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In these notes we construct the momentum-space potentials fromconfiguration-space using for the Fourier-transformation theGaussian-Expansion-Method (GEM). This has the advantage that the Fourier-Besselintegrals can be performed analytically, avoiding possible problems with theoscillations in the Bessel functions for large r, in particular for $p_f \neqp_i$. The mass parameters in the exponentials of the Gaussian base-functionsare fixed using the geometric progression recipe of Hiyama-Kamimura. Thefitting of the expansion coefficients is linearly and very fast. Application tonucleon-nucleon is given in detail for the recent Extended-soft-core modelESC08c. The NN phase shifts obtained by solving the Lippmann-Schwingerequations agree very well with those obtained in configuration-space solvingthe Schr\"{o}dinger equations.

Momentum-space Lippmann-Schwinger-Equation, Fourier-transform with Gauss-Expansion-Method