It has been suggested that chaotic motion inside the nucleus may significantly limit the accuracy with which nuclear masses can be calculated. Using a power spectrum analysis we show that the inclusion of additional physical contributions in mass calculations, through many-body interactions or local information, removes the chaotic signal in the discrepancies between calculated and measured masses. Furthermore, a systematic application of global mass formulas and of a set of relationships among neighboring nuclei to more than 2000 nuclear masses allows one to set an unambiguous upper bound for the average errors in calculated masses, which turn out to be almost an order of magnitude smaller than estimated chaotic components.

Excited states in ${}^{70}\mathrm{Br}$ were populated in the ${}^{40}\mathrm{Ca}{(}^{32}\mathrm{S},pn)$ reaction at $E_{\mathrm{beam}}=80\mathrm{}–100\hspace{0.5em}\mathrm{MeV}$ and the ${}^{40}\mathrm{Ca}{(}^{36}\mathrm{Ar},\alpha pn)$ reaction at $E_{\mathrm{beam}}=145\mathrm{}\hspace{0.5em}\mathrm{MeV}.$ The resulting gamma decay was detected using the Gammasphere array triggered by a 30-element neutron detector. The cross-bombardment allowed the unambiguous assignment of levels to ${}^{70}\mathrm{Br},$ comprising a total of 32 states built both on the $J^{\pi }{=0\mathrm{}}^{+}$ ground state and a previously known $J^{\pi }{=9\mathrm{}}^{+}$ isomer, which is located at an excitation energy of 2293 keV by the observation of linking transitions. The structures are discussed within the context of the two-quasiparticle plus rotor model, the IBM-4 model and the cranked Nilsson-Strutinsky formalism. The nonobservation of a doublet of $J=0,$ $T=1\mathrm{}$ and $J=1,$ $T=0\mathrm{}$ states at low excitation in ${}^{70}\mathrm{Br}$ is indicative that $T=0\mathrm{}$ proton-neutron pairing strength is weak in comparison to $T=1\mathrm{}$ pairing.

A key question concerning the spherical-vibrator attributes of states in cadmium isotopes is addressed by means of a boson Hamiltonian encompassing U(5) partial dynamical symmetry. The U(5) symmetry is preserved in a segment of the spectrum and is broken in particular nonyrast states, and the resulting mixing with the intruder states is small. The vibrational character is thus maintained in the majority of low-lying normal states as observed in ${}^{110}\mathrm{Cd}$.

A systematic study of energy spectra throughout the rare-earth region (even-even nuclei from 58Ce to 74W) is carried out in the framework of the interacting boson model (IBM), leading to an accurate description of the spherical-to-deformed shape transition in the different isotopic chains. The resulting IBM Hamiltonians are then used for the calculation of nuclear charge radii (including isotope and isomer shifts) and electric monopole transitions with consistent operators for the two observables. The main conclusion of this study is that an IBM description of charge radii and electric monopole transitions is possible for most of the nuclei considered but that it breaks down in the tungsten isotopes. It is suggested that this failure is related to hexadecapole deformation.

We show that the introduction of a ${\mathrm{U}}^{B+F}\mathrm{}\left(6\right)\mathrm{}$ group into the multi-$j$ supersymmetric scheme permits a better agreement with the energy spectrum of ${}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}$ and suggest two other possible supersymmetric classifications.

We discuss symmetries of the spherical shell model that make contact with the geometric collective model of Bohr and Mottelson. The most celebrated symmetry of this kind is SU(3), which is the basis of Elliott’s model of rotation. It corresponds to a deformed mean field induced by a quadrupole interaction in a single major oscillator shell N and can be generalized to include several major shells. As such, Elliott’s SU(3) model establishes the link between the spherical shell model and the (quadrupole component of the) geometric collective model. We introduce the analogue symmetry induced by an octupole interaction in two major oscillator shells and N , leading to an octupole-deformed solution of the spherical shell model. We show that in the limit of large oscillator shells, , the algebraic octupole interaction tends to that of the geometric collective model.