Feeding of hole states by proton decay of Gamow-Teller and isobaric analog state resonances.

Abstract

The study of giant resonances in nuclei is attracting much attention both experimentally and theoretically @1,2#. The importance of these studies is that they may provide information about the continuum part of nuclear spectra as well as an understanding of the nuclear dynamics in the continuum. However, there is not much experimental evidence regarding partial decay widths from giant resonances—even the theoretical results are scarce. The reason for this is that the processes of formation and decay of giant resonances are time dependent and a proper treatment of such processes is a very difficult task. Experimentally, it is not easy to subtract the interesting signals from the background. Moreover, if the resonance is not isolated what one measures is not related to the resonance itself but rather to the result of the contribution of all the overlapping resonances, including their interference. The relativistic random-phase approximation ~RRPA !@ 3 # is a natural extension of the random-phase approximation ~RPA! which allows for the treatment of particle-hole states in the continuum. The eigenvalues of the RRPA can be complex due to the admixture of bound and resonant states in the unperturbed particle-hole basis ~Berggren’s representation !. The imaginary part of a complex eigenvalue is associated with the escape width of the state @4#. The formalism has been presented in detail previously and several applications of it have been given, particularly for the description of charge-conserving multipole excitations in 208 Pb @7#. As has been discussed in @4# the residues of the S matrix at a complex energy v n are the partial decay widths of the resonance n if the resonance is isolated ~nonoverlapping!. For such a resonance there exists a direct correspondence between the total escape width and the imaginary part of the energy, i.e., G n522Im(v n). This result has been confirmed for the case of the decay of the giant monopole resonance in 208 Pb @7# .I n the present case we shall show that similar results are also valid for charge-exchange modes, i.e., the isobaric analog ~IAS! and Gamow-Teller giant resonances ~GTGR’s! in 208 Bi.