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Register a new userQuasi-SU(3) truncation scheme for even-even sd-shell nuclei
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C. E. Vargas Cinvestavn Mexico
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The Quasi-SU(3) symmetry was uncovered in full pf and sdg shell-model calculations for both even-even and odd-even nuclei. It manifests itself through a dominance of single-particle and quadrupole-quadrupole terms in the Hamiltonian used to describe well-deformed nuclei. A practical consequence of the quasi-SU(3) symmetry is an efficient basis truncation scheme. In a recent work was shown that when this type of Hamiltonian is diagonalized in an SU(3) basis, only a few irreducible represntations (irreps) of SU(3) are needed to describe the Yrast band, the leading S = 0 irrep augmented with the leading S = 1 irreps in the proton and neutron subspaces. In the present article the quasi-SU(3) truncation scheme is used, in conjunction with a realistic but schematic Hamiltonian that includes the most important multipole terms, to describe the energy spectra and B(E2) transition strengths of 20-Ne, 22-Ne, 24-Mg and 28-Si. The effect of the size of the Hilbert space on both sets of observables is discussed, as well as the structure of the Yrast band and the importance of the various terms in the Hamiltonian.
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The variational multiparticle-multihole configuration mixing approach (MPMH) to nuclei has been proposed about a decade ago. While the first applications followed rapidly, the implementation of the full formalism of this method has only been recently completed and applied in [C. Robin, N. Pillet, D. Pe~na Arteaga and J.-F. Berger, Phys. Rev. C 93, 024302 (2016)] to $^{12}$C as a test-case. The main objective of the present paper is to carry on the study that was initiated in that reference, in order to put the MPMH method to more stringent tests. To that aim we perform a systematic study of even-even sd-shell nuclei. The wave function of these nuclei is taken as a configuration mixing built on orbitals of the sd-shell, and both the mixing coefficients of the nuclear state and the single-particle wave functions are determined consistently from the same variational principle. The calculations are done using the D1S Gogny force. Various ground-state properties are analyzed. In particular, the correlation content and composition of the wave function as well as the single-particle orbitals and energies are examined. Binding energies and charge radii are also calculated and compared to experiment. The description of the first excited state is also examined and the corresponding transition densities are used as input for the calculation of inelastic electron and proton scattering. Special attention is paid to the effect of the optimization of the single-particle states consistently with the correlations of the system. Globally, the results are satisfying and encouraging. In particular, charge radii and excitation energies are nicely reproduced. However, the chosen valence-space truncation scheme precludes achieving maximum collectivity in the studied nuclei. Further refinement of the method and a better-suited interaction are necessary to remedy this situation.
The reanimation of the investigations dedicated to 0^{+} states energies and E0 transitions between them is provoked by new and more precise experimental techniques that not only made revision of the previous data but also gave a possibility to obtain a great amount of new 0^{+} states energies and conversion electrons data. We suggest one phenomenological model for estimation of the E0 transition nuclear matrix elements. Recently theoretical calculations [1] predicted existence of a 0^{+} state with energy 0.68 MeV in ^{160}Dy nucleus. Powerful enough arguments in favor of existence of 681.3 keV state in ^{160}Dy nucleus are presented.
A unitary description for wobbling motion in even-even and even-odd nuclei is presented. In both cases compact formulas for wobbling frequencies are derived. The accuracy of the harmonic approximation is studied for the yrast as well as for the excited bands in the even-even case. Important results for the structure of the wave function and its behavior inside the two wells of the potential energy function corresponding to the Bargmann representation are pointed out. Applications to $^{158}$Er and $^{163}$Lu reveal a very good agreement with available data. Indeed, the yrast energy levels in the even-even case and the first four triaxial super-deformed bands, TSD1,TSD2,TSD3 and TSD4, are realistically described. Also, the results agree with the data for the E2 and M1 intra- as well as inter-band transitions. Perspectives for the formalism development and an extensive application to several nuclei from various regions of the nuclides chart are presented.
Background: A global description of the ground-state properties of nuclei in a wide mass range in a unified manner is desirable not only for understanding exotic nuclei but for providing nuclear data for applications. Purpose: We demonstrate the KIDS functional describes the ground states appropriately with respect to the existing data and predictions for a possible application of the functional to all the nuclei by taking Nd isotopes as examples. Method: The Kohn-Sham-Bogoliubov equation is solved for the Nd isotopes with the neutron numbers ranging from 60 to 160 by employing the KIDS functionals constructed to satisfy both neutron-matter equation of state or neutron star observation and selected nuclear data. Results: Considering the nuclear deformation improves the description of the binding energies and radii. We find that the discrepancy from the experimental data is more significant for neutron-rich/deficient isotopes and this can be made isotope independent by changing the slope parameter of the symmetry energy. Conclusions: The KIDS functional is applied to the mid-shell nuclei for the first time. The onset and evolution of deformation are nicely described for the Nd isotopes. The KIDS functional is competent to a global fitting for a better description of nuclear properties in the nuclear chart.
We extend the ab initio coupled-cluster effective interaction (CCEI) method to deformed open-shell nuclei with protons and neutrons in the valence space, and compute binding energies and excited states of isotopes of neon and magnesium. We employ a nucleon-nucleon and three-nucleon interaction from chiral effective field theory evolved to a lower cutoff via a similarity renormalization group transformation. We find good agreement with experiment for binding energies and spectra, while charge radii of neon isotopes are underestimated. For the deformed nuclei $^{20}$Ne and $^{24}$Mg we reproduce rotational bands and electric quadrupole transitions within uncertainties estimated from an effective field theory for deformed nuclei, thereby demonstrating that collective phenomena in $sd$-shell nuclei emerge from complex ab initio calculations.
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