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One-body and Two-body Fractional Parentage Coefficients for Spinor Bose–Einstein Condensation |
| BAO Cheng-guang |
| Department of Physics, SUN Yet-sen University, Guangzhou 510275, China |
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Abstract A very effective tool, namely, the analytical expression of the fractional parentage coefficients (FPC), is introduced in this paper to deal with the total spin states of N-body spinor bosonic systems, where N is supposed to be large and the spin of each boson is one. In particular, the analytical forms of the one-body and two-body FPC for the total spin states with {N} and {N-1,1} permutation symmetries have been derived. These coefficients facilitate greatly the calculation of related matrix elements, and they can be used even in the case of N→∞. They appear as a powerful tool for the establishment of an improved theory of spinor Bose Einstein condensation, where the eigenstates have the total spin S and its Z-component being both conserved.
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Issue Date: 05 March 2006
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