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Register a new userApproximate transmission coefficients in heavy ion fusion
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In this paper we revisit the one-dimensional tunnelling problem. We consider different approximations for the transmission through the Coulomb barrier in heavy ion collisions at near-barrier energies. First, we discuss approximations of the barrier shape by functional forms where the transmission coefficient is known analytically. Then, we consider Kembles approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical continuation of the radial coordinate to the complex plane. We investigate the validity of the different approximations considered in this paper by comparing their predictions for transmission coefficients and cross sections of three heavy ion systems with the corresponding quantum mechanical results.
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We carefully compare the one-dimensional WKB barrier tunneling model, and the one-channel Schodinger equation with a complex optical potential calculation of heavy-ion fusion, for a light and a heavy system. It is found that the major difference between the two approaches occurs around the critical energy, above which the effective potential for the grazing angular momentum ceases to exhibit a pocket. The value of this critical energy is shown to be strongly dependent on the nuclear potential at short distances, on the inside region of the Coulomb barrier, and this dependence is much more important for heavy systems. Therefore the nuclear fusion process is expected to provide information on the nuclear potential in this inner region. We compare calculations with available data to show that the results are consistent with this expectation.
The nuclear fusion is a reaction to form a compound nucleus. It plays an important role in several circumstances in nuclear physics as well as in nuclear astrophysics, such as synthesis of superheavy elements and nucleosynthesis in stars. Here we discuss two recent theoretical developments in heavy-ion fusion reactions at energies around the Coulomb barrier. The first topic is a generalization of the Wong formula for fusion cross sections in a single-channel problem. By introducing an energy dependence to the barrier parameters, we show that the generalized formula leads to results practically indistinguishable from a full quantal calculation, even for light symmetric systems such as $^{12}$C+$^{12}$C, for which fusion cross sections show an oscillatory behavior. We then discuss a semi-microscopic modeling of heavy-ion fusion reactions, which combine the coupled-channels approach to the state-of-the-art nuclear structure calculations for low-lying collective motions. We apply this method to subbarrier fusion reactions of $^{58}$Ni+$^{58}$Ni and $^{40}$Ca+$^{58}$Ni systems, and discuss the role of anharmonicity of the low-lying vibrational motions.
In this paper we revisit the one-dimensional tunneling problem. We consider Kembles approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical continuation of the radial coordinate to the complex plane. We investigate the validity of this approximation by comparing their predictions for the cross section and for the barrier distribution with the corresponding quantum mechanical results. We find that the extended Kembles approximation reproduces the results of quantum mechanics with great accuracy.
We study the single electron spectra from $D-$ and $B-$meson semileptonic decays in Au+Au collisions at $sqrt{s_{rm NN}}=$200, 62.4, and 19.2 GeV by employing the parton-hadron-string dynamics (PHSD) transport approach that has been shown to reasonably describe the charm dynamics at RHIC and LHC energies on a microscopic level. In this approach the initial heavy quarks are produced by using the PYTHIA which is tuned to reproduce the FONLL calculations. The produced heavy quarks interact with off-shell massive partons in QGP with scattering cross sections which are calculated in the dynamical quasi-particle model (DQPM). At energy densities close to the critical energy density the heavy quarks are hadronized into heavy mesons through either coalescence or fragmentation. After hadronization the heavy mesons interact with the light hadrons by employing the scattering cross sections from an effective Lagrangian. The final heavy mesons then produce single electrons through semileptonic decay. We find that the PHSD approach well describes the nuclear modification factor $R_{rm AA}$ and elliptic flow $v_2$ of single electrons in d+Au and Au+Au collisions at $sqrt{s_{rm NN}}=$ 200 GeV and the elliptic flow in Au+Au reactions at $sqrt{s_{rm NN}}=$ 62.4 GeV from the PHENIX collaboration, however, the large $R_{rm AA}$ at $sqrt{s_{rm NN}}=$ 62.4 GeV is not described at all. Furthermore, we make predictions for the $R_{rm AA}$ of $D-$mesons and of single electrons at the lower energy of $sqrt{s_{rm NN}}=$ 19.2 GeV. Additionally, the medium modification of the azimuthal angle $phi$ between a heavy quark and a heavy antiquark is studied. We find that the transverse flow enhances the azimuthal angular distributions close to $phi=$ 0 because the heavy flavors strongly interact with nuclear medium in relativistic heavy-ion collisions and almost flow with the bulk matter.
A systematic analysis of correlations between different orders of $p_T$-differential flow is presented, including mode coupling effects in flow vectors, correlations between flow angles (a.k.a. event-plane correlations), and correlations between flow magnitudes, all of which were previously studied with integrated flows. We find that the mode coupling effects among differential flows largely mirror those among the corresponding integrated flows, except at small transverse momenta where mode coupling contributions are small. For the fourth- and fifth-order flow vectors $V_4$ and $V_5$ we argue that the event plane correlations can be understood as the ratio between the mode coupling contributions to these flows and and the flow magnitudes. We also find that for $V_4$ and $V_5$ the linear response contribution scales linearly with the corresponding cumulant-defined eccentricities but not with the standard eccentricities.
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