Number-conserving algebraic method for pairing theory

Several powerful approaches to the study of pairing interactions are based on the relation of seniority conservation to the number-nonconserving algebra of quasi spins. In this note, we develop an algebraic number-conserving treatment utilizing the simplest number-conserving algebra, nonlinear under commutation, which follows from the quasi-spin algebra. The development is carried out in detail for a two-level model and yields encouraging numerical results in the simplest viable approximation consistent with the limit of strong pairing interaction.