6.5 Inclusion of Continuum Couplings in the Pairing Model
287
−G(MeV )
10
−13
10
−11
10
−9
10
−7
10
−5
10
−3
10
−1
δ(Γ)
0.0
0.2
0.4
0.6
0.8
1.0
10
−14
10
−12
10
−10
10
−8
10
−6
10
−4
10
−2
δ(E)
Fig. 6.16 The relative error of the ground state energy δ(E ) and width δ(Γ ) which are calculated
using the pair energies E i given by the generalized Richardson equations (6.39) and exact solution
of the Gamow shell model. Results for 2 and 3 pairs of fermions are shown with solid and dashed
line, respectively (from Ref. [130])
continuum for the considered resonance. The contour consists of the segments
k 0 = 0, k 1 = (0.1549, −0.14), k 2 = 1, k max = 2, in units of fm −1 , and is discretized
using the Gauss-Legendre quadrature procedure. One may notice a spike of the
relative error for the ground state width at certain values of the pairing strength.
At this discrete value of G, the imaginary part of the complex total energy (6.38)
calculated using the generalized Richardson approach (6.39) is equal to the Gamow
shell model energy. In general, both real and imaginary parts of the relative error of
the complex energy exhibit spikes. These spikes in δ(E ) and/or δ(Γ ) are found only