One dimensional BCS Hamiltonian in Hg_3-δAsF₆

The structure of the linear chain compound Hg_3-δAsF₆ gives rise to an unusual electron-phonon interaction which leads to a reduced BCS Hamiltonian. The effective electron-electron interaction exists only when the two electrons of a Cooper-pair jump together from one chain to the next. The calculation on the paraconductivity due to this unusual Hamiltonian is briefly reviewed and the diamagnetic susceptibility is calculated. When the two-dimensional flucturation of Cooper-pairs along the a- and b-chains is assumed, the susceptibility χ_c for a field H in the c-direction is larger than χ_a,b (H in the a-b plane).