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Title: Nuclear three-body problem in the complex energy plane: Complex-scaling Slater method

Journal Article · · Physical Review. C. Nuclear Physics
 [1];  [2];  [3];  [4]
  1. Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy; Hungarian Academy of Sciences Inst. for Nuclear Research, Debrecen (Hungary)
  2. Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy; Univ. of Arizona, Tucson, AZ (United States). Dept. of Physics
  3. Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy; Oak Ridge National Lab. (ORNL), TN (United States). Physics Division; Univ. of Warsaw, Warsaw (Poland). Inst. of Theoretical Physics
  4. Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy; Michigan State Univ., East Lansing, MI (United States). National Superconducting Cyclotron Lab., and Dept. of Physics and Astronomy
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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. 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. 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. In this paper, 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. 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.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Univ. of Tennessee, Knoxville, TN (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
FG02-96ER40963
OSTI ID:
1565205
Journal Information:
Physical Review. C. Nuclear Physics, Vol. 89, Issue 1; ISSN 0556-2813
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 18 works
Citation information provided by
Web of Science

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Cited By (1)

Precise comparison of the Gaussian expansion method and the Gamow shell model text January 2014

Figures / Tables (18)

FIG. 1(p. 4)figure FIG. 1
FIG. 2(p. 6)figure FIG. 2
FIG. 3(p. 8)figure FIG. 3
FIG. 4(p. 9)figure FIG. 4
FIG. 5(p. 9)figure FIG. 5
TABLE I(p. 9)table TABLE I
FIG. 6(p. 10)figure FIG. 6
FIG. 7(p. 10)figure FIG. 7
TABLE II(p. 10)table TABLE II
FIG. 10(p. 11)figure FIG. 10
FIG. 8(p. 11)figure FIG. 8
FIG. 9(p. 11)figure FIG. 9
FIG. 11(p. 12)figure FIG. 11
FIG. 12(p. 12)figure FIG. 12
FIG. 13(p. 12)figure FIG. 13
FIG. 14(p. 13)figure FIG. 14
FIG. 15(p. 13)figure FIG. 15
FIG. 16(p. 13)figure FIG. 16

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