8.2 Benchmarking of No-Core Gamow Shell Model Against Other Methods
373
8.2
Benchmarking of No-Core Gamow Shell Model Against
Other Methods
To benchmark the no-core Gamow shell model, one will compare results for the
ground state energy of 3 H and 4 He obtained using the Jacobi–Davidson method
with results issued from the harmonic oscillator no-core shell model using the
Lanczos method. Both 3 H and 4 He are well-bound systems so that results of the nocore Gamow shell model can be compared against other well-known bound states
methods. The numerical task in solving a three and four nucleon system is relatively
easy so that one can check the convergence with respect to the maximal angular
momentum of the model space.
8.2.1 Binding Energies and Center-of-Mass Excitations
One will demonstrate in this section that the generalized variational principle can
be applied with the Berggren basis, i.e. that the binding energies of ground states in
truncated shell model spaces converge to their exact value in infinite space. One will
also study the center-of-mass properties of no-core Gamow shell model many-body
states in details.
In Fig. 8.1, one compares results of the no-core Gamow shell model with
results of the Faddeev calculations obtained using the Argonne υ 18 . Calculations
are performed using s 1/2 , p 3/2 , p 1/2 , d 3/2 , d 5/2 , f 7/2 , f 5/2 , g 9/2 , g 7/2 partial
Energy (MeV)
Fig. 8.1 (Color online) 3 H results as a function of the (maximum) angular momentum, in the
interval from = 0 to = 4 using the Argonne υ 18 interaction (from Ref. [94])
373
8.2
Benchmarking of No-Core Gamow Shell Model Against
Other Methods
To benchmark the no-core Gamow shell model, one will compare results for the
ground state energy of 3 H and 4 He obtained using the Jacobi–Davidson method
with results issued from the harmonic oscillator no-core shell model using the
Lanczos method. Both 3 H and 4 He are well-bound systems so that results of the nocore Gamow shell model can be compared against other well-known bound states
methods. The numerical task in solving a three and four nucleon system is relatively
easy so that one can check the convergence with respect to the maximal angular
momentum of the model space.
8.2.1 Binding Energies and Center-of-Mass Excitations
One will demonstrate in this section that the generalized variational principle can
be applied with the Berggren basis, i.e. that the binding energies of ground states in
truncated shell model spaces converge to their exact value in infinite space. One will
also study the center-of-mass properties of no-core Gamow shell model many-body
states in details.
In Fig. 8.1, one compares results of the no-core Gamow shell model with
results of the Faddeev calculations obtained using the Argonne υ 18 . Calculations
are performed using s 1/2 , p 3/2 , p 1/2 , d 3/2 , d 5/2 , f 7/2 , f 5/2 , g 9/2 , g 7/2 partial
Energy (MeV)
Fig. 8.1 (Color online) 3 H results as a function of the (maximum) angular momentum, in the
interval from = 0 to = 4 using the Argonne υ 18 interaction (from Ref. [94])