Gamow shell model and realistic nucleon-nucleon interactions

Hagen, G.; Hjorth‐Jensen, M.; Michel, N.

doi:10.1103/physrevc.73.064307

Cited by 79 publications

(118 citation statements)

References 57 publications

(159 reference statements)

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“…(35) and the two-body recoil term in Eq. (32) are expanded in a harmonic oscillator (HO) basis as their difference is short-ranged [14,41]. In our calculations, we took nine HO shells with the oscillator length b = 2 fm to carry out this expansion.…”

Section: Gsm Frameworkmentioning

confidence: 99%

Asymptotic normalization coefficients and continuum coupling in mirror nuclei

et al. 2012

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Background: An asymptotic normalization coefficient (ANC) characterizes the asymptotic form of a one-nucleon overlap integral required for description of nucleon-removal reactions.Purpose: We investigate the impact of the particle continuum on proton and neutron ANCs for mirror systems from p-and sd-shell regions. Method:We use the real-energy and complex-energy continuum shell model approaches.Results: We studied the general structure of the single-particle ANCs as a function of the binding energy and orbital angular momentum. We computed ANCs in mirror nuclei for different physical situations, including capture reactions to weakly-bound and unbound states. Conclusions:We demonstrated that the single-particle ANCs exhibit generic behavior that is different for charged and neutral particles. We verified the previously proposed relation [1] between proton and neutron mirror ANCs. We find minor modifications if the spectroscopic strength is either localized in a single state or broadly distributed. For cases when several states couple strongly to the decay channel, these modifications may reach 30%.

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Section: Gsm Frameworkmentioning

confidence: 99%

Asymptotic normalization coefficients and continuum coupling in mirror nuclei

et al. 2012

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“…In Ref. [8] it was also illustrated how matrix elements of the nucleon-nucleon interaction may be obtained in a Berggren basis by expanding the interaction in a finite oscillator basis, i.e. …”

Section: Gamow-hartree-fock Single-particle Basismentioning

confidence: 99%

“…However, the vector-bracket transformation coefficients are not easily continued in the complex kplane, and we therefore proceed via the numerically and mathematically simpler route outlined in Ref. [8]. In Ref.…”

Section: Gamow-hartree-fock Single-particle Basismentioning

confidence: 99%

“…The Berggren basis is an analytic continuation of the usual completeness relation in the complex energy plane. Recently, we reported the first results on loosely bound and resonant states in nuclei, starting from a realistic interaction and a Gamow-Hartree-Fock basis [8]. However, an ab-initio description of such nuclei within the Gamow shell model approach might presently not be feasible since the computational cost scales combinatorially with the number orbitals, and one typically needs a large number of orbitals for each partial wave in order to discretize the continuum integral accurately.…”

Section: Introductionmentioning

confidence: 99%

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Building nuclei from the ground up

Hagen¹,

Dean²,

Jensen³

et al. 2010

Proceedings of International Symposium on Nuclear Astrophysics - Nuclei in the Cosmos - IX — PoS(NIC-IX)

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We present ab-initio CCSD calculations of the 3−5 He ground states. We perform these calculations using a mixed basis of oscillator and complex Woods-Saxon states for chosen partial waves. From this starting point, we build a spherical Gamow-Hartree-Fock basis from a renormalized interaction of the low-momentum type generated from the N 3 LO two-body potential. The GamowHartree-Fock basis, which is a Berggren basis, treats bound, resonant, and continuum states on an equal footing, and is therefore optimal for the description of nuclear states which may be embedded in the continuum. Within this ab-initio approach, we are able to calculate that 3−4 He are stable against particle decay, while 5 He has a non-negligible width and is therefore unstable with respect to one neutron emission, as is the case experimentally. We illustrate from these calculations that the CCSD approach is as accurate for closed-shell nuclei as for open-shell nuclei with ±1 nucleon outside a closed-shell. Finally, we perform various tests on the convergence of our CCSD results. We find that our results are well converged with respect to basis size and discretization of the continuum integral defining our Berggren basis.

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“…The solution of the configuration-interaction problem in the presence of continuum states has been recently advanced in the real-energy continuum SM [4][5][6] and in the complex-energy SM, the so-called Gamow shell model (GSM) [7][8][9][10][11]. In the GSM, the s.p.…”

Section: Introductionmentioning

confidence: 99%

Density matrix renormalization group approach to two-fluid open many-fermion systems

et al. 2009

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We have extended the density matrix renormalization group (DMRG) approach to two-fluid open manyfermion systems governed by complex-symmetric Hamiltonians. The applications are carried out for three-and four-nucleon (proton-neutron) systems within the Gamow shell model (GSM) in the complex-energy plane. We study necessary and sufficient conditions for the GSM+DMRG method to yield the correct ground-state eigenvalue and discuss different truncation schemes within the DMRG. The proposed approach will enable configuration interaction studies of weakly bound and unbound strongly interacting complex systems, which, because of a prohibitively large size of Fock space, cannot be treated by means of the direct diagonalization.

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Gamow shell model and realistic nucleon-nucleon interactions

Cited by 79 publications

References 57 publications

Asymptotic normalization coefficients and continuum coupling in mirror nuclei

Asymptotic normalization coefficients and continuum coupling in mirror nuclei

Building nuclei from the ground up

Density matrix renormalization group approach to two-fluid open many-fermion systems

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