This study endeavors to develop an improved set of basis functions for nuclear shell-model calculations. The shell model, a well-established approach to understanding nuclear structure, typically employs the harmonic oscillator potential within the mean-field approximation. Given the extensive validation and consistency of harmonic oscillator results with experimental data, we propose a modification by incorporating a centrifugal term that converges toward the Davidson potential. This potential has been extensively studied, and we aim to extract relevant experimental data for the simplest cases in the shell model, namely one-particle and one-hole nuclei. A comprehensive comparison between the Davidson-based results and the harmonic oscillator calculations is presented to demonstrate the effectiveness of the new basis functions.

The Schrodinger equation with a Yukawa type of potential is solved analytically. When different boundary conditions are taken into account, a series of solutions are indicated as a Bessel function, the first kind of Hankel function and the second kind of Hankel function, respectively. Subsequently, the scattering processes of $K{\bar{K}}^{* }$ and $D{\bar{D}}^{* }$ are investigated. In the $K{\bar{K}}^{* }$ sector, the f₁(1285) particle is treated as a $K{\bar{K}}^{* }$ bound state, therefore, the coupling constant in the $K{\bar{K}}^{* }$ Yukawa potential can be fixed according to the binding energy of the f₁(1285) particle. Consequently, a $K{\bar{K}}^{* }$ resonance state is generated by solving the Schrodinger equation with the outgoing wave condition, which lies at 1417 − i18 MeV on the complex energy plane. It is reasonable to assume that the $K{\bar{K}}^{* }$ resonance state at 1417 − i18 MeV might correspond to the f₁(1420) particle in the review of the Particle Data Group. In the $D{\bar{D}}^{* }$ sector, since the X(3872) particle is almost located at the $D{\bar{D}}^{* }$ threshold, its binding energy is approximately equal to zero. Therefore, the coupling constant in the $D{\bar{D}}^{* }$ Yukawa potential is determined, which is related to the first zero point of the zero-order Bessel function. Similarly to the $K{\bar{K}}^{* }$ case, four resonance states are produced as solutions of the Schrodinger equation with the outgoing wave condition. It is assumed that the resonance states at 3885 − i1 MeV, 4029 − i108 MeV, 4328 − i191 MeV and 4772 − i267 MeV might be associated with the Zc(3900), the X(3940), the χ_c1(4274) and χ_c1(4685) particles, respectively. It is noted that all solutions are isospin degenerate.

The role of the delta isobar degrees of freedom in nucleon–nucleon scattering is revisited. We attempt to understand why the dimensionally regularized two-pion exchanges with the explicit delta isobar is much stronger than the ones with spectral function regularization. When the cut-off value of spectral function regularization is varied, the isoscalar central component exhibits a rather large cut-off variation. This reveals a surprisingly large numerical factor of the deltaful two-pion exchange potentials. The power counting is adjusted accordingly and we discuss the results and how to improve upon this finding.

The structure of the irreducible collective spaces of the group Sp(12, R), which many-particle nuclear states are classified according to the chain Sp(12, R) ⊃ U(6) ⊃ SO(6) ⊃ SU_pn(3) ⨂ SO(2) ⊃ SO(3) of the proton–neutron symplectic model (PNSM), is considered in detail. This chain of the PNSM was recently shown to correspond to a microscopic shell-model version of the Bohr–Mottelson collective model. The construction of the relevant shell-model representations of the Sp(12, R) group along this chain is considered for three nuclei with varying collective properties and from different mass regions. It is shown that the SU_pn(3) basis states of the Sp(12, R) representations belonging to the SO(6) irreps with seniority $\upsilon$ ≥ $\upsilon$₀, with $\upsilon$₀ denoting the maximal seniority SO(6) irrep contained in the Sp(12, R) bandhead, are always Pauli allowed, but organized in a different way into different SO(6) shells. This is in contrast to the case of filling the levels of the standard three-dimensional harmonic oscillator and using the plethysm operation. Although the SU_pn(3) multiplets within $\upsilon$ < $\upsilon$₀ are not all Pauli forbidden, it is safe to discard them. The results obtained in the present work are important for the practical application of the microscopic version of the Bohr–Mottelson collective model.

By using potential energy surface (PES) calculations in the three-dimensional space (β₂, γ, β₄) within the framework of the macroscopic-microscopic model, the fission trajectory and fission barrier for Z = 118(Og), 119, 120 nuclei has been systematically investigated. The calculated PES includes macroscopic liquid-drop energy, microscopic shell correction and pairing correction. Taking the ²⁹⁴Og₁₇₆ nucleus as an example, we discuss the next closed shell after Z = 82 and N = 126 with the calculated Woods–Saxon single-particle levels. Then, the results of PES in ²⁹⁴Og is illustrated from the (X, Y) scale to the (β₂, γ) scale. The γ degree of freedom reveals the shape evolution clearly during the fission process. The structure near the minimum and saddle point of the PES in the Z = 118, 119, 120 nuclei is demonstrated simultaneously. Based on the potential energy curves, general trends of the evolution of the fission barrier heights and widths are also studied. The triaxial deformation in these superheavy mass regions plays a vital role in the first fission barrier, showing a significant reduction in both triaxial paths. In addition, the model-dependent fission barriers of proton-rich nuclei ²⁹⁵Og, ²⁹⁶119, and ²⁹⁷120 are analyzed briefly. Our studies could be valuable for synthesizing the superheavy new elements in the forthcoming HIAF and other facilities.

The fusion barriers and cross sections of 15 colliding systems with 320 ≤ Z₁Z₂ ≤ 1512 are investigated in detail to understand the influence of the universal function of proximity potential formalism in the heavy-ion fusion mechanism. To realize this goal, we select three versions of the phenomenological proximity potentials, including Prox. 77, Zhang 2013, and Guo 2013, to calculate the nucleus–nucleus potential. The experimental fusion cross sections for the selected reactions are analyzed using the standard coupled-channel calculations, including couplings to the low-lying 2⁺ and 3⁻ states in the target and projectile. The calculated results show that the universal functions of the Guo 2013 and Prox. 77 models provide the lowest and highest fusion barriers, respectively. In addition, it is found that the height of the fusion barriers is enhanced by increasing the mass number of the projectile from light to heavy ones. The highest sensitivity to the mass number of the projectile belongs to the results of Prox. 77. A discussion is also presented on the influence of the universal function on the radial behavior of the interaction potential in the allowed region for overlapping configurations. Our results reveal that the best fit to the experimental data of the fusion cross sections for the reactions involving light and medium nuclei is obtained using the universal function of the Zhang 2013 model. For the heavier systems, the results of the Guo 2013 model at sub-barrier energies provide a good description of the available data.

We study the dissociation of ψ(3770), ψ(4040), ψ(4160), and ψ(4415) mesons in collision with nucleons, which takes place in high-energy proton-nucleus collisions. The quark interchange between a nucleon and a $c\bar{c}$ meson leads to the dissociation of the $c\bar{c}$ meson. We consider the reactions: ${pR}\to {{\rm{\Lambda }}}_{c}^{+}{\bar{D}}^{0}$, ${pR}\to {{\rm{\Lambda }}}_{c}^{+}{\bar{D}}^{* 0}$, ${pR}\to {{\rm{\Sigma }}}_{c}^{++}{D}^{-}$, ${pR}\to {{\rm{\Sigma }}}_{c}^{++}{D}^{* -}$, ${pR}\to {{\rm{\Sigma }}}_{c}^{+}{\bar{D}}^{0}$, ${pR}\to {{\rm{\Sigma }}}_{c}^{+}{\bar{D}}^{* 0}$, ${pR}\to {{\rm{\Sigma }}}_{c}^{* ++}{D}^{-}$, ${pR}\to {{\rm{\Sigma }}}_{c}^{* ++}{D}^{* -}$, ${pR}\to {{\rm{\Sigma }}}_{c}^{* +}{\bar{D}}^{0}$, and ${pR}\to {{\rm{\Sigma }}}_{c}^{* +}{\bar{D}}^{* 0}$, where R stands for ψ(3770), ψ(4040), ψ(4160), or ψ(4415). A reaction of a neutron and a $c\bar{c}$ meson corresponds to a reaction of a proton and the $c\bar{c}$ meson by replacing the up quark with the down quark and vice versa. Transition-amplitude formulas are derived from the S-matrix element. Unpolarized cross sections are calculated with the transition amplitudes for scattering in the prior form and in the post form. The cross sections relate to nodes in the radial wave functions of ψ(3770), ψ(4040), ψ(4160), and ψ(4415) mesons.

The effective liquid drop model (ELDM) is improved by introducing an accurate nuclear charge radius formula and an analytic expression for assaulting frequency. Within the improved effective liquid drop model (IMELDM), the experimental cluster radioactivity half-lives of the trans-lead region are calculated. It is shown that the accuracy of the IMELDM is improved compared with that of the ELDM. At last, the cluster radioactivity half-lives that are experimentally unavailable for the trans-lead nuclei are predicted by the IMELDM. These predictions may be useful for searching for new candidates for cluster radioactivity in future experiments.

Based on the potential-energy-surface calculation, the impact of different deformation degrees of freedom on a single-particle structure and binding energies in nuclei around ¹⁵²Nd, located on one of the hexadecapole-deformation islands, is analyzed in a multi-dimensional deformation space. Various energy maps, curves and tables are presented to indicate nuclear properties. The calculated equilibrium deformations and binding energies with different potential parameters are compared with experimental data and other theories. It is found that the inclusion of the hexadecapole deformations, especially the axial one, can improve the theoretical description of both nuclear shapes and masses. In addition, our calculated potential-energy curve shows that a critical deformation-point, β₂ ≈ 0.4, exists—the triaxial (hexadecapole) deformation effect can be neglectable but the hexadecapole (triaxial) one plays an important role before (after) such a critical point.

The nuclear modification factor for prompt photon production in proton-nucleus collisions is investigated within color dipole formalism. By means of the Glauber-Gribov approach, the nuclear effects are studied in various rapidity bins with the evolution equation-based saturation models and the phenomenological dipole models. The theoretical results are compared with the experimental data provided by PHENIX, ATLAS and CMS Collaborations. At forward rapidity and midrapidity, a reasonable agreement with the experimental data is shown for the theoretical results with the modified Kharzeev, Levin and Nardi model, and the Kowalski and Teaney model. Then, we analyze the influence of the initial state energy loss effect on the nuclear modification factor and find that it is obvious only at backward rapidity together with small p_T. Finally, the theoretical results are also compared with those of JETPHOX Monte Carlo program and the predictive results for the LHCb at very forward rapidities are presented.

We study the energy loss of a quark moving in a strongly coupled quark gluon plasma under the influence of anisotropy. The heavy quark drag force, diffusion coefficient, and jet quenching parameter are calculated using the Einstein-Maxwell-dilaton model, where the anisotropic background is characterized by an arbitrary dynamical parameter A. Our findings indicate that as the anisotropic factor A increases, the drag force and jet quenching parameter both increase, while the diffusion coefficient decreases. Additionally, we observe that the energy loss becomes more significant when the quark moves perpendicular to the anisotropy direction in the transverse plane. The enhancement of the rescaled jet quenching parameters near critical temperature T_c, as well as drag forces for a fast-moving heavy quark is observed, which presents one of the typical features of quantum chromodynamics phase transition.

The strong attractive interaction of the φ meson and the proton has recently been reported by the ALICE Collaboration. The corresponding scattering length f₀ is given as ${\rm{Re}}({f}_{0})=0.85\pm 0.34({\rm{stat}})\pm 0.14({\rm{syst}})$ and ${\rm{Im}}({f}_{0})=0.16\pm 0.10({\rm{stat}})\pm 0.09({\rm{syst}})$ fm. The fact that the real part is significant in contrast to the imaginary part indicates a dominant role of elastic scattering, whereas the inelastic process is less important. In this work, such scattering processes are inspected based on a unitary coupled-channel approach inspired by the Bethe–Salpeter equation. The φp scattering length is calculated based on this approach, and it is found that the experimental value of the φp scattering length can be obtained only if the attractive interaction of the φ meson and the proton is taken into account. A significant outcome of such attractive interaction is a two-pole structure in the φp scattering amplitude. One of the poles, located at (1969 − i283) MeV might correspond to N(1895)1/2⁻ or N(1875)3/2⁻ as listed in the review of the Particle Data Group (PDG). The other one, located at 1949 − i3 MeV should be a φN bound state, which has no counterpart in the PDG data.

A triaxially deformed relativistic Hartree–Bogoliubov theory in the Woods–Saxon basis is developed with the aim of treating the triaxial deformation, pairing correlations and continuum in a unified way. In order to consider the triaxial deformation, the deformed potentials are expanded in terms of spherical harmonic functions in the coordinate space. In order to take the pairing correlations into account and treat the continuum properly, by using the Dirac Woods–Saxon basis, which has correct asymptotic behavior, the relativistic Hartree–Bogoliubov equation with triaxial deformation is solved. The formalism of triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is presented. Taking an axially deformed nucleus ²⁴Ne and a triaxially deformed nucleus ⁷⁶Ge as examples, the numerical checks are performed. A weakly bound nucleus ¹¹²Ge is taken as an example to carry out the necessary converge checks for the numerical parameters. In addition, the ground-state properties of even–even germanium isotopes are investigated. The evolutions of two-neutron separation energy, deformation, root-mean-square radii and density distribution with mass number are analyzed. The comparison between the calculations from the relativistic Hartree–Bogoliubov theory based on harmonic-oscillator basis and the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is performed. It is found that the neutron drip line is extended from ¹¹⁴Ge to ¹¹⁸Ge in the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis.

Pronounced changes of nuclear charge radii provide a stringent benchmark on the theoretical models and play a vital role in recognizing various nuclear phenomena. In this work, the systematic evolutions of nuclear charge radii along even Z = 84-120 isotopic chains are first investigated by the recently developed new ansatz under the covariant density functional. The calculated results show that the shell closure effects of nuclear charge radii appear remarkably at the neutron numbers N = 126 and 184. Interestingly, the arch-like shapes of charge radii between these two strong neutron-closed shells are naturally observed. Across the N = 184 shell closure, the abrupt increase in charge radii is still evidently emerged. In addition, the rapid raise of nuclear charge radii from the neutron numbers N = 138 to N = 144 is disclosed clearly in superheavy regions due to the enhanced shape deformation.

We demonstrate an optical realization for the rotating BTZ black hole using the recent popular photon fluid model in an optical vortex but with a new proposed expression for the optical phase. We also give the numerical realization for the optical vortex to ensure that it can be generated experimentally. Different from the earlier suggestions for the analogue rotating black holes, our proposal includes an inner horizon in the analogue black hole structure. Such structure can keep for a long distance for the convenience of observing analogue Hawking or Penrose radiations.

The structure properties for even–even nuclei around ²³⁰U, located on the hexadecapole-deformation island, are investigated using the potential-energy-surface calculation within the framework of the macroscopic−microscopic model. The impact of different deformation degrees of freedom (including axial and nonaxial quadrupole and hexadecapole deformations) on total energy, shell, and pairing contributions is analyzed, based on the projected energy maps and curves. The single-particle structure is presented and briefly discussed. To a large extent, a much better agreement with experimental data and other theoretical results is obtained if the hexadecapole deformations, especially the axial one, are taken into account. These results could provide useful insights into understanding the effects of different quadrupole and hexadecapole deformations.

Based on the liquid-drop model and using the first derivative of the normalized Gaussian function to consider the shell correction, a simple α-decay energy formula is proposed for heavy and superheavy nuclei. The values of corresponding adjustable parameters are obtained by fitting α-decay energies of 209 nuclei ranging from Z = 90 to Z = 118 with N ≥ 140. The calculated results are in good agreement with the experimental data. The average and standard deviations between the experimental data and theoretical results are 0.141 and 0.190 MeV, respectively. For comparison, the reliable formulae proposed by Dong T K et al (2010, Phys. Rev. C 82, 034 320), Dong J M et al (2010, Phys. Rev. C 81, 064 309) and the WS3+ nuclear mass model proposed by Wang N et al (2011, Phys. Rev. C 84, 051 303) are also used. The results indicate that our improved 7-parameter formula is superior to these empirical formulae and is largely consistent with the WS3+ nuclear mass model. In addition, we extend this formula to predict the α-decay energies for nuclei with Z = 117, 118, 119 and 120. The predicted results of these formulae are basically consistent.

Based on the systematic studies for low-lying states of the odd-A ⁴⁹⁻⁵⁷Mn isotopes, the ground-states inversion and the rotational properties of a ground-state-based sequence are revealed and discussed. The energy levels of low-lying states and electromagnetic moments in odd-A ⁴⁹⁻⁵⁷Mn isotopes have been well reproduced in shell-model calculations, and the above phenomena could be understood with obviously different occupation numbers in proton orbitals such as πf_7/2 and πp_3/2, which changes similarly with the obtained quadrupole deformation in covariant density functional theory (CDFT). After considering the coupling of collective rotation and intrinsic single-particle motion, the available experimental magnetic moments in ⁵³Mn and adjacent nuclei can be well explained with CDFT. The present calculations suggest that the 5/2⁻ and 7/2⁻ states in ⁵³Mn are formed by π5/2⁻[312] and π7/2⁻[303] respectively. Together with the behavior of levels, this provides proofs for the level sequences of low-lying states in ⁵³Mn distinct from the K^π = 5/2⁻ rotational band in ⁴⁹Cr and other odd-A Mn isotopes.