J.W. Gibbs Professor of Physics, Yale University

Phone: 203-432-6944; Email: francesco.iachello@yale.edu

Nuclear and molecular structure: the interacting boson model

The research program of Francesco Iachello is devoted to the study of symmetries in complex systems and to the exploitation of these symmetries to construct models of physical systems based on algebraic structures. The most celebrated of these models is the Interacting Boson Model of the atomic nucleus, introduced in 1974 by Arima and Iachello, in which the fundamental constituents are correlated pairs of protons and neutrons treated as bosons [1]. The algebraic structure of this model is that of the unitary group in six dimensions, U(6). This model, together with the Nuclear Shell Model and the Liquid Drop Model, forms the basis for the description of all nuclear phenomena. Several aspects of nuclear structure physics are being investigated at the moment, including the nature of shape phase transitions [2], the origin of anharmonicites, and the occurrence of collective states in which protons and neutrons move out of phase. The concept of symmetry was enlarged in the 70’s to include a new type, called supersymmetry. One of the most important models which exploits the concept of supersymmetry is the Interacting Boson-Fermion Model of the nucleus, in which the fundamental constituents are correlated pairs (bosons) together with unpaired protons and neutrons (fermions). This model, introduced in 1980 by Iachello, forms the basis for the description of nuclei with an odd number of particles [3]. Many aspects of supersymmetry (a concept also employed in Particle Physics) and of the Interacting Boson-Fermion Model are being investigated, including the study of beta-decay and neutrino absorption. Another celebrated algebraic model is the Vibron Model, introduced in 1981 by Iachello to describe rotations and vibrations of molecules [4]. The fundamental constituents here are quanta of anharmonic vibration, called vibrons. Its algebraic structure is [4]. This model, together with the Force Field Model, forms the basis for the description of rotational and vibrational motion in molecules. Many aspects of the algebraic description of molecules are being investigated at the present time. In a research project carried in part at the Physics Department and in part at the Chemistry Department, symmetry and algebraic methods are being exploited to study complex polyatomic molecules. Aspects that are being investigated are the structure of aromatic molecules, the structure of fullerene-like molecules and the phenomenon of vibrational energy relaxation. Tools being used are infrared, Raman and Franck-Condon spectroscopy [5]. The use of symmetry and associated algebraic methods are now being extended to even more complex systems, such as polymers and macromolecules. The aim here is to understand the spectroscopy of polymers, including eventually biopolymers and the like. Symmetry is a fundamental concept in physics (and chemistry) which has led to crucial results. In particular, the concept of dynamical symmetry [i.e. symmetry of the interactions] developed by Francesco Iachello and exploited in the construction of the Interacting Boson and Boson-Fermion Models and of the Vibron and Vibron-Electron Models promises to provide crucial results for complex systems other than nuclei and molecules. It is the development of these models that will form the bulk of the future research program.

References:

[1] "Collective Nuclear States as Representations of an SU[6] Group," A. Arima and F. Iachello, Phys. Rev. Lett. 35, 1069 (1975); For a review see, "The Interacting Boson Model", F. Iachello and A. Arima, Cambridge University Press   (1987).

[2] "Phase Coexistence in Transitional Nuclei and the Interacting Boson Model," F. Iachello , N.V. Zamfir and R.F. Casten, Phys. Rev. Lett. 81, 1191 (1998).

[3] "Dynamical Supersymmetries in Nuclei," F. Iachello, Phys. Rev. Lett. 44, 77  (1980); For a review see, "The Interacting Boson-Fermion Model", F. Iachello and P. van Isacker, Cambridge University Press (1991).

[4] "Algebraic Methods for Molecular Rotation-Vibration Spectra," F. Iachello, Chem. Phys. Lett. 78, 581 (1981); For a review see, F. Iachello and R.D. Levine,"Algebraic Theory of Molecules," Oxford University Press (1995).

[5] "Analytic and Algebraic Evaluation of Franck-Condon Overlap Integrals," F. Iachello and M. Ibrahim, J. Phys. Chem. 102, 9427 (1998).