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A multi-energy phase shift analysis of all published proton-proton (pp) scattering data in the energy range T lab ≤ 30 MeV is presented. In the description of all partial waves the well-known long range interaction is included: the improved Coulomb, the vacuum polarization, and the one-pion-exchange potential. In the lower partial waves the energy-dependent analysis uses a P-matrix parametrization for the short range interaction. Special attention is paid to the electric interaction, the definition of the phase shifts and the selection of the data. The fit to the final data set comprising 360 scattering observables results in χ 2 /N df = 1.0, where N df is the number of degrees of freedom. The ppπ 0-coupling constant is determined to be g 2 ppπ 0 /4π = 14.5 ± 1.2, but there are several indications for a lower value. The optimum value for the P-matrix radius b ≈ 1.4 fm is satisfying. Single-energy phase shifts with second derivative matrices, and effective range parameters are given.

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In an energy-dependent phase-shift analysis of all low-energy np scattering data below 7^ -30 MeV we reach ^VTVDF^I.I, where /VDF is the number of degrees of freedom. In our fit we determine the Smatrix elements in the coupled 3 Si + 3 Z>i channels, which allows us to compute the residue at the deuteron pole. Expressed in terms of the deuteron parameters, we find for the asymptotic normalization of the 3 Si state ^5=0.8838(4) fm~1 /2 and for the asymptotic D/S ratio 77=0.027 12(22). Compared with other determinations, there seems to be some indication for the presence of closed isobar channels and/or energy-dependent potentials in the deuteron system. PACS numbers: 21.40.+d, 13.75.Cs, 27.10.+h For several years now there has been a renewed interest in the precise determination of the deuteron parameters. These serve as an important constraint on the description of the np interaction. Special attention 1_12 has been given to the asymptotic ZMo-S-state ratio r\ and, more recently, to the asymptotic normalization As of the S state. 13,14 Most of the determinations of these two quantities come from analyses of either pd elastic scattering or (d,p) stripping reactions and ip,d) pickup reactions on various nuclei. Some discrepancies between the various determinations have shown up, especially for the value of r/.In this Letter we present a very accurate determination of r\ and As with the help of an energy-dependent phase-shift analysis of all np scattering data below 7^ -30 MeV. In this way the values for As and r\ are obtained purely from the two-body np scattering data, thereby circumventing the typical many-body problems arising in many of the other analyses.In our phase-shift analysis the scattering matrix S and the K matrix are determined, where S s= (\+iK)(\ -iK)~x.To study the deuteron, special attention is given to the coupled 3 S\ + ^D\ channels. Time-reversal invariance allows us to choose the relative phases between the 3 S\ and the 3 D\ channel such that the S and K matrices are symmetric above as well as below the threshold £=0, with E = (k 2 + M?) U2 +(k 2 + Mt) l/2 -(M p + M n ) the cm. energy, k the relative cm. momentum, and M p and M n the proton and neutron mass, respectively. Unitarity requires that above the threshold (E > 0, k > 0) the S matrix is unitary, and therefore the K matrix Hermitean. Below the threshold (E < 0), the S matrix is real and the K matrix purely imaginary. The S and K matrices can be diagonalized simultaneously by a real, orthogonal matrix cose" -sine [sine cose-J'where e is the Blatt and Biedenharn 15 mixing parameter.The eigenvalues of S and K are ^=exp(2/^) and Kx=tand\ with X=0 or 2, and 8x the Blatt and Biedenharn eigenphase shifts. Next we introduce the projection operators P\*=P 2 on the scattering eigenstates, where Po+Pi-l and cos 2 e~ cosesine*[cose-sine sin z 6 J This allows us to write S =2ASJ 1 /\ and K^Y^xK^P^.The existence of the deuteron at 16 E = -B = -2.224575(9) MeV means that in the complex momentum plane the eigenvalue So has a pole at k =m, and so at ...

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