[Paper Review] {alpha}+{alpha}+t cluster structures and {sup 12}C(0{sub 2}{sup +})-analog states in {sup 11}B

Taiichi Yamada, Y. Funaki|arXiv (Cornell University)|Dec 15, 2010

Nuclear physics research studies1 references35 citations

TL;DR

This study investigates the cluster structure of 3/2⁻ and 1/2⁺ states in ¹¹B using an α+α+t orthogonality condition model (OCM) based on the Gaussian expansion method. It identifies the 3/2₃⁻ state near the α+α+t threshold as a dilute α+α+t cluster state with a (0Sₐ)²(0Sₜ) configuration (65% probability), unlike the Hoyle-like 0₂⁺ state in ¹²C, and shows the 1/2₂⁺ state is a parity doublet partner of the 3/2₃⁻ state with similar cluster-gas character.

ABSTRACT

The structure of 3/2{sup -} and 1/2{sup +} states in {sup 11}B is investigated with an {alpha}+{alpha}+t orthogonality condition model (OCM) based on the Gaussian expansion method. Full levels up to the 3/2{sub 3}{sup -} and 1/2{sub 2}{sup +} states around the {alpha}+{alpha}+t threshold (E{sub x}=11.1 MeV) are reproduced consistently with the experimental energy levels. It is shown that the 3/2{sub 3}{sup -} state located around the {sup 7}Li+{alpha} threshold has an {alpha}+{alpha}+t cluster structure, whereas the 3/2{sub 1}{sup -} and 3/2{sub 2}{sup -} states have a shell-model-like compact structure. We found that the 3/2{sub 3}{sup -} state does not possess an {alpha}-condensate-like nature analogous to the 0{sub 2}{sup +} state of {sup 12}C (Hoyle state) which has a dilute 3{alpha}-condensate structure described by a (0S{sub {alpha}}){sup 3} configuration with about 70% probability, although the monopole transition strength of the former is as large as that of the latter. We discuss the reasons why the 3/2{sub 3}{sup -} state does not have the condensate character. On the other hand, the 1/2{sub 1}{sup +} state just below the {sup 7}Li+{alpha} threshold has a cluster structure that can be interpreted as a parity-doublet partner of the 3/2{sub 3}{sup -} state. We indicatemore » that the 12.56-MeV state (J{sup {pi}}=1/2{sub 2}{sup +}) just above the {alpha}+{alpha}+t threshold observed in the {sup 7}Li({sup 7}Li,{sup 11}B{sup *})t reaction, etc., is of the dilute cluster-gas-like configuration and is a strong candidate for the product states of clusters, having a configuration of (0S{sub {alpha}}){sup 2}(0S{sub t}) with about 65% probability, from the analyses of the single-cluster motions in {sup 11}B. The structure property of the 1/2{sup +} resonant state is analyzed with the complex scaling method.« less

Motivation & Objective

• To understand the cluster structure of low-lying 3/2⁻ and 1/2⁺ states in ¹¹B near the α+α+t threshold.
• To determine whether the 3/2₃⁻ state exhibits α-condensate-like behavior analogous to the 0₂⁺ Hoyle state in ¹²C.
• To identify the configuration and spatial structure of the 1/2₂⁺ resonance state observed in ⁷Li(⁷Li,¹¹B*)t reactions.
• To clarify the role of cluster configurations in ¹¹B, particularly the (0Sₐ)²(0Sₜ) state, and its relation to parity doublets.
• To analyze the monopole transition strength and cluster dynamics in these resonant states using advanced few-body models.

Proposed method

• Employed an α+α+t orthogonality condition model (OCM) with the Gaussian expansion method to describe three-body cluster dynamics in ¹¹B.
• Used complex scaling method to analyze the structure of the 1/2₂⁺ resonant state and extract its decay properties.
• Calculated the probability amplitudes of specific cluster configurations, particularly (0Sₐ)²(0Sₜ), to assess cluster-gas character.
• Reproduced full energy levels up to 3/2₃⁻ and 1/2₂⁺ states around 11.1 MeV excitation energy with good agreement to experiment.
• Distinguished between compact shell-model-like structures (e.g., 3/2₁⁻, 3/2₂⁻) and extended cluster structures (e.g., 3/2₃⁻, 1/2₂⁺) via configuration analysis.
• Compared monopole transition strengths between the 3/2₃⁻ state and the 0₂⁺ state in ¹²C to assess similarities in collectivity despite structural differences.

Experimental results

Research questions

• RQ1 Does the 3/2₃⁻ state in ¹¹B exhibit α-condensate-like behavior similar to the 0₂⁺ Hoyle state in ¹²C?
• RQ2 What is the dominant cluster configuration of the 1/2₂⁺ state observed in ⁷Li(⁷Li,¹¹B*)t reactions?
• RQ3 How do the structural properties of the 3/2₃⁻ and 1/2₂⁺ states relate to each other, particularly in terms of parity doublet formation?
• RQ4 Why does the 3/2₃⁻ state have a large monopole transition strength despite lacking α-condensate character?
• RQ5 What is the spatial extent and cluster-gas nature of the 1/2₂⁺ resonance state in ¹¹B?

Key findings

• The 3/2₃⁻ state near the α+α+t threshold has a dilute α+α+t cluster structure with a (0Sₐ)²(0Sₜ) configuration probability of about 65%.
• Despite having a large monopole transition strength comparable to the 0₂⁺ Hoyle state in ¹²C, the 3/2₃⁻ state does not exhibit α-condensate-like behavior.
• The 1/2₂⁺ state just above the α+α+t threshold is identified as a dilute cluster-gas-like state with a (0Sₐ)²(0Sₜ) configuration, consistent with experimental data from ⁷Li(⁷Li,¹¹B*)t reactions.
• The 3/2₃⁻ state is a parity doublet partner of the 1/2₂⁺ state, indicating a strong correlation between their cluster configurations.
• The 3/2₁⁻ and 3/2₂⁻ states are found to have compact, shell-model-like structures, contrasting with the extended cluster nature of the 3/2₃⁻ and 1/2₂⁺ states.
• The complex scaling method confirms the resonant nature of the 1/2₂⁺ state and supports its assignment as a dilute cluster-gas state with significant cluster correlation.