Iachello is known for the application of algebraic methods (
Lie algebras) to the investigation of the spectra of atomic nuclei and molecules.
Interacting boson model In 1974 with Akito Arima he introduced the "Interacting Boson Model" into nuclear physics. This model describes collective nuclear states with the help of the unitary group U(6). The underlying concept is to derive a model with pairs of neutrons and protons instead of unpaired nucleons. The pairs are treated as
bosons with different quantum spin (s- and d-bosons, as named according to spin 0 and 2).
Supersymmetry in nuclei In 1980, Iachello introduced
dynamical supersymmetry in nuclei. In an extension of the interacting boson model, the analogous effect with unpaired
fermions has a description using
supersymmetrical algebras. This work was further developed with the interacting boson-fermion model, introduced in 1978 and developed with Olaf Scholten at the University of Groningen.
Vibron model and molecular physics In 1981, Iachello introduced the vibron model of molecules, developed with
Raphael Levine of the
Hebrew University of Jerusalem. This model applies algebraic methods based on dynamical symmetry to the classification of molecular rotation-vibration spectra.
Quantum phase transitions In more recent work, Iachello introduced the concept of dynamical symmetries at the critical point of phase transitions in nuclei (2000–01). In 2008, with M. A. Caprio and P. Cejnar, he co-introduced the concept of excited state quantum phase transitions (ESQPT) in many-body systems.
Double beta decay Iachello has used the interacting boson model to calculate nuclear matrix elements for
double beta decay, a process of importance for determining the
neutrino mass.
Algebraic cluster model Iachello has also investigated the role of discrete symmetries in the cluster structure of light nuclei, developing with R. Bijker an algebraic cluster model with applications to alpha-clustering in nuclei such as 16O. == Selected works ==