J. Jolie

Particle-hole excitations in the interacting boson model (I) General structure and symmetries

Abstract A version of the interacting boson model (IBM) is introduced that includes particle-like and hole-like bosons and allows the description of excitations across closed shells. The formal, algebraic aspects of the model are worked out in detail. Reduction of the dynamical algebra U p (6) ⊗ U h (6) leads to the definition of intruder or I spin which labels the character of the bosons (particle-like or hole-like). The I -spin properties of the Hamiltonian and electromagnetic transition operators are discussed. Embedding of U p (6) ⊗ U h (6) into a larger dynamical algebra gives rise to multiplets that connect either states in different nuclei with the same I spin [U(12)], or states that differ by two particles and two holes [U(6,6)], or states that differ by four particles or four holes [Sp(12)].

On the importance of the description for the interpretation of the first excited band in deformed nuclei

The decay properties of the lowest band in the SU(3) dynamical limit of the interacting boson model exhibit properties which are not compatible with the classical picture of a -vibration. Induced by this doubt, recent experimental work on and shows that the lowest band can be indeed of various origins in different nuclei.

Study of the vibrational nucleus 100Ru by the 98Mo(α,2nγ) and 99Ru(n,γ) reactions

The nuclear structure of 100Ru was investigated using the 99Ru(n,γ) and 98Mo(α,2nγ) reactions. In the in-beam spectroscopy study, the use of a coincidence system equipped with five Compton-suppression spectrometers allowed to place 207 transitions in the decay scheme. Spin and parity assignments of the states were determined using angular distribution analysis together with the excitation function slopes and side-feeding intensities. The photons following the neutron capture were observed using curved crystal and pair spectrometers. Using the results of both reactions, the level scheme was extended by 36 new levels. The interpretation of the resulting level scheme was performed in the framework of the spdf interacting boson model.

Erratum to “Study of the vibrational nucleus 100Ru by the 98Mo(α,2nγ) and 99Ru(n,γ) reactions” [Nucl. Phys. A 662 (2000) 3–43]

Abstract The nuclear structure of 100Ru was investigated using the 99Ru(n,γ) and 98Mo(α,2nγ) reactions. In the in-beam spectroscopy study, the use of a coincidence system equipped with five Compton-suppression spectrometers allowed to place 207 transitions in the decay scheme. Spin and parity assignments of the states were determined using angular distribution analysis together with the excitation function slopes and side-feeding intensities. The photons following the neutron capture were observed using curved crystal and pair spectrometers. Using the results of both reactions, the level scheme was extended by 36 new levels. The interpretation of the resulting level scheme was performed in the framework of the spdf interacting boson model.

Nuclear levels in 190Ir studied with the 192Os(p,3nγ) and 192Os(d,4ne−) reactions

Abstract Nuclear levels in 190 Ir have been investigated with the 192 Os(p,3n γ ) and 192 Os(d,4n e − ) reactions using beams of 18–31 MeV protons and 27.8 MeV deuterons. A series of measurements, including excitation functions, γγ and e − e − coincidences, and life time measurements, was performed. From the singles measurements, a total of 140 γ rays were assigned as belonging to the 192 Os(p,3n) 190 Ir channel. The results of the coincidence measurements show that many of these lines are multiplets. Using information from a previous isomer study and single-nucleon transfer reactions, a level scheme is proposed comprising of 112 γ rays placed between 76 levels. It is shown that most of the γ intensity arises from bands having K π ≥4 + . Several negative-parity bands are also proposed. Calculations performed using values of ϵ and γ characteristic of the region reproduce qualitatively some aspects of the level scheme.

Symmetry and Supersymmetry in Quantal Many-Body Systems

Symmetry, together with its mathematical formulation in terms of group theory, has played an increasingly pivotal role in quantum mechanics. Although symmetry ideas can be applied to classical physics, they have become of central importance in quantum mechanics. To illustrate the generic nature of the idea of symmetry, suppose one has an isolated physical system which does not interact with the outside world. It is then natural to assume that the physical laws governing the system are independent of the choice of the origin and the orientation of the coordinate system and of the origin of the time coordinate. The laws of (quantum) physics should thus be invariant with respect to certain transformations of our reference frame. This simple statement leads to three fundamental conservation laws which greatly simplify our description of nature: conservation of energy, linear momentum, and angular momentum. On these three conservation laws much of classical mechanics is built. These quantities are also conserved in isolated quantal systems. In some cases an additional space-inversion symmetry applies, yielding another conserved quantity called parity. In a relativistic framework the above transformations on space and time cannot be considered separately but become intertwined. The laws of nature are then invariant under the set of Lorentz transformations which operate in four-dimensional space–time.

Supersymmetry in Nuclear Physics

One particularly important extension of the interacting boson model (IBM) concerns odd-mass nuclei, achieved by considering, in addition to the bosons, a fermion coupled to the core with an appropriate boson–fermion interaction. The resulting interacting boson–fermion model (IBFM) is thus a specific version of the particle–core coupling model which has been widely used in nuclear physics to describe odd-mass nuclei. The characteristic feature of the IBFM is that it lends itself very well to a study based on symmetry considerations whereby certain classes of boson–fermion Hamiltonians can be solved analytically. Essential features of the IBFM are recalled in Sect. 4.1, while its symmetry structure is outlined in Sect. 4.2. Since the IBFM is described in detail in Iachello and Van Isacker (The interacting Boson–Fermion model. Cambridge University Press, Cambridge, 1991), no comprehensive review is given here. Two dynamical-symmetry limits of the IBFM which are of relevance in this and the remaining chapters are discussed in Sect. 4.3.

Supersymmetries with Neutrons and Protons

In this chapter we present the logical combination of ideas introduced previously. In Chap. 4 fermion degrees of freedom were introduced in the interacting boson model (IBM), leading to a description of odd-mass nuclei in the context of the interacting boson–fermion model (IBFM) and, after due consideration of the appropriate superalgebras, to a simultaneous description of even–even and odd-mass nuclei. The purpose of Chap. 5, on the other hand, was the introduction of the F-spin degree of freedom in the IBM to distinguish between neutron and proton bosons, with several consequences such as a better microscopic foundation of the IBM, the existence of F-spin multiplets of nuclei, and the occurrence of states with a mixed-symmetry character in neutrons and protons.

Symmetries with Neutrons and Protons

Atomic nuclei consist of neutrons and protons. This seemingly trivial observation has far-reaching consequences as far as the structure of nuclei is concerned. Neutrons and protons are the elementary building blocks of the nuclear shell model. They are always included in the model, either explicitly or via the formalism of isospin which assigns to each nucleon an intrinsic label T = 1∕2 with different projections for neutron and proton. While the neutron–proton degree of freedom is an essential part of the shell model, it is not always one of the interacting boson models (IBM). In fact, in the version of the model discussed in Chap. 3 no distinction is made between neutrons and protons and all bosons are considered as identical. Nevertheless, to make the model more realistic, it is essential to introduce this distinction. This is the main objective of the present chapter.