General form of the boson-fermion interaction in the interacting boson-fermion model-2

The boson-fermion interaction in the interacting boson-fermion model-2 (IBFM-2) is derived in a systematic and general form from a quadrupole-quadrupole force using several nondegenerate levels. The boson-fermion quadrupole operator employed is obtained from the boson-fermion image of the one nucleon transfer operator which in turn can be calculated following two alternative schemes: the Otsuka-Arima-Iachello and generalized Holstein-Primakoff schemes. Four different terms (two quadrupole and two exchange) were obtained. Application of the new expressions to a single-$j$ model is studied and analyzed.

Figure 1

Diagrammatic representation of the terms [Eqs. (9)–(12)] and the last term in Eq. (7).

Figure 2

Energies of a single $j$ calculation for $j=\frac{5}{2}$ (left), $\frac{9}{2}$ (middle), and $\frac{13}{2}$ (right) with $\kappa =-0.2$ MeV (top) and $\kappa =-0.5$ MeV (bottom). Red, $J=j-2$; magenta, $J=j-1$; green, $J=j+1$, and blue, $J=j+2$. The ground state was taken as zero energy and it is not shown to visualize the energies more clearly.

Figure 3

Same as Fig. 2, but considering just one of the terms in the boson-fermion interaction. The calculation were done with $\kappa =-0.5$ MeV and $j=9/2$.