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In fact, that paper reports the doublet and quartet p − d scattering lengths considering the Coulomb potential in s -wave (the given values are 0 . 16 fm and 13 . 75 fm, respectively). After the correction introduced by using the KVP and considering the complete Coulomb potential, the results from Ref. [16] are 0 . 003 fm and 13 . 95 fm, respectively. They are in close agreement with the results obtained here and given in Table II. It is worth noting that the use of the integral relations permits a correct computation of the p − d phase-shifts in the energy range [0 , E$_{d}$ ], after a diagonalization procedure of the Hamiltonian using square integrable basis functions. 

In the last example of this Section, we explore the possibility of extracting p − d phase- shifts from a calculation in which the Coulomb potential has been screened at a certain distance, as we have already done for the two body case. In the three nucleon system, we define the screened Coulomb potential as 

with r$_{ij}$ the interparticle distance between nucleons ( i, j ). Using the PHH method, we solve a p − d scattering problem using the screened potential and, therefore, the asymptotic behavior is of the form of Eq. (41), with F$_{0}$ and G$_{0}$ the regular and irregular Bessel functions. For different values of n and r$_{sc}$ we calculate the scattering wave function Ψ n,r$_{sc}$ k and, using the integral relations, we determine the Coulomb phase shift. Similarly to what we have done in the two-body case, the integral relations are 

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In H the unscreened Coulomb potential is included and the asymptotic functions F$_{k}$ and ˜ G$_{k}$ are given in Eq. (41) in terms of the Coulomb functions F$_{0}$, G$_{0}$ . The results are shown in Fig. 6 for the case of J = 3 / 2 + at E$_{cm}$ = 2 MeV. The second order estimates [tan δ$_{c,k}$ ] 2 nd are given for different values of n as a function of r$_{sc}$ . For n > 4 and r$_{sc}$ ≈ 30 fm, the results are in complete agreement with the value obtained solving the p − d case without any screening of the Coulomb potential, tan δ$_{c}$ = − 2 . 1037, which is shown as a straight line in the figure. This method can be compared to the method given in Ref. [20] in which the Coulomb potential was screened using the same screening function as in Eq. (47) and 

