Scattering amplitude and cross-section of 2 scattering centres

Assume we have 2 identical particles at $z_1$ and $z_2$ and an incident plane wave propagating along $z$.
The scattering amplitude $f(theta)$ and differential cross section $sigma(theta)$ of individual particles are known where most of the scattering happens at small scattering angles. The particles are far apart $z_2-z_1=10lambda$, $lambda$ being the wavelength of the incident wave.
The scattering is weak so the incident plane wave is hardly affected by the scatterers.

Since the particles are a multiple of a wavelength apart, they interfere constructively. Summing up naively their scattering amplitudes $f_{tot}(theta)=2f(theta)$ would result in a total cross section $sigma_{tot}=4sigma$ instead of $2sigma$.

Is this expected or should the scattering amplitude of the system be written differently?