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Oscillation modes of compact stars, in general, can serve as a fingerprint in determining the equation of state (EOS) of dense matter. In this study, we examine the impact of symmetry energy slope ($L$) on the oscillation frequencies of neutron stars (NSs) with nucleon-nucleon short range correlation (SRC) and admixed dark matter (DM) for the first time within the relativistic mean-field theory. By adjusting the $L$, we revise the EOS and coupling parameters in light of the SRC and DM effects, and construct the new sets. The results reveal that NSs containing SRC and DM inside are more likely to satisfy the observational constraints, and we find that smaller $L$ exhibits larger fundamental non-radial and radial frequencies, and that the effect on Large Separation (LG) is also mainly concentrated in the low-mass region. Moreover, we update the linear relationship between the non-radial frequency and mean density, and we further give empirical relations between non-radial and radial frequencies and tidal deformability at different $L$ for 1.4$M_{\odot}$ and 2$M_{\odot}$. These findings will enable us to more effectively confine the NS EOSs, in turn, also provide a strategy to place constraints on the $L$., 18 pages, 13 figures

Inspired by a recent Letter [S. R. Beane et al., Phys. Rev. Lett. 122, 102001(2019)], the entanglement generated in the elastic $S$-wave scattering of $p+{}^{3}\text{He}$ and $n+{}^3\text{H}$ is studied, where the proton, neutron, ${}^{3}$He, and ${}^3$H are all regarded as qubits. To deal with the Coulomb interaction between the proton and ${}^{3}$He, we derive the entanglement power, a physical quantity that measures the average entanglement generated by a scattering process, for charged qubits within the screening method. The entanglement power in the aforementioned two few-nucleon scatterings is found to be generally much smaller than that in the $S$-wave $n+p$ scattering at low energies, with the corresponding cluster effective field theories possessing an enhanced approximate $\text{SU}(2)_1\otimes\text{SU}(2)_{2}$ symmetry at leading order. Our study suggests that the entanglement generation capacities of effective interactions between nucleons and light nuclei could be more suppressed than realistic nucleon-nucleon interactions at low energies., 7 pages, 4 figures; published version

Superposition is one of unusual features in quantum mechanics. This paper investigates the properties of multi-component Schrödinger cat state, generated by amplitude dispersion. The geometrical imaginary of the multi-component Schrödinger cat state is studied, and the entropy of the geometrical imaginary is proposed. This entropy is inverse proportional to the amplitude of the initial coherent state in the large amplitude regime. Additionally, the superposition of the multi-component cat state can be vividly displayed by the Wigner function and the Pegg–Barnett phase operator.

The study of biologic effects of ionizing radiation is important in many fields. In this work, we build a DNA model from the atomic level and study the DNA damage caused by low energy electrons, protons and alpha particles with Geant4-DNA code. Damage yields, including total strand break yields (SBY), single strand break yields (SSBY), double strand break yields (DSBY) and SSB+ yields (SSB + Y), are calculated for each beam. According to the simulation results, direct strand break yields are almost independent of the projectile features and indirect strand break yields decrease with the LET for more radicals reacting with each other. Simple damage yields, like SSBY, decrease with the LET but the total yields of complex damage increase with the LET for the clustering of energy deposition events and radical productions. In the study, different physics and chemistry constructors are used to simulate the direct and indirect damages caused by electrons. Simulation results show that the direct SBY simulated by the physics option4 constructor are, on average, 6.7% and 30.9% higher than the option6 and option2 constructors, respectively, because of the different cross sections implemented in these models. The indirect SBY simulated by chemistry option1 constructor are about 18.3% less than that of the chemistry default constructor due to the different chemical parameters used in these constructors. A comparison with experiment data and other simulation works is also given. The trends of different works are in consistent with each other and the DSBY of protons simulated in this work agree well with the experiment data.

In the T-matrix form of the transfer reaction, the optical model potentials (OMPs) are used to compute the scattering wave function and transition operator. For most cases, the elastic scattering cross sections, normally used to generate the OMPs, are not directly given in the same experiment. Then, the global OMPs, which fit the experimental data over a broad mass and energy range, are widely used in the theoretical calculations. Different sets of global OMPs with different parameter sets can reproduce the scattering cross section equally well within the uncertainty. Here, we apply different global OMPs to calculate the (differential) cross sections of transfer reactions on the target nuclei , , , and at different energies. The results demonstrate that the effects of deuteron and nucleon global OMPs on transfer (differential) cross sections vary with energy and target mass. Furthermore, the influences of the spin-orbit coupling term of deuteron and nucleon global OMPs on the transfer cross sections are not negligible.

The nucleon-nucleon short-range correlation NN-SRC is one of the key issues of nuclear physics, which typically manifest themselves in high-momentum components of the nuclear momentum distributions. In this letter, the nuclear spectral functions based on the axially deformed relativistic mean-field model are developed to involve the NN-SRC. With the spectral functions, the inclusive electron scattering $ (e,e^{\prime}) $ cross sections are calculated within the PWIA framework, including the quasi-elastic (QE) part and $ \Delta $ production part. Especially in the $ \Delta $ production region, we reconsider the electromagnetic structures of the nucleon resonance $ \Delta $(1232) and the scattering mechanisms, thereby the theoretical calculations are improved effectively and the cross sections are well consistent with the experimental data. The theoretical $ (e,e^{\prime}) $ cross sections are further divided into NN-SRC and mean-field contributions. It is found that, at the kinematics $ 0.5 \,{\rm GeV}^{2}

The $\ensuremath{\alpha}$-core structure has been constructed to successfully interpret the band spectra of a series of nuclei above the double shell closure, plus the extension to the heavier cluster structure in the actinide region. By refining the binary cluster model, we show that such kind of picture can be applicable to more heavy nuclei, implying that there can exist cluster states in any heavy nuclei. As for superheavy nuclei, the involved cluster, analogous to the heavy particle radioactivity, is allowed to be above $Zg28$ plus the core $^{208}\mathrm{Pb}$. In this sense, besides some predictions on energy spectra of cluster states in superheavy nuclei, the very recently reported ${2}^{+}$ state of $^{282}\mathrm{Cn}$ is diagnosed to be not in the ground state rotational band via the present method. During the whole procedure, the uncertainty of the cluster model is determined for the first time, by the nonparametric resampling strategy, to make the whole theoretical results reliable and complete.

Nucleon momentum distribution (NMD), particularly its high-momentum components, is essential for understanding the nucleon--nucleon ($ NN $) correlations in nuclei. Herein, we develop the studies of NMD of $^{56}\text{Fe}$ from the axially deformed relativistic mean-field (RMF) model. Moreover, we introduce the effects of $ NN $ correlation into the RMF model from phenomenological models based on deuteron and nuclear matter. For the region $ kk_{\text{F}} $, the high-momentum components of the RMF model are modified by the effects of $ NN $ correlation, which agree with the experimental data. Comparing the NMD of relativistic and non-relativistic mean-field models, the relativistic effects on nuclear structures in momentum space are analyzed. Finally, by analogizing the tensor correlations in deuteron and Jastrow-type correlations in nuclear matter, the behaviors and contributions of $ NN $ correlations in $^{56}\text{Fe}$ are further analyzed, which helps clarify the effects of the tensor force on the NMD of heavy nuclei., Comment: 12 pages, 10 figures, This article has been published in SCIENCE CHINA Physics, Mechanics & Astronomy(SCPMA), and the original publication is available at www.scichina.com and www.springerlink.com

Background: Recently, novel statistical methods such as neural networks and Bayesian learning methods are implemented to describe the nuclear masses. Purpose: Based on previous studies, an improved naive Bayesian probability (iNBP) classifier is proposed to study the nuclear masses by refining the results of sophisticated nuclear models. Method: In the iNBP method, the prediction for nuclear masses is treated as a classification problem. The residuals are classified into several groups to generate prior and conditional probabilities, and the posterior probabilities are further determined by the Bayesian formula. We choose the expectation with maximum probability as the final prediction. Reliability of the iNBP method is assessed by analyzing the global optimizations and the extrapolating capabilities. Results: The iNBP method exhibits impressive improvements on global descriptions for different mass models. Moreover, the method shows robust extrapolating capabilities. Results demonstrate the iNBP method can be applied to predict the nuclear masses of unknown regions. Conclusions: Considering the local mass relations, the iNBP method can offer considerable fine-tuning of the mass descriptions from nuclear models. The methodology proposed in this paper can also be applied to other model-based extrapolations of nuclear observables.

Nucleon-nucleon short-range correlations (SRCs) result in the presence of high-momentum tail (HMT) above the Fermi surface in nucleon momentum distribution. In this work, we introduce HMT corrections in relativistic mean field (RMF) theory to make the theory compatible with the nucleon-nucleon SRCs. The properties of nucleonic stars and hyperon stars are studied within the RMF theory with HMT corrections. After introducing the HMT corrections, the equation of state (EoS) of the nucleonic star becomes softer and the maximum mass is smaller. The particle fractions of hyperon stars are significantly affected by the HMT corrections. The threshold densities of the presence of hyperons are changed dramatically. More importantly, with the introduction of HMT corrections, the mass-radius relations of nucleonic stars and hyperon stars can satisfy the stringent limits provided by the detection of gravitational wave.

We incorporate the nuclear medium effect into α-decay calculation through a reformulation of the conventional double-folding model. The improved model enables the α cluster to simultaneously change its size at different nuclear density during the Coulomb penetration process, thus reflecting the effect from the variation of nuclear mean field and Pauli blocking at the nuclear surface. To evaluate the result of such a dynamic effect, we perform a systematic calculation of α-decay half-lives for even-even α-emitters within a deformed cluster model. We found that the medium effect optimises the shape of α-nucleus potential at the surface region, leading to a remarkable reduction in the deviations between the theoretical and experimental decay rates. The result implies the importance of the dynamic aspect of α clustering in describing a realistic α-nucleus interaction. Keywords: α decay, Half-life, Nuclear medium effect, α clustering, α-preformation factor

α clustering plays an important role in studying not only nuclear structures but also nuclear reactions of light nuclei. In this work, we study the O 18 , 16 + 13 , 12 C fusion-evaporation reactions at the energy near the Coulomb barrier using a modified statistical model with the α-cluster structures taken into consideration explicitly in the nuclear level densities. This modified statistical model reproduces successfully the experimentally measured α-emission cross sections, and thus provides a possible way to resolve the underestimation discrepancy of the α emission in the original statistical model. Moreover, the modified statistical model could also describe well the angular distributions of the evaporation residues and the energy spectra of the emitted α particles. Therefore, our work shows that α-cluster structures could play an important role in the fusion-evaporation reactions of light ions, and the modified statistical model is a reliable theoretical model for these physical processes.

Background: Recently, the researches of cluster structure have attracted considerable attention. Many microscopic structure models have been applied to describe the cluster configurations.Purpose: To better analyze the cluster structure and associate with the experimental observations, comparative studies are carried out in this paper by combining the nuclear structure model with the electron scattering theory.Method: The density distributions for candidate nuclei of normal and cluster states are obtained from the deformed relativistic Hartree-Bogoliubov (RHB) model. Using some moderate approximations, the corresponding Coulomb form factors $|{F}_{C}{(q)|}^{2}$ and inclusive cross sections for different configurations are calculated by the distorted wave Born approximation (DWBA) and coherent density fluctuation model (CDFM), respectively.Results: Comparing the $|{F}_{C}{(q)|}^{2}$ and inclusive cross sections of different configurations, the effects of nuclear cluster structure can be revealed, due to the differences of nuclear charge radii ${R}_{C}$ in coordinate space and the discrepancies of Fermi momentum ${k}_{F}$ in momentum space.Conclusions: Results illustrate that the cluster structure can be reflected from the elastic and inclusive electron scattering. The studies conducted in this paper provide a new approach to analyze the cluster configurations, and are also helpful to guide future electron scattering experiments.

A new α-emitting isotope ^{214}U, produced by the fusion-evaporation reaction ^{182}W(^{36}Ar,4n)^{214}U, was identified by employing the gas-filled recoil separator SHANS and the recoil-α correlation technique. More precise α-decay properties of even-even nuclei ^{216,218}U were also measured in the reactions of ^{40}Ar, ^{40}Ca beams with ^{180,182,184}W targets. By combining the experimental data, improved α-decay reduced widths δ^{2} for the even-even Po-Pu nuclei in the vicinity of the magic neutron number N=126 are deduced. Their systematic trends are discussed in terms of the N_{p}N_{n} scheme in order to study the influence of proton-neutron interaction on α decay in this region of nuclei. It is strikingly found that the reduced widths of ^{214,216}U are significantly enhanced by a factor of two as compared with the N_{p}N_{n} systematics for the 84≤Z≤90 and N

In this paper, we calculate the cross sections for proton-induced reactions producing short-lived radionuclides like $^{7,10}\mathrm{Be}$, $^{26}\mathrm{Al}$, $^{53,54}\mathrm{Mn}$, etc., with the Li\`ege intranuclear cascade model (incl$++$). The results show that the incl model, when coupled with the proper deexcitation model, gives satisfactory results for most of the considered reactions. Generally, results for reactions with $(\mathrm{\ensuremath{\Delta}}N\ensuremath{-}\mathrm{\ensuremath{\Delta}}Z)$ equal to 0 or 1 are more likely to precisely match experimental data than those for reactions with larger or smaller $|\mathrm{\ensuremath{\Delta}}N\ensuremath{-}\mathrm{\ensuremath{\Delta}}Z|$. Our results can provide useful references for both the users and developers of incl and deexcitation models.

$\alpha$-cluster structures above double shell closures are among the cornerstones for nuclear $\alpha$-cluster physics. Semi-microscopic cluster models (SMCMs) are important theoretical models to study their properties. A crucial ingredient of SMCM is the effective potential between the alpha cluster and the doubly magic nucleus. We derive new double-folding potentials between $\alpha$ clusters and doubly magic nuclei from soft local chiral nucleon-nucleon potentials given by chiral effective field theory ($\chi$EFT) at the next-to-next-to-leading order. The $\alpha$-cluster structures in ${}^{8}\text{Be}$, ${}^{20}\text{Ne}$, ${}^{44,52}\text{Ti}$, and ${}^{212}\text{Po}$ are explored to validate these new double-folding potentials. The $\alpha$ decay of ${}^{104}\text{Te}$ is also studied in the light of recent experimental results. Our study shows that double-folding potentials from $\chi$EFT are the new reliable effective potentials for the SMCM approach to $\alpha$-cluster structures above double shell closures, with both conceptual and phenomenological merits., Comment: 9 pages, 2 figures; accepted by Physical Review C

We study the $\ensuremath{\alpha}$-decay energies (${Q}_{\ensuremath{\alpha}}$) taken from the Atomic Mass Evaluation 2016 within the valence correlation scheme (VCS). A linear trajectory of $\ensuremath{\alpha}$-decay energies, derived from the VCS for nucleon separation energies, is put forward in terms of $\ifmmode\pm\else\textpm\fi{}\ensuremath{\alpha}{N}_{\mathrm{p}}\ensuremath{\mp}\ensuremath{\beta}{N}_{\mathrm{n}}({N}_{\mathrm{p}}$ and ${N}_{\mathrm{n}}$ are the valence proton and neutron numbers, respectively, counted as particles or holes from the nearest shell closure). It is applicable well to all available $\ensuremath{\alpha}$ emitters including even-even, odd-$A$, and odd-odd nuclei. This relationship can be understood via the Taylor expansion method based on the Bethe-Weizs\"acker (BW) mass formula, leading to the recognition on the origin of the $\ensuremath{\alpha}$-decay energy to some extent as well. In fact, the present study can not only reconfirm the similar linear dependence of nucleon separation energies in the VCS, but also exhibit a regular pattern of $\ensuremath{\alpha}$-decay energy and provide a reasonable estimation on unknown ${Q}_{\ensuremath{\alpha}}$ values.

The nonlocalized clustering approach is generalized to $$^{8-11}$$ Be isotopes with isospin dependent spin–orbit potential. A new form of the Tohsaki-Horiuchi-Schuck-Ropke (THSR) wave function is introduced to provide a correct description for the $$\sigma $$ -binding neutron in $$^{11}$$ Be. Systematic calculations for $$^{8-11}$$ Be isotopes are performed and results fit well with experimental values. The low energy spectrum of $$^{11}$$ Be is also obtained, especially the correct spin-parity $$1/2^{+}$$ is reproduced for the intruder ground state. The exotic neutron halo structure of $$^{11}$$ Be is studied by calculations of root-mean-square radii and density distribution. The spectroscopic factor is also calculated and discussed for the $$1/2^+$$ ground state of $${}^{11}$$ Be.

Elliott's SU(3) model is at the basis of the shell-model description of rotational motion in atomic nuclei. We demonstrate that SU(3) symmetry can be realized in a truncated shell-model space if constructed in terms of a sufficient number of collective $S$, $D$, $G$, $\dots$ pairs (i.e., with angular momentum zero, two, four, $\dots$) and if the structure of the pairs is optimally determined either by a conjugate-gradient minimization method or from a Hartree-Fock intrinsic state. We illustrate the procedure for 6 protons and 6 neutrons in the $pf$ ($sdg$) shell and exactly reproduce the level energies and electric quadrupole properties of the ground-state rotational band with $SDG$ ($SDGI$) pairs. The $SD$-pair approximation without significant renormalization, on the other hand, cannot describe the full SU(3) collectivity. A mapping from Elliott's fermionic SU(3) model to systems with $s$, $d$, $g$, $\dots$ bosons provides insight into the existence of a decoupled collective subspace in terms of $S$, $D$, $G$, $\dots$ pairs.

The calculable $R$-matrix theory has been formulated successfully for regular boundary conditions with vanishing radial wave functions at the coordinate origins [P. Descouvemont and D. Baye, Rept. Prog. Phys. 73, 036301 (2010)]. We generalize the calculable $R$-matrix theory to the incoming wave boundary condition (IWBC), which is widely used in theoretical studies of low-energy heavy-ion fusion reactions to simulate the strong absorption of incoming flux inside the Coulomb barriers. The generalized calculable $R$-matrix theory also provides a natural starting point to extend eigenvector continuation (EC) [D. Frame et al., Phys. Rev. Lett. 121, 032501 (2018)] to fusion observables. The ${}^{14}\text{N}+{}^{12}\text{C}$ fusion reaction is taken as an example to validate these new theoretical tools. Both local and nonlocal potentials are considered in numerical calculations. Our generalizations of the calculable $R$-matrix theory and EC are found to work well for IWBC., Comment: 9 pages, 4 figures; accepted by Physical Review C

In this study, we determine the influence of the nucleon-nucleon short range correlation (SRC) on static spherically symmetric neutron stars (NSs) from the perspectives of radial and nonradial oscillations for the first time. We revise the equation of state and coupling parameters in the relativistic mean field theory after considering the SRC effect, and select the hyperon coupling parameters as the SU(3) model. For the non-radial oscillations, the SRC effect decreases the -mode frequency by kHz. For the radial oscillations, it decreases the fundamental radial frequency by 0.75 ~ 0.85 kHz. Additionally, we refit the linear relationship between the average density and -mode frequency for SRC. Combining the characteristics of the radial and non-radial frequencies, we provide a view of inferring the maximum mass of NSs. Owing to the characteristics of the SRC influence on the radial frequency, we expect that the SRC can be tested by future observation and can also be used as a probe for the structure inside NSs.

We study the ternary fission of various even-even $\ensuremath{\alpha}$-structured parent nuclei with $12\ensuremath{\le}A\ensuremath{\le}60$, such as $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{20}\mathrm{Ne}$, $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, $^{32}\mathrm{S}$, $^{36}\mathrm{Ar}$, $^{40}\mathrm{Ca}$, $^{44}\mathrm{Ti}$, $^{48}\mathrm{Cr}$, $^{52}\mathrm{Fe}$, $^{56}\mathrm{Ni}$, and $^{60}\mathrm{Zn}$, within a three-body decay approach. In the present study, we consider the three spherical ternary fission fragments with the lightest fragment ${A}_{3}$ at the middle of the other two main fission fragments, ${A}_{1}$ and ${A}_{2}$. The effects of hyperradius and the hypermomentum quantum number in the ternary fission potential energy barrier are also studied. Further, the total excitation energy and the ternary fission relative yields are calculated for the possible ternary fragmentation of each parent nuclei considered. From the results obtained, we find the emission of $\ensuremath{\alpha}$-structured ternary fragments is more favored than the other ternary fragment combinations.

A new, very short-lived neutron-deficient isotope $^{222}\mathrm{Np}$ was produced in the complete-fusion reaction $^{187}\mathrm{Re}(^{40}\mathrm{Ar},5\mathrm{n})^{222}\mathrm{Np}$, and observed at the gas-filled recoil separator SHANS. The new isotope $^{222}\mathrm{Np}$ was identified by employing a recoil-$\ensuremath{\alpha}$ correlation measurement, and six $\ensuremath{\alpha}$-decay chains were established for it. The decay properties of $^{222}\mathrm{Np}$ with ${E}_{\ensuremath{\alpha}}=10016(33)\text{ }\text{ }\mathrm{keV}$ and ${T}_{1/2}=38{0}_{\ensuremath{-}110}^{+260}\text{ }\text{ }\mathrm{ns}$ were determined experimentally. The $\ensuremath{\alpha}$-decay systematics of Np isotopes is improved by adding the new data for $^{222}\mathrm{Np}$, which validates the $N=126$ shell effect in Np isotopes. The evolution of the $N=126$ shell closure is discussed in the neutron-deficient nuclei up to Np within the framework of $\ensuremath{\alpha}$-decay reduced width.

We investigate the evolution of clustering structure through the momentum distributions in the $^{8\text{--}10}\mathrm{Be}$ isotopes. The nucleon dynamics within the intercluster antisymmetrization are discussed via the momentum distribution of a Brink type $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}$ wave function. For the state with a small $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}$ distance, we observe a significant depression with a dip structure at zero momentum and an enhanced tail in a relatively higher momentum region. In addition, we find the ``cluster structure'' in the intrinsic frame of momentum space, which is complementary to its significant $\ensuremath{\alpha}$-cluster dissolution in the coordinate space because of the strong antisymmetrization. For the physical $^{8\text{--}10}\mathrm{Be}$ isotopes, the Tohsaki-Horiuchi-Schuck-R\"opke (THSR) wave functions are adopted. The evolution from the dilute clustering state to the compact one is demonstrated by a successive depression at zero momentum of nucleon distribution for the two $\ensuremath{\alpha}$ clusters within $^{8\text{--}10}\mathrm{Be}$ isotopes. For the compact $^{10}\mathrm{Be}$ nucleus, the momentum distribution of all nucleons shows significant depression at zero momentum with a dip structure, which is found to be contributed by both the intercluster antisymmetrization and the $p$-orbit occupation of the valence neutrons. This study proposes a new window for the investigations of the $\ensuremath{\alpha}$-clustering effects via the low-momentum components of nuclei, which is expected to be extended to the heavier nuclear clustering states.

The $\ensuremath{\alpha}$ decays of exotic $N=125$, 126, and 127 isotones, including two new isotopes $^{219}\mathrm{Np}$ [Phys. Lett. B 777, 212 (2018)] and $^{220}\mathrm{Np}$ [Phys. Rev. Lett. 122, 192503 (2019)], are studied by using the improved Buck-Merchant-Perez cluster model with the charge-dependent $\ensuremath{\alpha}$-preformation factors. The experimental half-lives of $\ensuremath{\alpha}$ decays varying from $2.50\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ to $6.00\ifmmode\times\else\texttimes\fi{}{10}^{26}\phantom{\rule{0.28em}{0ex}}\mathrm{s}$ are reproduced within a factor of $\ensuremath{\approx}2$. Noticeably, the theoretical $\ensuremath{\alpha}$-decay half-lives of the new isotopes $^{219,220}\mathrm{Np}$ are also in good agreement with the experimental data. Furthermore, the $\ensuremath{\alpha}$-decay half-lives of some undiscovered $N=125$, 126 and 127 isotones are predicted, which could be useful for future experimental studies on the robustness of the magic number $N=126$.

The multichannel cluster model (MCCM) is generalized to investigate the effect of nuclear collective vibrations on the $\ensuremath{\alpha}$-decay fine structure. Vibrational excitations up to two-phonon states are taken into account and coupled-channels calculations are performed for vibrational Rn, Ra, Th, and U isotopes. Without introducing any additional adjustable parameter, the calculated $\ensuremath{\alpha}$-decay branching ratios to various vibrational states show good agreement with the experimental data. In particular, it is shown that the $\ensuremath{\alpha}$-decay fine structure is strongly correlated with vibrational excitations, offering an alternative tool to explore the phonon states in daughter nuclei. Despite the $N=126$ shell closure, the calculated $\ensuremath{\alpha}$-decay half-lives are also found to be in good agreement with the experimental data. A unified description of the $\ensuremath{\alpha}$-decay fine structure has been achieved by the MCCM for both rotational and vibrational nuclei.