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2025-3 Contents
2025, 49(3): 1-2.
Abstract:
PARTICLES AND FIELDS
Modification of the Sommerfeld effect due to coannihilator decays
Feng Luo
2025, 49(3): 033101. doi: 10.1088/1674-1137/ad93b9
Abstract:
In dark matter coannihilation scenarios, the Sommerfeld effect of coannihilators is usually important in the calculations of dark matter thermal relic abundance. Due to decays of coannihilators, two annihilating coannihilators can only approach each other from a finite initial separation. While conventional derivations of Sommerfeld factors essentially assume an infinite initial separation, Sommerfeld factors for a pair of annihilating coannihilators may be different. We find that the Sommerfeld factor for a pair of coannihilators is less prominent than that obtained without considering decays. Modification of the Sommerfeld factor may result in a change of the dark matter thermal relic abundance well beyond the percent level.
Soft pattern of Rutherford scattering from heavy target mass expansion
Yu Jia, Jia-Yue Zhang
2025, 49(3): 033102. doi: 10.1088/1674-1137/acdb56
Abstract:
We investigate the soft behavior of the tree-level Rutherford scattering process. We consider two types of Rutherford scattering processes: One in which a low-energy massless point-like projectile (say, a spin-\begin{document}${1/ 2}$\end{document} or spin-\begin{document}$ 0 $\end{document} electron) hits a static massive composite target particle carrying various spins (up to spin-\begin{document}$ 2 $\end{document}), and one where a slowly-moving light projectile hits a heavy static composite target. For the first type, the unpolarized cross sections in the laboratory frame are found to exhibit universal forms in the first two orders of \begin{document}$ 1/M $\end{document} expansion yet differ at the next-to-next-to-leading order (though some terms at this order still remain universal or depend on the target spin in a definite manner). For the second type, at the lowest order in electron velocity expansion, through all orders in \begin{document}$ 1/M $\end{document}, the unpolarized cross section is universal (also not sensitive to the projectile spin). The universality partially breaks down at relative order-\begin{document}$ v^2/M^2 $\end{document}, though some terms at this order are still universal or depend on the target spin in a specific manner. We also employ the effective field theory approach to reproduce the soft behavior of the differential cross sections for when the target particle is a composite spin-\begin{document}${1/ 2}$\end{document} fermion.
Fused model of the alternating spin chain from ABJM theory
Nan Bai, Fan Feng, Mao-Zhong Shao
2025, 49(3): 033103. doi: 10.1088/1674-1137/ada521
Abstract:
In this paper, we present an algebraic construction of the fused model for the ABJM spin chain by gluing two adjacent quantum spaces and two original auxiliary spaces. We prove the integrability of the fused model by demonstrating the validity of the Yang-Baxter equation. Owing to the regularity property of the fused R-matrix, we successfully construct the boost operator for the fused model and obtain the third-order charge accordingly. We also investigate the open spin chain Hamiltonian for the fused model and indicate the general common structures of the boundary terms which are further used to analyze the integrability of the flavored ABJM Hamiltonian.
Potential to identify neutrino mass ordering with reactor antineutrinos at JUNO
Angel Abusleme, Thomas Adam, Shakeel Ahmad, Rizwan Ahmed, Sebastiano Aiello, Muhammad Akram, Abid Aleem, Fengpeng An, Qi An, Giuseppe Andronico, Nikolay Anfimov, Vito Antonelli, Tatiana Antoshkina, Burin Asavapibhop, João Pedro Athayde Marcondes de André, Didier Auguste, Weidong Bai, Nikita Balashov, Wander Baldini, Andrea Barresi, Davide Basilico, Eric Baussan, Marco Bellato, Marco Beretta, Antonio Bergnoli, Daniel Bick, Lukas Bieger, Svetlana Biktemerova, Thilo Birkenfeld, Iwan Morton-Blake, David Blum, Simon Blyth, Anastasia Bolshakova, Mathieu Bongrand, Clément Bordereau, Dominique Breton, Augusto Brigatti, Riccardo Brugnera, Riccardo Bruno, Antonio Budano, Jose Busto, Anatael Cabrera, Barbara Caccianiga, Hao Cai, Xiao Cai, Yanke Cai, Zhiyan Cai, Stéphane Callier, Antonio Cammi, Agustin Campeny, Chuanya Cao, Guofu Cao, Jun Cao, Rossella Caruso, Cédric Cerna, Vanessa Cerrone, Chi Chan, Jinfan Chang, Yun Chang, Auttakit Chatrabhuti, Chao Chen, Guoming Chen, Pingping Chen, Shaomin Chen, Yixue Chen, Yu C
2025, 49(3): 033104. doi: 10.1088/1674-1137/ad7f3e
Abstract:
The Jiangmen Underground Neutrino Observatory (JUNO) is a multi-purpose neutrino experiment under construction in South China. This paper presents an updated estimate of JUNO’s sensitivity to neutrino mass ordering using the reactor antineutrinos emitted from eight nuclear reactor cores in the Taishan and Yangjiang nuclear power plants. This measurement is planned by studying the fine interference pattern caused by quasi-vacuum oscillations in the oscillated antineutrino spectrum at a baseline of 52.5 km and is completely independent of the CP violating phase and neutrino mixing angle θ23. The sensitivity is obtained through a joint analysis of JUNO and Taishan Antineutrino Observatory (TAO) detectors utilizing the best available knowledge to date about the location and overburden of the JUNO experimental site, local and global nuclear reactors, JUNO and TAO detector responses, expected event rates and spectra of signals and backgrounds, and systematic uncertainties of analysis inputs. We find that a 3σ median sensitivity to reject the wrong mass ordering hypothesis can be reached with an exposure of about 6.5 years × 26.6 GW thermal power.
NUCLEAR PHYSICS
Odd-even mass differences of well and rigidly deformed nuclei in the rare earth region: Test of a newly proposed fit for average pairing matrix elements
T. V. Nhan Hao, N. N. Bao Nguyen, D. Quang Tam, P. Quentin, L. Bonneau, Meng-Hock Koh
2025, 49(3): 034101. doi: 10.1088/1674-1137/ad8bb1
Abstract:
We present an analysis of a recent approach for determining the average pairing matrix elements within a specified interval of single-particle (sp) states around the Fermi level, denoted as λ. This method, known as the uniform gap method (UGM), highlights the critical importance of the averaged sp level density \begin{document}$\tilde{\rho}(e)$\end{document}. The pairing matrix elements within the UGM approach are deduced from microscopically calculated values of \begin{document}$\tilde{\rho}(e)$\end{document} and gaps obtained from analytical formulae of a semi-classical nature. Two effects generally ignored in similar fits are addressed: (a) a correction for a systematic bias introduced by fitting pairing gaps corresponding to equilibrium deformation solutions, as discussed by Möller and Nix [Nucl. Phys. A 476, 1 (1992)], and (b) a correction for a systematic spurious enhancement of \begin{document}$\tilde{\rho}(e)$\end{document} for protons in the vicinity of λ, caused by the local Slater approximation commonly employed in treating Coulomb exchange terms (e.g., [Phys. Rev. C 84, 014310 (2011)]). This approach has demonstrated significant efficiency when applied to Hartree-Fock + Bardeen-Cooper-Schrieffer (BCS) calculations (including the seniority force and self-consistent blocking for odd nuclei) of a large sample of well and rigidly deformed even-even rare-earth nuclei. The experimental moments of inertia for these nuclei were reproduced with an accuracy comparable to that achieved through direct fitting of the data [Phys. Rev. C 99, 064306 (2019)]. In this study, we extended the evaluation of our method to the reproduction of three-point odd-even mass differences centered on odd-N or odd-Z nuclei in the same region. The agreement with experimental data was found to be comparable to that obtained through direct fitting, as reported in [Phys. Rev. C 99, 064306 (2019)].
Systematic research on the ground state properties of medium-mass neutron-rich nuclei
Chen He, Xue-Neng Cao, Xian-Xian Zhou
2025, 49(3): 034102. doi: 10.1088/1674-1137/ad9014
Abstract:
The recently developed relativistic-mean-field in complex momentum representation with the functional NL3* was used to explore the exotic properties of neutron-rich Pd, Cd, Te, and Xe isotopes. The results were compared with those obtained using the relativistic Hartree-Bogoliubov (RHB) calculations and available experimental data. The single-particle levels were obtained for the bound and resonant states. The two neutron separation energies \begin{document}$ S_{2n} $\end{document} and root mean square (rms) radii agree with the experimental data. It is shown that there is a halo structure in extremely neutron-rich \begin{document}$ ^{164-180} $\end{document}Te and \begin{document}$ ^{164-182} $\end{document}Xe, as well as a thick neutron skin in extremely neutron-rich Pd and Cd isotopes. From the numbers of neutrons (\begin{document}$ N_{_\lambda} $\end{document}) and (\begin{document}$ N_{_0} $\end{document}) occupying the levels above the Fermi surface and zero-potential energy level, it was found that pairing correlations play an important role in the formation of halo phenomena. These findings are further supported by investigating \begin{document}$ S_{2n} $\end{document}, rms radii, occupation probabilities, contributions of single-particle levels to the neutron rms radii, and density distributions. The neutron rms radii increased sharply, evidently deviating from the traditional rule \begin{document}$ r\propto N^{1/3} $\end{document}, and the density distributions were very diffuse. Finally, the contributions of different single-particle levels to the total neutron density and wavefunction are discussed. It was found that the sudden increase in the neutron rms radii and diffuse density distributions mainly arise from the resonant levels with a lower orbital angular momentum near the continuum threshold.
Simulation of dark scalar particle sensitivity in η rare decay channels at HIAF
Yang Liu, Rong Wang, Zaiba Mushtaq, Ye Tian, Xionghong He, Hao Qiu, Xurong Chen
2025, 49(3): 034103. doi: 10.1088/1674-1137/ad9d1b
Abstract:
The search for dark portal particles is a prominent topic at the frontier of particle physics. We present a simulation study of an experiment suitable for searching for scalar portal particles at the Huizhou η factory. The high-intensity proton beam from HIAF and a high event-rate spectrometer are suggested to conduct this experiment, both of which are well-suited for the discovery of new physics. Under a conservative estimation, \begin{document}$5.9\times 10^{11}$\end{document} η events could be produced during a one-month operation of the experiment. The hadronic production of η mesons (\begin{document}$p + ^7\text{Li} \rightarrow \eta X$\end{document}) was simulated at a beam energy of 1.8 GeV using the GiBUU event generator. We searched for light dark scalar particles through rare decay channels, namely \begin{document}$\eta \rightarrow S \pi^0 \rightarrow \pi^+ \pi^- \pi^0$\end{document} and \begin{document}$\eta \rightarrow S \pi^0 \rightarrow e^+ e^- \pi^0$\end{document}. The detection efficiencies of the channels and the spectrometer resolutions were studied in the simulation. We also present the projected upper limits of the decay branching ratios of the dark scalar particle and the projected sensitivities to the model parameters.
Evaluation of fission fragment moments of inertia forspontaneous fission of CF-252
D. E. Lyubashevsky, P. V. Kostryukov, A. A. Pisklyukov, J. D. Shcherbina
2025, 49(3): 034104. doi: 10.1088/1674-1137/ad8d4d
Abstract:
In the present study, methods for estimating the moments of inertia of fission fragments resulting from the spontaneous fission of isotope Cf-252 were analyzed. In particular, two main approaches were examined: statistical and microscopic. The classical and superfluid approaches for calculating the moments of inertia were also examined, along with their implementations in a variety of nuclear models. In this context, the impact of diverse oscillation modes and nucleon exchange on the moments of inertia and spin distributions of fission fragments was assessed. This study emphasizes the need for a comparative analysis of theoretical predictions and experimental data, which would contribute to a more comprehensive understanding of the internal structure of nuclei and the mechanisms of fission.
Revisiting the alpha-decay reduced width of the lightest uranium isotope 214U
Shuangshuang Zhang, Yongjia Wang, Xiaotao He
2025, 49(3): 034105. doi: 10.1088/1674-1137/ad9302
Abstract:
The lightest uranium isotope \begin{document}$ {\rm^{214}U} $\end{document} has been produced at the Heavy Ion Research Facility in Lanzhou, China. The α-decay reduced width (\begin{document}$ \delta^{2} $\end{document}) of \begin{document}$ {\rm^{214}U} $\end{document} has been found to be significantly larger than those of other nuclei by a factor of 2. However, the extraction of \begin{document}$ \delta^{2} $\end{document} depends on the penetration probability (P) through the barrier, and P is related to the theoretical method of obtaining it and the form of the α-core potential. The aim of this study is to investigate whether the selections of the α-core potential and the method of calculating P can affect the above conclusion. Four different phenomenological α-core potentials and two microscopic double-folding potentials, together with the Wentzel-Kramers-Brillouin (WKB) approximation and transfer matrix (TM) approach, are used to obtain P. The value of P obtained using the WKB approximation is about 20%−40% smaller than the one obtained using the TM approach. Thus, the deduced \begin{document}$ \delta^{2} $\end{document} is overestimated. The choice of α-core potential can significantly affect the value of \begin{document}$ \delta^{2} $\end{document}. With the spherical form for the α-core potentials, the \begin{document}$ \delta^{2} $\end{document} of \begin{document}$ {\rm^{214}U} $\end{document} obtained with both the WKB and TM approaches are about twice as large as those of the surrounding nuclei. With the deformed double-folding potential, the ratio between \begin{document}$ \delta^{2} $\end{document} of \begin{document}$ {\rm^{214}U} $\end{document} and that of the surrounding nuclei is observed to be slightly below 2. The effects of nuclear deformation and the α-core potential should be considered when studying the α-decay reduced width in the \begin{document}$ N_{p}N_{n} $\end{document} systematics.
Enhanced empirical formulas for α-decay of heavy and superheavy nuclei: Incorporating deformation effects of daughter nuclei
M. Ismail, A. Adel, Asmaa Ibrahim
2025, 49(3): 034106. doi: 10.1088/1674-1137/ad9f46
Abstract:
The latest experimental data of α-decay half-lives for 573 nuclei within the range of \begin{document}$ 52 \leq Z \leq 118 $\end{document} are utilized to enhance empirical formulas with updated coefficients. These formulas are enhanced by analyzing the contributions of orbital angular momentum and isospin asymmetry. The effect of deformation of daughter nuclei on the α-decay half-life is modeled by incorporating two additional terms, dependent on the quadrupole and hexadecapole deformation parameters, into the empirical formulas for α-decay half-lives. Incorporating these deformation-dependent terms, along with angular momentum and isospin asymmetry, we improve the standard deviation by approximately 17%. The revised empirical formulas for α-decay half-lives demonstrate better agreement with experimental data when deformation factors are included. The modified formulas are validated through comparisons with recent experimental results and further theoretical predictions. This paper presents and compares α-decay half-life predictions for several isotopes of superheavy nuclei with \begin{document}$ Z = 120-126 $\end{document}, which are yet to be experimentally synthesized. For various isotopes of each element, the variation in \begin{document}$ \log_{10} T_{\alpha} $\end{document} with changes in the neutron number is also explored.
Investigation of decay mechanisms and associated aspects of exotic nobelium isotopes using the Skyrme energy density formalism
Shubhpreet Kaur, Raj Kumar, Manoj K. Sharma
2025, 49(3): 034107. doi: 10.1088/1674-1137/ad65dd
Abstract:
The search for heavy elements has yielded many surprises and enhanced our knowledge of nuclear synthesis and associated dynamical aspects. Although new elements and their associated isotopes have been synthesized, information concerning elements with \begin{document}$Z \geq 102 $\end{document}, remains scarce. Further, concerning the transfermium elements, the nuclear shell structure is key to ensuring nuclear stability. Hence, the shell effects have key implications on such nuclei. Many experimental and theoretical investigations have been conducted to examine the reactions induced by heavy ions and the subsequent decay mechanisms in the superheavy mass region. In addition, the region of transfermium elements is of great interest because of the neutron/proton shell effects. Here, our objective is to analyze the decay mechanisms of nuclides having Z = 102 nuclei, i.e., 248No* and 250No*. An extensive study was conducted using the dynamical cluster-decay model (DCM) based on Quantum Mechanical Fragmentation Theory (QMFT). The focus was to investigate compound nucleus (CN) and non-compound nucleus (nCN) mechanisms, including fusion-fission (ff), quasi-fission (QF), and fast fission (FF). The specific isotopes of interest are 248No* and 250No*, with attention given to the role of the center-of-mass energy \begin{document}$(E_{\rm c.m.})$\end{document} and angular momentum \begin{document}$ (\ell) $\end{document}. The nuclear interaction potential was derived using the Skyrme energy density formalism (SEDF) with the GSkI force parameters. The capture cross-sections were calculated using the \begin{document}$ \ell $\end{document}-summed Wong Model. The determination of the probability of compound nucleus formation (PCN) involved a function that is dependent upon the center-of-mass energy. The lifetimes of the ff and QF channels were also investigated. Here, CN and nCN decay mechanisms for two isotopes of Z = 102 nobelium were analyzed over the range of center-of-mass values \begin{document}$(E_{\rm c.m.})$\end{document} considering the quadrupole deformation \begin{document}$ (\beta_2) $\end{document} and optimum orientations \begin{document}$(\theta_{\rm opt.})$\end{document} of the decaying fragments. The fragmentation potential, preformation probability, neck length parameter, and reaction cross-sections were explored. Further, PCN was calculated to determine the mechanisms of decay of 248No* and 250No* isotopes. The obtained fusion–fission lifetimes and quasi-fission lifetimes are compared with the dinuclear system (DNS) approach. Among the considered isotopes having Z = 102, i.e., the 248No* formed in the 40Ca + 208Pb reaction and 250No* formed via two different entrance channels, 44Ca+206Pb and 64Ni+186W, show asymmetric fragmentation with the effect of \begin{document}$ \beta_2 $\end{document} deformation at the energies beyond the Coulomb barrier. Of note, the nCN (QF and FF) decay mechanisms compete with the CN fission channels. The calculations based on the DCM show a strong correlation with the experimental data. The most probable fragments, such as 122Sn and 128Te, were observed near the magic shell closure at Z = 50 and N = 82. Further, as the excitation energy increased, the fusion–fission and quasi-fission lifetimes decreased.
Time-reversal invariance violation effect in dd scattering
M. N. Platonova, Yu. N. Uzikov
2025, 49(3): 034108. doi: 10.1088/1674-1137/ad9b9f
Abstract:
A formalism is developed for calculating the signal of the violation of time-reversal invariance, provided that space-reflection (parity) invariance is conserved during the scattering of tensor-polarized deuterons on vector-polarized deuterons. The formalism is based on Glauber theory and fully considers the spin dependence of \begin{document}$ NN $\end{document} elastic scattering amplitudes and the spin structure of colliding deuterons. Numerical calculations are performed in the laboratory proton energy range \begin{document}$ T_p = 0.1 $\end{document}–1.2 GeV using the SAID database for spin amplitudes and in the energy region of the SPD NICA experiment corresponding to the invariant mass of the interacting nucleon pairs \begin{document}$\sqrt{s_{_{NN}}} = 2.5$\end{document}–25 GeV, using two phenomenological models of \begin{document}$ pN $\end{document} elastic scattering. It is found that only one type of the time-reversal non-invariant parity conserving \begin{document}$ NN $\end{document} interaction gives a non-zero contribution to the signal in question, which is important for isolating an unknown constant of this interaction from the corresponding data.
Coupled channel analysis of neutron transfer in 6,7Li induced reactions around the Coulomb barrier
Himanshu Sharma, Rishabh Kumar, Moumita Maiti
2025, 49(3): 034109. doi: 10.1088/1674-1137/ad99ae
Abstract:
The coupled reaction channel approach has proven to be quite effective in explaining the mechanism of nucleon transfer in heavy-ion reactions. Nevertheless, significant ambiguities remain regarding the selection of potential parameters and the states of the nuclei that should be coupled together for a specific reaction channel. In this study, the excitation functions for one- and two-neutron transfer in \begin{document}$^{6,7}$\end{document}Li-induced reactions on various targets were analyzed using the coupled reaction channel formalism. Spectroscopic amplitudes were taken from the existing literature and shell model calculations. The one-neutron transfer cross sections from \begin{document}$ ^{6} $\end{document}Li+\begin{document}$ ^{93} $\end{document}Nb and \begin{document}$ ^{7} $\end{document}Li+\begin{document}$ ^{115} $\end{document}In reactions were reasonably well reproduced by coupled reaction channel calculations. A reasonable match for the measured cross sections was also obtained for the two-neutron transfer in the \begin{document}$ ^{7} $\end{document}Li+\begin{document}$ ^{181} $\end{document}Ta reaction by employing the extreme cluster model.
PARTICLE AND NUCLEAR ASTROPHYSICS AND COSMOLOGY
Layout optimization and performance analysis of large array of imaging atmospheric Cherenkov telescopes
Zhipeng Zhang, Ruizhi Yang, Shoushan Zhang, Zhen Xie, Jiali Liu, Liqiao Yin, Yudong Wang, Lingling Ma, Zhen Cao
2025, 49(3): 035001. doi: 10.1088/1674-1137/ad8e3f
Abstract:
The large array of imaging atmospheric Cherenkov telescopes (LACT) is a planned array of 32 Cherenkov telescopes, each featuring 6-m diameter mirrors, to be constructed at the LHAASO site. This study focused on optimizing the array layout and analyzing the performance of LACT. Two observation modes were examined: large zenith angle observations for ultra-high energy events and small zenith angle observations for lower energy thresholds. For large zenith angles (60°), simulations indicate that an 8-telescope subarray can achieve an effective area of \begin{document}$ 3 \; \rm km^2 $\end{document} with excellent angular resolution. For small zenith angles, we optimized the layout of 4-telescope cells and the full 32-telescope array. The energy threshold of the full array is approximately 200 GeV, which is particularly crucial for studying transient phenomena such as gamma-ray bursts (GRBs) and active galactic nuclei (AGNs). This study provides essential guidance for finalizing the LACT layout design and estimating performance under various observational conditions. It also highlights the potential of LACT for conducting deep observations of ultra-high energy γ-ray sources, performing morphological studies of PeVatrons, and advancing time-domain γ-ray astronomy.
Gravitational waves and primordial black holes from axion domain walls in level crossing
Hai-Jun Li, Yu-Feng Zhou
2025, 49(3): 035101. doi: 10.1088/1674-1137/ada003
Abstract:
In this paper, we investigate the nano-Hertz gravitational wave (GW) emission and massive primordial black hole (PBH) formation from the light QCD axion scenario. We consider the axion domain wall formation from the level crossing induced by the mass mixing between the light \begin{document}$ Z_{\mathcal N} $\end{document} QCD axion and axion-like particle. A general mixing case in which the heavy and light mass eigenvalues do not necessarily have to coincide with the axion masses is considered. To form the domain walls, the axions should start to oscillate slightly before the level crossing. The domain walls must annihilate before dominating the Universe to avoid cosmological catastrophe. Then, we focus our attention on the GW emission from the domain wall annihilation and the PBH formation from the domain wall collapse. We show the predicted GW spectra with a peak frequency \begin{document}$\sim 0.2~ \rm nHz$\end{document} and peak amplitude \begin{document}$ \sim 5\times 10^{-9} $\end{document}, which can be tested by future pulsar timing array projects. In addition, during the domain wall annihilation, the closed walls could shrink to the Schwarzschild radius and collapse into the PBH. We find that PBHs in the mass range of \begin{document}$ \mathcal{O}(10^5-10^8) M_\odot $\end{document} could potentially form in this scenario and account for a small fraction (\begin{document}$ \sim 10^{-5} $\end{document}) of the cold dark matter.
Evolution of the universe prior to inflation in loop quantum cosmology
M. Shahalam
2025, 49(3): 035102. doi: 10.1088/1674-1137/ad9d1a
Abstract:
We studied the dynamics of pre-inflation with generic potentials, namely \begin{document}$ V(\phi) \propto \phi^{4} $\end{document} and \begin{document}$ V(\phi) \propto (1+\phi)^{2} $\end{document} , in the context of loop quantum cosmology, where the initial singularity is resolved by a non-singular quantum bounce. Initially, the background evolution is dominated by either kinetic or potential energy at the quantum bounce. In the case of kinetic energy dominated evolution at the bounce, we found three generic phases, namely bouncing, transition, and slow-roll inflation. The first two regimes vanish in the case of potential energy dominated evolution; however, slow-roll inflation remains. Therefore, we found physically viable initial conditions of the inflaton field, which must have a minimum number of \begin{document}$ e $\end{document} -folds of 60 to be compatible with observations. Additionally, we analyzed the phase space diagram for the models under consideration; we found that all the trajectories of the inflaton field start from the bounce and move toward stable attractor points.
Quantifying the memory and dynamical stability of magnetar bursts
Yu Sang, Hai-Nan Lin
2025, 49(3): 035103. doi: 10.1088/1674-1137/ad9d1c
Abstract:
The time series of energy and waiting time in magnetar bursts carry important information about the source activity. In this study, we investigate the memory and dynamical stability of magnetar bursts from four soft gamma repeater (SGR) sources: SGR 1806−20, SGR 1900+14, SGR J1935+2154, and SGR J1550−5418. Based on the rescaled range analysis, we quantify the memory in magnetar bursts for the first time and find that there exists long-term memory in the time series of both waiting time and energy. We investigate the dynamical stability in the context of randomness and chaos. For all four SGR samples, we find that the waiting time is not completely random; however, the energy of two SGRs is consistent with a total random organization. Furthermore, both waiting time and energy exhibit weak chaos. We also find no significant difference between SGRs and repeating fast radio bursts (FRBs) in the randomness-chaos phase space. The statistical similarity between SGRs and repeating FRBs hints that there may be potential physical connection between these two phenomena.
Complexity growth for AdS black holes in the presence of backreaction
Long Guo, Zi-qiang Zhang
2025, 49(3): 035104. doi: 10.1088/1674-1137/ada125
Abstract:
We investigate the holographic complexity in backreacted gravity backgrounds according to the complexity-action conjecture. The backreaction considered here originates from the presence of static strings evenly distributed over the system. We exploit a probe string in the bulk and evaluate the Nambu-Goto action and its dependence on backreaction. The results suggest that, for slower strings, the complexity increases with increasing backreaction, in accordance with the findings of holographic entanglement entropy. However, for faster strings, the situation is different. Furthermore, we analyze the relationship between complexity and space dimension as well as string velocity.
Schottky anomaly of Reissner-Nordström-de Sitter spacetime
Hai-Long Zhen, Yu-Bo Ma, Huai-Fan Li, Li-Chun Zhang, Yun-Zhi Du
2025, 49(3): 035105. doi: 10.1088/1674-1137/ad9f45
Abstract:
In the extended thermodynamics of black holes, there exists a thermodynamical pressure whose dual thermodynamical quantity is volume. Extensive studies have been conducted on the phase structure of numerous black holes, demonstrating striking similarities to the phase structures of various ordinary matter systems. From a comparison between the thermodynamic properties of spherically symmetric AdS black holes and ordinary thermodynamic systems, we know that the isovolumetric heat capacity of the former is zero, whereas that of the latter is non-zero. The intrinsic reason for this discrepancy is a topic of interest. For Reissner-Nördstrom-de Sitter (RN-dS) spacetime with the coexistence of the black hole and cosmological horizons, the effective thermodynamic quantities are presented alongside the interaction between two horizons. The heat capacity in RN-dS spacetime is then investigated, and it is demonstrated that the behavior of the heat capacity in RN-dS spacetime is analogous to that of Schottky specific heat. Treating two horizons in RN-dS spacetime as two distinct energy levels in a two-energy-level system, we investigate the thermodynamic properties in RN-dS spacetime by studying the thermodynamic properties in an ordinary two-energy system, thereby elucidating the intrinsic reasons for the occurrence of Schottky specific heat in RN-dS spacetime. The heat capacity observed in RN-dS spacetime is not only consistent with that of Schottky specific heat described by the effective thermodynamic quantities in RN-dS spacetime but also with that of an ordinary two-energy-level system. These results not only reveal the quantum properties of RN-dS spacetime but also provide a new avenue for further in-depth study of the quantum properties of black holes and dS spacetime.
Universal thermodynamic relations with constant corrections for five-dimensional de Sitter spacetime
Yubo Ma, Songtao Zheng, Jing Li
2025, 49(3): 035106. doi: 10.1088/1674-1137/ad9d1e
Abstract:
In this study, we built upon the method proposed by Goon and Penco for analyzing the universality of thermodynamic relations with corrections in de Sitter (dS) black holes. Additionally, based on our analysis of non-linear magnetically charged black holes in dS spacetime, five-dimensional dS hairy spacetime, and five-dimensional charged-dS rotating black holes, we demonstrate the universality of thermodynamic relations in dS black holes. This establishes a universal conjecture relating shifted thermodynamic quantities for arbitrary black-hole backgrounds. We consider that these universal relations will offer new insights into the realm of quantum gravity.
Effective potential and topological photon spheres: a novel approach to black hole parameter classification
Mohammad Ali S. Afshar, Jafar Sadeghi
2025, 49(3): 035107. doi: 10.1088/1674-1137/ada127
Abstract:
In this paper, we base our analysis on the assumption that the existence of a photon sphere is an intrinsic characteristic of any ultra-compact gravitational structure with spherical symmetry. Utilizing the concept of a topological photon sphere, we categorize the behaviors of various gravitational models based on the structure of their photon spheres. This innovative approach enables us to define boundaries for black hole parameters, subsequently enabling us to classify the model as either a black hole or naked singularity. We demonstrate that the presence of this interplay between the gravitational structure and the existence of a photon sphere is a unique advantage that can be utilized from both perspectives. Our observations indicate that a gravitational model typically exhibits the behavior of a horizonless structure (or naked singularity) when a minimum effective potential (a stable photon sphere) appears within the studied spacetime region. Additionally, in this study, we investigate the effect of this structure on the behavior of the photon sphere by selecting models that are affected by Perfect Fluid Dark Matter (PFDM). Finally, by analyzing a model with multiple event horizons, we show that the proposed method remains applicable even in such scenarios.
Holographic Einstein rings of AdS black holes in Horndeski theory
Zhi Luo, Ke-Jian He, Jin Li
2025, 49(3): 035108. doi: 10.1088/1674-1137/ada34c
Abstract:
Using the AdS/CFT correspondence and wave optics techniques, we conduct an extensive study of the imaging properties of holographic Einstein rings in the context of anti-de Sitter (AdS) black holes (BHs) in Horndeski theory. Our results indicate that the optical characteristics of these holographic Einstein rings are significantly influenced by the observer's position, physical parameters of the BH, nature of the wave source, and configuration of the optical system. Specifically, when the observer is positioned at the north pole of the AdS boundary, the holographic image prominently displays a ring structure aligning with the BH's photon sphere. We thoroughly analyze the effect of various physical parameters — including the observation position, event horizon radius, temperature, and the parameter γ in Horndeski theory — on the holographic Einstein rings. These parameters play a crucial role in determining the rings' radius and brightness, with variations potentially causing the ring structures to deform or even transform into bright spots. Furthermore, our comparative analysis between wave and geometric optics reveals a strong agreement in predicting the positions and brightness of both the photon and Einstein rings. This paper offers new insights into the spacetime geometry of BHs in Horndeski theory and proposes a promising framework for exploring the gravitational duals of strongly coupled systems.
Constraints on brane geometry from massive vector KK modes
Chun-E Fu, Heng Guo, Ye-Hao Yang
2025, 49(3): 035109. doi: 10.1088/1674-1137/ada5ca
Abstract:
We examine the gauge invariance of massive vector Kaluza-Klein (KK) modes within various 6D brane models. Our analysis reveals that additional constraints on the brane geometry are essential to maintain the gauge invariance of the massive vector KK modes. However, these conditions are not universally satisfied by brane solutions, leading to loss of gauge invariance. In instances in which the brane solutions align with the conditions, we compute the mass spectra of both vector and scalar KK modes and determine some resonances for the KK modes in one of the brane models. Our findings indicate that the presence of a single type of massive scalar KK mode will break the gauge invariance.
Thermodynamic topology of Kiselev-AdS black holes within f (R, T) gravity
Saeed Noori Gashti, Mohammad Ali S. Afshar, Mohammad Reza Alipoury, Yassine Sekhmani, Jafar Sadeghi, Javlon Rayimbaeva
2025, 49(3): 035110. doi: 10.1088/1674-1137/ada379
Abstract:
In this paper, we investigate the topological charge and conditions for the existence of the photon sphere in Kiselev-anti-de Sitter (AdS) black holes within \begin{document}$f(R, T)$\end{document} gravity. Furthermore, we establish their topological classifications. We employ two different methods based on Duan’s topological current ϕ-mapping theory viz analysis of temperature and the generalized Helmholtz free energy methods to study the topological classes of our black hole. Considering this black hole, we discuss the critical and zero points (topological charges and topological numbers) for different parameters. Our findings reveal that the Kiselev parameter ω and \begin{document}$f(R, T)$\end{document} gravity parameter γ influence the number of topological charges of black holes, providing novel insights into topological classifications. We observe that for given values of the free parameters, total topological charges (\begin{document}$Q_{\rm total} = -1$\end{document}) exist for the T method and total topological numbers (\begin{document}$W = +1$\end{document}) for the generalized Helmholtz free energy method. Our research findings elucidate that, in contrast to the scenario in which \begin{document}$\omega = 1/3$\end{document}, in other cases, increasing γ increases the number of total topological charges for the black hole. Interestingly, for the phantom field (\begin{document}$\omega = -4/3$\end{document}), we observe that decreasing γ increases the number of topological charges. Additionally, we study the results for the photon sphere. The studied models reveal that the simultaneous presence of γ and ω effectively expands the permissible range for γ. In other words, the model can exhibit black hole behavior over a larger domain. Additionally, we observe that with the stepwise reduction of ω, the region covered by singularity diminishes and becomes more restricted. However, an interesting point about all three ranges is the elimination of the forbidden region in this model. In other words, this model and the investigated areas appear to have no region in which both the ϕ and metric functions simultaneously lack solutions. Additionally, we fully check the curvatures singularities and energy conditions for the mentioned black hole.
Off-equatorial deflections and gravitational lensing in Kerr spacetime and the effect of spin
Tingyuan Jiang, Xiaoge Xu, Junji Jia
2025, 49(3): 035111. doi: 10.1088/1674-1137/ada34b
Abstract:
This paper investigates off-equatorial plane deflections and gravitational lensing of both null signals and massive particles in Kerr spacetime in the weak deflection limit, considering the finite distance effect of the source and detector. This is the effect caused by both the source and detector being located at finite distances from the lens although many researchers often use the deflection angle for infinite distances from sources and detectors. The deflection in both the \begin{document}$ \phi $\end{document} and \begin{document}$ \theta $\end{document} directions is computed as a power series of \begin{document}$ M/r_0 $\end{document} and \begin{document}$ r_0/r_{\mathrm{s,d}} $\end{document} , where \begin{document}$ M,\,r_{\mathrm{s,d}} $\end{document} are the spacetime mass and source and detector radii, respectively, and \begin{document}$ r_0 $\end{document} is the minimal radial coordinate of the trajectory. The coefficients of these series are simple trigonometric functions of \begin{document}$ \theta_ \mathrm{e} $\end{document} , the extreme value of the \begin{document}$ \theta $\end{document} coordinate of the trajectory. A set of exact gravitational lensing equations is used to solve for \begin{document}$ r_0 $\end{document} and \begin{document}$ \theta_ \mathrm{e} $\end{document} for given deviation angles \begin{document}$ \delta\theta $\end{document} and \begin{document}$ \delta\phi $\end{document} of the source, and two lensed images are always obtained. The apparent angles and their magnifications of these images and the time delays between them are solved. Additionally, their dependences on various parameters, particularly spacetime spin \begin{document}$ \hat{a} $\end{document} , are analyzed in depth. We find that generally two critical spacetime spin values exist that separate the case of test particles reaching the detector from different sides of the \begin{document}$ z $\end{document} axis from the cases in which the images appear from the same side in the celestial plane. Three potential applications of these results are discussed.
Erratum and Addendum
Erratum and Addendum: Analytical formula for the cross section of hadron production from e+e− collisions around the narrow charmouinum resonances (Chin. Phys. C, 48(11): 113104 (2024))
Yanan Wang, Yadi Wang, Ping Wang
2025, 49(3): 039001. doi: 10.1088/1674-1137/adb709
Abstract:
Chinese Physics C
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