results are shown in Fig. 7 as solid points on the effective range line. We observe a perfect agreement between the 23 points and the exact results given by the straight line. In the solution of the same problem using the PHH basis, we have used M = 24 (see Table III) and obtained six negative eigenvalues. With the HA expansion, using M = 60, we obtain a much denser spectrum covering the whole energy range [0 ,E$_{d}$ ] below the breakup into three particles. The description of scattering states from the KVP has not been used in the literature as much as the equivalent form for bound states, the Rayleight-Ritz variational principle. A possible explanation for this is the different care that is required at the moment of describing the asymptotic structure of the system. For example, when a complete basis is used to describe an A -body bound state, the main condition for the basis elements is that they be square integrable. Elements having gaussian or exponential tails are often used. It is well known that these bases do not describe correctly the asymptotic structures as the distances between the particles increase. However the error introduced by these configurations in the computation of the binding energies is small. Conversely the extraction of the asymptotic constants could be problematic if the number of basis states is not sufficiently high (see for example Refs. [3, 29]). The situation drastically changes when the KVP is considered. The asymptotic structure of the system has to be introduced in an exact form in the trial wave function Ψ$_{t}$ otherwise the matrix element < Ψ$_{t}$ | H − E | Ψ$_{t}$ > could well not be finite. In other words, Ψ$_{t}$ has to satisfy asymptotically that ( H − E )Ψ$_{t}$ = 0. Formally Ψ$_{t}$ can be decomposed in an internal and in an asymptotic part as in Eq. (13). Then, the internal part of Ψ$_{t}$ can be expanded over a square integrable basis. However, the necessity of taking care explicitly of the (sometimes very complicated) asymptotic structures has limited the application of the KVP. The reformulation of the KVP, given in Eq. (14), to the form given in Eq. (21) changes this situation. The KVP, given in terms of integral relations, does not necessitate the explicit introduction of the correct asymptotic behavior in Ψ$_{t}$. The two integrals involved, < Ψ$_{t}$ | H − E | F > and < Ψ$_{t}$ | H − E | ˜ G > , go very fast to zero since F and ˜ G are asymptotic solutions of the Schr¨ odinger equation. Therefore, the only condition necessary to obtain accurate second order estimates through the integral relations is that 20 VI. CONCLUSIONS