Dynamical Boson-Fermion symmetries in nuclei (original) (raw)

The shell model as a unified view of nuclear structure

Reviews of Modern Physics, 2005

The last decade has witnessed both quantitative and qualitative progresses in Shell Model studies, which have resulted in remarkable gains in our understanding of the structure of the nucleus. Indeed, it is now possible to diagonalize matrices in determinantal spaces of dimensionality up to 10^9 using the Lanczos tridiagonal construction, whose formal and numerical aspects we will analyze. Besides, many new approximation methods have been developed in order to overcome the dimensionality limitations. Furthermore, new effective nucleon-nucleon interactions have been constructed that contain both two and three-body contributions. The former are derived from realistic potentials (i.e., consistent with two nucleon data). The latter incorporate the pure monopole terms necessary to correct the bad saturation and shell-formation properties of the realistic two-body forces. This combination appears to solve a number of hitherto puzzling problems. In the present review we will concentrate on those results which illustrate the global features of the approach: the universality of the effective interaction and the capacity of the Shell Model to describe simultaneously all the manifestations of the nuclear dynamics either of single particle or collective nature. We will also treat in some detail the problems associated with rotational motion, the origin of quenching of the Gamow Teller transitions, the double beta-decays, the effect of isospin non conserving nuclear forces, and the specificities of the very neutron rich nuclei. Many other calculations--that appear to have ``merely'' spectroscopic interest--are touched upon briefly, although we are fully aware that much of the credibility of the Shell Model rests on them.

Dynamical symmetries in contemporary nuclear structure applications

2010

In terms of group theory Å the language of symmetries, the concept of spontaneous symmetry breaking is represented in terms of chains of groupÄsubgroup structures that deˇne the dynamical symmetry of the system under consideration. This framework enables exact analytic solutions of the associated eigenvalue problems. We review two types of applications of dynamical symmetries in contemporary theoretical nuclear structure physics:ˇrst for a classiˇcation of the many-body systems under consideration, with respect to an important characteristic of their behavior; and second for the creation of exactly solvable algebraic models that describe speciˇc aspects of this behavior. This is illustrated with the boson and fermion realizations of symplectic structures; in theˇrst case with an application of the sp(4, R) classiˇcation scheme of evenÄeven nuclei within the major nuclear shells and next with an application of the sp(4) microscopic model for the description of isovector pairing correlations.

Nuclear shell model and interacting boson fermion approximation

Physics Letters B, 1998

. The Interacting Boson-Fermion Model IBFM hamiltonian is derived starting from the shell-model interaction, by a straightforward extension of the Otsuka, Arima and Iachello mapping procedure to odd-mass systems. Employing a single j-shell model and identical many nucleon systems, systematic studies of spectra giving the comparison in the shell-model, Ž . SD pair truncated model and IBFM are carried out: i for various proportions of monopole pairing and Q P Q interactions Ž . which simulate vibrational-rotational transition; ii for a particular combination of these interactions together with the quadrupole pairing interaction, which conserves seniority. q 1998 Elsevier Science B.V.

Deriving the nuclear shell model from first principles

Journal of Physics: Conference Series, 2015

A procedure for calculating microscopically the input for standard shell-model calculations, i.e., the core and single-particle energies plus the two-body effective model-space interactions, is presented and applied to nuclei at the start of the sd-shell. Calculations with the JISP16 and Idaho χEFT N 3 LO nucleon-nucleon interactions are performed and yield consistent results, which also are similar to phenomenological results in the sd-shell as well as with other theoretical calculations, utilizing other techniques. All results show only a weak A-dependence.

Mixed Symmetry Nuclear Shell Model

2003

A mixed-symmetry nuclear shell-model scheme for carrying out calculations in regimes where there is a competition between two or more modes is proposed. A one-dimensional toy model is used to demonstrate the concept. The theory is then applied to 24Mg^{24}Mg24Mg and 44Ti^{44}Ti44Ti. For lower pf-shell nuclei such as 44−48Ti^{44-48}Ti44−48Ti and 48Cr^{48}Cr48Cr there is strong SU(3) symmetry breaking due to the spin-orbit interaction. However, the quadrupole collectivity as measured by B(E2) transition strengths in the yrast band remain high even though SU(3) appears to be broken. Some results for the so-called X(5) symmetry that falls along the U(5) leftrightarrow\leftrightarrowleftrightarrow SU(3) leg of the Interacting Boson Model are also considered. The results show that the mixed-symmetry concept is effective, even when strong symmetry breaking occurs.

Interacting boson models of nuclear and nucleon structure

1998

Interacting boson models provide an elegant and powerful method to describe collective excitations of complex systems by introducing a set of effective degrees of freedom. We review the interacting boson model of nuclear structure and discuss a recent extension to the nucleon and its excited states.

Frontiers and challenges of the nuclear shell model

The European Physical Journal A, 2002

Two recent developments of the nuclear shell model are presented. One is a breakthrough in computational feasibility owing to the Monte Carlo Shell Model (MCSM). By the MCSM, the structure of low-lying states can be studied with realistic interactions for a wide, nearly unlimited basically, variety of nuclei. The magic numbers are the key concept of the shell model, and are shown to be different in exotic nuclei from those of stable nuclei. Its novel origin and robustness will be discussed.

Mixed-symmetry shell-model calculations in nuclear physics

Arxiv preprint arXiv:1002.3200, 2010

We consider a novel approach to the nuclear shell model. The one-dimensional harmonic oscillator in a box is used to introduce the concept of an oblique-basis shell-model theory. By implementing the Lanczos method for diagonalization of large matrices, and the Cholesky algorithm for solving generalized eigenvalue problems, the method is applied to nuclei. The mixed-symmetry basis combines traditional spherical shell-model states with SU(3) collective configurations. We test the validity of this mixed-symmetry scheme on 24Mg and 44Ti. Results for 24Mg, obtained using the Wilthental USD intersection in a space that spans less than 10% of the full-space, reproduce the binding energy within 2% as well as an accurate reproduction of the low-energy spectrum and the structure of the states - 90% overlap with the exact eigenstates. In contrast, for an m-scheme calculation, one needs about 60% of the full space to obtain compatible results. Calculations for 44Ti support the mixed-mode scheme although the pure SU(3) calculations with few irreps are not as good as the standard m-scheme calculations. The strong breaking of the SU(3) symmetry results in relatively small enhancements within the combined basis. However, an oblique-basis calculation in 50% of the full pf-shell space is as good as a usual m-scheme calculation in 80% of the space. Results for the lower pf-shell nuclei 44-48Ti and 48Cr, using the Kuo-Brown-3 interaction, show that SU(3) symmetry breaking in this region is driven by the single-particle spin-orbit splitting. In our study we observe some interesting coherent structures, such as coherent mixing of basis states, quasi-perturbative behavior in the toy model, and enhanced B(E2) strengths close to the SU(3) limit even though SU(3) appears to be rather badly broken.

Towards an Extended Microscopic Theory for the Upper fp-shell nuclei

2008

An extended SU(3) shell model that for the first time explicitly includes unique-parity levels is introduced. Shell-model calculations for the isotopes of 64^{64}64Ge and 68^{68}68Se are performed where valence nucleons beyond the N=28=Z core occupy levels of the normal parity upper-$fp$ shell ($f_{5/2},p_{3/2},p_{1/2}$) and the unique parity g9/2g_{9/2}g9/2 intruder configuration. The levels of the upper-$fp$ shell are handled within the framework of an m-scheme basis as well as its pseudo-SU(3) counterpart, and respectively, the g9/2g_{9/2}g9/2 as a single level and as a member for the complete gdsgdsgds shell. It is demonstrated that the extended SU(3) approach allows one to better probe the effects of deformation and to account for many key properties of the system by using a highly truncated model space.