Influence of Structural Properties on Fusion Cross-Sections Using Proximity Potentials

The cross sections for capture, ionization, capture from pair production, and free pair production were measured for 0.96-GeV/nucleon U{sup 92+} and 0.405-, 0.96-, and 1.3-GeV/nucleon La{sup 57+} ions incident on Au, Ag, and Cu targets. The cross sections for capture from pair production, free pair production, ionization, and total capture (the sum of capture from pair production, radiative electron capture, and nonradiative capture) are analyzed as a function of collision energy, projectile, and target atomic numbers. We find that, when the collision energy is increased from 0.405 GeV/nucleon to 1.3 GeV/nucleon, the capture from pair production and the free pair production cross sections increase by almost a factor of 6, while the capture cross section decreases by two orders of magnitude. The ionization cross section is found to vary very weakly with the collision energy in the 1-GeV/nucleon energy range. We found a dependence of free pair production cross sections on the target and projectile atomic number to be close to Z{sup 2}, characteristic of an ionizationlike process. We also found a dependence of the capture from pair production cross sections on the target atomic number to be usually steeper than Z{sub t}{sup 2}, and on the projectile atomic number,more » somewhat steeper than the Z{sub p}{sup 5}, characteristic of a capturelike process. Theory and experiment are in some disagreement for capture from pair production, and free pair production, cross sections, but are in general agreement for the other capture processes and for ionization. {copyright} {ital 1997} {ital The American Physical Society}« less

The fusion barriers and cross sections of 15 colliding systems with 320 ≤ Z 1 Z 2 ≤ 1512 are investigated in detail to understand the influence of the universal function of proximity potential formalism in the heavy-ion fusion mechanism. To realize this goal, we select three versions of the phenomenological proximity potentials, including Prox. 77, Zhang 2013, and Guo 2013, to calculate the nucleus–nucleus potential. The experimental fusion cross sections for the selected reactions are analyzed using the standard coupled-channel calculations, including couplings to the low-lying 2+ and 3− states in the target and projectile. The calculated results show that the universal functions of the Guo 2013 and Prox. 77 models provide the lowest and highest fusion barriers, respectively. In addition, it is found that the height of the fusion barriers is enhanced by increasing the mass number of the projectile from light to heavy ones. The highest sensitivity to the mass number of the projectile belongs to the results of Prox. 77. A discussion is also presented on the influence of the universal function on the radial behavior of the interaction potential in the allowed region for overlapping configurations. Our results reveal that the best fit to the experimental data of the fusion cross sections for the reactions involving light and medium nuclei is obtained using the universal function of the Zhang 2013 model. For the heavier systems, the results of the Guo 2013 model at sub-barrier energies provide a good description of the available data.

Effect of deformation and orientation on interaction barrier and fusion cross-sections using various proximity potentials

Absolute $K$-shell ionization cross sections of Sb, Au, and Bi have been measured in collisions with highly charged C, O, and S ions having energies between 2 and $6.25\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕u$. The data are presented along with the earlier results with F and Si ions as projectiles. The measured data have been compared with theoretical models based on the semiclassical approximation including relativistic effect and perturbed stationary state approximation including the corrections for energy loss, Coulomb deflection, and relativistic effects. The data were analyzed in term of relativistic effect on $K$-ionization: its dependence on the projectile atomic number, target atomic number and projectile energy. The present data set along with our recently measured similar data for F and Si ions show that the relativistic effect increases with projectile atomic number and decreases with projectile velocity. A comparison of the experimental data and relativistic calculations, both normalized to nonrelativistic model, show the inadequacy of the theoretical models in describing the relativistic correction on $K$-shell ionization. For example, the theoretical predictions agree with experimental findings for O ions on Bi while the same theoretical predictions deviate from the experimental results by about a factor of 2 for Si and S on Bi, the theory being higher.

The 12C+12C fusion reaction plays a major role in the nucleosynthesis process of the star. However, this reaction takes place at extremely low energies where a direct experimental measurement of the reaction cross sections is almost impossible. Various theoretical developments have been put forward to predict the fusion cross section at such low energies. One of the models is the proximity potential which is well known for its simplicity and numerous applications in different fields. In recent years, several refinements and modifications have been made over the original proximity potential besides several different versions of the same model are also have been proposed. The fusion cross sections of the 12C+12C reaction are calculated and analysed in the present work using different versions of the proximity potential.

Fusion of 6Li with 152Sm: Role of projectile breakup versus target deformation

The present work provides a systematic study on the role of nuclear surface tension in the isotopic dependence of the fusion cross sections at below- and above-barrier energies over wide range of neutron content (0.5 < N/Z < 1.7). To realize our goal, we select three different versions of proximity-based potential, involving proximity potential 1977, 1988, and 2010, in order to calculate the nucleus-nucleus potential and ultimately the fusion barrier parameters. It is shown that the barrier positions, heights, and curvatures follow a (second-order) non-linear isotopic behavior with addition of neutrons which are dependent on the effect of variation in the nuclear surface tension. Our findings reveal that the sensitivity of isotopic dependence of the fusion barrier characteristics to the effect of surface energy coefficients γ increases by increasing the asymmetry of the colliding pair. In addition, we demonstrate the sensitivity toward the coefficient γ is seen more clearly from the more neutron-rich nuclei compared to the neutron-deficient ones. We discuss the isotopic dependence of the fusion cross sections at below- and above-barrier energies within the framework of the Wong model for a single potential barrier. For above-barrier energies, it is shown that the fusion cross sections follow an increasing (second-order) non-linear trend due to the addition of neutrons. While a decreasing (second-order) non-linear trend exists for the variation in the fusion cross sections at below-barrier energies. Simultaneous comparison the results obtained by the 3 versions of proximity potential for the isotopic dependence of fusion cross sections in the mentioned energy regions reveal the importance of the quantum tunneling and also nuclear structure effects.

Half-life time and branching ratio for cluster decay from various xenon isotopes are studied taking Coulomb and proximity potentials as interacting barrier. Inclusion of proximity potential reduces the height of potential barrier, which closely agrees with the experiments. It is found that4He,8Be,12C and16O emissions are well within the present upper limit for measurements (T 1/2 1030 s). Our predicted half-life time values lie close to those values reported by Gupta and collaborators based on preformed cluster model (PCM) and also with those values reported by Poenaruet al based on ASAFM. The calculated half-life time shows that8Be from108Xe and110Xe are most favourable for emission (T 1/2 ≈ 108 s). LowestT 1/2 value for8Be emission from108Xe stress the role of doubly magic100Sn daughter in cluster decay process. The logarithm of half-life time calculated for4He emission from110Xe is −0.39 s which is in good agreement with experimental value which is −0.40 s. Geiger-Nuttall plots for all clusters are studied and are found to be linear. Nuclear structure effect and shell effect are evident from the observed variation in slope and intercept of Geiger—Nuttall plots. It is found that neutron excess in the parent will slow down the cluster decay process.

Fusion reactions in the deuterium cycle (D+D, D+T and D+3He) are the main nucleus-nucleus interactions which occur in tokamaks and stellerators. These reactions are the limiting case between the Woods-Saxon potential field at nuclear distances and the Coulomb electrostatic potential (scattering) at longer distances. In this paper several fusion cross-sections, geometric, Gamow-Sommerfeld and astrophysical S-factors have been reviewed and compared with experimental data from the last ENDF/B-VIII.0 cross-section library. The XDC-fusion code has been developed to calculate fusion cross-sections, geometric, Gamow-Sommerfeld and S-factors of the deuterium-cycle (D-cycle), including resonance parameters (energy and partial width). The software estimates also fusion reaction heat (Q) and Woods-Saxon/Coulomb proximity potentials. Although relative differences between fusion cross-sections are lower than 5 %, S-factors present considerable differences between the energies and partial width (FWHM) of the single-level Breit-Wigner (SLBW) resonances. The energy at which is placed the maximum fusion cross-section is also different between cases. In conclusion, fusion reaction models for light nuclei (deuterium, tritium and helium) should be reviewed in order to apply fusion to energy production in safety conditions.

Multiple-electron transfer to highly charged noble gas ions in single ion-atom collisions

The behavior of projectile electron capture and ionization cross sections at ultrarelativistic energies (g10 GeV/amu) is discussed. Three mechanisms contribute to electron capture at these energies: radiative and nonradiative capture and the capture of the electron following electron-positron pair production. The radiative and nonradiative cross sections both fall off as ${\ensuremath{\gamma}}^{\mathrm{\ensuremath{-}}1}$ at high energies, (\ensuremath{\gamma}-1)${\mathrm{Mc}}^{2}$ being the ion energy. The vacuum capture cross sections increase as the ln\ensuremath{\gamma}. Projectile 1s ionization cross sections also increase as ln\ensuremath{\gamma} at high energies if target screening is negligible. However, when the projectile atomic number is smaller than the target atomic number, the transverse interaction giving the ln\ensuremath{\gamma} term is screened and reduced. Therefore, the total 1s ionization cross sections are dominated by Coulomb ionization, and are nearly constant with increasing projectile energy. Tables of reduced capture and ionization cross sections are given, and are applied to calculating the charge states of ions in matter and the lifetime of ions in storage rings.

Heavy-ion fusion cross sections of weakly bound 9Be on 27Al, 64Zn and tightly bound 16O on 64Zn target using Coulomb and proximity potential

Systematic study of proximity potentials for heavy-ion fusion cross sections

Heavy-ion collisons are typically characterized by the presence of many open reaction channels. In the energies around the Coulomb barrier, the main processes are elastic scattering, inelastic excitations of low-lying modes and fusion operations of one or two nuclei. The fusion process is generally defined as the effect of one-dimensional barrier penetration model, taking scattering potential as the sum of Coulomb and proximity potential. We have performed heay-ion fusion reactions with coupled-channel (CC) calculations. Coupled-channel formalism is carried out under barrier energy in heavy-ion fusion reactions. In this work fusion cross sections have been calculated and analyzed in detail for the five systems 16O + 147,148,150,152,154sm in the framework of coupled-channel approach (using the codes CCFUS and CCDEF) and Wong Formula. Calculated results are compared with experimental data, CC calculations using code CCFULL and with the cross section datas taken from ‘nrv’. CCDEF, CCFULL and Wong Formula explains the fusion reactions of heavy-ions very well, while using the scattering potential as WOODS-SAXON volume potential with Akyuz-Winther parameters. It was observed that AW potential parameters are able to reproduce the experimentally observed fusion cross sections reasonably well for these systems. There is a good agreement between the calculated results with the experimental and nrv[8] results.Heavy-ion collisons are typically characterized by the presence of many open reaction channels. In the energies around the Coulomb barrier, the main processes are elastic scattering, inelastic excitations of low-lying modes and fusion operations of one or two nuclei. The fusion process is generally defined as the effect of one-dimensional barrier penetration model, taking scattering potential as the sum of Coulomb and proximity potential. We have performed heay-ion fusion reactions with coupled-channel (CC) calculations. Coupled-channel formalism is carried out under barrier energy in heavy-ion fusion reactions. In this work fusion cross sections have been calculated and analyzed in detail for the five systems 16O + 147,148,150,152,154sm in the framework of coupled-channel approach (using the codes CCFUS and CCDEF) and Wong Formula. Calculated results are compared with experimental data, CC calculations using code CCFULL and with the cross section datas taken from ‘nrv’. CCDEF, CCFULL and Wong Formula exp...

The fusion cross section of $^{9}$Li + $^{70}$Zn reaction is studiedin an extensive manner within the framework of different theoreticalapproaches. For this purpose, three different methods which consistof proximity potentials, temperature dependent densities andtemperature dependent nuclear potentials are used in order todetermine the real part of the nuclear potential. The imaginary partis considered as Woods-Saxon potential. The calculated fusion crosssections are compared with the experimental data. The theoreticalresults describe the experimental data very well. It is seen thatthe applied approaches present to be different ways to study thereactions involving fusion cross sections.