  The J-matrix inverse scattering nucleon-nucleon potentials (JISP), describing
both two-nucleon data and bound and resonant states of light nuclei to high
accuracy, are tested on the total photoabsorption cross sections of Deuteron,
Triton, 3He and 4He. The calculations in the three- and four-body systems are
carried out via the Lorentz integral transform method and the hyperspherical
harmonics (HH) technique. To this end the HH formalism has been adapted to
accommodate non-local potentials. The cross sections calculated with the JISP
are compared to those obtained with more traditional realistic interactions,
which include two- and three-nucleon forces. While the results of the two kinds
of potential models do not differ significantly at lower energies, beyond the
resonance peak they show fairly large discrepancies, which increase with the
nuclear mass. We argue that these discrepancies may be due to a probably
incorrect long range behavior of the JISP, since the one pion exchange is not
manifestly implemented there.
