### Abstract

Background: The physics of open quantum systems is an interdisciplinary area of research. The nuclear "openness" manifests itself through the presence of the many-body continuum representing various decay, scattering, and reaction channels. As the radioactive nuclear beam experimentation extends the known nuclear landscape toward the particle drip lines, the coupling to the continuum space becomes exceedingly more important. Of particular interest are weakly bound and unbound nuclear states appearing around particle thresholds. Theories of such nuclei must take into account their open quantum nature. Purpose: To describe open quantum systems, we introduce a complex-scaling (CS) approach in the Slater basis. We benchmark it with the complex-energy Gamow shell model (GSM) by studying energies and wave functions of the bound and unbound states of the two-neutron halo nucleus 6He viewed as an α+n+n cluster system. Methods: Both CS and GSM approaches are applied to a translationally invariant Hamiltonian with the two-body interaction approximated by the finite-range central Minnesota force. In the CS approach, we use the Slater basis, which exhibits the correct asymptotic behavior at large distances. To extract particle densities from the back-rotated CS solutions, we apply the Tikhonov regularization procedure, which minimizes the ultraviolet numerical noise. Results: We show that the CS-Slater method is both accurate and efficient. Its equivalence to the GSM approach has been demonstrated numerically for both energies and wave functions of 6He. One important technical aspect of our calculation was to fully retrieve the correct asymptotic behavior of a resonance state from the complex-scaled (square-integrable) wave function. While standard applications of the inverse complex transformation to the complex-rotated solution provide unstable results, the stabilization method fully reproduces the GSM benchmark. We also propose a method to determine the smoothing parameter of the Tikhonov regularization. Conclusions: The combined suite of CS-Slater and GSM techniques has many attractive features when applied to nuclear problems involving weakly bound and unbound states. While both methods can describe energies, total widths, and wave functions of nuclear states, the CS-Slater method - if it can be applied - can provide additional information about partial energy widths associated with individual thresholds.

Original language | English |
---|---|

Article number | 014330 |

Journal | Physical Review C - Nuclear Physics |

Volume | 89 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 31 2014 |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physical Review C - Nuclear Physics*,

*89*(1), [014330]. https://doi.org/10.1103/PhysRevC.89.014330

**Nuclear three-body problem in the complex energy plane : Complex-scaling Slater method.** / Kruppa, A.; Papadimitriou, G.; Nazarewicz, W.; Michel, N.

Research output: Contribution to journal › Article

*Physical Review C - Nuclear Physics*, vol. 89, no. 1, 014330. https://doi.org/10.1103/PhysRevC.89.014330

}

TY - JOUR

T1 - Nuclear three-body problem in the complex energy plane

T2 - Complex-scaling Slater method

AU - Kruppa, A.

AU - Papadimitriou, G.

AU - Nazarewicz, W.

AU - Michel, N.

PY - 2014/1/31

Y1 - 2014/1/31

N2 - Background: The physics of open quantum systems is an interdisciplinary area of research. The nuclear "openness" manifests itself through the presence of the many-body continuum representing various decay, scattering, and reaction channels. As the radioactive nuclear beam experimentation extends the known nuclear landscape toward the particle drip lines, the coupling to the continuum space becomes exceedingly more important. Of particular interest are weakly bound and unbound nuclear states appearing around particle thresholds. Theories of such nuclei must take into account their open quantum nature. Purpose: To describe open quantum systems, we introduce a complex-scaling (CS) approach in the Slater basis. We benchmark it with the complex-energy Gamow shell model (GSM) by studying energies and wave functions of the bound and unbound states of the two-neutron halo nucleus 6He viewed as an α+n+n cluster system. Methods: Both CS and GSM approaches are applied to a translationally invariant Hamiltonian with the two-body interaction approximated by the finite-range central Minnesota force. In the CS approach, we use the Slater basis, which exhibits the correct asymptotic behavior at large distances. To extract particle densities from the back-rotated CS solutions, we apply the Tikhonov regularization procedure, which minimizes the ultraviolet numerical noise. Results: We show that the CS-Slater method is both accurate and efficient. Its equivalence to the GSM approach has been demonstrated numerically for both energies and wave functions of 6He. One important technical aspect of our calculation was to fully retrieve the correct asymptotic behavior of a resonance state from the complex-scaled (square-integrable) wave function. While standard applications of the inverse complex transformation to the complex-rotated solution provide unstable results, the stabilization method fully reproduces the GSM benchmark. We also propose a method to determine the smoothing parameter of the Tikhonov regularization. Conclusions: The combined suite of CS-Slater and GSM techniques has many attractive features when applied to nuclear problems involving weakly bound and unbound states. While both methods can describe energies, total widths, and wave functions of nuclear states, the CS-Slater method - if it can be applied - can provide additional information about partial energy widths associated with individual thresholds.

AB - Background: The physics of open quantum systems is an interdisciplinary area of research. The nuclear "openness" manifests itself through the presence of the many-body continuum representing various decay, scattering, and reaction channels. As the radioactive nuclear beam experimentation extends the known nuclear landscape toward the particle drip lines, the coupling to the continuum space becomes exceedingly more important. Of particular interest are weakly bound and unbound nuclear states appearing around particle thresholds. Theories of such nuclei must take into account their open quantum nature. Purpose: To describe open quantum systems, we introduce a complex-scaling (CS) approach in the Slater basis. We benchmark it with the complex-energy Gamow shell model (GSM) by studying energies and wave functions of the bound and unbound states of the two-neutron halo nucleus 6He viewed as an α+n+n cluster system. Methods: Both CS and GSM approaches are applied to a translationally invariant Hamiltonian with the two-body interaction approximated by the finite-range central Minnesota force. In the CS approach, we use the Slater basis, which exhibits the correct asymptotic behavior at large distances. To extract particle densities from the back-rotated CS solutions, we apply the Tikhonov regularization procedure, which minimizes the ultraviolet numerical noise. Results: We show that the CS-Slater method is both accurate and efficient. Its equivalence to the GSM approach has been demonstrated numerically for both energies and wave functions of 6He. One important technical aspect of our calculation was to fully retrieve the correct asymptotic behavior of a resonance state from the complex-scaled (square-integrable) wave function. While standard applications of the inverse complex transformation to the complex-rotated solution provide unstable results, the stabilization method fully reproduces the GSM benchmark. We also propose a method to determine the smoothing parameter of the Tikhonov regularization. Conclusions: The combined suite of CS-Slater and GSM techniques has many attractive features when applied to nuclear problems involving weakly bound and unbound states. While both methods can describe energies, total widths, and wave functions of nuclear states, the CS-Slater method - if it can be applied - can provide additional information about partial energy widths associated with individual thresholds.

UR - http://www.scopus.com/inward/record.url?scp=84894450130&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894450130&partnerID=8YFLogxK

U2 - 10.1103/PhysRevC.89.014330

DO - 10.1103/PhysRevC.89.014330

M3 - Article

VL - 89

JO - Physical Review C - Nuclear Physics

JF - Physical Review C - Nuclear Physics

SN - 0556-2813

IS - 1

M1 - 014330

ER -