The Interacting Boson-Fermion Model

Abstract

The interacting boson-fermion model has become in recent years the standard model for the description of atomic nuclei with an odd number of protons and/or neutrons. This book describes the mathematical framework on which the interacting boson-fermion model is built and presents applications to a variety of situations encountered in nuclei. The book addresses both the analytical and the numerical aspects of the problem. The analytical aspect requires the introduction of rather complex group theoretic methods, including the use of graded (or super) Lie algebras. The first (and so far only) example of supersymmetry occurring in nature is also discussed. The book is the first comprehensive treatment of the subject and will appeal to both theoretical and experimental physicists. The large number of explicit formulas for level energies, electromagnetic transition rates and intensities of transfer reactions presented in the book provide a simple but detailed way to analyse experimental data. This book can also be used as a textbook for advanced graduate students.

Critical-Point Symmetries in Boson-Fermion Systems: The Case of Shape Transitions in Odd Nuclei in a Multiorbit Model

“…Knowing the analytic form of the eigenfunctions, it is then easy to calculate spectroscopic observables, such as electromagnetic transition probabilities. To check the validity of the model, we will also present more microscopic calculations based on the interacting boson-fermion model (IBFM) [5], with a choice of the boson-fermion Hamiltonian that describes the same physical situation.…”

Lifetime measurements in mass regions A=100 and A=130 as a test for chirality in nuclear systems

“…[1,47] and of the IBFFM [49,50]. IBFFM model is based on the interacting boson model (IBM-1) [51,52] for even-even nuclei and the interacting boson-fermion model (IBFM-1) [53,54] for odd-A nuclei. A detailed procedure of this calculation and the parameter choice can be found in [55].…”

Construction of spherical harmonics and Clebsch–Gordan coefficients

“…Recall that this involves first constructing the function of γ appearing in the integrand of (11) or (24) and then evaluating the integral with respect to γ. The integrand is built from the generating functions (15), using (12) and (17). The integrand is thus a polynomial in the trigonometric functions cos γ, sin γ, cos 2γ, sin 2γ, cos 3γ, and sin 3γ or, therefore, by multiple-angle identities, a polynomial in cos γ and sin γ.…”

“…However, the monomials Φ N2t2L2 (γ, Ω) and Φ N1t1L1 (γ, Ω) must first themselves be constructed, from the definition (12). As noted in Sec.…”

“…The purpose of this code is to make calculations using the ACM routinely possible, without the need to reconstruct the SO(5) machinery for each new application. The SO(5) ⊃ SO(3) Clebsch-Gordan coefficients yielded by the code are also relevant to the U(6) interacting boson model (IBM) [11,12] which, in U(6) ⊃ U(5) ⊃ SO(5) and U(6) ⊃ SO(6) ⊃ SO(5) bases, is in close correspondence with the collective model in appropriate SU(1, 1) × SO(5) bases [13]. They can, furthermore, be used as seed coefficients in the generation of Clebsch-Gordan coefficients for the coupling of more general (non-symmetric) representations of SO (5) or Sp (4) in an SO(3) basis [14].…”