An approach without partial wave expansion to calculate scattering of spin-0 and spin- 1 2 $\frac{1}{2}$ particles in high energy regions and those governed by long range interactions

Scattering of spin-0 and spin- 1 2 $\frac{1}{2}$ particles is formulated in momentum space based on basis states being not expanded in partial waves. No sequential calculations with increasing angular momentum are performed to reach physical convergence, which depends on the scattering energy and the interaction range. Both nonrelativistic and relativistic cases are described. We put forward for consideration the utilization of this approach. By taking some simple interaction models we show some advantages in calculations representing those of high energy scattering as well as those of scattering governed by long range interactions.