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Published: , doi: 10.1088/1674-1137/44/9/094107
Abstract:
Inspired by the availability of recent experimental as well as theoretical data on the energy levels of odd-mass 151-161Pm and odd-odd 154,156Pm, we applied the theoretical framework of the projected shell model to further understand the nuclear structure of these nuclei. The calculations closely reproduced the experimental data reported for the yrast bands of these isotopes by assuming an axial (prolate) deformation of ~0.3. Other properties along the yrast line, such as transition energies and transition probabilities, have also been discussed. Band diagrams are plotted to understand their intrinsic multi-quasiparticle structure, which turn out to be dominated by 1-quasiparticle bands for the odd-mass Pm isotopes and 2-quasiparticle bands for the doubly-odd Pm isotopes under study. The present study not only confirms the recently reported experimental/theoretical data, but also extends the already available information on the energy levels and adds new information regarding the reduced transition probabilities.
Published: , doi: 10.1088/1674-1137/abab8c
Abstract:
We use an existing model of the $\Lambda\Lambda N - \Xi NN$ three-body system based on two-body separable interactions to study the $(I,J^P) = (1/2,1/2^+)$ three-body channel. For the $\Lambda\Lambda$, $\Xi N$, and $\Lambda\Lambda - \Xi N$ amplitudes, we have constructed separable potentials based on the most recent results of the HAL QCD Collaboration. They are characterized by the existence of a resonance just below or above the $\Xi N$ threshold in the H-dibaryon channel, $(i,j^p) = (0,0^+)$. A three-body resonance appears 2.3 MeV above the $\Xi d$ threshold. We show that if the $\Lambda\Lambda - \Xi N$ H-dibaryon channel is not considered, the $\Lambda\Lambda N - \Xi NN$ S wave resonance disappears. Thus, the possible existence of a $\Lambda\Lambda N - \Xi NN$ resonance would be sensitive to the $\Lambda\Lambda - \Xi N$ interaction. The existence or nonexistence of this resonance could be evidenced by measuring, for example, the $\Xi d$ cross section.
Published: , doi: 10.1088/1674-1137/abab8a
Abstract:
In this study, we apply two methods to consider the variation of massive black holes in both normal and extended thermodynamic phase spaces. The first method considers a charged particle being absorbed by the black hole, whereas the second considers a shell of dust falling into it. With the former method, the first and second laws of thermodynamics are always satisfied in the normal phase space; however, in the extended phase space, the first law is satisfied but the validity of the second law of thermodynamics depends upon the model parameters. With the latter method, both laws are valid. We argue that the former method's violation of the second law of thermodynamics may be attributable to the assumption that the change of internal energy of the black hole is equal to the energy of the particle. Finally, we demonstrate that the event horizon always ensures the validity of weak cosmic censorship in both phase spaces; this means that the violation of the second law of thermodynamics, arising under the aforementioned assumption, does not affect the weak cosmic censorship conjecture. This further supports our argument that the assumption in the first method is responsible for the violation and requires deeper treatment.
Published: , doi: 10.1088/1674-1137/aba58d
Abstract:
Within the context of the Fermi-bounce curvaton mechanism, we analyze the one-loop radiative corrections to the four-fermion interaction, generated by the non-dynamical torsion field in the Einstein-Cartan-Holst-Sciama-Kibble theory. We show that contributions that arise from the one-loop radiative corrections modify the energy-momentum tensor, mimicking an effective Ekpyrotic fluid contribution. Therefore, we call this effect quantum Ekpyrotic mechanism. This leads to the dynamical washing out of anisotropic contributions to the energy-momentum tensor, without introducing any new extra Ekpyrotic fluid. We discuss the stability of the bouncing mechanism and derive the renormalization group flow of the dimensional coupling constant ξ, checking whether any change of its sign takes place towards the bounce. This enforces the theoretical motivations in favor of the torsion curvaton bounce cosmology as an alternative candidate to the inflation paradigm.
Published: , doi: 10.1088/1674-1137/44/9/095107
Abstract:
Based on the dynamics of single scalar field slow-roll inflation and the theory of reheating, we investigate the generalized natural inflationary (GNI) model. We introduce constraints on the scalar spectral index $n_{s}$ and the tensor-to scalar ratio r for the $\Lambda$CDM $+r$ model, according to the latest data from Planck 2018 TT, TE, EE+low E+lensing (P18) and BICEP2/Keck 2015 season (BK15), i.e., with $n_{s}=0.9659\pm0.0044$ at 68% confidence level (CL), and $r<0.0623$ at 95% CL. We find that the GNI model is favored by P18 and BK15 in the ranges $\log_{10}(f/M_{p})= 0.62^{+0.17}_{-0.18}$ and $m=0.35^{+0.13}_{-0.23}$ at 68% CL. In addition, the corresponding predictions of generalized and two-phase reheating are discussed. It follows that the parameter m has significant effect on the model behavior.
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Abstract:
The ratio of $\gamma$ transition-intensities from the initial capture state to low-lying states may represent the model-independent $\gamma$-strength function, which reflects the effects of different neutron-capture reaction mechanisms. The extraordinary quenching of the $\gamma_{0}$ transition from the p-wave neutron radiative capture in $^{57}$Fe is observed, for the first time, from the pronounced enhancement of the $\gamma$-strength function ratios $f_{\gamma_{1}}/f_{\gamma_{0}}$ and $f_{\gamma_{2}}/f_{\gamma_{0}}$. The 2p-1h doorway excitation leads to suppression of the $\gamma_{0}$ transition to the ground state and the enhancement of the $\gamma_{1}$ and $\gamma_{2}$ transitions to the first and second excited states, respectively. The $fp$ sub-shells supply the exact number of spaces required for the 2p-1h configuration, which features the neutron capture mechanism in the vicinity of A = 55.
Published: , doi: 10.1088/1674-1137/44/9/093106
Abstract:
We reduce all the most complicated Feynman integrals in two-loop five-light-parton scattering amplitudes to basic master integrals, while other integrals can be reduced even easier. Our results are expressed as systems of linear relations in the block-triangular form, very efficient for numerical calculations. Our results are crucial for complete next-to-next-to-leading order quantum chromodynamics calculations for three-jet, photon, and/or hadron production at hadron colliders. To determine the block-triangular relations, we develop an efficient and general method, which may provide a practical solution to the bottleneck problem of reducing multiloop multiscale integrals.
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Abstract:
We study the effect of chemical potential and nonconformality on the jet quenching parameter in a holographic QCD model with conformal invariance broken by background dilaton. The presence of chemical potential and nonconformality both increase the jet quenching parameter, thus enhancing the energy loss, consistently with the findings of the drag force.
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Abstract:
In this study, the production of inclusive b-jet and $b\bar{b}$ dijets in Pb + Pb collisions has been investigated by considering the in-medium evolution of heavy and light quarks simultaneously. The initial hard processes of inclusive b-jet and $b\bar{b}$ dijets production are described using a next-to-leading order (NLO) plus parton shower Monte Carlo (MC) event generator, SHERPA, which can be well matched with the experimental data in p + p collisions. The framework uses the Langevin transport model to describe the evolution of the bottom quark. Furthermore, the collisional energy loss and higher-twist description are considered to determine the radiative energy loss from both the bottom and light quarks. We compare the theoretical simulation of the inclusive jet and b-jet $R_{\rm AA}$ in the Pb + Pb collisions at $\sqrt{s_{ NN}}=2.76$ TeV with the experimental data and present the theoretical simulation of the momentum balance of the $b\bar{b}$ dijet in the Pb + Pb collisions at $5.02$ TeV along with recent CMS data for the first time. A similar trend to that seen in inclusive dijets is observed in $b\bar{b}$ dijets; the distribution of the production shifts to smaller $x_{\rm J}$ owing to the jet quenching effect. Finally, we report the prediction of the normalized azimuthal angle distribution of the $b\bar{b}$ dijet in the Pb + Pb collisions at $5.02$ TeV. The medium-induced energy loss effect of the $b\bar{b}$ dijets will generally suppress its production; however, the same side ($\Delta \phi \to 0$ region) suffers more energy loss than the far side ($\Delta \phi \to \pi$ region), thus leading to suppression on the same side and enhancement on the far side in the normalized azimuthal angle distribution in A + A collisions.
Published: , doi: 10.1088/1674-1137/44/9/093107
Abstract:
Based on the prediction of a $D^*\bar{D}^*$ molecular state $Z_c(4000)$ with isospin $I=1$ in the coupled channel approach, we suggest the search for this state in the reaction $B^- \to J/\psi \rho^0 K^-$. By considering the final state interactions of $J/\psi \rho$ and $D^{*0}\bar{D}^{*0}$ and the contribution from the $K_1(1270)$ resonance, we observed that the $J/\psi\rho$ mass distribution shows a peak around 4000 MeV, which might be associated with the $D^*\bar{D}^*$ molecular state $Z_c(4000)$. The search for $Z_c(4000)$ in the reaction $B^- \to J/\psi \rho^0 K^-$ is critical for understanding the internal structures of exotic hadrons. Our predictions can be tested by the Belle II and LHCb in future studies.
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Abstract:
This work presents the subtraction procedure and the Regge cut in the logarithmic Regge pole approach. The subtraction mechanism leads to the same asymptotic behavior as previously obtained in the non-subtraction case. The Regge cut, in contrast, introduces a clear role to the non-leading contributions for the asymptotic behavior of the total cross-section. From these results, some simple parameterization is introduced to fit the experimental data for the proton-proton and antiproton-proton total cross-section above some minimum value up to the cosmic-ray. The fit parameters obtained are used to present predictions for the $\rho(s)$-parameter as well as to the elastic slope $B(s)$ at high energies.
Published: , doi: 10.1088/1674-1137/44/9/094108
Abstract:
In this work, we have performed Skyrme density functional theory (DFT) calculations of nuclei around 132Sn to study whether the abnormal odd–even staggering (OES) behavior of binding energies around N = 82 can be reproduced. With the Skyrme forces SLy4 and SkM*, we tested the volume- and surface-type pairing forces and also the intermediate between these two pairing forces, in the Hartree–Fock–Bogoliubov (HFB) approximation with or without the Lipkin–Nogami (LN) approximation or particle number projection after the convergence of HFBLN (PLN). The Universal Nuclear Energy Density Function (UNEDF) parameter sets are also used. The trend of the neutron OES against the neutron number or proton number does not change significantly by tuning the density dependence of the pairing force. Moreover, for the pairing force that is favored more at the nuclear surface, a larger mass OES is obtained, and vice versa. It appears that the combination of volume and surface pairing can give better agreement with the data. In the studies of the OES, a larger ratio of surface to volume pairing might be favored. Additionally, in most cases, the OES given by the HFBLN approximation agrees more closely with the experimental data. We found that both the Skyrme and pairing forces can influence the OES behavior. The mass OES calculated by the UNEDF DFT is explicitly smaller than the experimental one. The UNEDF1 and UNEDF2 forces can reproduce the experimental trend of the abnormal OES around 132Sn. The neutron OES of the tin isotopes given by the SkM* force agrees more closely with the experimental one than that given by the SLy4 force in most cases. Both SLy4 and SkM* DFT have difficulties in reproducing the abnormal OES around 132Sn. Using the PLN method, the systematics of OES are improved for several combinations of Skyrme and pairing forces.
Published: , doi: 10.1088/1674-1137/44/9/095105
Abstract:
The objective of the present work is to highlight the phenomena of strong gravitational lensing and deflection angle for the photon coupling with the Weyl tensor in a Kiselev black hole. Here, we have extended the prior work of Chen and Jing (S. Chen and J. Jing, JCAP, 10: 002 (2015)) for a Schwarzschild black hole to a Kiselev black hole. For this purpose, the equation of motion for the photons coupled to the Weyl tensor, null geodesic, and equation of photon sphere in a Kiselev black hole spacetime have been formulated. It is found that the equation of motion of the photons depends not only on the coupling between the photons and the Weyl tensor, but also on the polarization direction of the photons. There is a critical value of the coupling parameter, $\alpha$ , for the existence of the marginally circular photon orbit outside the event horizon, which depends on the parameters of the black hole and the polarization direction of the photons. Further, the polarization directions of the coupled photons and the coupling parameter, $\alpha$; both modify the features of the photon sphere, angle of deflection, and functions $(\bar{a}$ and $\bar{b})$ owing to the strong gravitational lensing in the Kiselev black hole spacetime. In addition to this, the observable gravitational lensing quantities and the shadows of the Kiselev black hole spacetime are presented in detail.
Published: , doi: 10.1088/1674-1137/ab97a9
Abstract:
High transverse momentum ($p_T$) particle production is suppressed owing to the parton (jet) energy loss in the hot dense medium created in relativistic heavy-ion collisions. Redistribution of energy at low-to-modest $p_T$ has been difficult to measure, owing to large anisotropic backgrounds. We report a data-driven method for background evaluation and subtraction, exploiting the away-side pseudorapidity gaps, to measure the jetlike correlation shape in Au+Au collisions at $\sqrt{s_{{NN}}} = 200$ GeV in the STAR experiment. The correlation shapes, for trigger particles $p_T>3\;{\rm{GeV}}/{\rm{c}}$ and various associated particle $p_T$ ranges within $0.5<p_T<10\;{\rm{GeV}}/{\rm{c}}$, are consistent with Gaussians, and their widths increase with centrality. The results indicate jet broadening in the medium created in central heavy-ion collisions.
Published: , doi: 10.1088/1674-1137/44/9/095106
Abstract:
We solve the condundrum on whether the molecules of the Reissner-Nordström black hole interact through the Ruppeiner thermodynamic geometry, basing our study on the concept of the black hole molecule proposed in [Phys. Rev. Lett. 115 (2015) 111302] and choosing the appropriate extensive variables. Our results show that the Reissner-Nordström black hole is indeed an interaction system that may be dominated by repulsive interaction. More importantly, with the help of a novel quantity, namely the thermal-charge density, we describe the fine micro-thermal structures of the Reissner-Nordström black hole in detail. Three different phases are presented, namely the free, interactive, and balanced phases. The thermal-charge density plays a role similar to the order parameter, and the back hole undergoes a new phase transition between the free phase and interactive phase. The competition between the free phase and interactive phase exists, which leads to extreme behavior of the temperature of the Reissner-Nordström black hole. For the extreme Reissner-Nordström black hole, the entire system is completely in the interactive phase. More importantly, we provide the thermodynamic micro-mechanism for the formation of the naked singularity of the Reissner-Nordström black hole.
Published: , doi: 10.1088/1674-1137/44/9/094106
Abstract:
In this study, we systematically investigate the $\alpha$ decay preformation factors, $P_{\alpha}$ , and the $\alpha$ decay half-lives of 152 nuclei around Z = 82, N = 126 closed shells based on the generalized liquid drop model (GLDM) with $P_{\alpha}$ being extracted from the ratio of the calculated $\alpha$ decay half-life to the experimental one. The results show that there is a remarkable linear relationship between $P_{\alpha}$ and the product of valance protons (holes) $N_p$ and valance neutrons (holes) $N_n$ . At the same time, we extract the $\alpha$ decay preformation factor values of the even–even nuclei around the Z = 82, N = 126 closed shells from the study of Sun ${et\ al.}$ [J. Phys. G: Nucl. Part. Phys., 45: 075106 (2018)], in which the $\alpha$ decay was calculated by two different microscopic formulas. We find that the $\alpha$ decay preformation factors are also related to $N_pN_n$ . Combining with our previous studies [Sun ${et\ al.}$ , Phys. Rev. C, 94: 024338 (2016); Deng ${et\ al.}$ , ibid. 96: 024318 (2017); Deng ${et\ al.}$ , ibid. 97: 044322 (2018)] and that of Seif ${et\ al.,}$ [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 $\alpha$ decay preformation factor data calculated by the GLDM, we calculate the $\alpha$ decay half-lives of these nuclei. The calculated results agree with the experimental data well.
Published: , doi: 10.1088/1674-1137/44/9/093105
Abstract:
By studying the $\eta_c$ exclusive decay to double glueballs, we introduce a model to phenomenologically mimic the gluon-pair-vacuum interaction vertices, namely the $0^{++}$ model. Based on this model, we study glueball production in pseudoscalar quarkonium decays, explicitly $\eta_c \to f_0(1500)\eta(1405)$, $\eta_b\to f_0(1500)\eta(1405)$ , and $\eta_b\to f_0(1710)\eta(1405)$ processes. Among them $f_0(1500)$ and $f_0(1710)$ are well-known scalars possessing large glue components, while $\eta(1405)$ is a potential candidate for a pseudoscalar glueball. The preliminary calculation results indicate that these processes are marginally accessible in the presently running experiments BES III, BELLE II, and LHCb.
Published: , doi: 10.1088/1674-1137/44/9/094105
Abstract:
Neutron–proton momentum correlation functions are constructed from a three-body photodisintegration channel, i.e., core$+ n + p$, and used to explore the spatial-time information of the non-clustering Woods–Saxon spherical structure as well as the $\alpha$-clustering structures of $^{12}{\rm{C}}$ or $^{16}{\rm{O}}$ based on an extended quantum molecular dynamics model. The emission time sequence of neutrons and protons is indicated by the ratio of velocity-gated neutron–proton correlation functions, demonstrating its sensitivity to $\alpha$-clustering structures. This work sheds light on a new probe for $\alpha$-clustering structures.
Published: , doi: 10.1088/1674-1137/44/9/095102
Abstract:
Quasinormal modes (QNMs) for massless and massive Dirac perturbations of Born-Infeld black holes (BHs) in higher dimensions are investigated. Solving the corresponding master equation in accordance with hypergeometric functions and the QNMs are evaluated. We discuss the relationships between QNM frequencies and spacetime dimensions. Meanwhile, we also discuss the stability of the Born-Infeld BH by calculating the temporal evolution of the perturbation field. Both the perturbation frequencies and the decay rate increase with increasing dimension of spacetime n. This shows that the Born-Infeld BHs become more and more unstable at higher dimensions. Furthermore, the traditional finite difference method is improved, so that it can be used to calculate the massive Dirac field. We also elucidate the dynamic evolution of Born-Infeld BHs in a massive Dirac field. Because the number of extra dimensions is related to the string scale, there is a relationship between the spacetime dimension n and the properties of Born-Infeld BHs that might be advantageous for the development of extra-dimensional brane worlds and string theory.
Published: , doi: 10.1088/1674-1137/44/9/095103
Abstract:
Banerjee-Ghosh's work shows that the singularity problem can be naturally avoided by the fact that black hole evaporation stops when the remnant mass is greater than the critical mass when including the generalized uncertainty principle (GUP) effects with first- and second-order corrections. In this paper, we first follow their steps to reexamine Banerjee-Ghosh's work, but we find an interesting result: the remnant mass is always equal to the critical mass at the final stage of black hole evaporation with the inclusion of the GUP effects. Then, we use Hossenfelder's GUP, i.e., another GUP model with higher-order corrections, to restudy the final evolution behavior of the black hole evaporation, and we confirm the intrinsic self-consistency between the black hole remnant and critical masses once more. In both cases, we also find that the thermodynamic quantities are not singular at the final stage of black hole evaporation.
Published: , doi: 10.1088/1674-1137/44/9/091001
Abstract:
In this study, we investigate the invariant-mass distribution of top-quark pairs near the 2mt threshold, which strongly influences the determination of the top-quark mass mt. Higher-order non-relativistic corrections lead to large contributions, which are not included in the state-of-the-art theoretical predictions. A factorization formula is derived to resum such corrections to all orders in the strong-coupling, and necessary ingredients are calculated to perform the resummation at next-to-leading power. We combine the resummation with fixed-order results and present phenomenologically relevant numerical results. The resummation effect significantly increases the differential cross-section in the threshold region and makes the theoretical prediction more compatible with experimental data. We estimate that using our prediction in the determination will lead to a value closer to the direct measurement result.
Published: , doi: 10.1088/1674-1137/44/9/093102
Abstract:
We investigate the strongly coupled minimal walking technicolor model (MWT) in the framework of a bottom-up holographic model, where the global $SU(4)$ symmetry breaks into $SO(4)$ subgroups. In the holographic model, we found that 125 GeV composite Higgs particles and small Peskin–Takeuchi S parameter can be achieved simultaneously. In addition, the model predicts a large number of particles at the TeV scale, including dark matter candidates Technicolor Interacting Massive Particles (TIMPs). If we consider the dark matter nuclear spin-independent cross-section in the range of $10^{-45}\sim 10 ^ {-48} \;{\rm{cm}}^2$, which can be detected by future experiments, the mass range of TIMPs predicted by the holographic technicolor model is $2 \sim 4$ TeV.
Published: , doi: 10.1088/1674-1137/44/9/094101
Abstract:
We develop a covariant kinetic theory for massive fermions in a curved spacetime and an external electromagnetic field based on quantum field theory. We derive four coupled semi-classical kinetic equations accurate to $O(\hbar)$, which describe the transports of particle number and spin degrees of freedom. The relationship with chiral kinetic theory is discussed. As an application, we study spin polarization in the presence of finite Riemann curvature and an electromagnetic field in both local and global equilibrium states.
Published: , doi: 10.1088/1674-1137/44/9/094103
Abstract:
We studied the chiral magnetic effect in AuAu, RuRu, and ZrZr collisions at $\sqrt{s_{{NN}}}=200\;{\rm{GeV}}$. The axial charge evolution was modeled with stochastic hydrodynamics, and geometrical quantities were calculated with the Monte Carlo Glauber model. By adjusting the relaxation time of the magnetic field, we found our results are in good agreement with background subtracted data for AuAu collisions at the same energy. We also made predictions for RuRu and ZrZr collisions. We found a weak centrality dependence on initial chiral imbalance, which implies that the centrality dependence of chiral magnetic effect signals results mainly from the effects of the magnetic field and volume factor. Furthermore, our results show an unexpected dependence on system size. While the AuAu system has larger chiral imbalance and magnetic field, it was observed to have a smaller signal for the chiral magnetic effect due to the larger volume suppression factor.
Published: , doi: 10.1088/1674-1137/44/9/094102
Abstract:
The survival probability of an excited compound nucleus was studied using two different approaches of the washing out of shell effects with excitation energy based on a superasymmetric reaction system. The estimated evaporation residue cross sections based on the two different methods are compared with the available experimental data. Both methods are in agreement with the experimental data to a certain extent for some specific reactions and $xn$ emission channels.
Published: , doi: 10.1088/1674-1137/44/9/095101
Abstract:
In this study, the scenario of a two-component warm tachyon inflation is considered, where the tachyon field plays the role of the inflaton by driving the inflation. During inflation, the tachyon scalar field interacts with the other component of the Universe, which is assumed to be photon gas, i.e., radiation. The interacting term contains a dissipation coefficient, and the study is modeled based on two different and familiar choices of the coefficient that were studied in the literature. By employing the latest observational data, the acceptable ranges for the free parameters of the model are obtained. For any choice within the estimated ranges, there is an acceptable concordance between the theoretical predictions and observations. Although the model is established based on several assumptions, it is crucial to verify their validity for the obtained values of the free parameters of the model. It is found that the model is not self-consistent for all values of the ranges, and for some cases, the assumptions are violated. Therefore, to achieve both self-consistency and agreement with the data, the parameters of the model must be constrained. Subsequently, we consider the recently proposed swampland conjecture, which imposes two conditions on the inflationary models. These criteria rule out some inflationary models; however, warm inflation is among those that successfully satisfy the swampland criteria. We conduct a precise investigation, which indicates that the proposed warm tachyon inflation cannot satisfy the swampland criteria for some cases. In fact, for the first case of the dissipation coefficient, in which, there is dependency only on the scalar field, the model agrees with observational data. However, it is in direct tension with the swampland criteria. Nevertheless, for the second case, wherein the dissipation coefficient has a dependency on both the scalar field and temperature, the model exhibits acceptable agreement with observational data, and suitably satisfies the swampland criteria.
Published: , doi: 10.1088/1674-1137/44/9/094001
Abstract:
The lifetime of the $2_{1}^{+}$ state in $^{106}$Cd populated via the $^{94}$Zr ($^{16}$O, 4n)$^{106}$Cd reaction has been measured with the Recoil Distance Doppler Shift technique in combination with the Differential Decay Curve Method. By subtracting the contamination in the data, the mean lifetime of the $I^{\pi}$=2$^{+}_{1}$ 633 keV state was determined as 9.9 (12) ps. The $B(E2)$ value calculated in this study is in good agreement with the experimental systematics and was compared to the shell model calculations.
Published: , doi: 10.1088/1674-1137/44/9/094104
Abstract:
The main purpose of this study is to interpret the possibilities of hybrid star configurations under different phase transition paths and provide a general description of the conditions and features of the different configurations. We assume that there are two possible phase transition paths, i.e., from a nuclear phase to a 2flavor(2f)/3flavor(3f) quark phase directly, or first from a nuclear phase to a 2f quark phase, and then from that phase to a 3f quark phase sequentially. In addition, we consider Maxwell and Gibbs constructions based on the assumption of a first-order transition, which yields multiple configurations of hybrid stars: N-2f, N-3f, and N-2f-3f for a Maxwell construction, and N-2fmix-2f, N-3fmix-3f, N-2f3fmix, and N-2fmix-3f for a Gibbs construction. From the radii analysis of different hybrid star configurations with the same mass of $1.95M_\odot$, the appearance of the quark matter (from nuclear to 2f or 3f quark matter) causes a radius difference of 0.5km~2km and provides the possibility of detection by NICER in the future. However, the sequential transition from 2f to 3f quark matter is difficult to detect because the transition does not lead to too high of a change in radius (far smaller than $0.5\; {\rm{km}}$). The dependence solely on the measurements of the stellar radii to probe the equation of state of dense matter in neutron stars causes difficulties. Multi-messenger observations can help us to infer the interior of a neutron star in the future.