The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing

Details The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing

2010-11-16

arxiv.org/abs/1011.3691v1

J.Phys.Conf.Ser.284:012020,2011

Physics

Nuclear Physics

Nuclear Theory

Submitted to the proceedings of the Group28 conference (Newcastle-upon-Tyne, UK). Journal of Physics: Conference Series

Scientific paper

10.1088/1742-6596/284/1/012020

A connection is made between the exact eigen states of the BCS Hamiltonian and the predictions made by the Tamm-Dancoff Approximation. This connection is made by means of a parametrised algebra, which gives the exact quasi-spin algebra in one limit of the parameter and the Heisenberg-Weyl algebra in the other. Using this algebra to construct the Bethe Ansatz solution of the BCS Hamiltonian, we obtain parametrised Richardson-Gaudin equations, leading to the secular equation of the Tamm-Dancoff Approximation in the bosonic limit. An example is discussed in depth.

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