On the Renormalization of the IBA by the g Boson

  • Bruce R. Barrett
  • Keith A. Sage
Part of the Ettore Majorana International Science Series book series (EMISS, volume 10)


The IBA-2 proton-neutron Hamiltonian is given byl–2
$${H_{IBA2}} = \varepsilon \left( {{n_{{d_\pi }}} + {n_{{d_v}}}} \right) + \kappa {Q_\pi } \cdot {Q_v} + {M_{\pi \nu }} + {V_{\pi \pi }} + {V_{vv}}$$
where κ < 0
$$\begin{gathered} {Q_{\pi \left( v \right)}} = \left( {{d^\dag }s + {s^\dag }\tilde d} \right)_{\pi \left( v \right)}^{\left( 2 \right)} + {\chi _{\pi \left( v \right)}}\left( {{d^\dag }\tilde d} \right)_{\pi \left( v \right)}^{\left( 2 \right)} \hfill \\ {V_{\pi \pi \left( {vv} \right)}} = \sum\limits_{L = 0,2,4} {\frac{1}{2}} {\left( {2L + 1} \right)^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}}}C_L^{\pi \left( v \right)}\left[ {\left( {{d^\dag }{d^\dag }} \right)_{\pi \left( v \right)}^{\left( L \right)}x\left( {\tilde d\tilde d} \right)_{\pi \left( v \right)}^{\left( L \right)}} \right]_0^0 \hfill \\ \end{gathered} $$
and Mπv is the Majorana operator which separates the totally symmetric proton-neutron states from states of mixed symmetry. This Hamiltonian has been used by several authors1–4 to do phenomenological analyses of nuclei in the mass region Z = 50−82 and N = 50 to N ≥ 126, in which the parameters ε, κ, χπ, χv (and perhaps the CL’s) are determined by fitting the low-lying energy spectra for an individual nucleus. One would like to obtain values for these parameters which vary smoothly with neutron (or proton) number and then to understand the physical origins of these parameters. Another interesting question is how these parameters are affected by terms left out of the model Hamiltonian, such as the g boson, i.e. proton or neutron pairs coupled to J = 4. One approach to studying this problem is to expand the symmetry group of the IBA from SU(6) to SU(15) in order to include the degrees of freedom associated with a g boson. One can avoid this difficult task by including the effects of a g boson on the s-d boson model space through second order perturbation theory.


Neutron Number Order Perturbation Theory Fermion Pair Boson State Neutron Pair 
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Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • Bruce R. Barrett
    • 1
  • Keith A. Sage
    • 2
  1. 1.Department of PhysicsUniversity of ArizonaTucsonUSA
  2. 2.Theoretical Physics DivisionUniversity of ArizonaTucsonUSA

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