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.
Categories: math-ph math.MP