Examples of rank two aCM bundles on smooth quartic surfaces in $\mathbb{P}^3$

Let \(F\subseteq {\mathbb {P}^{3}}\) be a smooth quartic surface and let \({\mathcal {O}}_F(h):={\mathcal {O}}_{{\mathbb {P}^{3}}}(1)\otimes {\mathcal {O}}_F\). In the present paper we classify locally free sheaves \({\mathcal {E}}\) of rank 2 on F such that \(c_1({\mathcal {E}})={\mathcal {O}}_F(2h), c_2({\mathcal {E}})=8\) and \(h^1\big (F,{\mathcal {E}}(th)\big )=0\) for \(t\in \mathbb {Z}\). We also deal with their stability.