# Four-Divergence of a massive vector field in the interaction term

In an exercise is given the following Lagrangian $$\mathcal{L} = -\frac{1}{4}F^{\mu\nu}F_{\mu\nu} + \frac{1}{2}MA^\mu A_\mu + \bar\psi(i\gamma^\mu\partial_\mu - m)\psi + \mathcal{L}_{int}$$ with the following interaction term $$\mathcal{L}_{int} = k\,\bar\psi(c_V+ic_A\gamma_5)\psi\,\partial_\mu A^\mu$$ Assuming that $$\mathcal H_{int} = -\mathcal L_{int}$$, it's asked at first, to evaluate the expected value: $$\langle0|\partial_\mu A^\mu|a_{(\lambda)}(k)\rangle$$ where $$|a_{(\lambda)}(k)\rangle$$ is a state with one vector particle of momentum $$k$$ and polarization $$\lambda$$.
Then it's asked to derive the Feynman rules for this theory.
How shall I deal with this kind of derivative interaction term, since I know that it has to vanish $$\partial_\mu A^\mu= 0$$ on the free field solution (also related to $$k^\mu \epsilon_\mu^\lambda = 0$$ for $$\lambda = 1,2,3$$)?