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F. J. de Swart, Phys. Rev. C 49,2950 (1994). 40 18. A. Coon and W. Glokle, Phys. Rev. C 23, 1790 (1981). 19. S. R. Pandharipande, J. B. Wiringa, Phys. Rev. Lett. 74, 4396 (1995). 20. E. Epelbaum, W. Glockle, and Ulf-G. Meissner, Nucl. Phys. A747, 362 (2005); E. Epelbaum, W. -G. Meissner, Eur. Phys. J. A 19, 401 (2004). 21. A. , Phys. Rev. C 65, 054003 (2002). 22. R. Lazauskas and J . Carbonell, Phys. Rev. C 70,044002 (2004) and private communication. 23. B. C. Pieper, J. R. Pandharipande, Phys.

The circles corresponds to the fully converged results, some of which are also reported in Table 1. 5 . Conclusions In this contribution we have applied the Khon variational principle in conjunction with an expansion on the HA basis to obtain variational bounds for scattering observables a t energies below the three-body breakup. We 47 Table 1. Convergence of the energies of the two bound states (in MeV), Eo and E l , the doublet scattering length a d (in fm), and the 1/2+ phase-shifts (in degrees) at four different energies below the breakup threshold in terms of the number of HA states umax.

J. C. Black, A. Kievsky, M. Viviani, and S. Rosati, Phys. Rev. C 74,034001 (2006). 26. R. Entem and R. Machleidt, Phys. Rev. C 68, 041001(R) (2003). 27. V. Efros, W. Leidemann, and G. Orlandini, Phys. Lett. B338, 130 (1994). 28. D. Andreasi, W. Leidemann, C. Reiss, and M. Schwamb, Eur. Phys. J. A 24, 361 (2006). 29. S. Quaglioni, V. D. Efros, W. Leidemann, and G. Orlandini, Phys. Rev. C 72, 064002 (2005). 30. D. Gazit, S. Bacca, N. Barnea, W. Leidemann, and G. Orlandini, Phys. Rev. Lett. 96, 112301 (2006).

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