1202.3986 (R. Id Betan)

Exact Eigenvalues of the Pairing Hamiltonian Using Continuum Level
Density    [PDF]

R. Id Betan

The pairing Hamiltonian constitutes an important approximation in many-body
systems, it is exactly soluble and quantum integrable. On the other hand, the
continuum single particle level density (CSPLD) contains information about the
continuum spectrum of energy of the system. The question if one could use the
constant pairing strength for particles correlations in the continuum is still
unanswered. In this paper we generalized the Richardson exact solution for the
pairing Hamiltonian in order to include correlation with the continuum spectrum
of energy. The resonant and non-resonant continuum is included through the
CSPLD relative to the free particles energy. The resonant correlations is made
explicit by using the Cauchy theorem. Low lying states with seniority zero and
two were calculated for the even Carbon isotopes. We concluded that energy
levels can be calculated with the constant pairing in the continuum using the
CSPLD. It was found that the nucleus $^{24}$C is unbound. The real and complex
energy representation of the continuum is developed and its differences are
shown. The trajectory of the pair energies in the continuum for the nucleus
$^{28}$C is shown.

View original: http://arxiv.org/abs/1202.3986