Background: The motivation for this study is the experimental evidence for rigid triaxial deformation at low energy in 76 Ge that was recently observed. Purpose: Quadrupole shapes and low-energy spectra of the isotopes 72-82 Ge are analyzed using a theoretical framework based on nuclear density functional theory. Method: The relativistic functional DD-PC1, supplemented by a finite-range pairing force, is used to perform constrained triaxial mean-field calculations of energy surfaces as functions of quadrupole deformation parameters. The corresponding collective Hamiltonian, based on DD-PC1, is employed in the calculation of excitation spectra and transition rates. Results: Model calculations reproduce the empirical trend of collective observables and predict the evolution of shapes from weakly triaxial in 74 Ge to γ soft in 78,80 Ge. For 76 Ge, in particular, the theoretical excitation spectrum is in good agreement with available data, the experimental ratio E(2 + 2)/E(2 + 1) is reproduced, as well as the pattern and amplitude of the staggering in energy between odd-and even-spin states in the γ band. Conclusions: The mean-field potential of 76 Ge appears to be γ soft. Collective correlations drive the nucleus toward triaxiality but do not stabilize a rigid triaxial shape. Both the experimental and theoretical staggering of levels in the γ band display a pattern consistent with triaxial shapes but the amplitudes are negligible and do not present evidence for rigid triaxiality.

The lowest positive-and negative-parity bands of 20 Ne and neutron-rich even-even Ne isotopes are investigated using a theoretical framework based on energy density functionals. Starting from a self-consistent relativistic Hartree-Bogoliubov calculation of axially-symmetric and reflectionasymmetric deformation energy surfaces, the collective symmetry-conserving states are built using projection techniques and the generator coordinate method. Overall a good agreement with the experimental excitation energies and transition rates is obtained. In particular, the model provides an accurate description of the excitation spectra and transition probabilities in 20 Ne. The contribution of cluster configurations to the low-energy states is discussed, as well as the transitional character of the ground state. The analysis is extended to 22 Ne and the shape-coexisting isotope 24 Ne, and to the drip-line nuclei 32 Ne and 34 Ne. The role of valence neutrons in the formation of molecular-type bonds between clusters is discussed. arXiv:1802.02873v1 [nucl-th] 8 Feb 2018 P J M K denotes the angular momentum projection operator:Pwhere the integral is carried out over the three Euler angles Ω = (α, β, γ), D J M K (Ω) = e −iM α d J M K (β)e −iKγ is the Wigner's D-matrix [32], and the active rotation operator readsR(Ω) = e −iαĴz e −iβĴy e −iγĴz . Good parity quantum number is restored by choosing the reflectionsymmetric basis, that is, by ensuring that for each