MULTIPLE PAIRING IN THE BCS MODEL

We study Cooper's paring for more than two particles in terms of the BCS model. We consider multiple pairing in terms of the BCS Hamiltonian in a quiescent Fermi sea model and in the BCS ground state. Although there is no interaction between Cooper's pairs in terms of the BCS Hamiltonian, yet we show that four particles are paired and form a bound state in the singlet state with just twice the bound state energy of a single Cooper's pair. Four-particle bound state - quartet only exists as a result of the Pauli principle and the sharp Fermi edge. We have also shown that the smearing of the Fermi edge due to Δ(k) as it is in the BCS ground state weakens the pairing of either two or four particles. We show that in the particle-hole channel there exists the multiple particle-hole resonance for four particles and four holes in a quiescent Fermi sea model similar to the resonance of two particles and two holes. There is no the particle-hole resonance in the BCS ground state as shown, which means that the particle-hole resonance is removed by Δ(k) due to smearing of the Fermi distribution. The wave function for the multiple pairing model is discussed as well.