390
8 No-Core Gamow Shell Model
potential. The method is iterated until convergence, by replacing V
(0)
aux by V aux and
restarting the previously described procedure, up to the physical value of V aux = 0.
This allows to follow Hamiltonian eigenstates adiabatically through the region
of very strong continuum couplings. The precision of this adiabatic identification
procedure has been checked to be nearly exact for a dineutron system [127].
One will calculate the ground states of trineutron and tetraneutron using the
auxiliary potential method. In these calculations, both resonance and continuum
basis states are included, so that one can calculate energies and widths of multineutron systems. Model spaces are defined by 3p-3h and 4p-4h truncations, as in
Sect. 8.3.1. One uses the so-called large model space, where Slater determinants
are built from s 1/2 , p 3/2 Berggren basis partial waves and p 1/2 , f 5/2 , f 7/2 , g 9/2
harmonic oscillator partial waves. In the small model space, one builds Slater
determinants using the same partial waves as in the large model space, but the
p 1/2 , d 3/2 , d 5/2 and f 5/2 , f 7/2 , g 9/2 partial waves are represented only with two
and one harmonic shells, respectively. Numerical tests showed that the dineutrons
channel does not open when decreasing V aux , so that eigenenergies can be expected
to smoothly vary when V aux → 0.
The Gamow shell model code based on the two-dimensional partitioning method
(see Sect. 5.8) has been employed to calculate the Hamiltonian ground state.
The single-particle Berggren basis is generated by the finite-depth Woods–Saxon
potential including spin–orbit coupling and the chiral two-body interaction N 3 LO
[132], as in Sect. 8.3.1.
As can be seen in Fig. 8.8, it was not possible to calculate tetraneutron energies
in the large model space beyond the value of V aux = −1.5 MeV. The physical region
(V aux = 0) could be reached only in truncated spaces, either using a reduced number
of shells, denoted as “small” in Fig. 8.8, or using 3p-3h truncations. Consequently,
one still does not have a definitive result for the tetraneutron energy with realistic
interactions, and one has to rely on extrapolations, as it was done in Sect. 8.3.1.
Both the auxiliary potential method and the density matrix renormalization
group approach (Sect. 8.3.1), predict similar tetraneutron energy, close to 2.6 MeV,
which is within the range of the experimental error [116]. The calculation of the
trineutron ground state is converged in a full space, i.e. without truncation on
the number of neutrons in the continuum, where one obtains E 3n = 1.29 MeV
and Γ 3n = 0.91 MeV. The energy and width of the trineutron, obtained with the
confining potential, is smaller than that of the tetraneutron, while being larger than
that of the dineutron. Consequently, it is plausible that the trineutron resonance
lives longer than the tetraneutron resonance and, hence, the chance to observe it
experimentally are bigger.
8 No-Core Gamow Shell Model
potential. The method is iterated until convergence, by replacing V
(0)
aux by V aux and
restarting the previously described procedure, up to the physical value of V aux = 0.
This allows to follow Hamiltonian eigenstates adiabatically through the region
of very strong continuum couplings. The precision of this adiabatic identification
procedure has been checked to be nearly exact for a dineutron system [127].
One will calculate the ground states of trineutron and tetraneutron using the
auxiliary potential method. In these calculations, both resonance and continuum
basis states are included, so that one can calculate energies and widths of multineutron systems. Model spaces are defined by 3p-3h and 4p-4h truncations, as in
Sect. 8.3.1. One uses the so-called large model space, where Slater determinants
are built from s 1/2 , p 3/2 Berggren basis partial waves and p 1/2 , f 5/2 , f 7/2 , g 9/2
harmonic oscillator partial waves. In the small model space, one builds Slater
determinants using the same partial waves as in the large model space, but the
p 1/2 , d 3/2 , d 5/2 and f 5/2 , f 7/2 , g 9/2 partial waves are represented only with two
and one harmonic shells, respectively. Numerical tests showed that the dineutrons
channel does not open when decreasing V aux , so that eigenenergies can be expected
to smoothly vary when V aux → 0.
The Gamow shell model code based on the two-dimensional partitioning method
(see Sect. 5.8) has been employed to calculate the Hamiltonian ground state.
The single-particle Berggren basis is generated by the finite-depth Woods–Saxon
potential including spin–orbit coupling and the chiral two-body interaction N 3 LO
[132], as in Sect. 8.3.1.
As can be seen in Fig. 8.8, it was not possible to calculate tetraneutron energies
in the large model space beyond the value of V aux = −1.5 MeV. The physical region
(V aux = 0) could be reached only in truncated spaces, either using a reduced number
of shells, denoted as “small” in Fig. 8.8, or using 3p-3h truncations. Consequently,
one still does not have a definitive result for the tetraneutron energy with realistic
interactions, and one has to rely on extrapolations, as it was done in Sect. 8.3.1.
Both the auxiliary potential method and the density matrix renormalization
group approach (Sect. 8.3.1), predict similar tetraneutron energy, close to 2.6 MeV,
which is within the range of the experimental error [116]. The calculation of the
trineutron ground state is converged in a full space, i.e. without truncation on
the number of neutrons in the continuum, where one obtains E 3n = 1.29 MeV
and Γ 3n = 0.91 MeV. The energy and width of the trineutron, obtained with the
confining potential, is smaller than that of the tetraneutron, while being larger than
that of the dineutron. Consequently, it is plausible that the trineutron resonance
lives longer than the tetraneutron resonance and, hence, the chance to observe it
experimentally are bigger.