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Using Multi-Layer Perceptrons (MLP) and Kolmogorov-Arnold Networks (KAN), we construct a holographic model based on lattice QCD data for the heavy-quark potential in the 2+1 system. The deformation factor $w(r)$ in the metric is obtained using the two types of neural network. First, we numerically obtain $w(r)$ using MLP, accurately reproducing the QCD results of the lattice, and calculate the heavy quark potential at finite temperature and the chemical potential. Subsequently, we employ KAN within the Andreev-Zakharov model for validation purpose, which can analytically reconstruct $w(r)$, matching the Andreev-Zakharov model exactly and confirming the validity of MLP. Finally, we construct an analytical holographic model using KAN and study the heavy-quark potential at finite temperature and chemical potential using the KAN-based holographic model. This work demonstrates the potential of KAN to derive analytical expressions for high-energy physics applications.

Within the framework of the Einstein-Maxwell-Dilaton (EMD) model, which incorporates information on the equation of state and baryon number susceptibility from lattice results, we have conducted a comprehensive analysis of the potential energy, running coupling, and dissociation time for heavy quark-antiquark pairs using gauge/gravity duality. This study encompasses various systems, including pure gluon systems, 2 flavor systems, 2+1 flavor systems, and 2+1+1 flavor systems under finite temperature and chemical potential. The results reveal that the linear component of the potential energy diminishes as the flavor increases. It is also found that our results are extremely close to the recent lattice results for 2+1 flavors at finite temperature. Moreover, we have thoroughly investigated the dissociation distance and running coupling constant of quark-antiquark pairs to gain a comprehensive understanding of their behavior across various flavors. Finally, we have examined real-time dynamics of quark dissociation. The findings indicate that the dissociation time of quark-antiquark pairs is dependent on temperature, chemical potential, and flavor of the systems.

In the present work, the cluster radioactivity preformation probability Pc in the scheme of NpNn 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 NpNn as well as the multiplication NpNnI of this product with the isospin asymmetry I. The calculations for Pc are both performed in microscopic and model-dependent way. Within the microscopic approach, based on our previous work [Chin. Phys. C 47,014101 (2023)], Pc is calculated in cluster formation model (CFM) combined with the exponential relationship of Pc to the alpha decay preformation probability P alpha when the mass number of the emitted cluster Ac less than 28. While Ac greater than 28, Pc is obtained through the charge-number dependence of Pc on the decay products proposed by Ren et al. [Phys. Rev. C 70,034304 (2004)]. In the model-dependent approach, Pc is extracted through the ratios from calculated cluster radioactivity half-lives in the framework of unified fission model (UFM) proposed by Dong et al. [Eur. Phys. J. A 41,197 (2009)] to experimental ones. Both of the results show Pc in logarithmic form are linear to NpNn as well as NpNnI. For comparison, the parent-mass-number dependence analytical formula as well as the model proposed by K. Wei and H. F. Zhang [Phys. Rev. C 96,021601(R)(2017)] are also used. Furthermore, the preformation mechanic for cluster radioactivity has also been discussed.

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

In the present work, we systematically study the spectroscopic factor of proton radioactivity ($S_p$) with $A>100$ using the deformed two-potential approach (D-TPA). It is found that there is a link between the quadrupole deformation parameter of proton emitter and $S_p$. Based on this result, we propose a simple analytic formula for estimating the spectroscopic factor of proton radioactivity. With the help of this formula, the calculated half-lives of proton radioactivity can reproduce the experimental data successfully within a factor of 2.77. Furthermore, we extend the D-TPA with this formula for evaluating the spectroscopic factor to predict the proton radioactivity half-lives of 12 proton radioactivity candidates whose radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020. For comparison, the universal decay law for proton radioactivity (UDLP) and the new Geiger-Nuttall law (NG-N) are also used. It turns out that all of the predicted results are basically consistent with each other.

In this work, based on the framework of the Coulomb and proximity potential model (CPPM), we systematically study the cluster radioactivity half-lives of 26 trans-lead nuclei by considering the cluster preformation probability which is found to possess a simple mass dependence on the emitted cluster by R. Blendowske and H. Walliser [Phys. Rev. Lett. 61, 1930(1988)]. Meanwhile, we investigate 28 different versions of the proximity potential formalisms, which are the most complete known proximity potential formalisms and have been proposed for the description of proton radioactivity, two-proton radioactivity, {\alpha} decay, heavy-ion radioactivity, quasi-elastic scattering, fusion reactions and other applications. The calculated results show that the modified forms of proximity potential 1977 denoted as Prox.77-12 and the proximity potential 1981 denoted as Prox.81 are the most appropriate proximity potential formalisms for the study of cluster radioactivity as the root-mean-square deviation between experimental data and relevant theoretical results obtained are least and the both values are 0.681. For comparison, a universal decay law (UDL) proposed by Qi et al. [Phys. Rev. C 80, 044326 (2009)], a unified formula of half-lives for {\alpha} decay and cluster radioactivity proposed by Ni et al. [Phys. Rev. C 78, 044310 (2008)] and a scaling law (SL) in cluster decay proposed by Horoi et al. [J. Phys. G 30, 945 (2004)] are also used. In addition, utilizing CPPM with Prox.77- 12, Prox.77-1, Prox.77-2 and Prox.81, we predict the half-lives of 51 potential cluster radioactive candidates whose cluster radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020. The predicted results are in the same order of magnitude with those obtained by using the compared semi-empirical and/or empirical formulae.

Differential cross sections of the elastic pion-proton scattering are investigated at very small momentum transfer in a holographic QCD model, considering both the strong and Coulomb interaction in the Regge regime. The strong interaction is described by the Pomeron and Reggeon exchange, and the Coulomb interaction is characterized by the one photon exchange. The two interactions are linked through an interference term and we only need to determine a single adjustable parameter involved in this term. As to the parameters for the strong interaction, we can utilize the values determined in the previous studies. The differential cross sections can be predicted without any additional parameters, and it is shown that our predictions are consistent with the experimental data. We explicitly show the momentum transfer dependence for the interference effect. The energy dependence of the contribution ratios for each component is also discussed., Comment: 24 pages, 5 figures, version accepted for publication in Phys. Rev. D

In the present work, based on Wentzel-Kramers-Brillouin theory, we systematically study the cluster radioactivity half-lives of 22 nuclei ranging from $^{221}$$\rm{Fr}$ to $^{242}$$\rm{Cm}$ by using a phenomenological model, which considers the screened electrostatic effect of Coulomb potential. In this model, there are two adjustable parameters i.e. the parameter $t$ and $g$, which are related to the screened electrostatic barrier and the strength of spectroscopic factor, respectively. The calculated results indicate this model can well reproduce the experimental data while the corresponding root-mean-square (rms) deviation is 0.660. In addition, we extend this model to predict the half-lives of possible cluster radioactive candidates whose cluster radioactivity are energetically allowed or observed but not yet quantified in the evaluated nuclear properties table NUBASE2020. The predicted results are consistent with the ones obtained by using other theoretical models and/or empirical formulae including the universal decay law (UDL) proposed by Qi \textit{et al.} [Phys. Rev. C 80, 044326 (2009)], a semi-empirical model for both $\alpha$ decay and cluster radioactivity proposed by Santhosh \textit{et al.} [J. Phys. G 35, 085102 (2008)] and a unified formula of half-lives for $\alpha$ decay and cluster radioactivity proposed by Ni \textit{et al.} [Phys. Rev. C 78, 044310 (2008)].

The differential cross sections of elastic proton-proton (pp) and proton-antiproton (pp\bar) scattering are studied in a holographic QCD model, considering the strong and Coulomb interaction in the Regge regime. Based on previous studies of strong interactions described in terms of Pomeron and Reggeon exchange, we add the contribution of Coulomb interaction described by photon exchange. We present the momentum transfer dependence of the contribution rates for each component, especially for the Coulomb-nuclear interference, which refers to the cross term between both interactions. For the adjustable parameters for the strong interaction, we can adopt the values determined in previous studies, and there are no extra adjustable parameters that need to be determined for the Coulomb interaction. It is presented that the resulting differential cross sections are consistent with the data for pp and pp\bar scattering., Comment: 19 pages, 6 figures

The effect of gluon condensate on the holographic entanglement entropy is investigated in an Einstein-Dilaton model at zero and finite temperature. There is a critical length for the difference of entanglement entropy between the connected and disconnected surfaces in this model, which is often regarded as a signal of phase transition. With the increase of gluon condensate, the critical length becomes small, which means the confinement becomes strong at zero temperature. Moreover, an entropic C-function suddenly jumps to zero at the critical length, where there are expected to be no entangled states. At finite temperatures, results show that the effect of gluon condensate on the critical length is qualitatively consistent with the case of zero temperature. We find that the entropic C-function increases as a function of $l$ at finite temperature, while it has competitive behaviors with large gluon condensate.

Using gauge/gravity duality, we first study the string breaking and melting of doubly heavy baryon at a finite chemical potential and temperature in this paper. The decay mode $\rm{Q Q q \rightarrow Q q q+Q \bar{q}}$ is investigated with the presence of temperature and chemical potential in this paper. With the increase of temperature and chemical potential, string breaking takes place at a smaller potential energy and the string-breaking distance will increase slightly. It is also found that the $\rm{QQq}$ melts at small separate distance with the increase of temperature and chemical potential. Then, we compare the screening distance of $\rm{QQq}$ with $\rm{Q \bar{Q}}$ under the same conditions. Finally, we draw the melting diagram of $\rm{QQq}$ and $\rm{Q \bar{Q}}$ in the $T-\mu$ plane., Comment: 24pages, 18 figures

In the present work, we systematically study the proton radioactivity half-lives of 33 spherical nuclei based on the relationship between the Skyrme parameters and the macroscopic quantities of nuclear matter. Using the two-potential approach with the spherical Skyrme-Hartree-Fock model, the correlation between proton radioactivity half-life and macroscopic quantities was analyzed. Moreover, we obtained a new Skyrme parameter set by fitting the two most weighted macroscopic quantities. Compared with Skyrme parameters MSL0 and the theoretical model of proton radioactivity UDLP, the theoretical proton radioactivity half-life calculated by the new Skyrme parameter set can better reproduce the experimental data., Comment: 8 pages, 3 figures

Considering the preformation probability of the two emitted protons in the parent nucleus, we extend the Coulomb and proximity potential model (CPPM) to systematically study two-proton (2p) radioactivity half-lives of the nuclei close to proton drip line. The proximity potential chosen is Prox. 81 proposed by Blocki et al. in 1981. Furthermore, we apply this model to predict the half-lives of possible 2p radioactive candidates whose 2p radioactivity is energetically allowed or observed but not yet quantified in the evaluated nuclear properties table NUBASE2016. The predicted results are in good agreement with those from other theoretical models and empirical formulas, namely the effective liquid drop model (ELDM), generalized liquid drop model (GLDM), Gamow-like model, Sreeja formula and Liu formula.

Using the gauge/gravity duality, we investigate the string breaking and dissolution of two heavy quarks coupled to a light quark at finite temperature. It is found that there exist three configurations of QQq with the increase of separate distance for heavy quarks in the confined phase. Besides, the string breaking occurs at the distance $L_{\rm{QQq}} = 1.27 \rm{fm}$($T = 0.1 \rm{GeV}$) for the decay mode $\rm{Q Q q \rightarrow Q q q+Q \bar{q}}$. In the deconfined phase, QQq will melt at a certain distance then becomes free quarks. At last, we compare the potential of QQq with that of $\rm{Q\bar{Q}}$ and find $\rm{Q\bar{Q}}$ is more stable than QQq at high temperature., Comment: 23 pages, 24 figures

In the present work, we systematically study the two-proton (2p) radioactivity half-lives of nuclei close to the proton drip line within a modified Gamow-like model. Using this model, the calculated 2p radioactivity half-lives can well reproduce the experimental data. Moreover, we use this model to predict the 2p radioactivity half-lives of 22 candidates whose 2p radioactivity is energetically allowed or observed but not yet quantied in evaluated nuclear properties table NUBASE2016. The predicted results are in good agreement with the ones obtained by using Gamow-like model, effective liquid drop model (ELDM), generalized liquid drop model (GLDM) as well as a four-parameter formula., Comment: 12 pages, 3 figures

In the present work we systematically study the half--lives of proton radioactivity for spherical proton emitters with ${Z\ge 69}$ based on two--potential approach. While the nuclear potential of the emitted proton--daughter nucleus is adopted by a parameterized cosh type, the parameters of the depth and diffuseness for nuclear potential are determined by fitting experimental data of 32 spherical proton emitters. In order to reduce the deviations between experimental half-lives and calculated ones, we propose a simple analytic expression for formation probability of proton radioactivity with the same orbital angular momentum $l$. The results indicate that the formation probability can be simply described by a formula of $A_d^{1/3}$. Moreover, the linear relationship between the formation probability and the fragmentation potential also exists. The calculated half-lives can well reproduce the experimental data., Comment: 9 pages,6 figures

In this work, we systematically study the two-proton($2p$) radioactivity half-lives using the two-potential approach while the nuclear potential is obtained by using Skyrme-Hartree-Fock approach with the Skyrme effective interaction of {SLy8}. For true $2p$ radioactivity($Q_{2p}$ $>$ 0 and $Q_p$ $< $0, where the $Q_p$ and $Q_{2p}$ are the released energy of the one-proton and two-proton radioactivity), the standard deviation between the experimental half-lives and our theoretical calculations is {0.701}. In addition, we extend this model to predict the half-lives of 15 possible $2p$ radioactivity candidates with $Q_{2p}$ $>$ 0 taken from the evaluated atomic mass table AME2016. The calculated results indicate that a clear linear relationship between the logarithmic $2p$ radioactivity half-lives $\rm{log}_{10}T_{1/2}$ and coulomb parameters [ ($Z_{d}^{0.8}$+$l^{0.25}$)$Q_{2p}^{-1/2}$] considered the effect of orbital angular momentum proposed by Liu $et$ $al$ [Chin. Phys. C \textbf{45}, 024108 (2021)] is also existed. For comparison, the generalized liquid drop model(GLDM), the effective liquid drop model(ELDM) and Gamow-like model are also used. Our predicted results are consistent with the ones obtained by the other models., Comment: 8 pages,2figures

In the present work, combining with the Geiger-Nuttall law, a two-parameter empirical formula is proposed to study the two-proton (2p) radioactivity. Using this formula, the calculated 2p radioactivity half-lives are in good agreement with the experimental data as well as the calculated ones obtained by Goncalves et al: ([Phys. Lett. B 774, 14 (2017)]) using the effective liquid drop model (ELDM), Sreeja et al: ([Eur. Phys. J. A 55, 33 (2019)]) using a four-parameter empirical formula and Cui et al: ([Phys. Rev. C 101: 014301 (2020)]) using a generalized liquid drop model (GLDM). In addition, this two-parameter empirical formula is extended to predict the half-lives of 22 possible 2p radioactivity candidates, whose the 2p radioactivity released energy Q2p>0, obtained from the latest evaluated atomic mass table AME2016. The predicted results have good consistency with ones using other theoretical models such as the ELDM, GLDM and four-parameter empirical formula., Comment: 6 pages, 2 figures

Proton radioactivity is an important and common process of the natural radioactivity of proton-rich nuclei. In our previous work [J. H. Cheng et al., Nucl. Rhys. A 997, 121717 (2020)], we systematically studied the proton radioactivity half-lives of 53< Z <83 nuclei within the two-potential approach with Skyrme-Hartree-Fock. The calculations can well reproduce the experimental data of spherical nuclei. The present work is an extension of the previous work. We systematically study 32 proton radioactivity half-lives of spherical nuclei with the two-potential approach with Skyrme-Hartree-Fock (TPA-SHF) within 115 different versions of the Skyrme interactions. The calculated results indicate that the SLy7 Skyrme interaction gives the lowest r.m.s. deviation in the description of the experimental data of the spherical proton emitters among all the different versions of the Skyrme interactions. In addition, we use this model with the SLy7 Skyrme interaction to predict the proton radioactivity half-lives of 7 spherical nuclei in the same region, whose proton radioactivity is energetically allowed or has been observed but is not yet quantified.

In this work, we systematically study the $\alpha$ decay preformation factors $P_{\alpha}$ and $\alpha$ decay half-lives of 152 nuclei around $Z$ = 82, $N$ = 126 closed shells based on a generalized liquid drop model while $P_{\alpha}$ is extracted from the ratio of the calculated $\alpha$ decay half-life to the experimental one. The results show that there is an obvious linear relationship between $P_{\alpha}$ and the product of valance protons (holes) $N_p$ and valance neutrons (holes) $N_n$. At the same time, we extract the $$P_{\alpha}$ values of even-even nuclei around $\emph{Z}$ = 82, $\emph{N}$ = 126 closed shells from the work of Sun \textit{et al.} [\href {https://doi.org/10.1088/1361-6471/aac981} {J. Phys. G: Nucl. Part. Phys. $\bm{45}$, 075106 (2018)}], in which the $P_{\alpha}$ can be calculated by two different microscopic formulas. We find that the $P_{\alpha}$ are also related to $N_pN_n$. Combining with our previous works [Sun \textit{et al.}, \href {https://doi.org/10.1103/PhysRevC.94.024338} {Phys. Rev. C $\bm{94}$, 024338 (2016)}; Deng \textit{et al.}, \href {https://doi.org/10.1103/ PhysRevC 96.024318} {ibid. $\bm{96}$, 024318 (2017)}; Deng \textit{et al.}, \href {https://doi.org/10.1103/PhysRevC.97.044322} {ibid. $\bm{97}$, 044322 (2018)}] and the work of Seif \textit{et al.} [\href {http://dx.doi.org/10.1103/PhysRevC.84.064608}{Phys. Rev. C $\bm{84}$, 064608 (2011)}], we suspect that this phenomenon of linear relationship for the nuclei around those closed shells is model independent. It may be caused by the effect of the valence protons (holes) and valence neutrons (holes) around the shell closures. Finally, using the formula obtained by fitting the $P_{\alpha}$ calculated by the generalized liquid drop model (GLDM), we calculate the $\alpha$ decay half-lives of these nuclei. The calculated results are agree with the experimental data well.

In the present work considering the contributions of the daughter nuclear charge and the orbital angular momentum taken away by the emitted proton, we propose a two-parameter formula of new Geiger-Nuttall law for proton radioactivity. A set of universal parameters of this law is obtained by fitting 44 experimental data of proton emitters in the ground state and isomeric state. The calculated results can reproduce the experimental data well. For a comparison, the calculations performed using other theoretical methods, such as UDLP proposed by Qi, et al. [https://journals.aps.org/prc/abstract/10.1103/PhysRevC.85.011303], the CPPM-Guo2013 analyzed by our previous work [Deng, et al., https://link.springer.com/article/10.1140/epja/i2019-12728-0] and the modified Gamow-like model proposed by us [Chen, et al., https://iopscience.iop.org/article/10.1088/1361-6471/ab1a56] are also included. Meanwhile, we extend this new Geiger-Nuttall law to predict the proton radioactivity half-lives for $51 \leq Z \leq 91$ nuclei, whose proton radioactivity is energetically allowed or observed but not yet quantified in NUBASE2016., Comment: 8 pages, 6 figures

In the present work we systematically study $\mathcal{\alpha}$ decay half-lives of $Z>51$ nuclei using the modified Gamow-like model which includes the effects of the centrifugal potential and electrostatic shielding. For the case of even-even nuclei, this model contains two adjustable parameters: the parameter $a$ related to the screened electrostatic barrier and the radius constant $r_0$, while for the case of odd-odd and odd-A nuclei, it is added a new parameter i.e. hindrance factor $h$ which is used to describe the effect of an odd-proton and/or an odd-neutron. Our calculations can well reproduce the experimental data. In addition, we use this modified Gamow-like model to predict the $\mathcal{\alpha}$-decay half-lives of seven even-even nuclei with $Z=120$ and some un-synthesized nuclei on their $\mathcal{\alpha}$ decay chains., Comment: 30 pages, 6 figures. This paper has been accepted by Nuclear Physics, Section A

In the present work we systematically study the half--lives of proton radioactivity for $51 \leq Z \leq 83$ nuclei based on the Gamow--like model with a screened electrostatic barrier. In this model there are two parameters while considering the screened electrostatic effect of Coulomb potential with the Hulthen potential i.e. the effective nuclear radius parameter r_0 and the screening parameter a. The calculated results can well reproduce the experimental data. In addition, we extend this model to predict the proton radioactivity half--lives of 16 nuclei in the same region within a factor of 2.94, whose proton radioactivity are energetically allowed or observed but not yet quantified. Meanwhile, studying on the proton radioactivity half-life by a type of universal decay law has been done. The results indicate that the calculated half--lives are linearly dependent on Coulomb parameter with the same orbital angular momentum., Comment: 12 pages, 5 figures, accepted by Journal of Physics G: Nuclear and Particle Physics

In this work we present a systematic study of the proton radioactivity half-lives of spherical proton emitters within the Coulomb and proximity potential model. We investigate 28 different versions of the proximity potential formalisms developed for the description of proton radioactivity, $\mathcal{\alpha}$ decay and heavy particle radioactivity. It is found that 21 of them are not suitable to deal with the proton radioactivity, because the classical turning points $r_{\text{in}}$ cannot be obtained due to the fact that the depth of the total interaction potential between the emitted proton and the daughter nucleus is above the proton radioactivity energy. Among the other 7 versions of the proximity potential formalisms, it is Guo2013 which gives the lowest rms deviation in the description of the experimental half-lives of the known spherical proton emitters. We use this proximity potential formalism to predict the proton radioactivity half-lives of 13 spherical proton emitters, whose proton radioactivity is energetically allowed or observed but not yet quantified, within a factor of 3.71., Comment: 10 pages, 5 figures. This paper has been accepted by The European Physical Journal A (in press 2019)

$\alpha$ decay is usually associated with both ground and low-lying isomeric states of heavy and superheavy nuclei, and the unpaired nucleon plays a key role on $\alpha$ decay. In this work, we systematically studied the $\alpha$ decay half-lives of odd-$A$ nuclei, including both favored and unfavored $\alpha$ decay within the two-potential approach based on the isospin dependent nuclear potential. The $\alpha$ preformation probabilities are estimated by using an analytic formula taking into account the shell structure and proton-neutron correlation, and the parameters are obtained through the $\alpha$ decay half-lives data. The results indicate that in general the $\alpha$ preformation probabilities of even-$Z$, odd-$N$ nuclei are slightly smaller than the odd-$Z$, even-$N$ ones. We found that the odd-even staggering effect may play a more important role on spontaneous fission than $\alpha$ decay. The calculated half-lives can well reproduce the experimental data.

In present work, the unfavored $\mathcal{\alpha}$ decay half-lives and $\mathcal{\alpha}$ preformation probabilities of closed shell nuclei related to ground and isomeric states around $Z=82$, $N=82$ and 126 shell closures are investigated by adopting two-potential approach from the perspective of valence nucleon (hole) and isospin asymmetry of the parent nucleus. The results indicate that $\mathcal{\alpha}$ preformation probability is linear dependence on $N_p N_n$ or $N_p N_n I$, the same as the case of favored $\mathcal{\alpha}$ decay in our previous work [X.-D. Sun \textit{et al.}, Phys. Rev. C 94, 024338 (2016)]. $N_p$, $N_n$, and $I$ represent the number of valence protons (holes), the number of valence neutrons (holes), and the isospin of the parent nucleus, respectively. Fitting the $\mathrm{\alpha}$ preformation probabilities data extracted from the differences between experimental data and calculated half-lives without a shell correction, we give two linear formulas of the $\mathcal{\alpha}$ preformation probabilities and the values of corresponding parameters. Based on the formulas and corresponding parameters, we calculate the $\mathrm{\alpha}$ decay half-lives for those nuclei. The calculated results can well reproduce the experimental data., Comment: 7 pages, 5 figures

In the present work, we systematically study the $\mathcal{\alpha}$ decay preformation factors $P_{\alpha}$ within the cluster-formation model and $\mathcal{\alpha}$ decay half-lives by the proximity potential 1977 formalism for nuclei around $Z=82$, $N=126$ closed shells. The calculations show that the realistic $P_{\alpha}$ is linearly dependent on the product of valance protons (holes) and valance neutrons (holes) $N_pN_n$. It is consistent with our previous works [X.-D. Sun \textit{et al.}, \href{https://journals.aps.org/prc/abstract/10.1103/PhysRevC.94.024338}{ Phys. Rev. C 94, 024338 (2016)}, J.-G. Deng \textit{et al.}, \href{https://journals.aps.org/prc/abstract/10.1103/PhysRevC.96.024318}{Phys. Rev. C 96, 024318 (2017)}], which $P_{\alpha}$ are model-dependent and extracted from the ratios of calculated $\mathcal{\alpha}$ half-lives to experimental data. Combining with our previous works, we confirm that the valance proton-neutron interaction plays a key role in the $\mathcal{\alpha}$ preformation for nuclei around $Z=82$, $N=126$ shell closures whether the $P_{\alpha}$ is model-dependent or microcosmic. In addition, our calculated $\mathcal{\alpha}$ decay half-lives by using the proximity potential 1977 formalism taking $P_{\alpha}$ evaluated by the cluster-formation model can well reproduce the experimental data and significantly reduce the errors., Comment: 4 figures, 7 tables; Accepted by Physical Review C

The present work is a continuations of our previous paper [J.-G. Deng, et al., Chin. Phys. C, {\bf41}: 124109 (2017)]. In present work, the $\mathcal{\alpha}$ decay half-life of unknown nucleus $^{296}$Og is predicted within the two-potential approach and the hindrance factors of all 20 even-even nuclei in the same region with $^{296}$Og, i.e. proton number $82