Journal of the Korean Physical Society, Vol. 64, No. 12, June 2014, pp. 1788∼1791 Inverse Scattering : Revisited S. A. Aldenfariya Department of Physics, University of Misurata, Misurata, Libya A. M. Awin ∗ Department of Mathematics, University of Tripoli, Tripoli, Libya (Received 21 March 2014, in final form 7 May 2014) Using recent data, we calculate the heavy-ion optical-model potential via an inversion solution that had been previously obtained based on the McIntyre parametrization of the S-matrix.The results are compared with previous works and with the recently-available experimental data for the 12 C - 12 C system. Moreover, the calculations were carried out for several energies not available before for the same system, these calculations need to be checked against future experimental data. PACS numbers: 25.55.Ci Keywords: Scattering potential, Woods-Saxon, Real part, Imaginary part, V(r), W(r) DOI: 10.3938/jkps.64.1788 I. INTRODUCTION The inversion solution to the heavy-ion optical-model potential was, given by Fayyad et al. [1] ,neglecting the Coulomb correction. The Coulomb correction was taken into account a little earlier than that by Rihan and Awin to get an approximate analytical expressions for the real part (V ) and the imaginary part (W ) of the potential [2]. The calculations were based on the McIntyre parametrization of the S-matrix; the obtained results are V (r)= -  4μE πkα  f (R ′ , Δ ′ ,r) (1) and W (r)= -  2E πkβ  f (R, Δ,r) (2) where f (x 0 ,a 0 ,x)= 1 1 + exp[(x - x 0 )/a 0 ] (3) E is the energy and k is the wave number.The other pa- rameters will be defined in conjunction with obtaining the potential. The above relations were obtained by in- version using the elastic-scattering s-matrix element χ(b) (b is the impact parameter) written in terms of the phase shift δ, which is directly related to the optical-model po- tential U (r) [1]. Note that V (r) and W (r) are of Woods- Saxon type potentials and are determined along with the ∗ E-mail: awinsus@yahoo.com parameters R, Δ, R ′ , and Δ ′ ; these with α and β are de- termined in terms of the phase shift parameters μ, b 0 , d, b ′ 0 , and d ′ . These details will be discussed in the next section. The results using the phase shift analysis [3] (available then) for three and five parameters were compared with the experimental Woods-Saxon potential for the sym- metric system of 12 C - 12 C at E lab = 1016 MeV and were found to be in good agreement [1,2]. Note that ignoring the Coulomb effects is justified by the fact that the en- ergy range of interest is in accordance with the Glauber’s high-energy approximation used for the present solutions [4]. In this paper, based on the light of recent phase-shift- analysis [5] data for the same system but now for many energies,we redo the calculations, ignoring the Coulomb effects, for three and five parameters and compare the results with the available experimental data [6,7].In the following section, we give some details regarding the sub- ject and in Section III we present our results. Finally we give a concluding discussion in Section IV. II. SOME DETAILS Using McIntyre parametrization [8] for the phase shift, one reaches the following relations between sets of the parameters : For the real part of the potential I 4 (R ′ , Δ ′ ) I 2 (R ′ , Δ ′ ) = 3 2 I 3 (b ′ 0 ,d ′ ) I 1 (b ′ 0 ,d ′ ) (4) -1788-