On the Relativistic Pseudoscalar Meson Theory of the Deuteron

The existence of stationary states of the neutron-proton system is discussed on the basis of a two-particle Dirac equation, including a retarded pseudoscalar interaction. This interaction (in which the possibility of creation of nucleons pairs is disregarded) is treated according to two different models: in the first one, the negative energy states of each nucleon are supposed to be filled, and the interaction is limited to transitions between positive energy states only; in the second model, which is the generalization of the "one-particle" theory, the negative energy states are considered as empty. It is shown that, in both cases, no stable stationary state exists with such an interaction.