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The triaxial dynamics of the quadrupole-deformed rotor model of both the rigid and the irrotational type have been investigated in detail. The results indicate that level patterns and E2 transitional characters of the two types of the model can be matched with each other to the leading order of the deformation parameter $beta$. Especially, it is found that the dynamical structure of the irrotational type with most triaxial deformation ($gamma=30^circ$) is equivalent to that of the rigid type with oblate deformation ($gamma=60^circ$), and the associated spectrum can be classified into the standard rotational bands obeying the rotational $L(L+1)$-law or regrouped into a new ground- and $gamma$-band with odd-even staggering in the new $gamma$-band commonly recognized as a signature of the triaxiality. The differences between the two types of the model in this case are emphasized especially on the E2 transitional characters.
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We discuss in depth the application of the classical concepts for interpreting the quantal results from the triaxial rotor core without and with odd-particle. The corresponding limitations caused by the discreteness and finiteness of the angular momentum Hilbert space and the extraction of the relevant features from the complex wave function and distributions of various angular momentum components are discussed in detail. New methods based on spin coherent states and spin squeezed states are introduced. It is demonstrated that the spin coherent state map is a powerful tool to visualize the angular momentum geometry of rotating nuclei. The topological nature of the concepts of transverse and longitudinal wobbling is clarified and the transitional axis-flipregime is analysed for the first time.
A reflection-asymmetric triaxial particle rotor model (RAT-PRM) with a quasi-proton and a quasi-neutron coupled with a reflection-asymmetric triaxial rotor is developed and applied to investigate the multiple chiral doublet (M$chi$D) bands candidates with octupole correlations in $^{78}$Br. The calculated excited energies, energy staggering parameters, and $B(M1)/B(E2)$ ratios are in a reasonable agreement with the data of the chiral doublet bands with positive- and negative-parity. The influence of the triaxial deformation $gamma$ on the calculated $B(E1)$ is found to be significant. By changing $gamma$ from 16$^circ$ to 21$^circ$, the $B(E1)$ values will be enhanced and better agreement with the $B(E1)/B(E2)$ data is achieved. The chiral geometry based on the angular momenta for the rotor, the valence proton and valence neutron is discussed in details.
With the Doppler Shift Attenuation Method, quadrupole transition moments, $Q_t$, were determined for the two recently proposed Triaxial Strongly Deformed (TSD) bands in $^{163}$Tm. The measured $Q_t$ moments indicate that the deformation of these bands is larger than that of the yrast, signature partners. However, the measured values are smaller than those predicted by theory. This observation appears to be valid for TSD bands in several nuclei of the region
We present a model-independent approach to electric quadrupole transitions of deformed nuclei. Based on an effective theory for axially symmetric systems, the leading interactions with electromagnetic fields enter as minimal couplings to gauge potentials, while subleading corrections employ gauge-invariant non-minimal couplings. This approach yields transition operators that are consistent with the Hamiltonian, and the power counting of the effective theory provides us with theoretical uncertainty estimates. We successfully test the effective theory in homonuclear molecules that exhibit a large separation of scales. For ground-state band transitions of rotational nuclei, the effective theory describes data well within theoretical uncertainties at leading order. In order to probe the theory at subleading order, data with higher precision would be valuable. For transitional nuclei, next-to-leading order calculations and the high-precision data are consistent within the theoretical uncertainty estimates. We also study the faint inter-band transitions within the effective theory and focus on the $E2$ transitions from the $0^+_2$ band (the $beta$ band) to the ground-state band. Here, the predictions from the effective theory are consistent with data for several nuclei, thereby proposing a solution to a long-standing challenge.
The wobbling spectrum of $^{163}$Lu is described through a novel approach, starting from a triaxial rotor model within a semi-classical picture, and obtaining a new set of equations for all four rotational bands that have wobbling character. Redefining the band structure in the present model is done by adopting the concepts of Signature Partner Bands and Parity Partner Bands. Indeed, describing a wobbling spectrum in an even-odd nucleus through signature and parity quantum numbers is an inedited interpretation of the triaxial super-deformed bands.
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