[Paper Review] Low energy 0+ excitations in 158Gd

Jorge G. Hirsch, Gabriela Popa+4 more|Redalyc (Universidad Autónoma del Estado de México)|May 18, 2005

Nuclear physics research studies22 references3 citations

TL;DR

This paper investigates the low-lying 0⁺ states in ¹⁵⁸Gd using the pseudo SU(3) model, successfully reproducing excitation energies of multiple 0⁺ states below 3.1 MeV. However, the model underestimates B(E2) transition strengths to the ground state band by two orders of magnitude, suggesting that inclusion of intruder orbital configurations and configuration mixing via pairing interactions is essential for accurate description of collectivity in these states.

ABSTRACT

High precision (p,t) studies of the deformed nucleus 158Gd allowed the observation of 13 excited 0+ states below an excitation energy of 3.1 MeV. This high density of low energy states, and particularly their measured B(E2) transition strengths to the first excited 2+ state challenge nuclear models. The pseudo SU(3) model, which successfully describes many excited bands in Dy isotopes, is used to analyze this nuclei. We have fairly good reproduction of most of the states but the absence of actively including nucleons occupying intruders orbits may be the reason for the observed limitations of the model.

Motivation & Objective

• To understand the origin of the high density of low-lying 0⁺ states in ¹⁵⁸Gd, which challenges standard nuclear models.
• To test the applicability of the pseudo SU(3) model in describing both the energy levels and electromagnetic transition strengths of these 0⁺ states.
• To identify the limitations of the pseudo SU(3) model in reproducing experimental B(E2) values, particularly for transitions to the ground state band.
• To explore whether inclusion of intruder orbitals and configuration mixing can improve the model's description of collectivity in these states.

Proposed method

• The pseudo SU(3) model is applied to ¹⁵⁸Gd using a deformed Nilsson potential with ε₂ = 0.25 to determine valence orbital occupancies.
• Many-body states are constructed as pseudo-SU(3) coupled states with good particle number and angular momentum, treating intruder orbitals via effective charges.
• The Hamiltonian includes rotor-like terms (a₀, a₂, a₃, a_sym) and K² terms to fit energy levels and moments of inertia.
• Calculations are performed in two basis configurations: a restricted space (Case 1) and an enlarged configuration space (Case 2) including pseudo-spin 0, 1, and 2 states.
• B(E2) transition strengths are calculated for transitions from 0⁺ states to the 2₁⁺ (ground state band) and 2γ⁺ (γ-band) states.
• Parameter optimization is performed by adjusting a₃ to fit the first 0⁺ state energy, a_sym to control level spacing, and K² coefficient to tune the 2γ⁺ state energy.

Experimental results

Research questions

• RQ1 Can the pseudo SU(3) model reproduce the excitation energies of the 13 observed 0⁺ states in ¹⁵⁸Gd below 3.1 MeV?
• RQ2 Why do the calculated B(E2) transition strengths from 0⁺ states to the ground state band (2₁⁺) fall significantly short of experimental values, which range from 0.9 to 6.4 W.u.?
• RQ3 To what extent does enlarging the configuration space improve the description of low-lying 0⁺ states and their electromagnetic transitions?
• RQ4 What role do intruder orbitals and configuration mixing play in enhancing B(E2) strengths to the ground state band?
• RQ5 Can the pseudo SU(3) model account for the observed fragmentation of collectivity in 0⁺ states, as indicated by B(E2) values below 3.1 MeV?

Key findings

• The pseudo SU(3) model with an enlarged configuration space reproduces 7 low-lying 0⁺ states below 3 MeV, with calculated energies in good agreement with experimental values.
• Calculated B(E2) strengths to the ground state band (2₁⁺) are all less than 0.08 W.u., which is two orders of magnitude smaller than experimental values ranging from 0.9 to 6.4 W.u.
• B(E2) strengths to the γ-bandhead (2γ⁺) are significantly larger, with values exceeding 1 W.u. in several cases (e.g., 7.79 W.u. in Case 2), suggesting stronger collectivity in γ-band transitions.
• The model's failure to reproduce B(E2) to the ground state band indicates that the wave functions of 0⁺ states lack sufficient admixture of configurations that would enhance E2 collectivity.
• The inclusion of intruder orbitals and configuration mixing via pairing interactions is identified as a necessary next step to improve the model's description of collectivity in these states.
• The results suggest that the absence of active intruder orbital contributions in the current pseudo SU(3) framework limits its ability to reproduce the observed fragmentation of B(E2) strengths.