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Low-lying resonances of 9 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
Cluster model for of 9 Be
Experimental data
From Review “Spectroscopy of Λ hypernuclei” O. Hashimoto, H. Tamura,
Progress in Particle and Nuclear Physics, 2006
Formalism
Merkuriev S P and Faddeev L D 1993
Quantum Scattering Theory for Several
Particle Systems (Dordrecht:Kluwer)
Faddeev equations in
configuration space
Formalism
(I Filikhin, V M Suslov, B Vlahovic,
2005 J. Phys. G. 31 1207)
2-4 nm
Formalism
2-4 nm
Formalism
2-4 nm
Model
aa-potential
S. Ali, A. R. Bodmer Nucl. Phys. 80 (1966) 99
a-potential
Y. Kurihara, Y. Akaishi, H. Tanaka, Phys. Rev. C 84 (1985) 971.
C. Daskaloyannis, M. Grypeos, H. Nassena,Phys. Rev. C 26 (1982) 702.
Model
Three-body potential
Method
Analytical continuation in a
parameter (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 levels
Calculations:
Numerical results
Bound states
Numerical results
Bound states
Numerical results
Energies of low-lying resonance and virtual levels
Calculations:
Numerical Results
Calculations:
Numerical Results
Calculations:
Numerical Results
Low-lying levels of aa system:calculation with the Gibson
potential
Numerical results
Cal.1 - Yamada, K. Ikeda, H. Bando, Prog. Theor. Phys. 73 (1985) 397
Cal.2 - our calculation with the Gibson potential
Cal.3 - our calculation with the Isle potential
Arrows - experimental data for (p+,K+) reaction
Numerical results
a+a+
Cal.1 -- calculation with “minimal” orbital momentum configuration
Cal.2 – with “maximal” orbital momentum configuration
Conclusion
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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.