Nucleon-antinucleon potential due to the annihilation of one gluon

The short-range part of the interaction between nucleon and antinucleon due to one-gluon exchange is explicitly calculated in the framework of the quark model. This is a first step towards treating anihilation channels for $N\overline{N}$ systems. It is found that it gives a spin- and isospin-dependent repulsion. The relativistic effect due to a large momentum of quarks is also considered and found to enhance the strength of the potential. It is argued in connection with the nucleon-nucleon potential that the one-gluon-exchange potential would provide almost none of the characteristics of the nucleon-antinucleon interaction at short distances expected in the meson-exchange theory.