the candidates for high-K ground states / K-isomers in Md - Rg nuclei.
Energies of nuclear configurations are calculated within the microscopic-macroscopic model with the Woods-Saxon potential in two scenarios: via blocking or/and using quasi-particle BCS method. Optimal deformations for a fixed configuration as well as for ground states are found by the four-dimensional energy minimization over deformations. Obtained excitation energies are discussed and compared with available experimental data.
The search for new elements has netted us six additions to the periodic table this decade, bringing the total to 118 known elements. These elements must be formed one-atom-at-a-time in complete-fusion evaporation reaction. Once formed, the atoms typically exist for just seconds or less before they decay into other elements. While we have made great progress in making and studying these elements, there is much that is still unknown – including things as basic as the proton and neutron numbers of the recently discovered elements.
Recently, the Berkeley Gas-filled Separator (BGS) at the Lawrence Berkeley National Laboratory (LBNL) was coupled to a new mass analyzer, FIONA. The goal of BGS+FIONA is to provide a M/$\Delta$M separation of ~300 and transport nuclear reaction products to a shielded detector station on the tens of milliseconds timescale. These upgrades will allow for direct A and Z identification of ii) new actinide and transactinide isotopes with ambiguous decay signatures such as electron capture or spontaneous fission decay and i) superheavy nuclei such as those produced in the $^{48}$Ca + actinide reactions. Here we will present recent results from first FIONA scientific experiments.
Very neutron-deficient isotopes were studied by means of in-beam gamma-ray spectroscopy, beta-decay spectroscopy, alpha-decay spectroscopy and isomeric-decay spectroscopy. The experiments were performed at ISOLDE and at cyclotron laboratory of the University of Jyväskylä. Unprecented rotational bands, based on 1h$_{11/2}$ proton-hole configurations, coupled with intruder 0⁺ states in even-even Hg cores, were identified in $^{177,179}$Au. Their band-heads de-excite with transitions that might have significant E0 components, although they were not unambiguously identified. In addition to that, in $^{179}$Au, two coexisting 9/2$⁻$ states connected with transition with possible E0 component were identified. They are based on coupling of 1h$_{9/2}$ proton-intruder configurations with two 0⁺ states in the $^{180}$Hg core.
method of determining the interacting boson model Hamiltonian based on the nuclear density functional theory is presented, with a focus on the recent applications to γ-soft transitional nuclei. The constrained self-consistent mean-field calculations using a universal energy density functional and pairing interaction provide microscopic inputs to determine strength parameters for the IBM Hamiltonian in general cases. The mapped Hamiltonian then yields relevant spectroscopic properties of a given nucleus, that is, excitation spectra and electromagnetic transition rates. The topics to be discussed include the descriptions of the quantum shape phase transitions, shape coexistence, and triaxial deformations in the neutron-rich N~60 γ-soft nuclei in the mass A~100 region, and the simultaneous inclusion of pairing and quadrupole triaxial shape vibrations in the calculation of the low-lying excited 0⁺ states of triaxially-deformed transitional nuclei in the mass A~190 and 130 regions.
Chirality is a well-known phenomenon in many fields, such as chemistry, biology, molecular physics, and particle physics. The study of nuclear chirality has attracted a lot of attention since it was originally suggested for triaxial nuclei in 1997 [1]. The experimental evidence of nuclear chirality is the so-called chiral doublet bands, which have been observed in many nuclei. Theoretically, there have been many approaches employed to study the chiral nuclei including the phenomenological approaches and the microscopic ones [2].
In a series of our recent works [3,4,5,6], we have developed the three-dimensional cranking relativistic density functional theory to study the chirality in triaxial nuclei. In particular, by overcoming the variational collapse and the fermion doubling problem, relativistic density functional theory has been solved in three-dimensional lattice space, and the corresponding time-dependent relativistic density functional theory has been established. It allows a unified description of the static and dynamic properties of nuclei without assuming any spatial symmetry restrictions. In this talk, I will review recent progress in the development of time-dependent relativistic density functional theory in space lattice and its application for the chiral structure and dynamics in triaxial nuclei.
[1] S. Frauendorf and J. Meng, Nucl. Phys. A 617, 131 (1997).
[2] S. Frauendorf, Rev. Mod. Phys. 73, 463 (2001).
[3] P. W. Zhao, Phys. Lett. B 773, 1 (2017).
[4] P. W. Zhao, Y. K. Wang, and Q. B. Chen, Phys. Rev. C 99, 054319 (2019).
[5] Z. X. Ren, P. W. Zhao, J. Meng, Phys. Lett. B 801, 135194 (2020).
[6] Z. X. Ren, P. W. Zhao, J. Meng, Phys. Rev. C 105, L011301 (2022).
The low-lying negative-parity bands of $^{135}$Pr were previously interpreted as the first case of zero-, one- and two-phonon transverse wobbling bands. In the present work, we re-investigated its structure via a high statistics JUROGAM experiment. It is shown that the mixing ratios of all analyzed connecting transitions between low-lying bands in$^{135}$Pr have absolute values smaller than one. This indicates predominant M1 magnetic character, which is incompatible with the proposed wobbling nature. All experimental observables are instead in good agreement with quasiparticle-plus-triaxial-rotor model calculations, which describe the bands as resulting from a rapid re-alignment of the total angular momentum from the short to the intermediate nuclear axis.
The neutron-deficient lead region has myriad competing configurations of differing nuclear shapes. This competition is greatest when approaching the N=104 midshell, where deformation driving residual interactions become strong enough to challenge the stabilising effects of the nearby proton shell closure. Here, spherical, prolate, and oblate shapes can all be found as either ground or low-lying excited states in the isotopes that inhabit this region of the nuclear chart.
In recent years, a wide-ranging study has been made at the CERN-ISOLDE facility, using the in-source laser spectroscopy technique. In these experiments, isotope shift and hyperfine structure measurements of long chains of isotopes have been made, from which the change in mean-squared charge radii and magnetic dipole moments can be extracted. This talk will present highlights from the experimental campaigns, along with recent theoretical developments that have been made in an attempt to describe the region in a consistent manner, using Hartree-Fock-Bogoliubov calculations involving configuration mixing between states of different deformation.
Precision measurements in exotic beam facilities deliver great amounts of new information on isotopic shifts of nuclear charge radii. The radii as such are usually well described by modern nuclear density functional theory (DFT) within their typical extrapolation uncertainty of 0.02 fm. However, trends of radii which are quantified by radius differences, as istopic shifts, or three point differences, as oddd-even staggerings, are much more sensitive observables and they reveal great differences in the performance of the various DFT functionals. Radius differences thus provide invaluable information for scrutinizing and further developing of nuclear DFT.
The talk addresses recent studies within the non-realtivistic Skyrme and Fayans functionals aiming at a better description of trends of charge radii. The tools are least-squares fits to ground state data extended by information on recently measured radius differences with subsequent statistical analysis to explore the sensitivity of the new data to the various aspects of a functional. The data call clearly for an improved description of pairing which is achieved by the Fayans pairing functional. The analysis also points to the need for further extensions of the functionals.
Laser spectroscopy experiments provide a precise measurement of the changes in the nuclear mean-square charge radii and the electromagnetic moments of isotopes. State-of-the-art techniques can routinely measure these properties of the ground state and long-lived isomers which are produced in minute samples at radioactive ion beam facilities. The region of the nuclear chart between the magic Ca (Z=20) and Ni (Z=28) isotopes is rich in nuclear structure changes and is perfectly placed to investigate the evolution of the nuclear shape and size in both neutron- and proton-rich isotopes, as well as the isospin symmetry in self-conjugate isotopes.
In this talk the nuclear charge radii in the Ca to Ni region will be presented, including the newly measured of $^{48-54}$Cr isotopes from the IGISOL laboratory. Recent developments for the laser spectroscopy of proton-rich Co and Fe will also be discussed.
A little more than ten years ago, the very first electron beam was produced with the ALTO electron LINAC. 50 MeV and 10 µA later, the induced photofission process allow the production of exotic neutron rich isotopes. Based on the ISOL technique, ALTO has shown its capability to produce radioactive ion beams in the $^{78}$Ni mass region. Since then, the Orsay team working with the facility developed a set of instruments dedicated to the study of neutron rich nuclei β -decay such as BEDO or the neutron counter named TETRA [1]. The availability of these setups allowed the investigation of possible existence of low-lying structures in the β -strength function above the neutron separation energy (Sn). This endeavor was further encouraged by two remarkable serendipities. The first one concerns the unexpected observation of “ultra”-high-energy γ-rays (8-9 MeV) [2] in the β-delayed emission products of $^{83}$Ga (Z=31 ; N=52 ; T1/2=312 ms ; Qb=11.7 MeV) sources collected at the BEDO station [3]. The second one concerns β-delayed neutron-emission probability (Pn) measurements of the $^{82,83,84}$Ga (N=51,52,53) precursors [4] using the neutron counter TETRA: quite unexpectedly, after a steep increase of the Pn values from N=51 to 52, the Pn falls down again at N=53 by a factor ~2. More recently, manifestation of Pygmy Dipole Resonances (PDR) was observed in $^{80}$Ge [5]. These results will be presented and discussed. It will be shown that they clearly point towards the existence of structures in the threshold region of the daughter-nucleus excitation spectrum, governing the decay properties in the $^{78}$Ni region. Perspectives for further investigation of these questions at ALTO using the PARIS, TETRA and MONSTER (γ and neutron) spectrometers will be presented.
Others β-decay activities of the Orsay research group will also be presented.
[1] D. Testov, D. Verney, B. Roussière et al., NIM A815, 96 (2016)
[2] A. Gottardo, D. Verney, I. Deloncle et al. PLB 772, 359 (2017)
[3] A. Etilé, D. Verney, N. N. Arsenyev et al. PRC 91, 064317 (2015)
[4] D. Verney, D. Testov, F. Ibrahim et al., PRC 95, 054320 (2017)
[5] R. Li, Ph. D. Thesis, Université Paris-Saclay (2022)
Using the axially deformed relativistic Hartree-Fock-Bogoliubov (D-RHFB) model, we explore the mechanism that triggers the novelties in $^{11}$Be, i.e., the parity inversion and one-neutron halo which are well reproduced by the RHF Lagrangian PKA1. Following the evolution from spherical to large prolate shapes, it is illustrated that the evidently enhanced $\pi$-pseudo-vector ($\pi$-PV) and $\rho$-tensor ($\rho$-T) couplings in PKA1 are crucial for correctly describing even-parity ground state (GS) of $^{11}$Be. By fragmentizing the even-parity orbit 1/2$_{\mskip 2mu 2}^{\mskip 1mu +}$, it is shown that the main fragment $1d_{5/2}$ strengthens the couplings with nuclear core to promise the even-parity GS, in which the $\rho$-T and $\pi$-PV couplings play an important role, and the other major one $2s_{1/2}$ remains weakly bound to form the halo in $^{11}$Be. Furthermore, it is found that the attractive inherent correlations between the $2s_{1/2}$ and $1d_{5/2}$ fragments are essential not only in determining the parity inversion but also in stabilizing the one-neutron halo of $^{11}$Be. Thus, an apparent picture of the deformed halo is achieved, which paves an efficient way to clarify the underlying mechanism responsible for the halos and other novelties in deformed unstable nuclei.
We study low-lying states of two-quasiparticle character in some well-deformed odd-odd nuclei around $^{178}$Hf within the framework of the Skyrme energy-density functional (SEDF) approach, including BCS pairing correlations with selfconsistent blocking. We use the SIII SEDF parametrization with time-odd terms and seniority pairing residual interaction as in a previous study of two-quasiparticle $K$-isomeric states in actinide and heavier nuclei [to be published in Phys. Rev. C]. The strength of the seniority interaction is determined through an overall fit on the first $2^{+}$ excitation energies [Phys. Rev. C \textbf{99}, 064306 (2019)]. Axial and parity symmetries are assumed throughout the Hartree--Fock--BCS calculations but time-reversal symmetry is broken.
After checking the relevance of the SIII single-particle spectrum by comparison with experimental bandhead states of low-lying one-quasiparticle states in odd-mass neighbors of $^{178}$Hf, we calculate two-quasiparticle states in doubly-odd neighboring nuclei for the relevant neutron and proton configurations. A special attention is drawn on the Gallagher--Moskowski splitting and a comparison with experiment and results obtained by Robledo, Bernard and Bertsch [Phys. Rev. C ${\bf 89}$, 021303(R) (2014)] with the Gogny EDF.
Isomers are the long-lived excited states of nuclei and are of particular interest due to their capacities to provide insights into the nuclear structure [1]. The reason behind their occurrence depends mostly upon the structural surroundings and can vary from region to region. Symmetries of pairing Hamiltonian for the shell model in terms of seniority and generalized seniority are known to play a crucial role in explaining the semi-magic spherical/ near-spherical isomers, particularly for the Sn isotopes [2, 3]. Our recent works provide more credence to the generalized seniority approach to decipher the decay probabilities as well as moments of isomers and other low-lying excited states [4–7]. In this conference, I will focus on the solution for the puzzle of finding consistent nuclear configurations to understand both the decay probabilities and moments of the 9/2−, 8+, and 21/2− isomers in and around N = 126 closed shell in terms of generalized seniority [8]. Though h9/2 is the dominant orbital for these isomers, the role of configuration mixing from the surrounding f7/2 and i13/2 orbitals is found to be very important for the consistent explanation of all the isomeric properties such as the B(E2) rates, Q−moments, and g−factors. Further, recent efforts to understand the B(E3) rates in both odd-A and even-A N = 80, 82, 84 isotones using the generalized seniority will also be discussed [9].
Acknowledgments
BM acknowledges the financial support from the Croatian Science Foundation and the ́Ecole Poly-technique F ́ed ́erale de Lausanne, under the project TTP-2018-07-3554 “Exotic Nuclear Structure and Dynamics”, with funds of the Croatian-Swiss Research Programme.
References
[1] A. K. Jain, B. Maheshwari, A. Goel, Nuclear Isomers - A Primer, Springer Nature, Switzerland (2021).
[2] B. Maheshwari and A. K. Jain, Phys. Lett. B 753, 122 (2016).
[3] B. Maheshwari, A. K. Jain and B. Singh, Nucl. Phys. A 952, 62 (2016).
[4] B. Maheshwari and A. K. Jain, Nucl. Phys. A 986, 232 (2019).
[5] B. Maheshwari, H. A. Kassim, N. Yusof and A. K. Jain, Nuclear Physics A 992, 121619 (2019).
[6] B. Maheshwari, European Physical Journal Special Topics 229, 2485 (2020).
[7] B. Maheshwari, D. Choudhury and A. K. Jain, Nucl. Phys. A 1014, 122277 (2021).
[8] B. Maheshwari, D. Choudhury and A. K. Jain, Phys. Rev. C 105, 024315 (2022).
[9] B. Maheshwari, et al., communicated.
The triaxial deformation and coupling with pairing vibration play important roles on the nuclear low-lying spectra and shape transitions. Here we have constructed a triaxial-and-pairing collective Hamiltonian that describes the triaxial shape vibrations, rotations, and coupling with pairing vibration, based on the covariant density functional theory (CDFT). The dynamics of the collective Hamiltonian is fully determined by the constrained CDFT calculations in the space of intrinsic shape and pairing deformations. The effect of coupling between shape and pairing degrees of freedom is analyzed in a study of low-energy spectra and transition rates of $^{156}$Gd, by comparing with the calculations from quadrupole collective Hamiltonian. Finally, the shape phase transitions and triaxial deformations in Xe isotopes have been studied in detail.
It will be shown within a relatively simple nuclear structure model framework [1] that the formation of the 8 eV "clock" isomer $^{229m}$Th may be the effect of single-neutron levels quasi-degeneracy stemming from a specific quadrupole octupole shape of the nucleus. The very fine interaction between collective and single-particle modes within narrow limits in the deformation space rather unambiguously determines the isomer formation conditions with the attendant B(M1), B(E2) decay rates and magnetic dipole moment in the isomeric state. Estimates based on a comprehensive model analysis of these isomer characteristics will be discussed.
It will be shown that the approach used provides a clear protocol for the search, prediction and identification of low-energy excitations in other nuclei opening a way to study similar effects and phenomena on the border between nuclear and atomic physics.
References
[1] N. Minkov and A. Palffy, Phys. Rev. Lett. ${\bf 118}$, 212501 (2017);
Phys. Rev. Lett.${\bf 122}$, 162502 (2019); Phys. Rev. C ${\bf 103}$, 014313 (2021).
Recently the DESPEC nuclear spectroscopy campaign started at the SIS/FRS facility at GSI as part of the FAIR/NUSTAR Phase-0 program. It aims at the investigation of exotic heavy nuclei produced in fragmentation reactions employing detectors and instrumentation developed for the FAIR facility. An important aspect of the program is the training of students and young researchers in the field. Despite the Covid-19 pandemic, a novel fast-timing spectroscopy set-up has been commissioned and first experiments have successfully been performed. Physics topics include the evolution of the shell structure around $^{100}$Sn, basic decay information of n-rich isotopes at N=126 below $^{208}$Pb and octupole correlations of n-rich actinide isotopes. Novel experimental techniques and first results will be presented.
This abstract reports results of the first experiment of the DESPEC Phase-0 campaign at GSI, which focused on the study of neutron-deficient nuclei approaching 100Sn. These data provide the first extended commissioning experiment for the DESPEC collaboration within NuSTAR. We present results on electromagnetic transition rates associated with the decays from excited states populated following the formation of I=8+ proton ‘seniority-isomer’ states in the N=50 isotones 94Ru and 96Pd. Direct half-life measurements via gamma-gamma coincidences using the FATIMA detector array consisting of 36 LaBr3(Ce) scintillators have determined the reduced matrix elements associated with decays between low-lying states in these semi-magic nuclei. The extracted half-lives for yrast spin/parity 6+ and 4+ states in 96Pd and the 6+ state in 94Ru are consistent with the published, highest-precision values for these nuclei.
One of the goals of modern nuclear physics research is to understand the origin of coexisting nuclear shapes and exotic excitations and their relation to the fundamental interactions between nuclear constituents. Despite of huge amount of both theoretical and experimental efforts, many open questions remain [1 and references therein]. In order to verify and understand these subjects in more detail, complementary approaches are needed.
This talk will give an insight into shape coexistence studies around neutron-deficient Pb nuclei. In particular, it will focus on series of simultaneous in-beam electron and gamma-ray spectroscopy experiments employing the SAGE spectrometer [2] at JYFL, Finland. Their relation to Coulomb excitation studies at Miniball [3] at HIE-ISOLDE, CERN [4] will also be discussed.
References
[1] K. Heyde and J.L. Wood, Rev. Mod. Phys. 83 1467 (2011).
[2] J. Pakarinen et al., Eur. Phys. J. A 50: 53 (2014).
[3] N. Warr et al., Eur. Phys. J. A 49, 40 (2013).
[4] P. Van Duppen, K. Riisager, J. Phys. G: Nucl. Part. Phys. 38, 024005 (2011).
Using covariant density functional theory with the DDME2 functional and labeling single particle energy orbitals by Nilsson quantum numbers [1], a search for particle-hole (p-h) excitations connected to the appearance of shape coexistence is performed for Z=38 to 84 nuclei. Islands of shape coexistence are found near the magic numbers Z=82 and Z=50, restricted in regions around the relevant neutron midshells N=104 and N=66 respectively, in accordance to the well accepted p-h interpretation of shape coexistence in these regions, which we call neutron induced shape coexistence, since the neutrons act as elevators creating holes in the proton orbitals. Similar but smaller islands of shape coexistence are found near N=90 and N=60, restricted in regions around the relevant proton midshells Z=66 and Z=39 respectively, related to p-h excitations across the 3-dimensional isotropic harmonic oscillator (3D-HO) magic numbers N=112 and N=70, which correspond to the beginning of the participation of the opposite parity orbitals 1i$_{13/2}$ and 1h$_{11/2}$ respectively to the onset of deformation.
We call this case proton induced shape coexistence, since the protons act as elevators creating holes in the neutron orbitals, thus offering a possible microscopic mechanism for the appearance of shape coexistence in these regions [2]. In the region around N=40, Z=40, an island is located on which both neutron p-h excitations and proton p-h excitations are present.
[1] K.E. Karakatsanis, G.A. Lalazissis, V. Prassa, and P. Ring, Phys. Rev. C 102 (2020) 034311.
[2] D. Bonatsos, K.E. Karakatsanis, A. Martinou, T.J. Mertzimekis, and N. Minkov, in preparation
Exotic nuclei exhibit various nuclear shapes depending on their shell structure.
In this talk, I will present our recent systematic analyses of the nuclear shapes
on neutron-rich nuclei using the density distributions of microscopic mean-field models.
First, I will discuss how the density profile is changed by nuclear deformation [1]
and show some examples of characteristic density profiles in the island of inversion
near N=40 [2]. This property is well reflected in the density distributions
near the nuclear surface. I will show that high-energy nucleus-nucleus collision
can be a promising tool to investigate such density profiles.
References
[1] W. Horiuchi and T. Inakura, Prog. Theor. Exp. Phys. 2021, 103D02 (2021).
[2] W. Horiuchi, T. Inakura, and S. Michimasa, Phys. Rev. C 105, 014316 (2022).
Despite the steady and remarkable progress in $\it{ ab initio}$ approaches to nuclear structure, Density Functional Theory remains a tool of broader applicability. It makes sense to derive an Energy Density Functional (EDF) from an underlying ab initio method: this is the topic addressed by a few contributions to the conference. At the same time, it is worth attempting other routes for improving current EDFs. We have started to make the first steps in the so- called inverse Kohn-Sham problem, that is, in grasping information on the effective nuclear potential and the associated energy functional by starting from the knowledge of the nuclear densities.
In particular, we have recently proposed a complete solution to the inverse Kohn-Sham (KS) problem. Our method consists of two steps. First, the effective KS potential is determined from the ground-state density of a given system. Then, the knowledge of the potentials along a path in the space of densities is exploited in a line integration formula to determine the KS energy of that system numerically. A possible choice for the density path is proposed. A benchmark in the case of a simplified yet realistic nuclear system is shown to be successful, so the method seems promising for future applications.
Ground-state electromagnetic moments are known in hundreds of odd and odd-odd nuclei. Very often, they have been measured by atomic spectroscopic methods up to very high precision. In nuclear DFT approaches, these essential observables have been rarely considered so far. At the same time, time-odd properties of nuclear density functionals, which crucially influence magnetic moments, are poorly known. In this talk, I will discuss recent DFT calculations of magnetic dipole and octupole, and electric quadrupole and Schiff moments.
The accuracy of an energy density functional determines the accuracy of the density functional calculation. Thus, it is highly motivated to improve the accuracy of an EDF.
Then, a question arises: Can we improve an EDF if we know the "exact" density?
To answer this question, recently, we proposed a method named "IKS-DFPT" to improve the known EDF using a combination of the inverse Kohn-Sham method and the density functional perturbation theory [1]. In Ref. [1], this method was benchmarked in atomic systems, while it was extended to the covariant density funcitonal theory for nuclear systems [2].
In this talk, I will introduce this method and its benchmark results.
References:
[1] T. Naito, D. Ohashi, and H. Liang. J. Phys. B 52, 245003 (2019).
[2] G. Accorto, T. Naito, H. Liang, T. Nikšić, and D. Vretenar. Phys. Rev. C 103, 044304 (2021).
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We compare the data on the lowest 0⁺ isomers in the half-life range greater than 10 ns and those in less than 1 ns [1-3]. In comparing the two group of isomers from even-even nuclei, we come across many similarities. This suggests that the 0⁺ states having half-life less than 1 ns have similar structure. The relationship of these states to shape coexistence will also be highlighted. We also consider couple of examples, which point to specific symmetries [4].
References:
1. A.K. Jain, B. Maheshwari, A. Goel, Nuclear Isomers-A Primer, Springer Nature, 2021.
2. K. Heyde and J.L. Wood, Rev. Mod. Phys. 83, 1655 (2011).
3. Swati, B. Maheshwari, Balraj Singh, Y. Sun, A. Goel, and A. K. Jain, Atlas of Isomers -2022, to be published.
4. Aagrah Agnihotri and A.K. Jain, B.Tech. Dissertation, 2022.
Alpha clustering is a well-known correlation in nuclei. We use the mean-field theory to investigate where in the nucleus and how probable the alpha particles are formed. In addition, the calculation approximately provides information how much the daughter nucleus is excited, when the alpha particle is knocked out.
We will discuss effect of the pairing and deformation of the parent nucleus.
The study of exotic nuclei far from the β-stability line has been at the forefront of nuclear physics research since 1980s. The relativistic density functional theory has achieved great success in the study of nuclear structure in recent years.
In order to explore the effects of triaxial deformation in exotic nuclei and the existence of triaxially deformed halo nuclei, a self-consistent triaxial relativistic Hartree-Bogoliubov theory in continuum (TRHBc) is developed. Possible triaxially deformed halo nuclei are explored by taking aluminum isotopes as examples. The binding energies, nucleon separation energies, and charge radii are well reproduced. It is predicted that the experimentally observed nucleus, $^{42}$Al, is a triaxially deformed halo nucleus, and there is a triaxial shape decoupling between its core and halo. Potential energy surfaces are constructed by the constrained calculations to verify the ground states obtained from unconstrained calculations.
High-spin rotational bands in rare-earth Er, Tm and Yb isotopes are investigated by (1) the cranked relativistic Hartree Bogoliubov approach with Lipkin-Nogami method, (2) the cranking covariant density functional theory with pairing correlations treated by a shell-model-like approach or the so called particle-number conserving (PNC) method, and (3) cranked shell model (CSM) with pairing correlations treated by the PNC method. A detailed comparison between these three models in the description of the ground state bands of even-even Er and Yb isotopes is performed. The similarities and differences between these models in the description of the moments of inertia, the band crossings, equilibrium deformations and pairing energies of even-even nuclei under study are discussed. On average, a comparable accuracy of the description of available experimental data is achieved in these models.
However, the differences between model predictions become larger above the first band crossings. Because of time consuming nature of the two CDFT-based models, systematic study of the rotational properties of both ground state and excited state bands in odd-mass Tm nuclei is carried out only by the PNC-SCM. With few exceptions, the rotational properties of experimental 1-quasiparticle and 3-quasiparticle bands in $^{165,167,169,171}$Tm are reproduced reasonably well.