Title: Analytical continuation from bound to resonant states in the Dirac equation with quadrupole-deformed potentials

Abstract

Here, resonances with pronounced single-particle characteristics are crucial for quantitative descriptions of exotic nuclei near and beyond the drip lines, and often impact halo formation and nucleon decay processes. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold can lead to improved descriptions of exotic nuclei. Develop a method to study single-particle resonant orbital structure in the Dirac equation with a quadrupole-deformed Woods-Saxon potential. Determine the structure evolution of bound and resonant levels with deformation in this scheme, and examine the impact on halo formation in loosely bound systems, with a focus on the recent halo candidate nucleus ³⁷Mg. Analytical continuation of the coupling constant (ACCC) method is developed on the basis of the Dirac equation with a deformed Woods-Saxon potential. The scalar and vector terms in the deformed potential are determined by the energies of the valence neutron and nearby orbitals, which are extracted from a self-consistent relativistic Hartree-Bogoliubov (RHB) calculation with the PC-PK1 density functional. As a result, we compare the energies and widths of resonant orbitals in the recent halo nucleus candidate ³⁷Mg using the ACCC method based on the Dirac coupled-channel equations with those determined from the scattering phasemore » shift (SPS) method. It is found that the results from the two methods agree well for narrow resonances, whereas the SPS method fails for broad resonances. Nilsson levels for bound and resonant orbitals from the ACCC method are calculated over a wide range of deformations and show some decisive hints of halo formation in ³⁷Mg. In conclusion, in our ACCC model for deformed potentials in the coupled-channel Dirac equations, the crossing of the configuration 1/2[321] and 5/2[312] orbitals at a deformation of approximately 0.5 enhances the probability to occupy the 1/2[321] orbital coming from 2_p3/2 thereby explaining the recent observation of a p-wave one-neutron halo configuration in ³⁷Mg. The resonant 1/2[301] configuration plays a crucial role in halo formation in the magnesium isotopes beyond A = 40 for a wide range of deformations larger than 0.2.« less

Authors:

Xu, Xu -Dong ^[1]; Zhang, Shi -Sheng ^[2]; Signoracci, Angelo J. ^[3]; Smith, Michael Scott  ^[3];

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Li, Zhi Pan ^[4]

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+ Show Author Affiliations

1. Beihang Univ., Beijing (China)
2. Beihang Univ., Beijing (China); Chinese Academy of Sciences (CAS), Beijing (China); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
4. Southwest Univ., Chongqing (China)

Publication Date:

Fri Aug 28 00:00:00 EDT 2015

Research Org.:

Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:

USDOE

OSTI Identifier:

1462914

Alternate Identifier(s):

OSTI ID: 1213285

Grant/Contract Number:  

AC05-00OR22725

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review C, Nuclear Physics

Additional Journal Information:

Journal Volume: 92; Journal Issue: 2; Journal ID: ISSN 0556-2813

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

73 NUCLEAR PHYSICS AND RADIATION PHYSICS