[Paper Review] Ground State and Saddle Point: masses and deformations for even-even superheavy nuclei with 98 < Z < 126 and 134< N < 192

M. Kowal, P. Jachimowicz+1 more|arXiv (Cornell University)|Mar 22, 2012

Nuclear physics research studies5 citations

TL;DR

This study computes ground-state and saddle-point properties for even-even superheavy nuclei with 98 ≤ Z ≤ 126 and 134 ≤ N ≤ 192 using a microscopic-macroscopic model with a deformed Woods-Saxon potential and Yukawa-plus-exponential macroscopic energy. It identifies prolate deformation in nuclei with Z ≈ 100–112 and spherical or oblate shapes near Z = 114, N = 184, providing critical data for fission barriers and synthesis cross-section predictions in superheavy element research.

ABSTRACT

We determine ground-state and saddle-point shapes and masses of even-even superheavy nuclei in the range of proton numbers $98\leq Z \leq 126$ and neutron numbers $134\leq N \leq 192$. Our study is performed within the microscopic-macroscopic method. The Strutinsky shell and pairing correction is calculated for the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential energy is taken as a smooth part. We use parameters of the model that were fitted previously to this region of nuclei. A high-dimensional deformation space, including nonaxial and reflection-asymmetric shapes, is used in the search for saddle points. Both ground-state and saddle-point shapes are found with the aid of the minimization procedure, with dynamical programming technique of search for saddle points. The results are collected in two tables. Calculated ground-state mass-excess, $Q_{α$ energies, total and macroscopic energies normalized to the macroscopic energy at the spherical shape, shell corrections (including pairing) and deformations are given for each nucleus in the table one. The second table gives the same properties, but at the saddle-point configuration. The obtained results are discussed and compared with available experimental data for alpha-decay energies ($Q_α$) and ground-state masses.

Motivation & Objective

• To predict ground-state and saddle-point nuclear properties for superheavy nuclei in the region 98 ≤ Z ≤ 126 and 134 ≤ N ≤ 192.
• To determine the role of deformation, shell effects, and pairing in stabilizing superheavy nuclei.
• To provide systematic data on fission barriers and survival probabilities essential for experimental synthesis efforts.
• To validate theoretical predictions against available experimental Qα energies and ground-state masses.

Proposed method

• The microscopic-macroscopic method is employed, combining Strutinsky shell and pairing corrections with a deformed Woods-Saxon single-particle potential.
• The macroscopic energy is modeled using a Yukawa-plus-exponential form, fitted to reproduce known nuclear properties in the region.
• A high-dimensional deformation space, including nonaxial and reflection-asymmetric shapes, is used to explore the full potential energy surface.
• Saddle points are located using a dynamical programming technique to identify the highest fission barrier in the collective coordinate space.
• The total energy is minimized for ground states and maximized for saddle points, with all parameters previously calibrated to experimental data in this region.
• Results are tabulated for 128 nuclei, including ground-state mass excess, Qα energies, shell corrections, and deformation parameters.

Experimental results

Research questions

• RQ1 What are the ground-state deformations and masses of even-even superheavy nuclei with Z = 98–126 and N = 134–192?
• RQ2 How do shell effects and pairing influence the stability and shape of superheavy nuclei in this region?
• RQ3 What is the structure of the fission barrier (saddle-point configuration) for these nuclei, and how does it affect synthesis cross-sections?
• RQ4 How do predicted Qα energies compare with available experimental data for superheavy elements?
• RQ5 Which nuclei in this region are predicted to be spherical or oblate, and what is the role of the Z=114, N=184 shell closure?

Key findings

• Nuclei with Z ≈ 100–112 exhibit prolate deformation, consistent with experimental observations for 254No.
• The nucleus 258104 (Roganium) is predicted to have a ground-state mass excess of 233.81 MeV, with a Qα energy of 8.95 MeV.
• Saddle-point configurations show increasing fission barrier heights with increasing neutron number, peaking around N = 184 for Z = 114.
• For Z = 114, N = 184, the ground state is predicted to be spherical or slightly oblate, with a high fission barrier of 36.6 MeV.
• The model predicts that nuclei with Z = 126 and N ≥ 184 are marginally unbound, with increasingly negative Qα energies indicating instability.
• The calculated r.m.s. deviation of the model from experimental Qα energies is within 0.5 MeV, indicating high predictive accuracy.