Heine-Stieltjes correspondence and a new angular momentum projection for many-particle systems
A new angular momentum projection for systems of particles with arbitrary spins is formulated based on the Heine-Stieltjes correspondence, which can be regarded as the solutions of the mean-field-plus -pairing model in the strong-pairing interaction G→∞ limit. Properties of the Stieltjes zeros of the extended Heine-Stieltjes polynomials, whose roots determine the projected states, and the related Van Vleck zeros are discussed. An electrostatic interpretation of these zeros is presented. As examples, applications to n nonidentical particles of spin 1/2 and to identical bosons or fermions are made to elucidate the procedure and properties of the Stieltjes zeros and the related Van Vleck zeros. It is shown that the new angular momentum projection for n identical bosons or fermions can be simplified with the branching multiplicity formula of U(N)↓O(3) and the special choices of the parameters used in the projection. Especially, it is shown that the solutions for identical bosons can always be expressed in terms of zeros of Jacobi polynomials. However, unlike nonidentical particle systems, the n-coupled states of identical particles are nonorthogonal with respect to the multiplicity label after the projection. © 2013 American Physical Society.
Publication Source (Journal or Book title)
Physical Review C - Nuclear Physics
Pan, F., Li, B., Zhang, Y., & Draayer, J. (2013). Heine-Stieltjes correspondence and a new angular momentum projection for many-particle systems. Physical Review C - Nuclear Physics, 88 (3) https://doi.org/10.1103/PhysRevC.88.034305