It should be observed that in the present case, due to the definition of the asymptotic behavior of Ψ$_{k}$, we have ( m/ ℏ $^{2}$) < Ψ$_{k}$ |G k > = 1. In Table II, the $^{3}$H and $^{3}$He bound states and the doublet and quartet n-d and p-d scat- tering lengths, corresponding to the MT I-III potential, are given in terms of the number M of Laguerre polynomials used in the expansion of the hyperradial functions. The calculations have been done using K = 16 which corresponds to 18 (9) hyperradial functions in the case of J = 1 / 2 + ( J = 3 / 2 $^{+}$). With M = 24, an accuracy better than 1 keV is obtained for the bound state energies and of the order of 0 . 001 fm for the scattering lengths. In Figs. 4 and 5 the J = 1 / 2 $^{+}$, 3 / 2 $^{+}$, l = 0, phase shifts δ are given as a function of the energy in the form of the effective range functions for n − d and p − d , respectively. Following Ref. [27], for n − d scattering this function is defined as ( E 0 = E − E$_{d}$ ) whereas for p − d scattering it is defined as where η is the Coulomb parameter, C 2 0 = 2 πη/ (e 2 πη − 1) and h ( η ) = − ln( η ) + Re ψ (1 + iη ) ( ψ is the digamma function). The solid line in the figures represents these two functions obtained solving Eqs.(42,43) for several values of the center of mass energy E 0 in the interval [0 , | E$_{d}$ | ]. The solid points in the figures are the results obtained from the integral relations using bound state wave functions as explained below. The capability of the PHH to produce a very accurate description of bound and scattering states can be used to study different applications of the integral relations. The lowest eigenvalue after the diagonalization procedure of Eq. (40) corresponds to the three-nucleon bound state energy of $^{3}$H ( T$_{z}$ = − 1 / 2) or $^{3}$He ( T$_{z}$ = 1 / 2). However more negative eigenvalues could appear. For example, in the case of K = 16, M = 24 and β = 1 fm − $^{1}$, six negative eigenvalues E$_{n}$ appear satisfying | E$_{n}$ | < | E$_{d}$ | . They are given in Table III transformed to the positive energies E 0 n = E$_{n}$ − E$_{d}$ . The corresponding eigenvectors Ψ$_{n}$ approximately describe a scattering process at the center of mass energy E 0 $_{n}$, though asymptotically they go to zero. In the following we use the index n to label these approximate scattering states and reserve the continuous index k to label those scattering states having the correct asymptotic behavior, as given by Eq. (41). We now consider the diagonalization of the Hamiltonian 15 K ( E $^{0}$) = C 2 $_{0}$( η ) k cot δ + 2 kηh ( η ) , (45) K ( E $^{0}$) = k cot δ (44)