“Super-radiance” and the width of exotic baryons N. Auerbach V. Zelevinsky A. Volya This work is supported by NSF grant PHY and in part by a grant from the US-Israel Binational Science Foundation.

Superradiance, collectivization by decay Dicke coherent state N identical two-level atoms coupled via common radiation Analog in nuclei Interaction via continuum Trapped states ) self-organization Volume ¿ 3 g ~ D and few channels Nuclei far from stability High level density (states of same symmetry) Far from thresholds

Superradiance in resonant spectra Narrow resonances and broad superradiant state in 12 C D Pentaquark as a possible candidate for superradiance Stepanyan et.al. hep-ex/ Bartsch et.al. Eur. Phys. J. A 4, 209 (1999)

Two interacting resonances

Q + pentaquark as a two-state interference Effective Hamiltonian

Poles of scattering matrix Decay Amplitudes, considering Kn scattering Consider scattering on a square well potential 1 fm size, depth adjusted to resonant energy

Decay Amplitude Near threshold (small) width parameterization (l>0) Parameterization - cutoff at high energy

Scattering and cross section near threshold Scattering Matrix Cross section Solution in two-level model

Kn scattering crossection Sensible parameters under requirement Resonant energy E r =1540 MeV Kn threshold energy Width of broad peak e 1 =1535 MeV g 1 (E r ) =120 MeV e 2 =1560 MeV g 2 (E r ) =60 MeV v=1 MeV L=300 (green), 500 (red) MeV

Summary Hamiltonian picture Projection formalism (exclusion of continuum) Exact diagonalization –Conservation laws –Unitarity Continuum coupling and reaction problem Near-threshold behavior To appear in Phys. Lett. B.; available at paper nucl-th/ http://arxiv.org/