# Feynman diagrams for neutron-neutron scattering

Neutron-neutron scattering can be described using the phenomenological Lagrangian $$\mathcal L_I=g \pi^0(x)\bar\psi_n(x)\gamma^5\psi_n(x).$$ Since the Lagrangian contains three fields and the process $$n+n\to n+n$$ involves four particles (let $$p_1,k_1$$ and $$p_2,k_2$$ be the momenta of the 'in' and 'out' pairs respectively), the terms in $$g^2$$ are the lowest that contribute to the scattering amplitude: the corresponding Feynman diagrams are

However, I have a small doubt. Why is there no diagram with $$p_1$$ and $$k_1$$ entering the same internal vertex?

There is no s-channel scattering between neutrons because it would require the intermediate steps $$\rm nn\to\pi^0$$ and $$\pi^0 \to \rm nn$$, which violate baryon number conservation.