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Register a new userQuantal diffusion approach for multi-nucleon transfers in Xe + Pb collisions
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Employing a quantal diffusion description based on the stochastic mean-field (SMF) approach, we analyze the mass distribution of the primary fragments in the collisions of ${}^{136} text{Xe}+{}^{208} text{Pb}$ system at the bombarding energy $E_text{c.m.} =526$~MeV. This quantal approach provides a good description of the primary fragment distribution without any adjustable parameter, including the effects of shell structure.
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Employing the stochastic mean-field (SMF) approach, we develop a quantal diffusion description of the multi-nucleon transfer in heavy-ion collisions at finite impact parameters. The quantal transport coefficients are determined by the occupied single-particle wave functions of the time-dependent Hartree-Fock equations. As a result, the primary fragment mass and charge distribution functions are determined entirely in terms of the mean-field properties. This powerful description does not involve any adjustable parameter, includes the effects of shell structure and is consistent with the fluctuation-dissipation theorem of the non-equilibrium statistical mechanics. As a first application of the approach, we analyze the fragment mass distribution in $^{48}mathrm{Ca}+{}^{238}mathrm{U}$ collisions at the bombarding energy $E_{text{c.m.}}=193$ MeV and compare the calculations with the experimental data.
Quantal diffusion mechanism of nucleon exchange is studied in the central collisions of several symmetric heavy-ion collisions in the framework of the Stochastic Mean-Field (SMF) approach. Since at bombarding energies below the fusion barrier, di-nuclear structure is maintained, it is possible to describe nucleon exchange as a diffusion process familiar from deep-inelastic collisions. Quantal diffusion coefficients, including memory effects, for proton and neutron exchanges are extracted microscopically employing the SMF approach. The quantal calculations of neutron and proton variances are compared with the semi-classical results.
The yields of over 200 projectile-like fragments (PLFs) and target-like fragments (TLFs) from the interaction of (E$_{c.m.}$=450 MeV) $^{136}$Xe with a thick target of $^{208}$Pb were measured using Gammasphere and off-line $gamma$-ray spectroscopy, giving a comprehensive picture of the production cross sections in this reaction.The measured yields were compared to predictions of the GRAZING model and the predictions of Zagrebaev and Greiner using a quantitative metric, the theory evaluation factor, {bf tef}. The GRAZING model predictions are adequate for describing the yields of nuclei near the target or projectile but grossly underestimate the yields of all other products. The predictions of Zagrebaev and Greiner correctly describe the magnitude and maxima of the observed TLF transfer cross sections for a wide range of transfers ($Delta$Z = -8 to $Delta$Z = +2). However for $Delta$Z =+4, the observed position of the maximum in the distribution is four neutrons richer than the predicted maximum. The predicted yields of the neutron-rich N=126 nuclei exceed the measured values by two orders of magnitude. Correlations between TLF and PLF yields are discussed.
Employing the quantal diffusion mechanism for multi-nucleon transfer, the double differential cross-sections are calculated for production of primary projectile-like and target-like fragments in collisions of ${}^{136}text{Xe}+{}^{208}text{Pb}$ system at $E_text{c.m.} =514$ MeV. Including de-excitation due to neutron emission, the cross-section for production of ${}^{210}text{Po}$, ${}^{222}text{Rn}$ and ${}^{224}text{Ra}$ isotopes are estimated and compared with data.
As an extension of previous work, we calculate the production cross-section of heavy neutron-rich isotopes by employing the quantal diffusion description to ${}^{48} text{Ca} + {}^{238} text{U}$ collisions. The quantal diffusion is deduced from stochastic mean-field approach, and transport properties are determined in terms of time-dependent single-particle wave functions of the time-dependent Hartree-Fock (TDHF) theory. As a result, the approach allows for prediction of production cross-sections without any adjustable parameters. The secondary cross-sections by particle emission are calculated with the help of the statistical GEMINI++ code.
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