Everything you always wanted to know about SUSY, but were afraid to ask.pdf

a r X i v : n u c l - t h / 0 3 0 4 0 3 3 v 1 1 2 A p r 2 0 0 3 EVERYTHING YOU ALWAYS WANTED TO KNOW ABOUT SUSY, BUT WERE AFRAID TO ASK R. BIJKER1, J. BAREA1 AND A. FRANK1,2 1 ICN-UNAM, AP 70-543, 04510 Me?xico, DF, Me?xico 2 CCF-UNAM, AP 139-B, 62251 Cuernavaca, Morelos, Me?xico New experimental tests of nuclear supersymmetry are suggested. They involve the measurement of one- and two-nucleon transfer reactions between nuclei that belong to the same supermultiplet. These reactions provide a direct test of the ‘fermionic’ sector, i.e. of the operators that change a boson into a fermion or vice versa. We present some theoretical predictions for the supersymmetric quartet of nuclei: 194Pt, 195Pt, 195Au and 196Au. 1 Introduction Dynamical supersymmetries were introduced 1 in nuclear physics in 1980 by Franco Iachello in the context of the Interacting Boson Model (IBM) 2 and its extensions. The spectroscopy of atomic nuclei is characterized by the interplay between col- lective (bosonic) and single-particle (fermionic) degrees of freedom. The IBM de- scribes collective excitations in even-even nuclei in terms of a system of interacting monopole and quadrupole bosons with angular momentum l = 0, 2. The bosons are associated with the number of correlated proton and neutron pairs, and hence the number of bosons N is half the number of valence nucleons. For odd-mass nuclei the IBM has been extended to include single-particle de- grees of freedom 3. The Interacting Boson-Fermion Model (IBFM) has as its build- ing blocks N bosons with l = 0, 2 and M = 1 fermion with j = j1, j2, . . .. The IBM and IBFM can be unified into a superalgebra U(n/m), where n = ∑ l(2l+1) = 6 is the dimension of the boson space andm = ∑ j(2j+1) of the fermion space 4. In this framework, even-even and odd-mass nuclei form the members of a supermultiplet. The inclusion of the neutron-proton degree of freedom leads to supersymmetric quartets of nuclei consisting of an even-even, an odd-even, an even