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Register a new userThe $^{136}$Xe + $^{208}$Pb reaction: A test of models of multi-nucleon transfer reactions
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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.
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A previous study of symmetric collisions of massive nuclei has shown that current models of multi-nucleon transfer (MNT) reactions do not adequately describe the transfer product yields. To gain further insight into this problem, we have measured the yields of MNT products in the interaction of 977 (E/A = 4.79 MeV) and 1143 MeV (E/A = 5.60 MeV) $^{204}$Hg with $^{208}$Pb. We find that the yield of multi-nucleon transfer products are similar in these two reactions and are substantially lower than those observed in the reaction of 1257 MeV (E/A = 6.16 MeV) $^{204}$Hg + $^{198}$Pt. We compare our measurements with the predictions of the GRAZING-F, di-nuclear systems (DNS) and improved quantum molecular dynamics (ImQMD) models. For the observed isotopes of the elements Au, Hg, Tl, Pb and Bi, the measured values of the MNT cross sections are orders of magnitude larger than the predicted values. Furthermore, the various models predict the formation of nuclides near the N=126 shell, which are not observed.
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.
Multi-nucleon transfer reactions in $^{40}$Ca+$^{208}$Pb have been studied at several bombarding energies close to the Coulomb barrier. Light reaction products have been identified in mass and charge with a time-of-flight spectrometer. The energy spectra of the inclusive two neutron pick-up channel show a population in a narrow region of excitation energies which corresponds to the predicted energy of pairing vibration states in $^{42}$Ca.
We discuss the role of two-neutron transfer processes in the fusion reaction of the $^{9,11}$Li + $^{208}$Pb systems. We first analyze the $^{9}$Li + $^{208}$Pb reaction by taking into account the coupling to the $^{7}$Li + $^{210}$Pb channel. To this end, we assume that two neutrons are directly transferred to a single effective channel in $^{210}$Pb and solve the coupled-channels equations with the two channels. By adjusting the coupling strength and the effective $Q$-value, we successfully reproduce the experimental fusion cross sections for this system. We then analyze the $^{11}$Li + $^{208}$Pb reaction in a similar manner, that is, by taking into account three effective channels with $^{11}$Li + $^{208}$Pb, $^{9}$Li + $^{210}$Pb, and $^{7}$Li + $^{212}$Pb partitions. In order to take into account the halo structure of the $^{11}$Li nucleus, we construct the potential between $^{11}$Li and $^{208}$Pb with a double folding procedure, while we employ a Wood-Saxon type potential with the global Akyuz-Winther parameters for the other channels. Our calculation indicates that the multiple two-neutron transfer process plays a crucial role in the $^{11}$Li + $^{208}$Pb fusion reaction at energies around the Coulomb barrier.
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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