[Paper Review] New cluster approach on properties of 8-11Be isotopes with isospin-dependent spin-orbit potential

Mengjiao Lyu, Zhongzhou Ren+8 more|arXiv (Cornell University)|Jun 20, 2017

Nuclear physics research studies1 references3 citations

TL;DR

This paper introduces a new isospin-dependent spin-orbit interaction within an improved nonlocalized cluster approach using the Tohsaki-Horiuchi-Schuck-R"opke (THSR) wave function to accurately describe the structure of 8-11Be isotopes. The method successfully reproduces the intruder 1/2⁺ ground state of 11Be, its large neutron halo radius (~5.5 fm RMS), and a spectroscopic factor of 0.907 for the 2s_{1/2} orbital, matching experimental trends and outperforming traditional shell model predictions.

ABSTRACT

The nonlocalized clustering approach is generalized to 8-11Be isotopes with isospin dependent spin-orbit potential. A new form of the Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function is introduced to provide a correct description for the σ-binding neutron in 11Be. Systematic calculations for 8-11Be isotopes are performed and results fit well with experimental values. The low energy spectrum of 11Be is also obtained, especially the correct spin-parity 1/2+ is reproduced for the intruder ground state. The exotic neutron halo structure of 11Be is studied by calculations of root-mean-square radii and density distribution. We obtain a large spatial distribution for the last valence neutron of 11Be, which fits the phenomenological extracted value from experimental data. The spectroscopic factor is also calculated and discussed for the 1/2+ ground state of 11Be.

Motivation & Objective

• To develop a new cluster model approach that incorporates isospin-dependent spin-orbit interactions for accurate description of neutron-rich 8-11Be isotopes.
• To address the challenge of correctly reproducing the intruder 1/2⁺ ground state of 11Be, which has positive parity and is difficult to describe with standard models.
• To provide a microscopic explanation for the large spatial distribution of the valence neutron in 11Be, consistent with experimental halo structure.
• To calculate and analyze the spectroscopic factor for the 2s_{1/2} orbital in 11Be's ground state, improving upon shell model results.

Proposed method

• A new form of the THSR wave function is introduced, explicitly incorporating the valence neutron's nodal surface structure via a modified creation operator for the σ-orbital in 11Be.
• An isospin-dependent spin-orbit interaction strength $ V_{ls}^{*} = 3200 \, \text{MeV} $ is implemented to better describe spin-orbit coupling effects in neutron-rich systems.
• The method uses angular momentum projection and norm-conserving techniques to extract spectroscopic factors from the many-body THSR state.
• The Hamiltonian includes a central interaction with optimized parameters to enhance α-α clustering, leading to stronger attraction and reduced α-α distance.
• Root-mean-square (RMS) radii and density distributions are calculated in the x-z plane to visualize the extended halo structure of the valence neutron.
• Systematic calculations are performed across 8-11Be isotopes, comparing ground state energies, separation energies, and low-lying spectra with experimental data.

Experimental results

Research questions

• RQ1 Can a nonlocalized cluster approach with isospin-dependent spin-orbit interaction correctly describe the 1/2⁺ intruder ground state of 11Be?
• RQ2 How does the inclusion of a modified THSR wave function improve the description of the valence neutron's spatial distribution and halo structure in 11Be?
• RQ3 What is the spectroscopic factor for the 2s_{1/2} orbital in the 1/2⁺ ground state of 11Be, and how does it compare to shell model predictions and experimental data?
• RQ4 How does the new spin-orbit coupling strength $ V_{ls}^{*} $ affect the spectroscopic factor and the configuration mixing in the 11Be ground state?
• RQ5 To what extent does the improved model reproduce the experimental single-neutron separation energies and low-lying spectra of 8-11Be isotopes?

Key findings

• The calculated ground state energy and single-neutron separation energy for 11Be agree well with experimental values, confirming the model's accuracy.
• The 1/2⁺ intruder ground state of 11Be is correctly reproduced, with the correct spin-parity and positive parity, a non-trivial achievement for cluster models.
• The root-mean-square radius of the last valence neutron in 11Be reaches approximately 5.5 fm, indicating a large spatial distribution consistent with experimental phenomenological extraction.
• The spectroscopic factor for the 2s_{1/2} orbital in the 1/2⁺ ground state is calculated as 0.907, which is higher than shell model predictions (55–74%) and within the range of experimental values (46–87%) with large error bars.
• Reducing the spin-orbit strength to 2000 MeV increases the spectroscopic factor to 0.933, showing that the new $ V_{ls}^{*} = 3200 \, \text{MeV} $ reduces the 2s_{1/2} component and enhances mixing with the 1d_{5/2} orbital, crucial for the intruder state.
• The density distribution of the valence neutron shows a giant halo with significant amplitude extending up to 8 fm in both x and z directions, confirming the halo nature of 11Be.