Systematic study of the α decay preformation factors of the nuclei around the Z = 82, N = 126 shell closures within the generalized liquid drop model

In this study, we systematically investigate the \begin{document}$\alpha$\end{document} decay preformation factors, \begin{document}$P_{\alpha}$\end{document} , and the \begin{document}$\alpha$\end{document} decay half-lives of 152 nuclei around Z = 82, N = 126 closed shells based on the generalized liquid drop model (GLDM) with \begin{document}$P_{\alpha}$\end{document} being extracted from the ratio of the calculated \begin{document}$\alpha$\end{document} decay half-life to the experimental one. The results show that there is a remarkable linear relationship between \begin{document}$P_{\alpha}$\end{document} and the product of valance protons (holes) \begin{document}$N_p$\end{document} and valance neutrons (holes) \begin{document}$N_n$\end{document} . At the same time, we extract the \begin{document}$\alpha$\end{document} decay preformation factor values of the even–even nuclei around the Z = 82, N = 126 closed shells from the study of Sun \begin{document}${et\ al.}$\end{document} [J. Phys. G: Nucl. Part. Phys., 45: 075106 (2018)], in which the \begin{document}$\alpha$\end{document} decay was calculated by two different microscopic formulas. We find that the \begin{document}$\alpha$\end{document} decay preformation factors are also related to \begin{document}$N_pN_n$\end{document} . Combining with our previous studies [Sun \begin{document}${et\ al.}$\end{document} , Phys. Rev. C, 94: 024338 (2016); Deng \begin{document}${et\ al.}$\end{document} , ibid. 96: 024318 (2017); Deng \begin{document}${et\ al.}$\end{document} , ibid. 97: 044322 (2018)] and that of Seif \begin{document}${et\ al.,}$\end{document} [Phys. Rev. C, 84: 064608 (2011)], we suspect that this phenomenon of linear relationship for the nuclei around the above closed shells is model-independent. This 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 \begin{document}$\alpha$\end{document} decay preformation factor data calculated by the GLDM, we calculate the \begin{document}$\alpha$\end{document} decay half-lives of these nuclei. The calculated results agree with the experimental data well.     

Calculations of the α-decay properties of Z = 120, 122, 124, 126 isotopes

The \begin{document}$\alpha$\end{document}-decay properties of even-Z nuclei with Z = 120, 122, 124, 126 are predicted. We employ the generalized liquid drop model (GLDM), Royer's formula, and universal decay law (UDL) to calculate the \begin{document}$\alpha$\end{document}-decay half-lives. By comparing the theoretical calculations with the experimental data of known nuclei from Fl to Og, we confirm that all the employed methods can reproduce the \begin{document}$\alpha$\end{document}-decay half-lives well. The preformation factor \begin{document}$P_{\alpha}$\end{document} and \begin{document}$\alpha$\end{document}-decay energy \begin{document}$Q_{\alpha}$\end{document} show that \begin{document}$^{298,304,314,316,324,326,338,348}$\end{document}120, \begin{document}$^{304,306,318,324,328,338}$\end{document}122, and \begin{document}$^{328,332,340,344}$\end{document}124 might be stable. The \begin{document}$\alpha$\end{document}-decay half-lives show a peak at Z = 120, N = 184, and the peak vanishes when Z = 122, 124, 126. Based on detailed analysis of the competition between \begin{document}$\alpha$\end{document}-decay and spontaneous fission, we predict that nuclei nearby N = 184 undergo \begin{document}$\alpha$\end{document}-decay. The decay modes of \begin{document}$^{287-339}$\end{document}120, \begin{document}$^{294-339}$\end{document}122, \begin{document}$^{300-339}$\end{document}124, and \begin{document}$^{306-339}$\end{document}126 are also presented.     

Systematic calculations of cluster radioactivity half-lives in trans-lead nuclei

In the present work, based on the Wentzel-Kramers-Brillouin (WKB) theory, considering the cluster preformation probability (\begin{document}$ P_{c} $\end{document}), we systematically investigate the cluster radioactivity half-lives of 22 trans-lead nuclei ranging from ²²¹Fr to ²⁴²Cm. When the mass number of the emitted cluster \begin{document}$ A_{c} $\end{document} \begin{document}$ < $\end{document} 28, \begin{document}$P_{c} $\end{document} is obtained by the exponential relationship of \begin{document}$ P_{c} $\end{document} to the α decay preformation probability (\begin{document}$ P_{\alpha} $\end{document}) proposed by R. Blendowskeis \begin{document}$ et $\end{document} \begin{document}$ al. $\end{document} [Phys. Rev. Lett. 61, 1930 (1988)], while \begin{document}$ P_{\alpha} $\end{document} is calculated through the cluster-formation model (CFM). When \begin{document}$ A_{c} $\end{document} \begin{document}$ \ge $\end{document} 28, \begin{document}$ P_{c} $\end{document} is calculated through the charge-number dependence of \begin{document}$ P_{c} $\end{document} on the decay products proposed by Ren \begin{document}$ et $\end{document} \begin{document}$ al. $\end{document} [Phys. Rev. C 70, 034304 (2004)]. The half-lives of cluster radioactivity have been calculated by the density-dependent cluster model [Phys. Rev. C 70, 034304 (2004)] and by the unified formula of half-lives for alpha decay and cluster radioactivity [Phys. Rev. C 78, 044310 (2008)]. For comparison, a universal decay law (UDL) proposed by Qi \begin{document}$ et $\end{document} \begin{document}$ al. $\end{document} [Phys. Rev. C 80, 044326 (2009)], a semi-empirical model for both α decay and cluster radioactivity proposed by Santhosh [J. Phys. G: Nucl. Part. Phys. 35, 085102 (2008)], and a unified formula of half-lives for alpha decay and cluster radioactivity [Phys. Rev. C 78, 044310 (2008)] are also used. The calculated results of our work, Ni's formula , and the UDL can well reproduce the experimental data and are better than those of Santhosh's model. In addition, we extend this model to predict the half-lives for 51 nuclei, whose cluster radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020.     

Calculation of double-β decay half-lives using an improved Primakoff-Rosen formula

A systematic analysis on experimental data of the half-lives of nuclear double-β decays with two neutrinos(2vββ) is performed based on the analytical formula proposed by Primakoff and Rosen.We improve the formula by considering the shell effects and refining the energy dependence of the phase-space factor.This improved formula can closely describe all available experimental half-lives of 2vβ~-β~-decays,both for ground-state transitions and transitions from ground states of parent nuclei to the first 0~+ excited states of daughter nuclei.The calculated half-lives agree with the experimental data of ground-state transitions of all known eleven nuclei with an average factor of 2.3.Further predictions are provided for 2vββ-decay candidates with decay energies above 0.5 MeV.We compare different theoretical predictions and emphasize the importance of experimental measurements on the half-lives of double-β transitions between the ground state of ~(48)Ca,~(76)Ge,and ~(136)Xe and the first 0~+ excited states of their corresponding daughter nuclei,which will be very useful for understanding the underlying mechanisms of double-β decays and for further studying the shell effects on nuclear transition matrix elements.     

Theoretical study on the favored alpha-decay half-lives of deformed nuclei

A systematic study on the α-decay half-lives of nuclei in the range \begin{document}$93\leqslant Z \leqslant 118$\end{document} is performed by employing various versions of proximity potentials. To obtain more reliable results, deformation terms are included up to hexadecapole (\begin{document}$\beta_{4}$\end{document}) in the spherical-deformed nuclear and Coulomb interaction potentials. First, the favored α-decay processes in this region are categorized as even-even, odd A, and odd-odd nuclei. Second, they are grouped into two transitions: ground state to ground state and ground state to isomeric states. Owing to the comparison of their root-mean-square deviations (RMSD's), \begin{document}$Bass 77$\end{document} and \begin{document}$Ngo 80$\end{document} have the lowest values and better reproduce experimental data. Moreover, by considering preformation probability within the cluster formation model, the results validate the significant reduction in root-mean-square deviations obtained for different versions of proximity. Hence, the deviation between the calculated and experimental data is detracted.     

New behaviors of α-particle preformation factors near doubly magic 100Sn

The \begin{document}$ \alpha $\end{document}-particle preformation factors of nuclei above doubly magic nuclei \begin{document}$ ^{100} $\end{document}Sn and \begin{document}$ ^{208} $\end{document}Pb are investigated within the generalized liquid drop model. The results show that the \begin{document}$ \alpha $\end{document}-particle preformation factors of nuclei near self-conjugate doubly magic \begin{document}$ ^{100} $\end{document}Sn are significantly larger than those of analogous nuclei just above \begin{document}$ ^{208} $\end{document}Pb, and they will be enhanced as the nuclei move towards the \begin{document}$ N = Z $\end{document} line. The proton–neutron correlation energy \begin{document}$ E_{p-n} $\end{document} and two protons–two neutrons correlation energy \begin{document}$ E_{2p-2n} $\end{document} of nuclei near \begin{document}$ ^{100} $\end{document}Sn also exhibit a similar situation, indicating that the interactions between protons and neutrons occupying similar single-particle orbitals could enhance the \begin{document}$ \alpha $\end{document}-particle preformation factors and result in superallowed \begin{document}$ \alpha $\end{document} decay. This also provides evidence of the significant role of the proton–neutron interaction on \begin{document}$ \alpha $\end{document}-particle preformation. Also, the linear relationship between \begin{document}$ \alpha $\end{document}-particle preformation factors and the product of valence protons and valence neutrons for nuclei around \begin{document}$ ^{208} $\end{document}Pb is broken in the \begin{document}$ ^{100} $\end{document}Sn region because the \begin{document}$ \alpha $\end{document}-particle preformation factor is enhanced when a nucleus near \begin{document}$ ^{100} $\end{document}Sn moves towards the \begin{document}$ N = Z $\end{document} line. Furthermore, the calculated \begin{document}$ \alpha $\end{document} decay half-lives fit well with the experimental data, including the recent observed self-conjugate nuclei \begin{document}$ ^{104} $\end{document}Te and \begin{document}$ ^{108} $\end{document}Xe [Phys. Rev. Lett. 121, 182501 (2018)].     

Note on rare Z-boson decays to double heavy quarkonia

Within the standard model, we have investigated rare Z-boson decays into double heavy quarkonia, \begin{document}$ Z\to VV $\end{document} and \begin{document}$ Z\to VP $\end{document}, with V and P denoting vector and pseudoscalar quarkonia, respectively. It is assumed that the leading-order QCD diagrams would give the dominant contributions to these processes, and the corresponding branching fractions, for instance, \begin{document}$ {\cal B}(Z\to J/\Psi J/\Psi) $\end{document}, have been estimated to be approximately\begin{document}$ 10^{-13} $\end{document} in literature. However, these decays could also happen through electromagnetic transitions \begin{document}$ Z\to V\gamma^* $\end{document} and \begin{document}$ Z\to P\gamma^* $\end{document}, with the virtual photon transforming into V. Interestingly, the smallness of the vector quarkonium mass can give rise to a large factor \begin{document}$ m_Z^2/m_V^2 $\end{document} relative to the QCD contributions, which thus counteracts the suppression from the electromagnetic coupling. We systematically include these two types of contributions in our calculation to predict branching fractions for these decays. Particularly, owing to the virtual photon effects, it is found that \begin{document}$ {\cal B}(Z\to J/\Psi J/\Psi) $\end{document} will be significantly enhanced, up to \begin{document}$ 10^{-10} $\end{document}.     

Nuclear mass parabola and its applications

We propose a method for extracting the properties of the isobaric mass parabola based on the total doubleβ-decay energies of isobaric nuclei.Two important parameters of the mass parabola,the location of the most β-stable nuclei Z_A and the curvature parameter b_A,are obtained for 251 A values,based on the total double β-decay energies of nuclei compiled in the AME2016 database.The advantage of this approach is that the pairing energy term P_A caused by the odd-even variation can be removed in the process,as well as the mass excess M(A,Z_A) of the most stable nuclide for the mass number A,which are employed in the mass parabolic fitting method.The Coulomb energy coefficient a_c=0.6910 MeV is determined by the mass difference relation for mirror nuclei,and the symmetry energy coefficient is also studied by the relation a_(sym)(A)=025 b_AZ_A.     

One-loop formulas for H → Zνlνl for l = e, μ, τ in 't Hooft-Veltman gauge

In this paper, we present analytical results for one-loop contributions to the decay processes \begin{document}$ H\rightarrow Z \nu_l\bar{\nu}_l $\end{document} (for \begin{document}$ l = e, \mu, \tau $\end{document}). The calculations are performed within the Standard Model framework in the 't Hooft-Veltman gauge. One-loop form factors are then written in terms of scalar one-loop functions in the standard notations of \begin{document}$ {\tt LoopTools}$\end{document}. As a result, one-loop decay rates for the decay channels can be evaluated numerically by using the package. Furthermore, we analyze the signals of \begin{document}$ H\rightarrow Z \nu_l\bar{\nu}_l $\end{document} via the production processes \begin{document}$ e^-e^+ \rightarrow ZH^* \rightarrow Z (H^* \rightarrow Z \nu_l\bar{\nu}_l) $\end{document}, including the initial beam polarizations at future lepton colliders. The Standard Model backgrounds, such as the processes \begin{document}$ e^-e^+ \rightarrow \nu_l\bar{\nu}_l ZZ $\end{document}, are also examined in this study. Numerical results indicate that one-loop corrections make contributions of approximately 10% to the decay rates. These are sizeable contributions and should be taken into account at future colliders. We show that the signals \begin{document}$ H\rightarrow Z\nu_l\bar{\nu}_l $\end{document} are clearly visible at the center-of-mass energy \begin{document}$ \sqrt{s}=250 $\end{document} GeV and are difficult to probe in higher-energy regions owing to the dominant backgrounds.     

Research on convergence of the nuclear matrix elements for 2νββ decays

In this work, the characteristics of \begin{document}$2\nu\beta\beta$\end{document} decays for six nuclei (\begin{document}$^{36}$\end{document}Ar, \begin{document}$^{46}$\end{document}Ca, \begin{document}$^{48}$\end{document}Ca, \begin{document}$^{50}$\end{document}Cr, \begin{document}$^{70}$\end{document}Zn, and \begin{document}$^{136}$\end{document}Xe) in a mass range from \begin{document}$A = 36$\end{document} to \begin{document}$A = 136$\end{document} are studied within the nuclear shell model (NSM) framework. Calculations are presented for the half-lives, nuclear matrix elements (NMEs), phase space factors (\begin{document}$G_{2\nu}$\end{document}), and convergence of the NMEs. The theoretical results agree well with the experimental data. In addition, we predict the half-lives of \begin{document}$2\nu\beta\beta$\end{document} decays for four nuclei. We focus on the convergence of the NMEs by analyzing the number of contributing intermediate \begin{document}$1^{+}$\end{document} states (\begin{document}$N_{\rm{C}}$\end{document}) for the nuclei of interest. We assume that \begin{document}$N_{\rm{C}}$\end{document} is safely determined when the accumulated NMEs saturate 99.7% of the final calculated magnitude. From the calculations of the involved nuclei, we discover a connection between \begin{document}$N_{\rm{C}}$\end{document} and the total number of intermediate \begin{document}$1^{+}$\end{document} states (\begin{document}$N_{\rm{T}}$\end{document}). According to the least squares fit, we conclude that the correlation is \begin{document}$N_{\rm{C}}=\left( 10.8\pm 1.2\right) \times N_{\rm{T}}^{\left( 0.29\pm 0.02\right)}$\end{document}.     

Determining the nuclear temperature dependence on source neutron-proton asymmetry in heavy-ion reactions at intermediate energy

In this article, we investigate the dependence of nuclear temperature on emitting source neutron-proton (\begin{document}$ N/Z $\end{document}) asymmetry with light charged particles (LCPs) and intermediate mass fragments (IMFs) generated from intermediate-velocity sources in thirteen reaction systems with different \begin{document}$ N/Z $\end{document} asymmetries, \begin{document}$ ^{64} \rm{Zn} $\end{document} on \begin{document}$ ^{112} \rm{Sn} $\end{document}, and \begin{document}$ ^{70} \rm{Zn} $\end{document}, \begin{document}$ ^{64} \rm{Ni} $\end{document} on \begin{document}$ ^{112,124} \rm{Sn} $\end{document}, \begin{document}$ ^{58,64} \rm{Ni} $\end{document}, \begin{document}$ ^{197} \rm{Au} $\end{document}, and \begin{document}$ ^{232} \rm{Th} $\end{document} at 40 MeV/nucleon. The apparent temperature values of LCPs and IMFs from different systems are deduced from the measured yields using two helium-related and eight carbon-related double isotope ratio thermometers, respectively. Then, the sequential decay effect on the experimental apparent temperature deduction with the double isotope ratio thermometers is quantitatively corrected explicitly with the aid of the quantum statistical model. The present treatment is an improvement compared to our previous studies in which an indirect method was adopted to qualitatively consider the sequential decay effect. A negligible \begin{document}$ N/Z $\end{document} asymmetry dependence of the real temperature after the correction is quantitatively addressed in heavy-ion reactions at the present intermediate energy, where a change of 0.1 units in source \begin{document}$ N/Z $\end{document} asymmetry corresponds to an absolute change in temperature of an order of 0.03 to 0.29 MeV on average for LCPs and IMFs. This conclusion is in close agreement with that inferred qualitatively via the indirect method in our previous studies.     

Systematic study of two-proton radioactivity half-lives using the two-potential and Skyrme-Hartree-Fock approaches

In this work, we systematically study the two-proton (\begin{document}$2p$\end{document}) radioactivity half-lives using the two-potential approach, and the nuclear potential is obtained using the Skyrme-Hartree-Fock approach and the Skyrme effective interaction of SLy8. For true \begin{document}$2p$\end{document} radioactivity (\begin{document}$Q_{2p}$\end{document} \begin{document}$>$\end{document} 0 and \begin{document}$Q_p$\end{document} \begin{document}$< $\end{document}0, where \begin{document}$Q_p$\end{document} and \begin{document}$Q_{2p}$\end{document} are the released energies of the one-proton and two-proton radioactivity, respectively), 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 \begin{document}$2p$\end{document} radioactivity candidates with \begin{document}$Q_{2p}$\end{document} \begin{document}$>$\end{document} 0 obtained from the evaluated atomic mass table AME2016. The calculated results indicate a clear linear relationship between the logarithmic \begin{document}$2p$\end{document} radioactivity half-lives (\begin{document}${\log}_{10}T_{1/2}$\end{document}) and coulomb parameters [(\begin{document}$Z_{d}^{0.8}$\end{document}+\begin{document}${l}^{\,0.25}$\end{document})\begin{document}$Q_{2p}^{-1/2}$\end{document}] considering the effect of orbital angular momentum proposed by Liu \begin{document}$et$\end{document} \begin{document}$al.$\end{document} [Chin. Phys. C 45, 024108 (2021)]. For comparison, the generalized liquid drop model (GLDM), effective liquid drop model (ELDM), and Gamow-like model are also used. Our predicted results are consistent with those obtained using other relevant models.     

Fusion of spherical-octupole pairs of colliding nuclei for compact and elongated configurations

The deformation and associated optimum/uniquely fixed orientations play an important role in the syn-thesis of compound nuclei via cold and hot fusion reactions,respectively,at the lowest and highest barrier energies.The choice of optimum orientation(0_op)for the'cold or elongated'and hot or cormpact'fusion configurations of quadrupole(β₂)deformed nuclei depends only on the+/-signs ofβ₂-deformation[J.Phys.G:Nucl.Part.Phys.31,631-644(2005)].In our recent study[Phys.Rev.C 101,051601(R)2020],we proposed a new sct of Oopt(iferent from the values reported for quadrupole deformed nuclei)after the inclusion of octupole deformation(up to B3)ef-fects.Using the respective 0op1 of B3-deformed nuclei for cold and hot optimum orientations,we analyzed the im-pact of the soft-and rigid-pear shapes of octupole deformed nuclei on the fusion barrier characterstics(barrier height Vg and barrier position RB).This analysis is applied to approximately 200 spherical-plus B3 deformed nucle-ar partners,that is,¹⁶O,¹⁸Cat octupole deformed nuclei.Compared with the compact configuration,the elongated fu-sion configuration has a relatively larger impact on the fusion barrier and cross sections ow ing to the inclusion of de-formations up to B3.Its agreement with available experimental data for the¹⁶O+¹⁵⁰Sm reaction(β₂₂-0.205,β₃₂=0.055)also improves when the optimum orientation degree of freedom is fixed in view of octupole deformations.This reinforces the fact that nuclear structure effects play an important role in the nuclear fusion process.Thus,octu-pole deformed nuclei can be used for the synthesis of heavy and superheavy nuclei.     

Relative probabilities of breakup channels in reactions of ~(6,7)Li with ~(209)Bi at energies around and above the Coulomb barrier

Coincidence measurements of breakup fragments in reactions of~ (6,7) Li with ~(209)Bi at energies around and above the Coulomb barrier were carried out using a large solid-angle covered detector array. Through the Q values along with the relative energies of the breakup fragments, different breakup components(prompt breakups and delayed breakups) and different breakup modes(α + t, α + d, α + p, and α + α) are distinguished. A new breakup mode, α + t, is observed in ~6Li-induced reactions at energies above the Coulomb barrier. Correlations between breakup modes and breakup components as well as their variations with the incident energy are investigated. The results will help us better understand the breakup effects of weakly bound nuclei on the suppression of a complete fusion, particularly for the above-barrier energies.     

Evolution of intrinsic nuclear structure in medium mass even-even Xenon isotopes from a microscopic perspective

In this study, the multi-quasiparticle triaxial projected shell model (TPSM) is applied to investigate \begin{document}$\gamma$\end{document}-vibrational bands in transitional nuclei of \begin{document}$^{118-128}{\rm{Xe}}$\end{document}. We report that each triaxial intrinsic state has a \begin{document}$\gamma$\end{document}-band built on it. The TPSM approach is evaluated by the comparison of TPSM results with available experimental data, which shows a satisfactory agreement. The energy ratios, B(E2) transition rates, and signature splitting of the \begin{document}$\gamma$\end{document}-vibrational band are calculated.     

Reaction 55Mn + 159Tb : preparation for the synthesis of new elements

The complete fusion reaction of \begin{document}$^{55}$\end{document}Mn + \begin{document}$^{159}$\end{document}Tb was studied on the gas-filled recoil separator SHANS2. Nineteen ER - α\begin{document}$_{1}$\end{document} - α\begin{document}$_{2}$\end{document} decay chains from \begin{document}$^{210}$\end{document}Th produced from the 4n evaporation channel were observed. The α-particle energy and half-life of \begin{document}$^{210}$\end{document}Th were determined as 7922(14) keV and 14(4) ms, respectively. In addition, the decay properties of \begin{document}$E_{\alpha}$\end{document} = 7788(14) keV and \begin{document}$T_{1/2}$\end{document} = 36\begin{document}$^{+15}_{-8}$\end{document} ms were obtained for \begin{document}$^{211}$\end{document}Th. The measured α decay properties of \begin{document}$^{210}$\end{document}Th and \begin{document}$^{211}$\end{document}Th were consistent with literature data. The cross sections were measured to be 0.59\begin{document}$^{+0.25}_{-0.23}$\end{document} nb and 0.19\begin{document}$^{+0.12}_{-0.09}$\end{document} nb for \begin{document}$^{210}$\end{document}Th and \begin{document}$^{211}$\end{document}Th, respectively. The equilibrium charge state of the recoiled nucleus \begin{document}$^{210}$\end{document}Th was determined experimentally. The new data were helpful for estimating the equilibrium charge states of elements 119 and 120, which could be produced via the \begin{document}$^{240}$\end{document}Pu(\begin{document}$^{55}$\end{document}Mn, 3n)\begin{document}$^{292}$\end{document}119 and \begin{document}$^{243}$\end{document}Am(\begin{document}$^{55}$\end{document}Mn, 3n)\begin{document}$^{295}$\end{document}120 reactions, respectively.     

Microscopic study of higher-order deformation effects on the ground states of superheavy nuclei around 270Hs

We investigate the effects of higher-order deformations \begin{document}$\beta_\lambda$\end{document} (\begin{document}$\lambda=4,6,8,$\end{document} and 10) on the ground state properties of superheavy nuclei (SHN) near the doubly magic deformed nucleus \begin{document}$^{270}{\rm{Hs}}$\end{document} using the multidimensionally-constrained relativistic mean-field (MDC-RMF) model with five effective interactions: PC-PK1, PK1, NL3^*, DD-ME2, and PKDD. The doubly magic properties of \begin{document}$^{270}{\rm{Hs}}$\end{document} include large energy gaps at \begin{document}$N=162$\end{document} and \begin{document}$Z=108$\end{document} in the single-particle spectra. By investigating the binding energies and single-particle levels of \begin{document}$^{270}{\rm{Hs}}$\end{document} in the multidimensional deformation space, we find that, among these higher-order deformations, the deformation \begin{document}$\beta_6$\end{document} has the greatest impact on the binding energy and influences the shell gaps considerably. Similar conclusions hold for other SHN near \begin{document}$^{270}{\rm{Hs}}$\end{document}. Our calculations demonstrate that the deformation \begin{document}$\beta_6$\end{document} must be considered when studying SHN using MDC-RMF.