Cluster radioactivity preformation probability of trans-lead nuclei in the N p N n scheme

In this study, considering the modified preformation probability to be , where and are the α-particle preformation probability and an adjustable parameter proposed by Wang et al. [Chin. Phys. C 45, 044111 (2021)], respectively, we extend a new simple model put forward by Bayrak [J. Phys. G 47, 025102 (2020)] to systematically study the cluster radioactivity half-lives of 28 trans-lead nuclei ranging from to , which is based on the Wentzel-Kramers-Brillouin approximation and Bohr–Sommerfeld quantization condition. For comparison, a universal decay law proposed by Qi et al. [Phys. Rev. C 80, 044326 (2009)], a three-parameter model-independent formula put forward by Balasubramaniam et al. [Phys. Rev. C 70, 017301 (2004)], and the semi-empirical model proposed by Tavares et al. [Eur. Phys. J. A 49, 1 (2013)] are used. Our calculated results reproduce the experimental data well, with a standard deviation of 0.818. Furthermore, we use this model to predict the cluster radioactivity half-lives of 51 possible cluster radioactive candidates whose cluster radioactivities are energetically allowed or observed but not yet quantified in NUBASE2020.

Section: ±10supporting

confidence: 66%

“…As is well known, cluster radioactivity is closely related to the shell effect, which has prompted widespread [68,71,72]. To verify the shell effect in the cluster radioactivity process, we calculate the cluster radioactivity half-lives of the emitter cluster from isotopes and from isotopes, which give the daughters and .…”

Section: ±10mentioning

confidence: 99%

Simple model for cluster radioactivity half-lives in trans-lead nuclei*

Zhu 朱,

Luo 骆,

Qi 亓

et al. 2023

“…Since most proton emitters are spherical or moderately deformed, the calculations of proton emission halflives are usually simplified by assuming a spherical shape for the daughter nucleus. Furthermore, the Wentzel-Kramers-Brillouin (WKB) approximation is capable of handling proton emission because it shares the same physical processes as α decay [26][27][28][29][30], cluster radioactivity [31][32][33][34], and two-proton emission [35][36][37][38], which can be handled through barrier penetration. Based on the WKB approximation, various calculations for spherical proton emitters with different models or potentials can obtain similar values, which closely match the experimental half-lives [39][40][41][42][43][44][45][46][47][48][49].…”

Section: Q Pmentioning

confidence: 99%

Theoretical calculations of proton emission half-lives based on a deformed Gamow-like model*

Zhang 张,

Hu 胡,

Qi 亓

et al. 2024

In the present study, proton emission half-lives have been investigated for the deformed proton emitters of proton number range $53\leq Z \leq 83$ within the deformed Gamow-like model, where the deformation effect has been included in the Coulomb potential. The calculated results can reproduce the experimental half-lives successfully within a factor of 3.45. For comparison, we also perform calculations with other different models, including the universal decay law for proton emission and the new Geiger-Nuttall law. Furthermore, the relevance of the half-lives to the angular momentum $l$ for $^{117}$La, $^{121}$Pr, $^{135}$Tb and $^{141}$Ho has been analysed as well as corresponding possible reference values of $l$ has been put forward: $l=$3, 3, 4, 4.

“…One of the main challenges in cluster radioactivity is calculating the cluster preformation factor . Currently, the most common method is to extract the cluster preformation factor from the experimental data of the cluster radioactivity half-life [20,[27][28][29][30]. In 1988, Blendowske and Walliser considered the extracted cluster preformation factor to depend on the α preformation factor and proposed the preformation law of cluster radioactivity…”

Section: Introduction ǎmentioning

confidence: 99%

“…For , is determined using the analytic formula [14]. In the second approach, is extracted through the ratios of the calculated cluster radioactivity half-lives employed in the unified fission model (UFM) to the experimental data [29], where in the UFM, the total interaction between the emitted cluster and daughter nucleus consists of the Coulomb, nuclear proximity, and centrifugal potentials [29]. The generalized liquid drop model (GLDM) differs from the CFM [34][35][36] and UFM [29] in its treatment of cluster radioactivity.…”

Section: Introduction ǎmentioning

confidence: 99%

Systematic study of cluster radioactivity within the generalized liquid drop model*

Deng 邓,

Cheng 程,

Bao 包

et al. 2024

The cluster radioactivity is studied within the Generalized Liquid Drop Model (GLDM), in which the shell correction energy, the pairing energy, and the cluster preformation factor are considered. The calculations show significant improvements and can reproduce the experimental data within a factor of 8.04 after the consideration of these physical effects. In addition, the systematic trend of cluster preformation factors $P_c$ is discussed in terms of the $N_pN_n$ scheme to study the influence of valence proton-neutron interaction and shell effect on cluster radioactivity. It is strikingly found that the $\log_{10}{P_c}$ is linearly related to the $N_pN_n$. It is in agreement with the recent work [L. Qi \textit{et al.}, \href{https://journals.aps.org/prc/abstract/10.1103/PhysRevC.108.014325}{Phys. Rev. C 108, 014325 (2023)}], in which $\log_{10}{P_c}$, obtained by using different theoretical models and treatment methods from this work, also has a linear relationship with $N_pN_n$. Combined with recent work by Qi \textit{et al.}, this work suggests that the linear relationship between $\log_{10}{P_c}$ and $N_pN_n$ is model-independent and that both the shell effect and the valence proton-neutron interaction play essential roles in cluster radioactivity. An analytical formula is proposed to calculate the cluster preformation factor based on the $N_pN_n$ scheme. In addition, the cluster preformation factors and cluster radioactivity half-lives of some heavy nuclei are predicted, which can provide references for experiments in the future.