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Register a new userMomentum-dependent potential and collective flows within the relativistic quantum molecular dynamics approach based on relativistic mean-field theory
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Relativistic quantum molecular dynamics based on the relativistic mean field theory (RQMD.RMF) is extended by including momentum-dependent potential. The equation of state (EoS) dependence of the directed and the elliptic flow of protons in the beam energy range of $2.3 < sqrt{s_{NN}}< 20$ GeV is examined. It is found that the directed flow depends strongly on the optical potential at high energies,$sqrt{s_{NN}} > 3 $ GeV, where no information is available experimentally. The correlation between effective mass at saturation density and the optical potential is found: smaller values of effective mass require smaller strengths of the optical potential to describe the directed flow data.This correlation can also be seen in the beam energy dependence of the elliptic flow at $sqrt{s_{NN}}>3$ GeV, although its effect is rather weak. On the other hand, stiff EoS is required to describe the elliptic flow at lower energies.Experimental constraints on the optical potential from $pA$ collisions will provide important information on the EoS at high energies.The proton directed and the elliptic flow are well described in the RQMD.RMF model from $sqrt{s_{NN}}=2.3$ to 8.8 GeV. In contrast,to reproduce the collapse of the directed flow above 10 GeV, pressure has to be reduced, which indicates a softening of the EoS around $sqrt{s_{NN}} =10 $ GeV.
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In this paper, we compare the RMF theory and the model of deformed oscillator shells (DOS) in description of the quantum properties of the bound states of the spherically symmetric light nuclei. We obtain an explicit analytical relation between differential equations for the RMF theory and DOS model, which determine wave functions for nucleons. On such a basis we perform analysis of correspondence of quantum properties of nuclei. We find: (1) Potential $V_{RMF}$ of the RMF theory for nucleons has the wave functions $f$ and $g$ with joint part $h$ coincident exactly with the nucleon wave function of DOS model with potential $V_{rm shell}$. But, a difference between $V_{RMF}$ and $V_{rm shell}$ is essential for any nucleus. (2) The nucleon wave functions and densities obtained by the DOS and RMF theories are essentially different. The nucleon densities of the RMF theory contradict to knowledge about distribution of the proton and neutron densities inside the nuclei obtained from experimental data. This indicates that $g$ and $f$ have no sense of the wave functions of quantum physics. But, $h$ provides proper description of quantum properties of nucleons inside the nucleus. (3) We calculate meson function $w^{0}$ and potential $V_{w}$ in RMF theory based on the found nucleon density. (4) $f$ and $g$ are not solutions of Dirac equation with $V_{w}$. If the meson theory describes quantum properties of nucleus well, then a difference between $V_{w}$ and $V_{RMF}$ should be as small as possible. We introduce new quantum corrections characterizing difference between these potentials. We find that (a) The function $w^{0}$ should be reinforced strongly, (b) The corrections are necessary to describe the quantum properties of the nuclei.
For the first time, we apply the temperature dependent relativistic mean field (TRMF) model to study the ternary fission of heavy nucleus using level density approach. The probability of yields of a particular fragment is obtained by evaluating the convolution integrals which employ the excitation energy and the level density parameter for a given temperature calculated within the TRMF formalism. To illustrate, we have considered the ternary fissions in 252Cf, 242Pu and 236U with fixed third fragment A3 = 48Ca, 20O and 16O respectively. The relative yields are studied for the temperatures T = 1, 2 and 3 MeV. For the comparison, the relative yields are also calculated from the single particle energies of the finite range droplet model (FRDM). In general, the larger phase space for the ternary fragmentation is observed indicating that such fragmentations are most probable ones. For T = 2 and 3 MeV, the Sn + Ni + Ca is the most probable combination for the nucleus 252Cf. However, for the nuclei 242Pu and 236U, the maximum fragmentation yields at T = 2 MeV differ from those at T = 3 MeV. For T = 3 MeV, the closed shell (Z = 8) light mass fragments with its corresponding partners has larger yield values. But, at T = 2 MeV Si/P/S are favorable fragments with the corresponding partners. It is noticed that the symmetric binary fragmentation along with the fixed third fragment for 242Pu and 236U are also favored at T = 1 MeV. The temperature dependence of the nuclear shape and the single particle energies are also discussed.
A new parameter set is generated for finite and infinite nuclear system within the effective field theory motivated relativistic mean field (ERMF) formalism. The isovector part of the ERMF model employed in the present study includes the coupling of nucleons to the {delta} and r{ho} mesons and the cross-coupling of r{ho} mesons to the {sigma} and {omega} mesons. The results for the finite and infinite nuclear systems obtained using our parameter set are in harmony with the available experimental data. We find the maximum mass of the neutron star to be 2.03Modot? and yet a relatively smaller radius at the canonical mass, 12.69 km, as required by the available data.
Relativistic quantum molecular dynamics with scalar and vector interactions based on the relativistic mean meson field theory, RQMD.RMF, is developed.It is implemented into the microscopic transport code JAM.The sensitivity of the directed and of the elliptic proton flow in high energy heavy-ion collisions on the stiffness of the RMF equation of state (EoS) is examined. These new calculations are compared to experimental data at mid-central Au + Au collisions in the beam energy range $2.5 < sqrt{s_{NN}} < 20$ GeV. This new RQMD model with the relativistic mean field scalar and vector meson interactions does describe consistently, with one RMF parameter set,the beam energy dependence of both the directed flow and the elliptic flow,from SIS18 to AGS and RHIC BES-II energies, $sqrt{s_{NN}}< 10$ GeV.There are different sensitivities of these different kinds of flow to the EoS: elliptic flow is most sensitive to the nuclear incompressibility constant,at the moderate beam energies $sqrt{s_{NN}}<3$ GeV,whereas the directed flow is most sensitive to the effective baryon mass at saturation density at $3< sqrt{s_{NN}}<5 $ GeV. Matters abruptly change in the next higher energy range,$sqrt{s_{NN}}gtrsim 10-20$ GeV:the directed flow data show a double change of sign of the slope of $v_1$, inverting twice in this energy range,in sudden contradiction to the RQMD.RMF calculation for a monotonous, stiff EoS. This surprising oscillating behavior,a double change of sign of the $v_1$ slope, points to the appearance of a hitherto unknown first-order phase transition in excited QCD matter at high baryon densities in mid-central Au + Au collisions.
Initial geometrical distribution and fluctuation can affect the collective expansion in relativistic heavy-ion collisions. This effect may be more evident in small system (such as B + B) than in large one (Pb + Pb). This work presents the collision system dependence of collective flows and discusses about effects on collective flows from initial fluctuations in a framework of a multiphase transport model. The results shed light on system scan on experimental efforts to small system physics.
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