  A semi-relativistic Pauli-Fierz model is defined by the sum of the free
Hamiltonian $H_{\rm f}$ of a Boson Fock space, an nuclear potential $V$ and a
relativistic kinetic energy: $$
H=\sqrt{[\sigma\cdot(\mathbf{p}+e\mathbf{A})]^2+M^2} - M + V + H_{\rm f}. $$
Let $-e_0<0$ be the ground state energy of a semi-relativistic Schr\"odinger
operator $$ H_{\rm p}=\sqrt{\mathbf{p}^2+M^2} - M + V. $$
  It is shown that the ionization energy $E^{\rm ion}$ of $H$ satisfies
$$E^{\rm ion}\geq e_0>0$$ for all values of both of the coupling constant
$e\in\mathbb{R}$ and the rest mass $M\geq 0$. In particular our result includes
the case of M=0.
