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25 pages, 7 figures, 5 tables, Accepted for publication in J. of Physics G; International audience; We present an analysis of effective operators in the shell model with up to three-body interactions in the Hamiltonian and two-body terms in electromagnetic transition operators when the nucleons are either neutrons or protons occupying a single-j orbital. We first show that evidence for an effective three-body interaction exists in the N = 50 isotones and in the lead isotopes but that the separate components of such interaction are difficult to obtain empirically. We then determine higher-order terms on more microscopic grounds. The starting point is a realistic two-body interaction in a large shell-model space together with a standard one-body transition operator, which, after restriction to the dominant orbital and with use of stationary perturbation theory, are transformed into effective versions with higher-order terms. An application is presented for the lead isotopes with neutrons in the 1g 9/2 orbital.

A cluster supersymmetry scheme based on a core+α configuration is applied to nuclei with mass numbers A = 20, 19 and 18. The bosonic sector of the superalgebra of the model describes the relative motion of the clusters, while its fermionic sector is associated with the internal structure of the core. In the application considered, the core is a p-shell nucleus, leading to an underlying superalgebra U(4|12). For each of the six nuclei included in the analysis, the best-known α-cluster bands are considered. To gauge the validity of the supersymmetry approximation, electric quadrupole transition rates and one-nucleon transfer intensities are computed in two different ways: first for each nucleus separately and then jointly for the six nuclei. The analysis of the experimental data confirms the approximate validity of the U(4|12) supersymmetry for the six nuclei considered here.

After a brief review of early developments, two recent examples of applications of symmetries in nuclear physics are presented: (i) pseudo-spin symmetry which can be used to extend Wigner's supermultiplet model to heavy nuclei; (ii) symmetries of the interacting boson model with isoscalar and isovector bosons which can be used to analyze the problem of deuteron transfer in N = Z nuclei.

The use of spectrum generating algebras in the description of the nuclear many-body system is reviewed. General notions of symmetry and dynamical symmetry in quantum mechanics are introduced with the help of simple examples. It is then indicated how techniques based on symmetry considerations can be used to find the analytical solutions for the problem of an aggregate of interacting particles (bosons and/or fermions). Some older ideas due to Wigner, Racah and Elliott are succinctly summarized to put more recent advances in a proper perspective. It is then shown that similar techniques are used in a model of the nucleus in terms of interacting bosons due to Arima and Iachello. Subsequent extensions of this model to odd-mass nuclei lead to the consideration of mixed systems of bosons and fermions and, most notably, to supersymmetry.

The connection between competing LS and jj coupling schemes and competing T = 0 and T = 1 correlated pairs is recalled and discussed in the light of a shell-model pseudo-SU(4) symmetry which follows from the combined invariance in pseudo-spin and isospin.

We discuss two related models of generalized pairing in nuclei. One is a fermion model based on the algebra SO(8). The other is an IBM-4 model restricted to L = 0 bosons. Both models accommodate isovector and isoscalar pairing on an equal footing. We develop in detail the group structure of the IBM-4 with L = 0 bosons and then discuss its relation to the SO(8) model through the use of boson mapping techniques. We show that a Dyson boson mapping of the SO(8) model leads to a version of IBM-4 very similar to the boson model we developed. Indeed, in the SU(4) limit that is common to the two models, we find that they are equivalent. In the two SO(5) limits of the SO(8) model, involving pure isoscalar and pure isovector pairing respectively, equivalence of the models can likewise be shown. Away from these symmetry limits, however, the assumption that the Hamiltonian of IBM-4 with L = 0 bosons is Hermitian and has at most two-boson interactions implies some differences with respect to the SO(8) model.

We discuss the experimental evidence for many-particle many-hole excitations (mp-nh) at and near to closed shells. Besides a shell-model approach and in order to understand the salient features of the general behaviour of the 0+ intruder band heads, we mainly concentrate on a group theoretical classification. Using the boson model, various possibilities to classify intruder mp-nh excitations can be shown to exist. Ample evidence for the realization of these new symmetries is given in (i) the Z = 50 mass region and, in (ii) the Z = 82 Pb mass region. Finally, a possible extension to encompass also mp-nh excitations in light nuclei is presented.

Isospin invariant boson models, IBM-3 and IBM-4, applicable in nuclei with neutrons and protons in the same valence shell, are reviewed. Some basic results related to these models are discussed: the mapping onto the shell model, the relation to Wigner's supermultiplet scheme, the boson-number and isospin dependence of parameters, etc. These results are examined for simple single-j shell situations (e.g. f7/2) and their extension to the fp shell is investigated. Other extensions discussed here concern the treatment of odd-mass nuclei and the classification of particle-hole excitations in light nuclei. The possibility of a pseudo-SU(4) supermultiplet scheme in fp-shell nuclei is discussed.

A review is given of some of the more topical extensions of the interacting boson model of collective nuclear excitations. After introducing some elementary and basic ideas which illuminate the general principles of the algebraic approach, their application to nuclear structure in the context of the various extensions of the interacting boson model is presented: the introduction of the neutron-proton degree of freedom and its relevance to a recently discovered class of collective states (so-called 'scissors' states); the coupling of a fermion to a system of interacting bosons to describe nuclei with odd numbers of neutrons and/or protons; and the inclusion of the isospin degree of freedom in the model, necessary in light nuclei where neutrons and protons occupy the same valence shell. These different developments are summarized with special emphasis on the new features and quantum numbers appearing specifically as a result of the algebraic method. The final part of this paper reviews a general algebraic framework for describing scattering phenomena, which is inspired by the methods used in structure phenomena.

Two-band model calculations are presented which describe the 01+ and 02+ levels of the platinum isotopes as linear combinations of pure states with definite deformation-near-spherical and a deformed one, the latter becoming the ground configuration near the neutron-mid shell. The mixing amplitudes between the spherical and deformed configurations and the corresponding mixing matrix elements have been derived. A comparison of the calculations with the experimental data is presented.

The democratic mapping is used for the calculation of low-lying states of nuclei in the sd and fp shells. In addition to demonstrating the applicability of the method in realistic cases where many non-degenerate levels are present, the method allows for the ranking of the various bosons according to their importance as building blocks of low-lying states. It is proven that the s and d bosons are the most important building blocks, followed by the d' and g bosons. Thus one of the basic assumptions of the interacting boson model (IBM) is proven to be correct. Very good agreement between the boson calculation and the shell-model results is obtained for A=20 nuclei when 12 bosons are taken into account, while an even larger number of bosons is required to reproduce the low-lying states of the A=44 nuclei. In order to obtain equally good results with a smaller number of bosons one needs to introduce effective boson Hamiltonians which correspond to truncated fermion spaces.

An extension of the interacting boson model (IBM) is suggested by introducting both the particle-hole character and the charge character of the bosons as supplementary degrees of freedom. This allows us to consider an SU(4) symmetry. Within this new classification scheme, three applications are worked out.

An extension of the interacting boson model (IBM) is suggested to treat both particle-hole and regular excitations on an equal footing. Particle and hole bosons are introduced, each corresponding to a unitary U(6) algebra. Reduction of the corresponding product algebra leads to the definition of intruder-spin (I-spin). Embedding of the latter into a larger dynamical algebra U(12) gives rise to multiplets that connect states in different nuclei with the same I-spin. Similarly, embedding into a non-compact algebra leads to the classification of multi-particle-multi-hole excitations within one nucleus.

It is argued that $N\sim Z$ nuclei with $90\leq A\leq100$ can be interpreted in terms of aligned neutron--proton pairs with angular momentum $J=2j$ and isospin T=0. Based on this observation, a version of the interacting boson model is formulated in terms of isoscalar high-spin bosons. To illustrate its possible use, the model is applied to the $21^+$ isomer in $^{94}$Ag.

International audience; Seniority isomers are nuclear states with an electromagnetic decay that is hindered by selection rules related to the seniority quantum number. A simple analysis is presented of their possible formation with reference to the nickel isotopes 70−76Ni and the N = 50 isotones from molybdenum to cadmium. It is shown that the existence of seniority isomers in a j = 9/2 shell is predominantly governed by the quadrupole pairing matrix element of the nucleon-nucleon interaction. The analysis is generalized to shells with larger j.

It is shown that the three-body forces in the $1f_{7/2}$ shell, for which recently evidence was found on the basis of spectroscopic properties of the Ca isotopes and $N=28$ isotones, can be most naturally explained as an effective interaction due to excluded higher-lying shells, in particular the $2p_{3/2}$ orbit.}, Comment: 5 pages, 1 tables, accepted for publication in Europhysics Letters

Measurements of the internal conversion electron spectrum and the identification of EO transitions linking the excited O+ states in 172Yb provide new information on the level structure of this nucleus. The (n,e-) reaction with a Yb2O3 target enriched in 171Yb was used and all possible EO transitions were searched for. Several new low-energy EO transitions were observed and evidence was found for a new 0+ level at 1920 keV. This may be due to pair excitation, which is also a possible explanation for the 1405 keV 0+ level. The authors show that an alternative explanation for the 1405 keV level is that it is the head of a Kpi =0+ mixed symmetry band with band members at 1477 keV (2+) and 1633 keV (4+). The level energies, B(E2) values, multipole mixing ratios and X values are compared with the predictions of the DDM and the IBA-2.

The coupling of isoscalar monopole and quadrupole resonances and their decay to the nuclear ground state are studied within the framework of the interacting boson model. Results for transitional samarium isotopes are presented.

Mixed-symmetry assignments are made to the 1.570 (l;), 1.573 (2:) and 1.659 (3:) MeV levels in 2wHg. The characteristics of the 2: level are shared with nearby 2+ levels at 1.254 and 1.593 MeV. An interacting boson approximation (IBA-2) analysis examines the sensitivity of the mixed-symmetry states to the E, parameters of the Majorana term and finds that both the magnitude and sign of the d(E2iM1) mixing ratio of 2'-2: transitions are well reproduced at the values of the tt parameters used to obtain a level energy fit. The IBA-2 calculations also give a satisfactory fit to the energy levels and in general provide X(EOiE2) values close to the experimental data. These calculations agree with the known oblate deformation of the ground state which we find to be predicted by Kumar's dynamic deformation model. Experimental data from n, yy(0) experiments together with internal conversion coef- ficient (ICC) results allow 1+ levels to be unambiguously established at 1.570, 1.631, 1.718, 2.061, 2.370, 2.640 and 2.979 MeV. The measurements also provide precise 6 values of many transitions while event-by-event coincidence information permits the decay scheme to the developed with previous unlocated transitions now firmly assigned.

The concept of a dynamical symmetry is re-examined. Starting from elementary considerations, it is shown that dynamical symmetries also occur in transitional Hamiltonians of the interacting boson model. Examples are given for the IBM-1 and IBM-2. Next, the breaking of dynamical symmetries is discussed. One specific case, namely the breaking of F spin, is of importance in the study of magnetic dipole properties, and is analyzed in detail with reference to observed E2/M1 mixing ratios in deformed rare-earth nuclei.

In the interacting boson-fermion model for odd nuclei it is shown that mixed- symmetry boson states may occur at low excitation when neutrons and protons occupy the same shell-model orbits. In any of the forms of the interacting boson model (l, 21 IBM~, -3 or -4 in which there is more than one type of boson, it is possible to have states which are less than fully symmetric in the separate orbital and intrinsic spaces. Such states are said to be of mixed symmetry and are labelled by a partition of the boson number N. Calculations for even-even nuclei show that low-lying states are dominated by full symmetry and that the lowest states of mixed symmetry have the partition (N- 1, 11. These states of mixed symmetry have been identified experimentally, mainly through their Ml properties, and examples are the I+ states (3) at 3.08 MeV excitation in lshGd and the 2+ state (4) at 1.99 MeV in 14"Ba. The boson model (5) for an odd nucleus (IBFM) consists of a single nucleon coupled to the boson structure for the even-mass core. In the IBM~ version of the model, which is appropriate for heavy nuclei with valence neutrons and protons in different orbits, each nucleus has a unique assignment of neutron and proton boson numbers N, and N, and a unique charge for the single nucleon. In this situation the states of the odd nucleus in which the bosons have mixed symmetry would be expected to lie at about the same excitation as in even-even nuclei (see above). However, in lighter nuclei, with valence neutrons and protons filling the same orbits, it is necessary to extend the boson model to IBM~ by introducing a third type of boson composed of a neutron and a proton in order to preserve isospin symmetry. Odd nuclei may also be described (6) in this region (IBFM~) but the single nucleon must now be vector coupled, in isospin, to the bosons. This implies that, in an odd-neutron nucleus, for example, the single nucleon spends part of its time as a neutron with an even-even boson core and part of its time as a proton with an odd-odd boson core. The question of the excitation energy of the mixed-symmetry states in the odd nuclei is then a more delicate one. Here we explore that question and show that in certain odd nuclei the mixed-symmetry states are at lower excitation than in the even-even nuclei. Consider a nucleus with an odd number n of nucleons beyond a double closed shell such as 40Ca or 56NNi. The number of bosons is then N= f(n - 1) and we shall discuss states with full symmetry (NI and with the lowest mixed symmetry (N- 1, 11. The possible total isospin may take the values T=tn, 3n- 1, in-2, . . ., and, from