Bayesian inference on isospin splitting of nucleon effective mass from giant resonances in ~(208)Pb

From a Bayesian analysis of the electric dipole polarizability,the constrained energy of isovector giant dipole resonance,the peak energy of isocalar giant quadrupole resonance,and the constrained energy of isocalar giant monopole resonance in ~(208)Pb,we extract the iso scalar and isovector effective masses in nuclear matter at saturation density p_0 as m_(s,0)~*/m=0.87_(-0.04)~(+0.04) and m_(v,0)~*/m=0.78_(-0.05)~(+0.06),respectively,at 90% confidence level.The constraints obtained on m_(s,0)~* and m_(v,0)~* lead to a positive iso spin splitting of nucleon effective mass in asymmetric nuclear matter of iso spin asymmetry δ at p_0 as m_(n-p)~*/m=(0.20_(-0.14)~(+0.15))δ.In addition,the symmetry energy at the subsaturation density p~*=0.05 fm~(-3) is determined to be E_(sym)(p~*)=16.7±1.3 MeV at 90% confidence level.     

The quark condensate in relativistic nucleus-nucleus collisions

We compute the modification of the quark condensate <ˉq q> in relativistic nucleus-nucleus collisions and estimate the 4-volume, where the quark condensate is small (<ˉqq>/<ˉqq>⁰≤ 0.1–0.3) using hadron phase-space distributions obtained with the quark-gluon string model. As a function of the beam energy the 4-volume rises sharply at a beam energy E^lab/A ≃ (2–5) GeV, remains roughly constant up to beam energies ≃ 20 GeV and rises at higher energies. At low energies the reduction of the condensate is mainly due to baryons, while at higher energies the rise of the 4-volume is due to the abundant mesons produced. Based on our results we expect that moderate beam energies on the order of 10 GeV per nucleon are favourable for studying the restoration of chiral symmetry in a baryon-rich environment in nucleus-nucleus collisions. Received: 4 December 1997 / Revised version: 31 July 1998     

Isospin splitting of nucleon effective mass and symmetry energy in isotopic nuclear reactions

Within an isospin and momentum dependent transport model, the dynamics of isospin particles(nucleons and light clusters) in Fermi-energy heavy-ion collisions are investigated for constraining the isospin splitting of nucleon effective mass and the symmetry energy at subsaturation densities. The impacts of the isoscalar and isovector parts of the momentum dependent interaction on the emissions of isospin particles are explored, i.e., the mass splittings of m_n~*=m_p~* and m_n~* m_p~*(m_n~* m_p~*). The single and double neutron to proton ratios of free nucleons and light particles are thoroughly investigated in the isotopic nuclear reactions of ~(112)Sn+~(112)Sn and ~(124)Sn+~(124)Sn at incident energies of 50 and 120 MeV/nucleon, respectively. It is found that both the effective mass splitting and symmetry energy impact the kinetic energy spectra of the single ratios, in particular at the high energy tail(larger than 20 Me V). The isospin splitting of nucleon effective mass slightly impacts the double ratio spectra at the energy of 50 MeV/nucleon. A soft symmetry energy with stiffness coefficient of γ_s =0.5 is constrained from the experimental data with the Fermi-energy heavy-ion collisions.     

Key factor for determining relation between radius and tidal deformability of neutron stars: Slope of symmetry energy

The constraints on tidal deformability Λ of neutron stars were first extracted from GW170817 by LIGO and Virgo Collaborations.However,the relationship between the radius R and tidal deformability Λ is still under debate.Using an isospin-dependent parameterized equation of state(EOS),we study the relation between R andΛand its dependence on parameters of symmetry energy E_(sym) and EOS of symmetric nuclear matter E_0 when the mass is fixed at 1.4 M_⊙,1.0 M_⊙,and 1.8 M_⊙.We find that,although the changes of high order parameters of E_(sym) and E _0 can shift individual values of R_(1.4) and Λ_(1.4),the R_(1.4)～Λ_(1.4) relation remains approximately at the same fitted curve.The slope L of the symmetry energy plays the dominant role in determining the R_(1.4)～Λ_(1.4) relation.By investigating the mass dependence of the R～Λ relation,we find that the well fitted R～Λ relation for 1.4 M_⊙ is broken for massive neutron stars.     

Systematic Study on System Size Dependence of Global Stopping: Role of Momentum-Dependent Interactions and Symmetry Energy

Using the isospin-dependent quantum molecular dynamical model, we systematically study the role of symme- try energy with and without momentum-dependent interactions on the global nuclear stopping. We simulate the reactions by varying the total mass of the system from 80 to 394 at different beam energies from 30 to 1000 Me V/nucleon over central and semi-central geometries. The nuclear stopping is found to be sensitive towards the momentum-dependent interactions and symmetry energy at low incident energies. The momentum-dependent interactions are found to weaken the finite size effects in nuclear stopping.     

Emissions of fragments and mesons produced in heavy-ion collisions at CSR and related energies

Using a multisource ideal gas (MSIG) model, we reconstruct the transverse emission source in the momentum space for light fragments produced in reactions ⁸⁶Kr-¹²⁴Sn at 25 MeV/nucleon and b=7—10 fm based on the theoretical predictions of the Isospin-Dependent Quantum Molecular Dynamics (IDQMD) model. We show that the MSIG model can reasonably describe the IDQMD-predicted results for the azimuthal distribution and the transverse momentum dependence of elliptic flow v₂ and fourth-order anisotropic flow v₄ but can only qualitatively describe the transverse momentum spectra. The azimuthal distributions of nuclear fragments produced in heavy-ion collisions at intermediate energies are studied by the MSIG model. The calculated results are compared and found to be in agreement with the experimental data of Ca-Ca, Nb-Nb, and Au-Au collisions at 150—800 MeV/nucleon beam energies. Meanwhile, the angular distributions of pions and kaons produced in heavy-ion collisions at the low-energy end (1—2 GeV/nucleon) of high energies are investigated by the MSIG model, too. The calculated results are compared and found to be in agreement with the experimental data of the KaoS Collaboration.     

金核-金核与质子-质子对撞中矢量介子K*0(892)和φ(1020)的自旋排列

We present the preliminary results on the spin alignment matrix elementρ_(00)for vector mesons K~(*0)(892)andφ(1020)in mid-central(20%—60%)Au Au and p p collisions at S_(NN)~(1/2)=200GeV.The values ofρ_(00)with respect to reaction plane in Au Au collisions are 0.36±0.02(stat)±0.13(sys)for K~(*0)(892)and 0.38±0.01(stat)±0.04(sys)forφ(1020).No evident global spin alignment with respect to reaction plane is observed in the measured p_T region up to 5GeV/c with current sensitivity,ρ_(00)with respect to the production plane of the vector meson is also measured for K~(*0)(892)andφ(1020)in Au Au collisions,and forφ(1020)in p p collisions.No significant difference for theρ_(00)between Au Au and p p collisions is observed with our data sample.     

Collective Transverse Flow in Intermediate Energy Heavy-Ion Collisions

Within the hadronic transport model IBUU04, we study the density-dependent symmetry energy by using the neutron-proton differential flow from the 132Sn＋124Sn reactions at beam energies of 200, 400, 600 and 800MeV per nucleon. The strong effect of the symmetry energy is shown at the incident beam energy of 400MeV/A. The small medium-effect of the neutron-proton differential flow is also found. We also study the neutron-proton differential flows with impact parameters of 3, 5, 7fm. It is found that in semi-central collisions the sensitivity of the neutron-proton differential flow to the symmetry energy is larger.     

Effect of Wigner energy on the symmetry energy coefficient in nuclei

The nuclear symmetry energy coefficient(including the coefficient a_(sym)~((4)) of the I~4 term) of finite nuclei is extracted by using the differences of available experimental binding energies of isobaric nuclei.It is found that the extracted symmetry energy coefficient a_(sym)~*(A,I) decreases with increasing isospin asymmetry I,which is mainly caused by Wigner correction,since e_(sym)~* is the summation of the traditional symmetry energy e_(sym) and the Wigner energy ew.We obtain the optimal values J = 30.25±0.10 MeV,a_(ss)=56.18±1.25 MeV,a_(sym)~((4)) = 8.33±1.21 MeV and the Wigner parameter x= 2.38 ±0.12 through a polynomial fit to 2240 measured binding energies for nuclei with20 ≤ A ≤ 261 with an rms deviation of 23.42 keV.We also find that the volume symmetry coefficient J■ 30 MeV is insensitive to the value x,whereas the surface symmetry coefficient a_(ss) and the coefficient a_(sym)~((4)) are very sensitive to the value of x in the range 1≤x≤4.The contribution of the a_(sym)~((4)) term increases rapidly with increasing isospin asymmetry I.For very neutron-rich nuclei,the contribution of the a_(sym)~((4)) term will play an important role.     

Symmetry energy and experimentally observed cold fragments in intermediate heavy-ion collisions

An attempt is made to study the symmetry energy at the time of primary fragment formation from the experimentally observed cold fragments for a neutron-rich system of ~(64)Ni + ~9Be at 140 MeV/nucleon,utilizing the recent finding that the excitation energy becomes lower for more neutron-rich isotopes with a given Z value.The extracted α_(sym)/T values from the cold fragments,based on the Modified Fisher Model(MFM),are compared to those from the primary fragments of the antisymmetrized molecular dynamics(AMD) simulation and become consistent with the simulation when the I = N —Z value becomes larger,indicating that the excitation energy of these neutron-rich isotopes is indeed lower.     

Simple Woods-Saxon-type form for Ωα and Ξα interactions using folding model

We derive a simple Woods-Saxon-type form for potentials between Y=Ξ,Ωandαusing a single-folding potential method,based on a separable Y-nucleon Potential.The PotentialsΞ+αandΩ+αare accordingly obtained using the ESC08 c Nijmegens potential(in 3 S1 channel)and HAL QCD collaborationΩN interactions(in lattice QCD),respectively.In deriving the potential between Y andα,the same potential between Y and N is employed.The binding energy,scattering length,and effective range of the Y particle on the alpha particle are approximated by the resulting potentials.The depths of the potentials inΩαandΞαsystems are obtained at-61 MeV and-24.4 MeV,respectively.In the case of theΞαpotential,a fairly good agreement is observed between the single-folding potential method and the phenomenological potential of the Dover-Gal model.These potentials can be used in 3-,4-and 5-body cluster structures ofΩandΞhypernuclei.     

Astrophysical ~(22)Mg(p,γ)~(23)Al reaction rates from asymptotic normalization coefficient of ~(23)Ne→~(22)Ne+n

The radionuclide ~(22)Na generates the emission of a characteristic 1.275 MeV γ-ray. This is a potential astronomical observable, whose occurrence is suspected in classical novae. The ~(22)Mg(p, γ)~(23)Al reaction is relevant to the nucleosynthesis of ~(22)Na in Ne-rich novae. In this study, employing the adiabatic distorted wave approximation and continuum discretized coupled channel methods, the squared neutron asymptotic normalization coefficients(ANCs)231 for the virtual decay of Ne → ~(22)Ne + n were extracted, and determined as(0.483 ± 0.060) fm~(-1) and(9.7 ± 2.3) fm~(-1) for the ground state and the first excited state from the experimental angular distributions of ~(22)Ne(d, p)~(23)Ne populating the ground state and the first excited state of ~(23)Ne, respectively. Then, the squared proton ANC of ~(23)Al_(g.s.) was obtained as C_(d5/2)~(2)(~(23)Al)(2.65 ± 0.33) × 10~3 fm~(-1) according to the charge symmetry of the strong interaction. The astrophysical S-factors and reaction rates for the direct capture contribution in ~(22)Mg(p, γ)~(23)Al were also presented. Furthermore, the proton width of the first excited state of ~(23)Al was derived to be(57 ± 14) eV from the neutron ANC of its mirror state in ~(23)Ne and used to compute the contribution from the first resonance of ~(23)Al. This result demonstrates that the direct capture dominates the ~(22)Mg(p, γ)~(23)Al reaction at most temperatures of astrophysical relevance for 0.33 T_9 0.64.     

The angular distributions of elastic scattering of 12,13C+Zr

To obtain the neutron spectroscopic amplitudes for \begin{document}${}^{90-96}$\end{document}Zr overlaps, experimental data of elastic scattering with small experimental errors and precise optical potentials were analyzed. In this study, the elastic scattering angular distributions of \begin{document}${}^{12,13}$\end{document}C + \begin{document}${}^{A} {\rm{Zr}}$\end{document} (A = 90, 91, 92, 94, 96) were measured using the high-precision Q3D magnetic spectrometer in the Tandem accelerator. The S?o Paulo potential was used for the optical potential. The optical model and coupled channel calculations were compared with the experimental data. The theoretical results were found to be very close to the experimental data. In addition, the possible effects of the couplings to the inelastic channels of the \begin{document}${}^A {\rm{Zr}}$\end{document} targets and \begin{document}${}^{12, 13}$\end{document}C projectiles on the elastic scattering were studied. It was observed that the couplings to the inelastic channels of the \begin{document}${}^{12,13}$\end{document}C projectiles could improve the agreement with the experimental data, while the inelastic couplings to the target states are of minor importance. The effect of the one-neutron stripping in the \begin{document}${}^{13}$\end{document}C+\begin{document}${}^A {\rm{Zr}}$\end{document} elastic scattering was also studied. The one-neutron stripping channel in \begin{document}${}^{13}$\end{document}C + \begin{document}${}^A {\rm{Zr}}$\end{document} was found to be not relevant and did not affect the elastic scattering angular distributions. Our results also show that in the reactions with the considered zirconium isotopes, the presence of the extra neutron in \begin{document}${}^{13}$\end{document}C does not influence the reaction mechanism, which is governed by the collective excitation of the \begin{document}${}^{12}$\end{document}C core.     

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.     

Analysis of Pcs(4338) and related pentaquark molecular states via QCD sum rules

In this study, we tentatively identify \begin{document}$ P_{cs}(4338) $\end{document} as the \begin{document}$ \bar{D}\Xi_c $\end{document}molecular state and distinguish the isospins of current operators to explore in detail the\begin{document}$ \bar{D}\Xi_c $\end{document}, \begin{document}$ \bar{D}\Lambda_c $\end{document}, \begin{document}$ \bar{D}_s\Xi_c $\end{document}, \begin{document}$ \bar{D}_s\Lambda_c $\end{document}, \begin{document}$ \bar{D}^*\Xi_c $\end{document}, \begin{document}$ \bar{D}^*\Lambda_c $\end{document}, \begin{document}$ \bar{D}^*_s\Xi_c $\end{document}, and \begin{document}$ \bar{D}^*_s\Lambda_c $\end{document} molecular states without strange, with strange, and with double strange in the framework of QCD sum rules. The present exploration favors identifying \begin{document}$ P_{cs}(4338) $\end{document} (\begin{document}$ P_{cs}(4459) $\end{document}) as the \begin{document}$ \bar{D}\Xi_c $\end{document} (\begin{document}$ \bar{D}^*\Xi_c $\end{document}) molecular state with the spin-parity \begin{document}$ J^P={\dfrac{1}{2}}^- $\end{document} (\begin{document}$ {\dfrac{3}{2}}^- $\end{document}) and isospin \begin{document}$ (I,I_3)=(0,0) $\end{document}, and the observation of their cousins with the isospin \begin{document}$ (I,I_3)=(1,0) $\end{document} in the \begin{document}$ J/\psi\Sigma^0/\eta_c\Sigma^0 $\end{document} invariant mass distributions would decipher their inner structures.     

Z0 boson associated b-jet production in high-energy nuclear collisions

The production of vector boson tagged heavy quark jets potentially provides new tools to probe the jet quenching effect. In this paper, we present the first theoretical study on the angular correlations (\begin{document}$ \Delta\phi_{bZ} $\end{document}), transverse momentum imbalance (\begin{document}$ x_{bZ} $\end{document}), and nuclear modification factor (\begin{document}$ I_{AA} $\end{document}) of \begin{document}$ Z^0 $\end{document} boson tagged b-jets in heavy-ion collisions, which was performed using a Monte Carlo transport model. We find that the medium modification of the \begin{document}$ \Delta\phi_{bZ} $\end{document} for \begin{document}$ Z^0$\end{document} + b-jet has a weaker dependence on \begin{document}$ \Delta\phi_{bZ} $\end{document} than that for \begin{document}$ Z^0$\end{document} + jet, and the modification patterns are sensitive to the initial jet \begin{document}$ p_T $\end{document} distribution. Additionally, with the high purity of the quark jet in \begin{document}$ Z^0$\end{document} + (b-) jet production, we calculate the momentum imbalance \begin{document}$ x_{bZ} $\end{document} and the nuclear modification factor \begin{document}$ I_{AA} $\end{document} of \begin{document}$ Z^0$\end{document} + b-jet in Pb+Pb collisions. We observe a smaller \begin{document}$ \Delta \langle x_{jZ} \rangle $\end{document} and larger \begin{document}$ I_{AA} $\end{document} of \begin{document}$ Z^0$\end{document} + b-jet in Pb+Pb collisions relative to those of \begin{document}$ Z^0$\end{document} + jet, which may be an indication of the mass effect of jet quenching and can be tested in future measurements.     

Is X(3872) a bound state?

All existing experimental evidence for the bound state nature of X(3872) relies on observing its decay products,which are measured with a finite experimental mass resolution that is typically △m≥2 MeV,and much larger than its alleged binding energy,B_X=0.00(18) MeV.On the other hand,we have found recently that there is a clear cancellation in the 1~(++) channel of the invariant DD~*mass around the threshold between continuum and the bound state.This is very much like a similar cancellation in the proton-neutron continuum with the deuteron in the1~(++) channel.Based on comparative fits with a common Tsallis distribution of the experimental cross-sections for prompt production of deuterons and X(3872) in pp collisions with a finite p_T,we find a strong argument for questioning the bound state nature of this state,which also suggests that the large observed production rate could be consistent with a half-bound state.     

Exact recession velocity and cosmic redshift based on cosmological principle and Yang-Mills gravity

Based on the cosmological principle and quantum Yang-Mills gravity in the super-macroscopic limit, we obtain an exact recession velocity and cosmic redshift z, as measured in an inertial frame F ≡ F(t, x, y, z). For a matter-dominated universe, we have the effective cosmic metric tensor G_(μν)(t) =(B~2(t),-A~2(t),-A~2(t),-A~2(t)),A ∝ B ∝ t~(1/2), where t has the operational meaning of time in F frame. We assume a cosmic action S ≡ S cos involving Gμν(t) and derive the ‘Okubo equation' of motion, G μν(t)?μS ?νS-m2= 0, for a distant galaxy with mass m. This cos-√mic equation predicts an exact recession velocity, ■, where H = A˙(t)/A(t) and Co = B/A, as observed in the inertial frame F. For small velocities, we have the usual Hubble's law r≈ rH for recession velocities. Following the formulation of the accelerated Wu-Doppler effect, we investigate cosmic redshifts z as measured in F. It is natural to assume the massless Okubo equation, G μν(t)?μψe?νψe= 0, for light emitted from accelerated distant galaxies. Based on the principle of limiting continuation of physical laws, we obtain a transformation for covariant wave 4-vectors between and inertial and an accelerated frame, and predict a relationship for the exact recession velocity and cosmic redshift, z = [(1 + V_r)/(1-V_r~2)~(1/2)]-1, where Vr= r˙/Co 1, as observed in the inertial frame F. These predictions of the cosmic model are consistent with experiments for small velocities and should be further tested.     

Gluon-pair-creation production model of strong interaction vertices

By studying the \begin{document}$\eta_c$\end{document} exclusive decay to double glueballs, we introduce a model to phenomenologically mimic the gluon-pair-vacuum interaction vertices, namely the \begin{document}$0^{++}$\end{document} model. Based on this model, we study glueball production in pseudoscalar quarkonium decays, explicitly \begin{document}$\eta_c \to f_0(1500)\eta(1405)$\end{document}, \begin{document}$\eta_b\to f_0(1500)\eta(1405)$\end{document} , and \begin{document}$\eta_b\to f_0(1710)\eta(1405)$\end{document} processes. Among them \begin{document}$f_0(1500)$\end{document} and \begin{document}$f_0(1710)$\end{document} are well-known scalars possessing large glue components, while \begin{document}$\eta(1405)$\end{document} 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.