- th / 0 40 40 42 v 1 1 6 A pr 2 00 4 Classification of states of single - j fermions with J - pairing interaction

uc l - th / 0 40 40 42 v 2 7 J ul 2 00 4 Classification of states of single - j fermions with J - pairing interaction

In this paper we show that a system of three fermions is exactly solvable for the case of a single-j in the presence of an angular momentum-J pairing interaction. On the basis of the solutions for this system, we obtain new sum rules for six-j symbols. When the Hamiltonian contains only an interaction between pairs of fermions coupled to spin J = J max = 2j − 1, the " non-integer " eigenvalues ...

ar X iv : n uc l - th / 0 40 40 46 v 1 1 6 A pr 2 00 4 Analytical relationship for the cranking inertia

The wave function of a spheroidal harmonic oscillator without spin-orbit interaction is expressed in terms of associated Laguerre and Hermite polynomials. The pairing gap and Fermi energy are found by solving the BCS system of two equations. Analytical relationships for the matrix elements of inertia are obtained function of the main quantum numbers and potential derivative. They may be used to...

0 30 40 38 v 1 1 4 A pr 2 00 3 Number of states with fixed angular momentum for identical fermions and bosons

We present in this paper empirical formulas for the number of angular momentum I states for three and four identical fermions or bosons. In the cases with large I we prove that the number of states with the same M and n but different J is identical if I ≥ (n − 2)J − 1 2 (n − 1)(n − 2) for fermions and I ≥ (n − 2)J for bosons, and that the number of states is also identical for the same M but di...

ar X iv : n uc l - th / 0 30 40 52 v 1 1 6 A pr 2 00 3

- th / 0 40 40 46 v 2 1 8 A pr 2 00 4 Analytical relationship for the cranking inertia

The wave function of a spheroidal harmonic oscillator without spin-orbit interaction is expressed in terms of associated Laguerre and Hermite polynomials. The pairing gap and Fermi energy are found by solving the BCS system of two equations. Analytical relationships for the matrix elements of inertia are obtained function of the main quantum numbers and potential derivative. They may be used to...