Low-lying resonances of Be: Faddeev calculation with Pade’-

approximates

B. Vlahovic, V. Suslov, I. Filikhin,

Department of Physics, North Carolina Central University, Durham, NC 27707, USA

FB18 August 21-26, 2006 Santos, SP, Brazil

9

Cluster model for of Be9

Experimental dataFrom Review “Spectroscopy of Λ hypernuclei” O. Hashimoto, H. Tamura, Progress in Particle and Nuclear Physics, 2006

FormalismMerkuriev S P and Faddeev L D 1993 Quantum Scattering Theory for Several Particle Systems (Dordrecht:Kluwer)

Faddeev equations in configuration space

2-4 nm

Formalism

(I Filikhin, V M Suslov, B Vlahovic,2005 J. Phys. G. 31 1207)

2-4 nm

Formalism

2-4 nm

Formalism

Model

potentialS. Ali, A. R. Bodmer Nucl. Phys. 80 (1966) 99potentia

l

Y. Kurihara, Y. Akaishi, H. Tanaka, Phys. Rev. C 84 (1985) 971.

C. Daskaloyannis, M. Grypeos, H. Nassena,Phys. Rev. C 26 (1982) 702.

Three-body potentialModel

MethodAnalytical continuation in aparameter (coupling constant) of additional three-body potential

Kukulin V. I., Krasnopol’sky V. M. and Horacek J. Theory of Resonances (Kluwer, Dordrecht) 1989

Numerical Results Energies of low-lying resonance and virtual levelsCalculations:

Numerical results

Bound states

Numerical results

Bound states

Numerical results

Energies of low-lying resonance and virtual levelsCalculations:

Numerical Results Calculations:

Numerical Results Calculations:

Numerical ResultsLow-lying levels of system:calculation with the Gibson potential

Numerical results

Cal.1 - Yamada, K. Ikeda, H. Bando, Prog. Theor. Phys. 73 (1985) 397Cal.2 - our calculation with the Gibson potentialCal.3 - our calculation with the Isle potential Arrows - experimental data for K+) reaction

Numerical results

Cal.1 -- calculation with “minimal” orbital momentum configurationCal.2 – with “maximal” orbital momentum configuration

Conclusion

Configuration space Faddeev equations have been applied to study the 9Lambda Be hypernucleus in the alpha-alpha-Lambda cluster model with phenomenological pair potentials.

The method of analytical continuation in coupling constant was successfully applied to estimate spectrum of low-lying resonances.

The calculations with the Gibson alpha-Lambda potential have qualitative agreement with the (pi+,K+) data.

We predict 2+ resonance state close to the alpha+alpha+Lambda threshold.

We also found the 0+ and 4+ virtual states formed by the (alpha+Lambda)+alpha configuration.