By employing separable potentials for the binary, i.e., n-n and n-core subsystems, we compute the threebody integral equations to solve for the 2n-separation energies in the ground and excited states of halo nuclei like 19 B, 22 C, and 20 C. We show through numerical analysis and also from analytical considerations that Borromean-type halo nuclei like 19 B and 22 C, where n-n and n-core are both unbound, are much less vulnerable to respond to the existence of the Efimov effect. On the contrary, those nuclei, like 20 C in which the halo neutron is supposed to be in the intruder low lying bound state with the core, appear to be the promising candidates to search for the occurrence of Efimov states at energies below the n-(nc) breakup threshold which can be within the experimental limits to measure.

Asymmetric resonances in elastic n+19C scattering are attributed to Efimov states of such neutron-rich nuclei, that is, three-body bound states of the n+n+18C system when none of the pairs is bound or some of them are only weakly bound. By fitting to the general resonance shape described by Fano, we extract the resonance position, width, and the "Fano profile index." While Efimov states have been discussed extensively in many areas of physics, there is only one very recent experimental observation in trimers of cesium atoms. The conjunction that we present of the Efimov and Fano phenomena may lead to experimental realization in nuclei.

Using the exact three-body formalism with separable potentials proposed sometime ago by us, the scattering lengths and low-energy phase shifts in n-d scattering have been evaluated. The nature of the contribution of the so-called "potential scattering" to the scattering lengths has also been examined within this formalism and found not to exceed 10% of the "nucleon exchange'' contribution.S OME time ago one of the authors (A.N.M.)proposed an exact formalism for the three-body problem 1 as a means of studying the properties of the triton. Subsequently this formalism was extended by two of us (ANM and VSB) to the problem of neutrondeuteron scattering. 2 The preliminary results on the n-d scattering lengths in the S=f and S='| states were given in Ref.(2), which we refer to here as A. The formalism of the three-body problem as given in these two papers can be cast almost without modification in the language of Faddeev's three-particle theory. 3 In the case 5=f, for example, the Faddeev wave function ^( 1) for the scattering of particle 1 by the composite of 2 and 3 is expressible in terms of the wave function F(Pi) of A [see Eqs. (3.5)] by the relation ^( 1) (P23,Pi) = ^(^3)^(P 1 )[^23 2 +!Pi 2 -M£]~1. (1)

A three body model for 11 Li proposed earlier ͓S. Dasgupta et al., Phys. Rev. C 50, R510 ͑1994͔͒ employing separable potentials for n-n and n-9 Li interactions has been extended to study the recently observed excited states in 11 Li above the three body breakup threshold. The n-9 Li potential used here includes both s-and p-state interactions so as to incorporate the virtual s-state and p-wave resonance observed experimentally. The resulting coupled integral equations for the spectator functions have been computed using the method of rotating the integral contour of the kernels in the complex plane. The model predicts the ground state energy as well as the three excited states in reasonable agreement with the data recently obtained. Dynamical content of the two body input potentials in the three body wave function has also been analyzed through the threedimensional plots.

The three-body formalism, using separable potentials in s and p states of nucleon pairs, is set up under the conditions of full antisymmetrization of the three-nucleon wave function. The formalism is applied to the problem of n-d scattering, where the effects of "polarization" are fully taken into account. The amplitudes for quartet and doublet scattering are found to satisfy two-and four-coupled one-dimensional integral equations, respectively. The quartet scattering length is found to agree with the figure for the so-called experimental set I for this parameter. The doublet scattering length, on the other hand, is found to be much more sensitive to the details of the potentials, thus preventing a theoretical resolution of its ambiguity within the present formalism without tensor forces.