Exactly solvable models of nuclei

In this paper a review is given of a class of sub-models of both approaches, characterized by the fact that they can be solved exactly, highlighting in the process a number of generic results related to both the nature of pair-correlated systems as well as collective modes of motion in the atomic nucleus.Comment: 34 pages, 8 figures accepted for publication in Scholarpedi

Criticality in the configuration-mixed interacting boson model : (1) U(5)−Q^(χ)⋅Q^(χ)U(5)-\hat{Q}(\chi)\cdot\hat{Q}(\chi) mixing

The case of U(5)--$\hat{Q}(\chi)\cdot\hat{Q}(\chi)$ mixing in the configuration-mixed Interacting Boson Model is studied in its mean-field approximation. Phase diagrams with analytical and numerical solutions are constructed and discussed. Indications for first-order and second-order shape phase transitions can be obtained from binding energies and from critical exponents, respectively

Pairing and Isospin Symmetry in Proton-Rich Nuclei

Unlike their lighter counterparts, most odd-odd N=Z nuclei with mass A > 40 40 have ground states with isospin T=1, suggesting an increased role for the isovector pairing interaction. A simple SO(5) seniority-like model of this interaction reveals a striking and heretofore unnoticed interplay between like-particle and neutron-proton isovector pairing near N=Z that is reflected in the number of each kind of pair as a function of A and T. Large scale shell-model calculations exhibit the same trends, despite the simultaneous presence of isoscalar pairs, deformation, and other correlations.Comment: 8 pages + 2 postscript figures, in RevTeX. Discussion of isospin projection in HFB added. This version to appear in Phys. Lett.

Two-neutron separation energies, binding energies and phase transitions in the interacting boson model

In the framework of the interacting boson model the three transitional regions (rotational-vibrational, rotational-$\gamma$-unstable and, vibrational-$\gamma$-unstable transitions) are reanalyzed. A new kind of plot is presented for studying phase transitions in finite systems such as atomic nuclei. The importance of analyzing binding energies and not only energy spectra and electromagnetic transitions, describing transitional regions is emphasized. We finally discuss a number of realistic examples.Comment: 34 pages, TeX (ReVTeX). 12 ps figures. 3 tables. Submitted to Nucl. Phys.

O(12) limit and complete classification of symmetry schemes in proton-neutron interacting boson model

It is shown that the proton-neutron interacting boson model (pnIBM) admits new symmetry limits with O(12) algebra which break F-spin but preserves the quantum number M_F. The generators of O(12) are derived and the quantum number `v' of O(12) for a given boson number N is determined by identifying the corresponding quasi-spin algebra. The O(12) algebra generates two symmetry schemes and for both of them, complete classification of the basis states and typical spectra are given. With the O(12) algebra identified, complete classification of pnIBM symmetry limits with good M_F is established.Comment: 22 pages, 1 figur

Identification of the slow E3 transition 136mCs -> 136Cs with conversion electrons

We performed at ISOLDE the spectroscopy of the decay of the 8- isomer in 136Cs by and conversion-electron detection. For the first time the excitation energy of the isomer and the multipolarity of its decay have been measured. The half-life of the isomeric state was remeasured to T1/2 = 17.5(2) s. This isomer decays via a very slow 518 keV E3 transition to the ground state. In addition to this, a much weaker decay branch via a 413 keV M4 and a subsequent 105 keV E2 transition has been found. Thus we have found a new level at 105 keV with spin 4+ between the isomeric and the ground state. The results are discussed in comparison to shell model calculations.Comment: Phys. Rev. C accepted for publicatio

Rotating ground states of trapped Bose atoms with arbitrary two-body interactions

In a k-dimensional system of weakly interacting Bose atoms trapped by a spherically symmetric and harmonic external potential, an exact expression is obtained for the rotating ground states at a fixed angular momentum. The result is valid for arbitrary interactions obeying minimal physical requirements. Depending on the sign of a modified scattering length, it reduces to either a collective rotation or a condensed vortex state, with no alternative. The ground state can undergo a kind of quantum phase transition when the shape of the interaction potential is smoothly varied.Comment: Talk given at the International Conference on Theoretical Physics (TH2002),Paris, UNESCO, 22-27 July; 11 pages, 3 figures, few typos fixe

SU(3) realization of the rigid asymmetric rotor within the IBM

It is shown that the spectrum of the asymmetric rotor can be realized quantum mechanically in terms of a system of interacting bosons. This is achieved in the SU(3) limit of the interacting boson model by considering higher-order interactions between the bosons. The spectrum corresponds to that of a rigid asymmetric rotor in the limit of infinite boson number.Comment: 9 pages, 2 figures, LaTeX, epsfi

Nuclear masses set bounds on quantum chaos

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 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.Comment: 4 pages, Accepted for publication in Physical Review Letter