Solution to the eigenstates of pairing Hamiltonian in finite nuclei

YU Yi; GUO Jian-You

doi:10.1088/1674-1137/33/S1/042

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2024年10月30日

Chinese Physics C> 2009, Vol. 33> Issue(S1) : 134-136 DOI: 10.1088/1674-1137/33/S1/042

Solution to the eigenstates of pairing Hamiltonian in finite nuclei

YU Yi ^, ,
GUO Jian-You

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Abstract：
We apply the algebraic Bethe technique to the nuclear pairing problem with certain limits. We obtain the exact energies and eigenstates, and find the symmetry between the states corresponding to less and more than half full shell. We also proved that the problem of solving BAE can be transformed into the problem of finding the roots of a hypergeometric polynomial, which is much
simpler.

References

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. Richardson R W. Phys. Rev., 1967, 159: 7922. Kerman A K. Ann. Phys. (NY), 1961, 12: 300; Kerman AK, Lawson R D, MacFarlane M H. Phys. Rev., 1961, 124:1623. Balantekin A B, Dereli T, Pehlivan Y. J. Phys. G, 2004,30: 12254. Stieltjes T J. 1914 Sur Quelques Theoremess d'Algebre,Oeuvres Completes, V.11 (Groningen:Noordho )5. Higher Transcendental Functions, Volume 1. Ed. A. Erde-lyi, McGraw-Hill, 19536. PAN F, Draayer J P, Ormand W E. Phys. Lett. B, 1998,422: 1

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YU Yi and GUO Jian-You. Solution to the eigenstates of pairing Hamiltonian in finite nuclei[J]. Chinese Physics C, 2009, 33(S1): 134-136. doi: 10.1088/1674-1137/33/S1/042

YU Yi and GUO Jian-You. Solution to the eigenstates of pairing Hamiltonian in finite nuclei[J]. Chinese Physics C, 2009, 33(S1): 134-136. doi: 10.1088/1674-1137/33/S1/042 shu

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Received: 2008-10-23
Revised: 1900-01-01

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Solution to the eigenstates of pairing Hamiltonian in finite nuclei

YU Yi ^,
GUO Jian-You

Corresponding author: YU Yi,

Received Date: 2008-10-23
Accepted Date: 1900-01-01
Available Online: 2009-01-10

Abstract: We apply the algebraic Bethe technique to the nuclear pairing problem with certain limits. We obtain the exact energies and eigenstates, and find the symmetry between the states corresponding to less and more than half full shell. We also proved that the problem of solving BAE can be transformed into the problem of finding the roots of a hypergeometric polynomial, which is much
simpler.