Interaction and fusion of deformed nuclei

It is shown that the height of the barrier and its position, as well the depth of the capture well, are highly sensitive to the relative orientation of colliding strongly deformed nuclei. It is found that the fusion/capture cross sections and the nucleus-nucleus potential for heavy nuclear systems depend greatly on the magnitude and sign of the quadrupole deformation of nuclear surfaces. In order to describe correctly the cross section for the capture of heavy strongly deformed nuclei, it is necessary to perform averaging over all three angles that describe their relative orientation. Allowance for a hexadecapole deformation leads to a significant increase in the capture cross section for very heavy nucleus-nucleus systems.     

Heavy-ion fusion at low energies

Through precision measurements of fusion cross sections at energies close to the Coulomb barrier and through the application of the method of “experimental barrier distributions” which these permit, many recent advances have been made in our understanding of the dynamical processes occurring during a heavy-ion collision. It is now clear that the target and projectile reach one another in superpositions of states which correspond to different orientations for rotational nuclei or to different induced deformations for vibrational nuclei. The creation of a neck of neutron matter has also long been postulated and by studying the isotopic dependence of the fusion reaction, some recent results in the ¹⁰Ca+^90,96Zr systems appear to confirm this result. For large Z ₁ Z ₂ a type of extra-push effect can arise from the same inelastic entrance-channel effects which enhance the fusion of lighter systems, though this will be absent in cases where the enhancement arises from neutron transfers. The existence of different barriers will of course influence all other reaction channels. Fusion simply allows one to visualise the barriers most easily, since for this process, the total cross section is an incoherent sum of the contributions from all relevant eigenchannels. Some effects in other channels have already been observed. Other possible effects will be discussed. These include; the exploitation of the lowest-energy barrier to produce exotic evaporation residues and strongly deformed high-spin states at low excitation energy.     

Anomalies in orientation interaction of slow neutrons with nuclei and the problem of neutron molecule existence

Based on the Dirac equation, the features of long-range electromagnetic orientational interaction of slow neutrons with even-even and even-odd nuclei are considered. This interaction is controlled by a narrow potential barrier arranged beyond the nucleus. The barrier height is U _tot = 20–40 eV and depends on Z, A, and the nucleus magnetic moment μ_nucl. The barrier formation is associated with the ponderomotive nonlinear interaction of the anomalous neutron moment with the nucleus electric field. The barrier transparency for thermal neutrons is D(E) ≈ 0.8–0.95. For cold neutrons, the barrier transparency and their reaction cross sections with nuclei sharply decrease and, at E → 0, their cross sections tend toward zero. It was shown that the combined effect of the magnetic dipole-dipole and ponderomotive interaction of the neutron and even-odd nucleus results in the formation of removed symmetrically positioned potential wells for neutrons beyond the nucleus. The presence of these wells results in the possible existence of short-lived or virtual nucleus-neutron molecules and the “neutron halo” effect beyond the nucleus.     

Nucleon--nucleon interactions in the double folding model for fusion reactions

Nucleus--nucleus potentials are determined in the framework of double folding model for M3Y--Reid and M3Y--Paris effective nucleon--nucleon (NN) interactions. Both zero-range and finite-range exchange parts of NN interactions are considered in the folding procedure. In this paper the spherical projectile--spherical target system ¹⁶O+²⁰⁸Pb is selected for calculating the barrier energies, fusion cross sections and barrier distributions with the density-independent and density-dependent NN interactions on the basis of M3Y--Reid and M3Y--Paris NN interactions. The barrier energies become lower for Paris NN interactions in comparison with Reid NN interactions, and also for finite-range exchange part in comparison with zero-range exchange part. The density-dependent NN interactions give similar fusion cross sections and barrier distributions, and the density-independent NN interaction causes the barrier distribution moving to a higher position. However, the density-independent Reid NN interaction with zero-range exchange part gives the lowest fusion cross sections. We find that the calculated fusion cross sections and the barrier distributions are in agreement with the experimental data after renormalization of the nuclear potential due to coupled-channel effect.     

Nuclear Potential and Fusion Cross Sections for Synthesizing Super-Heavy Elements in Di-nuclear Systems

A double foMing method with simplified Skyrme-type nucleon nucleon interaction is used to calculate the nuclear interaction potential between two nuclei. The calculation is performed in tip-to-tip orientation of the two nuclei if they are deformed. Based on this method, the potential energy surfaces~ the fusion probabilities and the evaporation residue cross sections for some cold fusion reactions leading to super-heavy elements within di-nuclear system model are evaluated. It is indicated that after the improvement, the exponential decreasing systematics of the fusion probability with increasing charge number of projectile on the Pb based target become better and the evaporation residue cross sections are in better agreement with the experimental data.     

Fusion around the barrier in 11,9Be +209Bi

The ⁹Be +²⁰⁹Bi fusion cross sections were measured in the range 37.5 MeV ≤ E _lab ≤ 45.0 MeV at the Munich Tandem via the observation of ground state α-decay of the evaporation residues. Fusion cross sections of ²⁰⁹Bi with the “halo”¹¹Be unstable projectile in the region around the Coulomb barrier were deduced from an experiment done with the same technique at the RIKEN Ring Cyclotron. Above the Coulomb barrier the ¹¹Be cross sections are larger than the ⁹Be ones in agreement with theoretical predictions based on the larger ¹¹Be halo radius. Also below the barrier these theories foresee the same behavior in disagreement with the experimental results, since the two cross sections are rather similar. Received: 2 April 1998     

The interaction and fusion of arbitrarily oriented deformed nuclei

The fusion/capture cross sections between various deformed nuclei are calculated. It is shown that quadrupole and hexadecapole deformations of heavy nuclei are important for evaluating the barrier height, capture well depth, and fusion/capture cross sections of heavy nuclei. It is found that calculations of the capture cross section of two heavy deformed nuclei must be performed with averaging over all possible mutual orientations of the colliding nuclei.     

β-delayed proton decays near the proton drip line

We briefly reviewed the experimental study on β-delayed proton decays near the proton drip line published by our group during the period of 1996–2004, namely the first observation of the β-delayed proton decays of 9 new nuclides in the rare-earth region and the new measurements of β-delayed proton decays of 5 nuclides in the mass ∼90 region near theN=Z line with the aid of the “p-y” coincidence in combination with a He-jet tape transport system. In the meantime some important experimental technique details were supplemented. The experimental results, including the half-lives, spins, parities, deformations and production reaction cross sections for the 14 nuclei were summarized and compared with the current nuclear-model predictions, and then the following points were represented. (1) The experimental half-lives for⁸⁵Mo and⁹²Rh as well as the predicted “waiting point” nuclei⁸⁹Ru and⁹³Pd are 5–10 times longer than the theoretical predictions given by M?ller et al. using a macroscopic-microscopic model. It considerably influences the predictions of the abundances of the nuclides produced in the rp-process. (2) The current-model predictions are not consistent with the experimental assignments of the spins and parities for the proton drip-line nuclei¹⁴²Ho and¹²⁸Pm. However, the nuclear potential energy surface (PES) calculated by using a Woods-Saxon-Strutinsky method reproduced the experimental results. (3) The Alice code overestimated the production reaction cross sections of the studied 9 rare-earth nuclei by one order of magnitude or two, while HIVAP code overestimated them by one order of magnitude approximately.     

Sensitivity of cross sections for elastic nucleus-nucleus scattering to halo nucleus density distributions

In order to clear up the sensitivity of the nucleus-nucleus scattering to the nuclear matter distributions in exotic halo nuclei, we have calculated differential cross sections for elastic scattering of the ⁶He and ¹¹Li nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon with different assumed nuclear density distributions in ⁶He and ¹¹Li.     

Hindrance of heavy-ion fusion due to nuclear incompressibility

We propose a new mechanism to explain the unexpected steep falloff of fusion cross sections at energies far below the Coulomb barrier. The saturation properties of nuclear matter are causing a hindrance to large overlap of the reacting nuclei and consequently a sensitive change of the nuclear potential inside the barrier. We report in this Letter a good agreement with the data of coupled-channels calculation for the 64Ni + 64Ni combination using the double-folding potential with Michigan-3-Yukawa-Reid effective N - N forces supplemented with a repulsive core that reproduces the nuclear incompressibility for total overlap.     

Search for signatures of phase transition and critical point in heavy-ion collisions

The general concepts in the critical phenomena related with the notions of “scaling” and “universality” are considered. Behavior of various systems near a phase transition is displayed. Search for clear signatures of the phase transition of the nuclear matter and location of the critical point in heavy-ion collisions (HIC) is discussed. The experimental data on inclusive spectra measured in HIC at RHIC and SPS over a wide range of energies s _{N N} ^1/2 = 9–200 GeV are analyzed in the framework of z-scaling. A microscopic scenario of the constituent interactions is presented. Dependence of the energy loss on the momentum of the produced hadron, energy and centrality of the collision is studied. Self-similarity of the constituent interactions described in terms of momentum fractions is used to characterize the nuclear medium by “specific heat” and colliding nuclei by fractal dimensions. Preferable kinematical regions to search for signatures of the phase transition of the nuclear matter produced in HIC are discussed. Discontinuity of the “specific heat” is assumed to be a signature of the phase transition and the critical point.     

140A MeV~(40,48)Ca和~(58,64)Ni炮弹碎裂反应产物的统计擦碎模型计算

用统计擦碎模型计算了140AMeV40,48Ca+9Be和58,64Ni+9Be弹核碎裂反应产物的截面.通过对碎片截面计算结果和实验测量结果的比较发现,采用自由空间的核子-核子反应截面计算时,对非中心反应产物的截面拟合很好,而对中心反应产物的截面有较大高估,而采用饱和密度相关的核子-核子反应截面计算时,对非周边反应产物的截面拟合较好,而对周边反应产物的截面有一定程度的低估.在统计擦碎模型中,对核子-核子反应截面进行细致的介质密度关联,可能会改进计算值与实验值的符合程度.     

Clustering phenomena in radioactive and stable nuclei and in heavy-ion collisions

A theory for clustering formation in nuclei and in heavy-ion collisions has been worked out in terms of the quantum-mechanical fragmentation process. Treating the mass fragmentation and relative separation coordinates as weakly coupled, the spontaneous cluster-decay of radioactive nuclei has been considered as a two-step process of clustering formation and tunnelling of the confining nuclear interaction barrier. This model has also been applied to “stable” nuclei, lighter than lead. The effects of adding more and more neutrons to collidingN =Z,A = 4n nuclei are studied for theα-clustering transfer phenomenon.     

Parton distributions for the LHC

We present updated leading-order, next-to-leading order and next-to-next-to-leading order parton distribution functions (“MSTW 2008”) determined from global analysis of hard-scattering data within the standard framework of leading-twist fixed-order collinear factorisation in the [`(MS)]\overline{\mathrm{MS}} scheme. These parton distributions supersede the previously available “MRST” sets and should be used for the first LHC data taking and for the associated theoretical calculations. New data sets fitted include CCFR/NuTeV dimuon cross sections, which constrain the strange-quark and -antiquark distributions, and Tevatron Run II data on inclusive jet production, the lepton charge asymmetry from W decays and the Z rapidity distribution. Uncertainties are propagated from the experimental errors on the fitted data points using a new dynamic procedure for each eigenvector of the covariance matrix. We discuss the major changes compared to previous MRST fits, briefly compare to parton distributions obtained by other fitting groups, and give predictions for the W and Z total cross sections at the Tevatron and LHC.     

Semi-classical model of neutron rearrangement using quantum coupled-channel approach

A quantum coupled-channel approach with collective degrees of freedom (the rotation of deformed nuclei and/or their surface vibrations) is combined with an empirical coupled-channel model to add neutron rearrangement channels to vibrational and rotational excitations. The calculated fusion cross sections and the barrier distribution functions for several combinations of nuclei are in good agreement with experimental data.     

Barrier distributions derived from quasielastic backscattering of 48Ti, 54Cr, 56Fe, 64Ni, and 70Zn projectiles on a 208Pb target

In order to study the nucleus-nucleus interaction in Pb-based cold fusion, we have measured excitation functions for quasielastic scattering of 48Ti, 54Cr, 56Fe, 64Ni, and 70Zn projectiles on a 208Pb target at backward angles. The barrier distributions were derived from the first derivative of measured quasielastic scattering cross sections relative to the Rutherford scattering cross section. The centroids of the barrier distributions show a deviation from several predicted barrier heights toward the low energy side. The shape of the barrier distributions is well reproduced by the results of a coupled-channel calculation taking account of the coupling effects of two phonon excitations of the quadrupole vibration for the projectiles and of the octupole vibration for the 208Pb target.     

Inelastic scattering of heavy ions at intermediate energies with excitations of nuclear collective states

Excitation of low-lying nuclear collective states upon scattering of heavy ions with energies of several tens of MeV/nucleon has been studied. The interaction potential leading to excitation is chosen in the form of a derivative of the microscopic (or semimicroscopic) nucleus-nucleus double-folding optical potential. Elastic and inelastic scattering cross sections have been calculated within the high-energy approximation; the inelastic scattering amplitude was obtained in the first order in the deformation parameter. The cross sections are compared with the experimental data on scattering of ¹⁷O from a series of nuclei with excitation of the 2⁺ level.     

Formation of heavy compound nuclei,their survival,and correlation with longtime-scale fission

Fusion of two massive nuclei with formation of a superheavy compound nucleus is driven by the potential energy gradient, as follows from the analysis of nuclear reaction cross sections. The conservative energy of the system is deduced in a simple approximation using regularized nuclear mass and interaction barrier values. Different reactions for the synthesis of Z = 110−118 nuclei are compared and favorable conditions are found for fusion of the stable W-Pt isotopes with radioactive fission fragment projectiles, like ⁹⁴Kr or ¹⁰⁰Sr. Thus, the cold-fusion method can be extended for a synthesis of elements with Z > 113. Survival of the evaporation residue is defined by the neutron-to-fission probability ratio and by the successful emission of gammas at the final step of the reaction. Numerical estimates are presented. Fixation of evaporation residue products must correlate with longtime-scale fission, and available experimental results are discussed. The text was submitted by the authors in English.