A Universal Four-Fermion Formation Framework and Odd-Even Staggering in $α$ Decay

Abstract

Clustering phenomena are common in many physical systems across multiple scales. The nuclear $α$ decay is one of the earliest observed evidences of clustering in quantum systems, yet its formation process remains poorly understood even today. In this letter, we propose a novel global odd-even staggering (OES) feature in $α$ decay, which emerges during the clustering process. To unveil its origin, we develop a Universal Four-Fermion Formation Framework (U4F), which describes the formation of any four-nucleon cluster, such as $α$ particle, from a general microscopic wave function, without assuming the preexistence of clustering or pairing. By combining U4F with the large-scale configuration-interaction approach, we demonstrate that the OES effect in $α$ decay arises from the suppression of clustering correlations due to unpaired nucleons. These findings significantly advance our understanding of cluster formation in nuclei and have important implications for the production of new elements and nuclear synthesis in the universe.

Figures (3)

• Figure 1: Distribution of $\Delta Q_\alpha$, $\Delta \log_{10}T_\alpha$, and $\Delta F_\alpha$ for nuclides with even-$N$, odd-$N$, even-$Z$, and odd-$Z$. The upper (lower) panels display data for isotopic (isotonic) chains, denoted as $\Delta_{n(p)}$. Each panel also indicates the proportions of positive and negative values of $\Delta$. The experimental values of $Q_\alpha$ and $T_\alpha$ are collected from AME2020 wang2021ame2020 and NUBASE2020 kondev_nubase2020_2021, respectively.
• Figure 2: Illustration of the microscopic mechanism of the formation process of an $\alpha$ particle in motion of the $L_\alpha$ wave in nucleus. Key components include the selection of orbitals, represented by the quartet amplitude $\mathcal{S}_\alpha$, and the center of mass mapping process. The latter includes transformations such as the $jj$ to $ls$ transformation $\gamma$ and $\widetilde{\gamma}$, as well as the Talmi-Moshinsky transformation $M$.
• Figure 3: Panels ($a$-$b$): The $\alpha$ formation probability of isotopes $^{202-210}$Po and $^{205-211}$At, both extracted from experimental data by Eq. (\ref{['f_exp']}) and estimated theoretically by Eq. (\ref{['f_th']}) using two groups of Hamiltonian (Int.1 and Int.2). Panels ($c$-$d$): Total Quartet Energy and the pairing correlation energy from like-particle spin-zero ($I=0$) pairs of Po and At isotopes extracted according to Eq. (\ref{['eq:QE']}).