In the present work, we systematically study the α decay half-lives of neptunium ( Z = 93) isotopes within a one-parameter model (OPM). The calculated results are in reasonable agreement with the experimental data. Noticeably, the recently measured α decay half-life value of 380 − 110 + 260 ns for ²²² Np [ Phys. Rev. Lett. 125 , 032 502 (2020)] has been fairly reproduced by the OPM as 780 ns within a factor of ≈2. In addition, we extend this model to predict α decay half-lives of neptunium isotopes whose α decay is energetically allowed or observed but not yet quantified in NUBASE2016. Meanwhile, it is found that the half-life between the neutron number N = 126 and N = 128 in Np drop sharply, this result shows that the N = 126 shell closure is still very robust at Z = 93. At last, α particle preformation probability P α extd are extracted in two cases with α transition orbital angular momentum l = 0 and l = 1, we find a amazing phenomenon that the P α extd are basically the same for α transition with the same orbital angular momentum l .

In the present work, the cluster radioactivity preformation probability $P_c$ in the scheme of $N_p{N}_n$ for the effective number of the valence particles (holes) in trans-lead nuclei has been systematically investigated. This quantity has been explored in the simplified parametrization of $N_p{N}_n$ as well as the multiplication $N_p{N}_{n}I$ of this product with the isospin asymmetry $I$. The calculations for $P_c$ are both performed in microscopic and model-dependent way. Within the microscopic approach, based on our previous work [ Chin. Phys. C 47, 014101 (2023)], $P_c$ is calculated in cluster formation model combined with the exponential relationship of $P_c$ to the $\alpha$ decay preformation probability $P_{\alpha }$ when the mass number of the emitted cluster $A_c\le$ 28. While $A_c\ge$ 28, $P_c$ is obtained through the charge-number dependence of $P_c$ on the decay products proposed by Ren et al. [ Phys. Rev. C 70, 034304 (2004)]. In the model-dependent approach, $P_c$ is extracted through the ratios from calculated cluster radioactivity half-lives in the framework of unified fission model proposed by Dong et al. [ Eur. Phys. J. A 41, 197 (2009)] to experimental ones. Both of the results show $P_c$ in logarithmic form are linear to $N_p{N}_n$ as well as $N_p{N}_{n}I$. For comparison, the parent-mass-number dependence analytical formula as well as the model proposed by Wei and Zhang [ Phys. Rev. C 96, 021601(R) (2017)] are also used. Furthermore, the preformation mechanic for cluster radioactivity has also been discussed.

In this study, based on Wentzel-Kramers-Brillouin theory, we systematically investigate the cluster radioactivity half-lives of 22 nuclei ranging from to using a phenomenological model that considers the screened electrostatic effect of the Coulomb potential. In this model, there are two adjustable parameters, t and g, which are related to the screened electrostatic barrier and the strength of the spectroscopic factor, respectively. The calculated results indicate that this model can effectively reproduce the experimental data, with a corresponding root-mean-square deviation of 0.660. In addition, we extend this model to predict the half-lives of possible cluster radioactive candidates whose cluster radioactivities are energetically allowed or observed but not yet quantified in the evaluated nuclear properties table NUBASE2020. The predicted results are consistent with those obtained using other theoretical models and/or empirical formulas, including the universal decay law proposed by Qi et al. [Phys. Rev. C 80, 044326 (2009)], a semi-empirical model for both α decay and cluster radioactivity proposed by Santhosh et al. [J. Phys. G 35, 085102 (2008)], and a unified formula for the half-lives of α decay and cluster radioactivity proposed by Ni et al. [Phys. Rev. C 78, 044310 (2008)].

In this study, the potential applications of perfect boron carbide (BC₃) nanosheet and single-vacancy defect BC₃ nanosheets (SVBC₃-B and SVBC₃-C), as the drug delivery vehicle for 6-mercaptopurine (6-MP), are investigated based on the calculation of the density functional theory (DFT). The interactions of the 6-MP drug with the BC₃ nanosheet, SVBC₃-B and SVBC₃-C are simulated in the gas phase, water solvent and acidic solvent, respectively. The results demonstrated that the 6-MP drug tends to adsorb parallel on the surface of the BC₃ nanosheet, and the adsorption energy on SVBC₃-B is the largest, followed by the perfect BC₃. The interactions between the 6-MP drug and the perfect BC₃ nanosheet, SVBC₃-B and SVBC₃-C will be weakened in a water solvent. Furthermore, the interaction force between the 6-MP drug and the perfect BC₃ nanosheet or SVBC₃-B nanosheet in an acidic solvent is more significant than that in a water solvent, which is not conducive to separating the 6-MP drug from the two kinds of BC₃ nanosheets. But, the adsorption energy of the 6-MP drug on SVBC₃-C in the acidic solvent is much lesser than that in the water solvent, which indicates that the 6-MP drug can be easily separated from SVBC₃-C in the acidic environment. The PH value of cancer tissue is just acidic, which provides an ideal environment for separating 6-MP. Generally, the results confirmed the possibility of SVBC₃-C as a delivery vehicle for the 6-MP drug. GRAPHICAL ABSTRACT