**What is meant by the "general formula for the scattering process"?**

To be more concrete, in an old exercise my lecturer gave me, I am told to give the general formula for the scattering process $a_1 + a_2 \to b_1 + b_2$ , based on the Lagrangian for a scalar Yukawa Scattering:

$$\mathcal{L}= \frac{1}{2} \partial_\mu \phi \partial ^\mu \phi - \frac{1}{2} m^2 \phi^2 + \partial_\mu \varphi^* \partial^\mu \varphi - M^2 \varphi^* \varphi - g \varphi^* \varphi \phi - g\phi^3$$

*where $\varphi ,\bar{\varphi}$ are associated to a complex scalar field and $\phi$ is associated to a real scalar field.*

**Is the general formula for the scattering process the amplitude for the process, or has it got a completely different meaning?**