] Nuclear Physics A133 (1969) 590--592; (~) North-HollandPublishiny Co., Amsterdam 1.B I Not to be reproduced by photoprint or microfilm without written permission from the publisher TEST OF THE NEW TABAKIN N-N SEPARABLE POTENTIALS IN THE 3-N SYSTEM V. A. ALESSANDRINI International Centre for Theoretical Physics, Trieste, Italy on leave of absence from Universidad de La Plata, Argentina and C. A. GARC[A CANAL tt International Centre for Theoretical Physics, Trieste, Italy on leave of absence from Universidad de La Plata, Aryentina Received 13 February 1969 Abstract: A new set of rank one nucleon-nucleon separable potentials, which contain both a short- range repulsion and a long-range attraction suggested by Tabakin, are studied by using them in solving the Faddeev equations for the three-nucleon system. It is a well-known fact that, using separable potentials to describe the two-body interactions, the three-body problem can be reduced to a multichannel two-body problem (and solved exactly using numerical techniques), the number of channels being proportional to the rank of the two-body separable potential 1). In the past few years, separable potentials have been used extensively to perform calculations in the three-nucleon system 2). An excellent description of the properties of the 3-N system at low energies can be obtained by using Yamaguchi type potentials with ten- sor forces in the 3S1 state, and a rank two potential in the 1So state to describe a long- range attraction and a short-range repulsion (hard-core effect) a). It has been recently suggested by Tabakin 3) that it is possible to describe a long- range attraction together with a short-range repulsion using only a rank one separable potential. This amounts to a great simplification in the three-body problem. The potential proposed by Tabakin is of the form h z 1 V(k, k') = 9(k)g(k'), (1) m 2z~ z and the form factors are given by o(k) = h(k2-k z) k2+d2 1 (2) k2+b z k4+a 4 The zero of 9(k) at k = k c produces a change of sign in the phase shift at the cor- responding energy of Ec = hZk2/m. As shown by Tabakin, ~/2a-1 is the range of t Member of the National Research Council of Argentina. *t Fellow of the National Research Council of Argentina. 59O