Why do Nilsson quantum numbers remain good at moderate deformations?

The Nilsson model is a simple microscopic model which has been extensively used over the years for the interpretation of a bulk of experimental results. The single particle orbitals in this model are labeled by quantum numbers which are good in the limit of large nuclear deformations. However, it is generally admitted that these quantum numbers remain good even at moderate deformations. We show that this fact is due to the existence of an underlying approximate symmetry, called the proxy-SU(3) symmetry. The implications of proxy-SU(3) on various aspects of nuclear structure will be discussed.Comment: 11 pages, 1 figure, to appear in Nuclear Theory '37, Proceedings of the 37th International Workshop on Nuclear Theory (Rila 2018), ed. M. Gaidarov and N. Minko

Particle-hole symmetry breaking due to Pauli blocking

Particle-hole symmetry has been used on several occasions in nuclear structure over the years. We prove that particle-hole symmetry is broken in nuclear shells possessing the proxy-SU(3) symmetry. The breaking of the symmetry is rooted in the Pauli principle and the short range nature of the nucleon-nucleon interaction. The breaking of the symmetry explains the dominance of prolate over oblate shapes in deformed nuclei and determines the regions of prolate to oblate shape transitions in the nuclear chart. Furthermore, it is related to the existence of specific regions of shape coexistence across the nuclear chart, surrounded by regions in which shape coexistence does not occur.Comment: 9 pages, 2 figures, to appear in HNPS: Advances in Nuclear Physics: Proceedings of the 27th Annual Symposium of the Hellenic Nuclear Physics Society (Athens, 2018), ed. T. Mertzimekis, G. Souliotis, and E. Styliari

Nucleon numbers for nuclei with shape coexistence

We consider two competing sets of nuclear magic numbers, namely the harmonic oscillator (HO) set (2, 8, 20, 40, 70, 112, 168, 240,...) and the set corresponding to the proxy-SU(3) scheme, possessing shells 0-2, 2-4, 6-12, 14-26, 28-48, 50-80, 82-124, 126-182, 184-256... The two sets provide 0+ bands with different deformation and band-head energies. We show that for proton (neutron) numbers starting from the regions where the quadrupole-quadrupole interaction, as derived by the HO, becomes weaker than the one obtained in the proxy-SU(3) scheme, to the regions of HO shell closure, the shape coexistence phenomenon may emerge. Our analysis suggests that the possibility for appearance of shape coexistence has to be investigated in the following regions of proton (neutron) numbers: 8, 18-20, 34-40, 60-70, 96-112, 146-168, 210-240,...Comment: 8 pages, 1 figure, to appear in HNPS: Advances in Nuclear Physics: Proceedings of the 27th Annual Symposium of the Hellenic Nuclear Physics Society (Athens, 2018), ed. T. Mertzimekis, G. Souliotis, and E. Styliari

Magic numbers for shape coexistence

The increasing deformation in atomic nuclei leads to the change of the classical magic numbers (2,8,20,28,50,82..) which dictate the arrangement of nucleons in complete shells. The magic numbers of the three-dimensional harmonic oscillator (2,8,20,40,70...) emerge at deformations around epsilon=0.6. At lower deformations the two sets of magic numbers antagonize, leading to shape coexistence. A quantitative investigation is performed using the usual Nilsson model wave functions and the recently introduced proxy-SU(3) scheme.Comment: 9 pages, 4 figures, to appear in HNPS: Advances in Nuclear Physics: Proceedings of the 27th Annual Symposium of the Hellenic Nuclear Physics Society (Athens, 2018), ed. T. Mertzimekis, G. Souliotis, and E. Styliari

Foundations of the proxy-SU(3) symmetry in heavy nuclei

We show that within the proxy-SU(3) scheme the wave functions of the normal parity orbitals in a given nuclear shell are affected very little as a result of the replacement of the abnormal parity orbitals by their 0[110] proxy-SU(3) counterparts.Comment: 9 pages, 5 tables, to appear in the proceedings of the Workshop on Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects (SDANCA17, Sofia 2017), ed. N. Minko

Parameter free predictions within the proxy-SU(3) model

Using a new approximate analytic parameter-free proxy-SU(3) scheme, we make predictions of shape observables for deformed nuclei, namely beta and gamma deformation variables, and compare them with empirical data and with predictions by relativistic and non-relativistic mean-field theories. Furthermore, analytic expressions are derived for B(E2) ratios within the proxy-SU(3) model, free of any free parameters, and/or scaling factors. The predicted B(E2) ratios are in good agreement with the experimental data for deformed rare earth nuclides.Comment: 12 pages, 5 figures, to appear in the proceedings of the Workshop on Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects (SDANCA17, Sofia 2017), ed. N. Minko

Proxy-SU(3) symmetry in heavy nuclei: Prolate dominance and prolate-oblate shape transition

Using a new approximate analytic parameter-free proxy-SU(3) scheme, simple predictions for the global feature of prolate dominance and for the locus of the prolate-oblate shape transition have been made and compared with empirical data. Emphasis is placed on the mechanism leading to the breaking of the particle-hole symmetry, which is instrumental in shaping up these predictions. It turns out that this mechanism is based on the SU(3) symmetry and the Pauli principle alone, without reference to any specific Hamiltonian.Comment: 10 pages, 4 tables, to appear in the proceedings of the Workshop on Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects (SDANCA17, Sofia 2017), ed. N. Minko

Parameter-independent predictions for nuclear shapes and B(E2) transition rates in the proxy-SU(3) model

Using a new approximate analytic parameter-free proxy-SU(3) scheme, we make predictions of shape observables for actinides and superheavy elements, namely beta and gamma deformation variables, and compare these with predictions by relativistic and non-relativistic mean-field theories. Furthermore, we make predictions for B(E2) transition rates of deformed nuclei and compare these with existing data and predictions of other theoretical approaches.Comment: 6 pages, 3 figures, to appear in the proceedings of the 26th Annual Symposium of the Hellenic Nuclear Physics Society (HNPS2017), Anavyssos, Greece, 9-10 June 2017, ed. Ch. Tsabaris, R. Vlastou, M. Kokkoris, and D. Patiris. arXiv admin note: text overlap with arXiv:1711.09201, arXiv:1711.0859

Proxy-SU(3): A symmetry for heavy nuclei

The SU(3) symmetry realized by J. P. Elliott in the sd nuclear shell is destroyed in heavier shells by the strong spin-orbit interaction. On the other hand, the SU(3) symmetry has been used for the description of heavy nuclei in terms of bosons in the framework of the Interacting Boson Approximation, as well as in terms of fermions using the pseudo-SU(3) approximation. A new fermionic approximation, called the proxy-SU(3), has been recently introduced and applied to the even rare earths. We show that the applicability of proxy-SU(3) can be extended to even nuclei in the 28-50 proton shell, to even superheavy elements, as well as to odd-odd and odd rare earths. Parameter free predictions for the beta and gamma deformation parameters are presented and compared to alternative theoretical predictions and to existing data.Comment: 13 pages, 9 figures, to appear in the proceedings of the Workshop on Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects (SDANCA17, Sofia 2017), ed. N. Minko

Manifestations of SU(3) symmetry in heavy deformed nuclei

The rapid increase of computational power over the last several years has allowed detailed microscopic investigations of the structure of many nuclei in terms of Relativistic Mean Field theories as well as in the framework of the no-core Shell Model. In heavy deformed nuclei, in which microscopic calculations remain a challenge, algebraic models based on the SU(3) symmetry offer specific predictions, parameter-independent in several cases, directly comparable to experimental data. Two different approximate models for heavy deformed nuclei based on the SU(3) symmetry, the pseudo-SU(3) and the proxy-SU(3) schemes will be discussed and the compatibility between their predictions for the nuclear deformation parameters will be shown. In particular, the dominance of prolate over oblate shapes in the ground states of even-even nuclei and the prolate to oblate shape phase transition occurring in heavy rare earths will be considered.Comment: 11 pages, 1 figure, 4 table