Electron-electron interactions in a thin toroid

A free-electron gas confined to a thin toroid is studied. Due to the cylindrical symmetry, the longitudinal angular momentum (L) is conserved in the electron-electron interactions. The Coulomb matrix elements, which satisfy the conservation of the transverse angular momentum (J), are much larger than the others. Therefore, the electronic excitations are well described by L and J. The L- and J-decoupled plasmons are investigated by evaluating the dielectric function within the random-phase approximation (RPA). They, respectively, correspond to the coherent plasma oscillations along the longitudinal and transverse directions. For the (L, J = 0) plasmons, the RPA results are almost the same with those of the Tomonaga model.