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HK: Hadronen und Kerne
HK 43: Nuclear Forces III, Reactions, Resonances
HK 43.3: Group Report
Tuesday, March 17, 1998, 17:30–18:00, J
Saturation of resonance and spreading widths caused by resonance trapping* — •E. Persson, T. Gorin, and I. Rotter — Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden and Technische Universität Dresden, Institut für Theoretische Physik, D-01062 Dresden
Resonance states are described in a formalism taking the continuum of decay channels into account. The effective hamiltonian is Heff=H−iAAT where H is the hamiltonian of the closed system and A is a (N× K) matrix describing the coupling of the N resonance states to the K channels. The complex eigenvalues of Heff give the energies ER and widths ΓR of the resonances. The system is studied as a function of the parameter κ=2Γ/(KD) where D is the mean level distance and Γ the mean width. For κ < 1, all widths grow with increasing κ whereas at κ≈ 1 a reorganisation takes place, as a result of which K states collect almost all of the sum of the widths. This is called resonance trapping.
In many studies of Heff, the widths of the N−K long-lived states decrease as a function of κ for κ > 1. This decrease is often considered as an unphysical artifact of the model caused by the broad states overlapping regions outside the spectrum of H. In [1] systems are considered with additional channels being weaker coupled to the system than the other ones. We show that in this case the widths of the narrow states saturate as a function of κ for κ > 1. Further, we demonstrate by using an H with a band-structure, that resonance trapping takes place before the broad states overlap regions outside the discrete spectrum.
A widely discussed problem in nuclear physics is the saturation of the
spreading widths as a function of the level density, see e.g. [2].
We formulate an Heff
model for the doorway states taking the continuum into account. Only
the doorway state is coupled to the decay channel. The background of
complicated states is coupled through a real coupling vector V to the
doorway state. The spreading width is directly calculated as the sum of the
widths of the narrow states.
We show that resonance trapping in combination with a realistic scaling of the
real coupling elements Vi with the level density gives an explanation
of the saturation of the spreading widths.
[1] E. Persson, T. Gorin and I. Rotter, E-Print at http://www.mpipks-
dresden.mpg.de/publ/year97/97.html, Nr. 9708011
[2] J. Reiter and H.L. Harney, Z. Phys. A 337, 121 (1990)
*Supported by DFG (Ro 922)