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Register a new userPhenomenological Scaling of Rapidity Dependence for Anisotropic Flows in 25 MeV/nucleon Ca + Ca by Quantum Molecular Dynamics Model
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Anisotropic flows ($v_1$, $v_2$, $v_3$ and $v_4$) of light fragments up till the mass number 4 as a function of rapidity have been studied for 25 MeV/nucleon $^{40}$Ca + $^{40}$Ca at large impact parameters by Quantum Molecular Dynamics model. A phenomenological scaling behavior of rapidity dependent flow parameters $v_n$ (n = 1, 2, 3 and 4) has been found as a function of mass number plus a constant term, which may arise from the interplay of collective and random motions. In addition, $v_4/{v_2}^2$ keeps almost independent of rapidity and remains a rough constant of 1/2 for all light fragments.
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Momentum correlation functions of the nucleon-nucleon pairs are presented for reactions with C isotopes bombarding a $^{12} rm C$ target within the framework of the isospin-dependent quantum molecular dynamics model. The binding-energy dependence of the momentum correlation functions is also explored, and other factors that have an influence on momentum correlation functions are investigated. These factors include momentum-dependent nuclear equation of state, in-medium nucleon-nucleon cross sections, impact parameters, total pair momenta, and beam energy. In particular, the rise and the fall of the strength of momentum correlation functions at lower relative momentum are shown with an increase in beam energy.
We investigate the possible occurrence of the highly-elongated shapes near the yrast line in $^{40}$Ca and $^{41}$Ca at high spins on the basis of the nuclear energy-density functional method. Not only the superdeformed (SD) yrast configuration but the yrare configurations on top of the SD band are described by solving the cranked Skyme-Kohn-Sham equation in the three-dimensional coordinate-space representation. It is suggested that some of the excited SD bands undergo band crossings and develop to the hyperdeformation (HD) beyond $J simeq 25 hbar$ in $^{40}$Ca. We find that the change of triaxiality in response to rotation plays a decisive role for the shape evolution towards HD, and that this is governed by the signature quantum number of the last occupied orbital at low spins. This mechanism can be verified in an experimental observation of the positive-parity SD yrast signature-partner bands in $^{41}$Ca, one of which ($alpha=+1/2$) undergoes crossings with the HD band while the other ($alpha=-1/2$) shows the smooth evolution from the collective rotation at low spins to the non-collective rotation with oblate shape at the termination.
For $^{48}$Ca, we determined $r_{m}$fm and $r_{rm skin}$fm from the central values of $sigma_{rm R}({rm EXP})$ of p+$^{48}$Ca scattering, using the chiral (Kyushu) $g$-matrix folding model with the GHFB+AMP densities. For $^{40}$Ca, Zenihiro {it et al.} determined $r_n({rm RCNP})=3.375$~fm and $r_{rm skin}({rm RCNP})=-0.01 pm 0.023$fm from the differential cross section and the analyzing powers for p+$^{40}$Ca scattering. For $^{40}$Ca, $sigma_{rm R}({rm EXP})$ are available with high accuracy. Our aim is to determine matter radius $r_{m}^{40}$ and skin $r_{rm skin}^{40}$ from $sigma_{rm R}({rm EXP})$ by using the Kyushu $g$-matrix folding model with the GHFB+AMP densities. We first determine $r_m({rm RCNP})=3.380$fm from the central value -0.01~fm of $r_{rm skin}({rm RCNP})$ and $r_p({rm RCNP})=3.385$fm. The folding model with the GHFB+AMP densities reproduces $sigma_{rm R}({rm EXP})$ in $30 leq E_{rm in} leq 180$MeV, in 2-$sigma$ level. We scale the GHFB+AMP densities so as to $r_p({rm AMP})=r_p({rm RCNP})$ and $r_n({rm AMP})=r_n({rm RCNP})$. The $sigma_{rm R}({rm RCNP})$ thus obtained agrees with the original one $sigma_{rm R}({rm AMP})$ for each $E_{rm in}$. For $E_{rm in}=180$MeV, we define $F$ as $F=sigma_{rm R}({rm EXP})/sigma_{rm R}({rm AMP})=0.929$. The $Fsigma_{rm R}({rm AMP})$ be much the same as the center values of $sigma_{rm R}({rm EXP})$ in $30 leq E_{rm in} leq 180$MeV. We then determine $r_{rm m}^{40}({rm EXP})$ from the center values of $sigma_{rm R}({rm EXP})$, using $sigma_{rm R}({rm EXP})=C r_{m}^{2}({rm EXP})$ with $C=r_{m}^{2}({rm AMP})/(Fsigma_{rm R}({rm AMP}))$. The $r_{m}({rm EXP})$ are averaged over $E_{rm in}$. The averaged value is $r_{m}({rm EXP})=3.380$fm. Eventually, we obtain $r_{rm skin}({rm EXP})=-0.01$fm from the averaged $r_{rm m}({rm EXP})$~fm and $r_p({rm PCNP})=3.385$fm.
In our previous paper, we predicted $r_{rm skin}$, $r_{rm p}$, $r_{rm n}$, $r_{rm m}$ for $^{40-60,62,64}$Ca after determining the neutron dripline, using the Gogny-D1S HFB (GHFB) with and without the angular momentum projection (AMP). Using the chiral $g$-matrix folding model, we predicted $sigma_{rm R}$ for Ca scattering on a $^{12}$C target at 280 MeV/nucleon, since Tanaka {it el al.} measured interaction cross sections $sigma_{rm I} (approx sigma_{rm R})$ for $^{42-51}$Ca in RIKEN. After our prediction, they determine $r_{rm m}({rm RIKEN})$, $r_{rm skin}({rm RIKEN})$, $r_{rm n}({rm RIKEN})$. In this paper, we reanalyses the $sigma_{rm I}$, since they assumed the Wood-Saxon densities for $^{42-51}$Ca. The $sigma_{rm R}$ calculated with the folding model with GHFB and GHFB+AMP densities almost reproduce the $sigma_{rm I}$. We then scale proton and neutron densities so that $r_{rm p}$ and $r_{rm n}$ may agree with the central values of $r_{rm p}(rm exp)$ and $r_{rm n}({rm RIKEN})$, respectively. The $sigma_{rm R}$ calculated with the scaled densities do not reproduce the central values of $sigma_{rm I}$ perfectly. We then determine the $r_{rm m}$ that agree with the central values of $sigma_{rm I}$, using the chiral $g$-matrix folding model. The fitted $r_{rm m}$ do not reproduce the central values of $r_{rm m}({rm RIKEN})$ perfectly, but are in one $sigma$ level. Finally, we show the $r_{rm skin}$, $r_{rm n}$ determined from the fitted $r_{rm m}$ are close to the original ones except for $r_{rm skin}^{48}$. The fitted $r_{rm skin}^{48}$ is 0.105 fm, while the central value of $r_{rm m}^{48}({rm RIKEN})$ is 0.146 fm. When we fit $r_{rm m}$ to the upper bound of $sigma_{rm I}$, the fitted $r_{rm skin}^{48}$ is 0.164~fm and near the central vale 0.17 fm of the high-resolution $E1$ polarizability experiment.
In this review article, we first briefly introduce the transport theory and quantum molecular dynamics model applied in the study of the heavy ion collisions from low to intermediate energies. The developments of improved quantum molecular dynamics model (ImQMD) and ultra-relativistic quantum molecular dynamics model (UrQMD), are reviewed. The reaction mechanism and phenomena related to the fusion, multinucleon transfer, fragmentation, collective flow and particle production are reviewed and discussed within the framework of the two models. The constraints on the isospin asymmetric nuclear equation of state and in-medium nucleon-nucleon cross sections by comparing the heavy ion collision data with transport models calculations in last decades are also discussed, and the uncertainties of these constraints are analyzed as well. Finally, we discuss the future direction of the development of the transport models for improving the understanding of the reaction mechanism, the descriptions of various observables, the constraint on the nuclear equation of state, as well as for the constraint on in-medium nucleon-nucleon cross sections.
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