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For cold (neutronless) fission we consider an analytical model of quantum tunneling with dissipation through a barrier U(q) evaluated with a M3Y nucleon-nucleon force. We calculate the tunneling spectrum, i.e., the fission rate as a function of the total kinetic energy of the fragments. The theoretical results are compared with the experimental data obtained for the fine structure of two cold fission modes of 252Cf: 148Ba+104Mo and 146Ba+106Mo. Taking into account the dissipative coupling of the potential function U(q) and of the momentum p with all the other neglected coordinates, we obtain a remarkable agreement with the experimental data. We conclude that the cold fission process is a spontaneous decay with a spectrum determined by the shape of the barrier and an amplitude depending on the strength of the dissipative coupling.
The molecular particle-core model is applied to the scattering of 13C on 13C. The model divides the 13C+ 13C system into two 12C cores and two valence neutrons. The valence neutrons are described with molecular eigenfunctions of the symmetric two-center shell model. Coupled channel calculations are carried out for the inelastic single and mutual excitation of the first (1/2+ state of 13C and the neutron transfer to the 12C+14C system. The results reproduce the experimental data. The analysis of the S matrix shows that the gross structure of the transfer excitation function is related to resonances in the relative motion of the elastic and transfer channels.
The inelastic excitation of the (1/2)+ (871 keV) state of 17O in the reaction of 13C on 17O is described by a time-dependent quantum mechanical model with two diabatic states and a classical treatment of the radial relative motion. The structures in the angle-integrated cross section are interpreted as caused by the barriers of the angular momentum-dependent potentials. The transition strength is enhanced by the Landau-Zener effect between the levels considered.
On the basis of the two-center shell model a molecular reaction theory is applied to the reaction 13C(13C, 12C)14C. Prominent structures in the measured differential cross sections can be reproduced by this theory.
For the scattering of 28Si on 28Si coupled channel calculations of the elastic scattering and inelastic single excitation of the first 2+ state of 28Si are carried out. The real coupling potentials are calculated in the framework of an adiabatic model. The resulting cross sections reveal structures in agreement with the observed ones and support their interpretation as nuclear molecular resonances.
Quasimolecular resonance structures in the 12C-12C system are studied in the framework of the coupled channel formalism in the energy range Ec.m.=5-14 MeV. The influence of the coupling of the first excited 2+ state in 12C on the resonance structures is investigated by choosing various types of coupling potentials. The intermediate structures in the reflection and transition coefficients and cross sections can be interpreted with the double resonance mechanism. NUCLEAR REACTIONS 12C(12C, 12C), quasimolecular states, coupling potentials, coupled channel calculations for σ(θ).
On the basis of the two-center shell model a theory is developed for the excitation of loosely bound nucleons in heavy ion collisions. These nucleons move in the two-center shell model potential generated by all the nucleons and are described by molecular wave functions. The model is applied to calculate the cross sections for the elastic and inelastic 13C-13C scattering. The cross sections show intermediate structures caused by the excitation of quasibound resonances in the molecular nucleus-nucleus potential. NUCLEAR REACTIONS 13C(13C,13C) molecular wave functions, dynamical two-center shell model, quasimolecular resonances, radial and Coriolis coupling, coupled channel calculations for σ(θ).
The theory of nucleon transfer in heavy ion reactions is formulated on the basis of the molecular particlecore model for a system consisting of two cores and one extracore nucleon. The extracore nucleon is described by the molecular wave functions of the asymmetric two-center shell model. The cores, which are assumed to be collectively excitable, are treated with vibrator-rotator models. Potentials for shape polarization are contained in the asymmetric two-center shell model and the interaction between the cores. The excitation and transfer of the extracore nucleon is induced by the radial and rotational couplings. The coupled channel equations, which include the recoil effects in first approximation, are derived in a form suitable for numerical calculations of cross sections. NUCLEAR REACTIONS Heavy ion scattering, theory of nucleon transfer, molecular wave functions, two-center shell model, collective and single-particle excitation.
Determination of the effective 12C + 12C potential from the sub-Coulomb single-particle resonances
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The sub-Coulomb resonances observed in the total reaction yield of the 12C + 12C system at 4.9, 5.6, and 6.2 MeV are explained as single-particle resonances. The "true" effective 12C + 12C potential is determined directly as the real potential which reproduces best the position and the spacing of the observed sub-Coulomb resonances. This potential is found from a parametrization of the two limiting adiabatic and sudden potentials.
It is shown that nuclear matter is compressed during the encounter of heavy ions. If the relative velocity of the nuclei is larger than the velocity of first sound in nuclear matter (compression sound for isospin T=0), nuclear shock waves occur. They lead to densities which are 3-5 times higher than the nuclear equilibrium density ρ0, depending on the energy of the nuclei. The implications of this phenomenon are discussed.
By introducing charge asymmetry as a new dynamical collective coordinate in the asymmetric two-center shell model, the nuclear charge dispersion in the fission of 236U is calculated without using any free parameter. The agreement between theory and experiment is quite good.
A general formalism for the scattering of heavy ions, which is especially convenient to study the antisymmetrization effects, is developed. Antisymmetrization effects are investigated by expanding the completely antisymmetrized wave function according to the number of exchanged nucleons. The particle-core model for the scattering of nuclei with loosely bound nucleons is presented. A formula for the additional contribution to the effective potential due to antisymmetrization effects is obtained by calculating the expectation value of the Hamiltonian with intrinsic wave functions. Application of the formalism is illustrated for the 14N + 14N scattering problem and its usefulness is demonstrated.
It is suggested that the experimentally observed intermediate structure in the cross section of elastic O16 + O16 scattering is due to quasibound molecular states of the ion-ion system while the gross structure originates from virtually bound molecular states.
With a schematic model for the nuclear matter we give a unified treatment of the real and imaginary parts of the elastic O16-O16 scattering potential. The model connects the parameters of the potential with the density and binding properties of the O16-O16 system and reproduces the structure of the excitation function quite well. It is shown that the nuclear compressibility can be obtained from the scattering data, and in the case of the S32 compound system there results an effective compressibility (finite quenching of the nuclei) of about 200 MeV.
The study of the azimuthal anisotropy of inclusive muons produced in p-Pb collisions at sNN−−−√=8.16 TeV, using the ALICE detector at the LHC is reported. The measurement of the second-order Fourier coefficient of the particle azimuthal distribution, v2, is performed as a function of transverse momentum pT in the 0-20% high-multiplicity interval at both forward (2.03<yCMS<3.53) and backward (−4.46<yCMS<−2.96) rapidities over a wide pT range, 0.5<pT<10 GeV/c, in which a dominant contribution of muons from heavy-flavour hadron decays is expected at pT>2 GeV/c. The v2 coefficient of inclusive muons is extracted using two different techniques, namely two-particle cumulants, used for the first time for heavy-flavour measurements, and forward-central two-particle correlations. Both techniques give compatible results. A positive v2 is measured at both forward and backward rapidities with a significance larger than 4.7σ and 7.6σ, respectively, in the interval 2<pT<6 GeV/c. Comparisons with previous measurements in p-Pb collisions at sNN−−−√=5.02 TeV, and with AMPT and CGC-based theoretical calculations are discussed. The findings impose new constraints on the theoretical interpretations of the origin of the collective behaviour in small collision systems.
In ultraperipheral collisions (UPCs) of relativistic nuclei without overlap of nuclear densities, the two nuclei are excited by the Lorentz-contracted Coulomb fields of their collision partners. In these UPCs, the typical nuclear excitation energy is below a few tens of MeV, and a small number of nucleons are emitted in electromagnetic dissociation (EMD) of primary nuclei, in contrast to complete nuclear fragmentation in hadronic interactions. The cross sections of emission of given numbers of neutrons in UPCs of 208Pb nuclei at sNN−−−√=5.02 TeV were measured with the neutron zero degree calorimeters (ZDCs) of the ALICE detector at the LHC, exploiting a similar technique to that used in previous studies performed at sNN−−−√=2.76 TeV. In addition, the cross sections for the exclusive emission of one, two, three, four, and five forward neutrons in the EMD, not accompanied by the emission of forward protons, and thus mostly corresponding to the production of 207,206,205,204,203Pb, respectively, were measured for the first time. The predictions from the available models describe the measured cross sections well. These cross sections can be used for evaluating the impact of secondary nuclei on the LHC components, in particular, on superconducting magnets, and also provide useful input for the design of the Future Circular Collider (FCC-hh).
Measurements of the production of electrons from heavy-flavour hadron decays in pp collisions at s√=13 TeV at midrapidity with the ALICE detector are presented down to a transverse momentum (pT) of 0.2 GeV/c and up to pT=35 GeV/c, which is the largest momentum range probed for inclusive electron measurements in ALICE. In p−Pb collisions, the production cross section and the nuclear modification factor of electrons from heavy-flavour hadron decays are measured in the pT range 0.5<pT<26 GeV/c at sNN−−−√=8.16 TeV. The nuclear modification factor is found to be consistent with unity within the statistical and systematic uncertainties. In both collision systems, first measurements of the yields of electrons from heavy-flavour hadron decays in different multiplicity intervals normalised to the multiplicity-integrated yield (self-normalised yield) at midrapidity are reported as a function of the self-normalised charged-particle multiplicity estimated at midrapidity. The self-normalised yields in pp and p−Pb collisions grow faster than linear with the self-normalised multiplicity. A strong pT dependence is observed in pp collisions, where the yield of high-pT electrons increases faster as a function of multiplicity than the one of low-pT electrons. The measurement in p−Pb collisions shows no pT dependence within uncertainties. The self-normalised yields in pp and p−Pb collisions are compared with measurements of other heavy-flavour, light-flavour, and strange particles, and with Monte Carlo simulations.
The correlations between different moments of two flow amplitudes, extracted with the recently developed asymmetric cumulants, are measured in Pb-Pb collisions at √sNN = 5.02 TeV recorded by the ALICE detector at the CERN Large Hadron Collider. The magnitudes of the measured observables show a dependence on the different moments as well as on the collision centrality, indicating the presence of nonlinear response in all even moments up to the eighth. Furthermore, the higher-order asymmetric cumulants show different signatures than the symmetric and lower-order asymmetric cumulants. Comparisons with state-of-the-art event generators using two different parametrizations obtained from Bayesian optimization show differences between data and simulations in many of the studied observables, indicating a need for further tuning of the models behind those event generators. These results provide new and independent constraints on the initial conditions and transport properties of the system created in heavy-ion collisions.
The production of π±, K±, and (p¯¯¯)p is measured in pp collisions at s√=13 TeV in different topological regions. Particle transverse momentum (pT) spectra are measured in the ``toward'', ``transverse'', and ``away'' angular regions defined with respect to the direction of the leading particle in the event. While the toward and away regions contain the fragmentation products of the near-side and away-side jets, respectively, the transverse region is dominated by particles from the Underlying Event (UE). The relative transverse activity classifier, RT=NT/⟨NT⟩, is used to group events according to their UE activity, where NT is the measured charged-particle multiplicity per event in the transverse region and ⟨NT⟩ is the mean value over all the analysed events. The first measurements of identified particle pT spectra as a function of RT in the three topological regions are reported. The yield of high transverse momentum particles relative to the RT-integrated measurement decreases with increasing RT in both the toward and away regions, indicating that the softer UE dominates particle production as RT increases and validating that RT can be used to control the magnitude of the UE. Conversely, the spectral shapes in the transverse region harden significantly with increasing RT. This hardening follows a mass ordering, being more significant for heavier particles. The pT-differential particle ratios (p+p¯¯¯)/(π++π−) and (K++K−)/(π++π−) in the low UE limit (RT→0) approach expectations from Monte Carlo generators such as PYTHIA 8 with Monash 2013 tune and EPOS LHC, where the jet-fragmentation models have been tuned to reproduce e+e− results.