272
6 Physical Applications of the Gamow Shell Model
1.2
1.3
1.4
1.5
1.6
1.7
-5.5
-5.0
-4.5
-4.0
-3.5
2
3
4
5
6
7
8
9 10
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
0
+
6 He g.s.
1
+
6 Li g.s.
0
+
6 Be g.s.
E (MeV)
GCC
GSM
(a)
(b)
(c)
Fig. 6.12 Comparison of convergence rates for ground state energies with respect to different
maximum angular momenta max in A = 6 nuclei: 6 Be (panel (a)), 6 Li (panel (b)), and 6 He
(panel (c)). Calculations are performed in the three-body model using Jacobi coordinates (denoted
as GCC, for Gamow translationally invariant coupled channels) and cluster orbital shell model
coordinates (denoted as GSM, for Gamow shell model). max denotes the maximal single-particle
orbital angular momentum for cluster orbital shell model and max( x , y ) for the three-body model
using Jacobi coordinates. The error bars stand for the decay widths (from Ref. [95])
Figure 6.12 illustrates the convergence rate for the ground state energies with
respect to model spaces bearing different maximal angular momentum max in the
three-body model in Jacobi coordinates and cluster orbital shell model coordinates.
The ground state energies of 6 He and 6 Be are in good agreement with experimental
data. On the contrary, 6 Li is overbound because the Minnesota interaction has no
explicit dependence on the isospin T of two-nucleon systems. The model spaces
of cluster orbital shell model and Jacobi-coordinate framework are not exactly
the same since different coordinate systems are used in these two approaches.