Angular Distributions Of Evaporation Residues Research Articles

Examination of break-up fusion in the O16+Nd148 system through measurements of forward recoil range distributions and angular distributions

The forward recoil range distributions and angular distributions of several evaporation residues produced via complete and incomplete fusion (ICF) dynamics in $^{16}\mathrm{O}+^{148}\mathrm{Nd}$ system at energy $\ensuremath{\approx}6$ MeV/nucleon were measured. The measured forward recoil range distributions of various reaction products show the presence of incomplete fusion components apart from complete fusion. Full and partial linear momentum transfer components of reaction products were found in the interaction of $^{16}\mathrm{O}$ with $^{148}\mathrm{Nd}$. These results were also confirmed by the measurements of angular distributions of evaporation residues. The measured angular distributions of the evaporation residues populated through complete and incomplete fusion channels were found to be distinctly different. The evaporation residues populated via complete fusion channels were trapped in the narrow angular zone as compared to incomplete fusion channels. A systematic study of the dependence of incomplete fusion dynamics on well-known entrance channel parameters shows that the incomplete fusion fraction grows exponentially with mass asymmetry $({\ensuremath{\mu}}_{EC}^{AS})$, Coulomb factor $({Z}_{P}{Z}_{T})$ and $\ensuremath{\alpha}\ensuremath{-}Q$ value of the projectile. The present observations suggest an exponential rise of ICF fraction with entrance channel parameters in contrast with the linear pattern reported in some earlier measurements. Further, the correlation of incomplete fusion fraction with the structure of target (T) was investigated employing four different parameters viz. deformation parameter $({\ensuremath{\beta}}_{2}^{T})$, interaction radius $({R}^{T})$, deformation length $({\ensuremath{\beta}}_{2}^{T}{R}^{T})$ and excess of neutrons ${(N\ensuremath{-}Z)}^{T}$ in the target. In the present study, the ICF fraction was found to rise exponentially with these parameters, independently for different projectiles. The three parameters ${\ensuremath{\beta}}_{2}^{T}, {\ensuremath{\beta}}_{2}^{T}{R}^{T}$, and ${(N\ensuremath{-}Z)}^{T}$ were found more sensitive and effective to investigate the entire picture about the influence of projectile and target deformation along with their relative orientations on incomplete fusion dynamics at low projectile energy. Moreover, the interaction radius of target $({R}^{T})$ is suitable to explain the characteristics of ICF dynamics in the spherical-spherical collisions. These present results show that incomplete fusion dynamics is strongly affected by the structure of projectile along with the target.

Isotopic effects in sub-barrier fusion of Si + Si systems

Background: Recent measurements of fusion cross sections for the 28Si+28Si system revealed a rather unsystematic behavior ; i.e., they drop faster near the barrier than at lower energies. This was tentatively attributed to the large oblate deformation of 28Si because coupled-channels (CC) calculations largely underestimate the 28Si+28Si cross sections at low energies, unless a weak imaginary potential is applied, probably simulating the deformation. 30Si has no permanent deformation and its low-energy excitations are of a vibrational nature. Previous measurements of this system reached only 4 mb, which is not sufficient to obtain information on effects that should show up at lower energies. Purpose: The aim of the present experiment was twofold: (i) to clarify the underlying fusion dynamics by measuring the symmetric case 30Si+30Si in an energy range from around the Coulomb barrier to deep sub-barrier energies, and (ii) to compare the results with the behavior of 28Si+28Si involving two deformed nuclei. Methods: 30Si beams from the XTU tandem accelerator of the Laboratori Nazionali di Legnaro of the Istituto Nazionale di Fisica Nucleare were used, bombarding thin metallic 30Si targets (50 μg/cm2) enriched to 99.64% in mass 30. An electrostatic beam deflector allowed the detection of fusion evaporation residues (ERs) at very forward angles, and angular distributions of ERs were measured. Results: The excitation function of 30Si+30Si was measured down to the level of a few microbarns. It has a regular shape, at variance with the unusual trend of 28Si+28Si. The extracted logarithmic derivative does not reach the LCS limit at low energies, so that no maximum of the S factor shows up. CC calculations were performed including the low-lying 2+ and 3− excitations. Conclusions: Using a Woods-Saxon potential the experimental cross sections at low energies are overpredicted, and this is a clear sign of hindrance, while the calculations performed with a M3Y + repulsion potential nicely fit the data at low energies, without the need of an imaginary potential. The comparison with the results for 28Si+28Si strengthens the explanation of the oblate shape of 28Si being the reason for the irregular behavior of that system.

Fusion hindrance for the positive Q -value system C12+Si30

Background: The fusion reaction 12C+30Si is a link between heavier cases studied in recent years, and the light heavy-ion systems, e.g., 12C+12C, 16O+16O that have a prominent role in the dynamics of stellar evolution. 12C+30Si fusion itself is not a relevant process for astrophysics, but it is important to establish its behavior below the barrier, where couplings to low-lying collective modes and the hindrance phenomenon may determine the cross sections. The excitation function is presently completely unknown below the barrier for the 12C+30Si reaction, thus no reliable extrapolation into the astrophysical regime for the C+C and O+O cases can be performed. Purpose: Our aim was to carry out a complete measurement of the fusion excitation function of 12C+30Si from well below to above the Coulomb barrier, so as to clear up the consequence of couplings to low-lying states of 30Si, and whether the hindrance effect appears in this relatively light system which has a positive Q value for fusion. This would have consequences for the extrapolated behavior to even lighter systems. Methods: The inverse kinematics was used by sending 30Si beams delivered from the XTU Tandem accelerator of INFN-Laboratori Nazionali di Legnaro onto thin 12C (50μg/cm2) targets enriched to 99.9% in mass 12. The fusion evaporation residues (ER) were detected at very forward angles, following beam separation by means of an electrostatic deflector. Angular distributions of ER were measured at Ebeam=45, 59, and 80 MeV, and they were angle integrated to derive total fusion cross sections. Results: The fusion excitation function of 12C+30Si was measured with high statistical accuracy, covering more than five orders of magnitude down to a lowest cross section ≃3μb. The logarithmic slope and the S factor have been extracted and we have convincing phenomenological evidence of the hindrance effect. These results have been compared with the calculations performed within the model that considers a damping of the coupling strength well inside the Coulomb barrier. Conclusions: The experimental data are consistent with the coupled-channels calculations. A better fit is obtained by using the Yukawa-plus-exponential potential and a damping of the coupling strengths inside the barrier. The degree of hindrance is much smaller than the one in heavier systems. Also a phenomenological estimate reproduces quite closely the hindrance threshold for 12C+30Si, so that an extrapolation to the C+C and O+O cases can be reliably performed.

Fusion ofSi28+Si28,30: Different trends at sub-barrier energies

Background: The fusion excitation function of the system $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$ at energies near and below the Coulomb barrier is known only down to $\ensuremath{\simeq}15$ mb. This precludes any information on both coupling effects on sub-barrier cross sections and the possible appearance of hindrance. For $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{30}\mathrm{Si}$ even if the fusion cross section is measured down to $\ensuremath{\simeq}50$ $\ensuremath{\mu}\mathrm{b}$, the evidence of hindrance is marginal. Both systems have positive fusion $Q$ values. While $^{28}\mathrm{Si}$ has a deformed oblate shape, $^{30}\mathrm{Si}$ is spherical.Purpose: We investigate 1. the possible influence of the different structure of the two Si isotopes on the fusion excitation functions in the deep sub-barrier region and 2. whether hindrance exists in the $\text{Si}\phantom{\rule{4.pt}{0ex}}+\phantom{\rule{4.pt}{0ex}}\text{Si}$ systems and whether it is strong enough to generate an $S$-factor maximum, thus allowing a comparison with lighter heavy-ion systems of astrophysical interest.Methods: $^{28}\mathrm{Si}$ beams from the XTU Tandem accelerator of the INFN Laboratori Nazionali di Legnaro were used. The setup was based on an electrostatic beam separator, and fusion evaporation residues (ER) were detected at very forward angles. Angular distributions of ER were measured.Results: Fusion cross sections of $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$ have been obtained down to $\ensuremath{\simeq}600$ nb. The slope of the excitation function has a clear irregularity below the barrier, but no indication of a $S$-factor maximum is found. For $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{30}\mathrm{Si}$ the previous data have been confirmed and two smaller cross sections have been measured down to $\ensuremath{\simeq}4$ $\ensuremath{\mu}\mathrm{b}$. The trend of the $S$-factor reinforces the previous weak evidence of hindrance.Conclusions: The sub-barrier cross sections for $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$ are overestimated by coupled-channels calculations based on a standard Woods-Saxon potential, except for the lowest energies. Calculations using the M3Y+repulsion potential are adjusted to fit the $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$ and the existing $^{30}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{30}\mathrm{Si}$ data. An additional weak imaginary potential (probably simulating the effect of the oblate $^{28}\mathrm{Si}$ deformation) is required to fit the low-energy trend of $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$. The parameters of these calculations are applied to predict the ion-ion potential for $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{30}\mathrm{Si}$. Its cross sections are well reproduced by also including one- and successive two-neutron transfer channels, besides the low-lying surface excitations.

Determination of the angular distribution of evaporation residues following transmission through the superconducting solenoidal separator SOLITAIRE

A highly efficient superconducting solenoidal fusion product separator has been developed at the Australian National University in order to enable separation and detection of evaporation residues following heavy-ion collisions. The determination of absolute fusion cross-sections requires an accurate knowledge of the transmission efficiency of evaporation residues through the superconducting solenoid, which in turn depends on the angular distribution of evaporation residues exiting the target. Two methods have been developed to extract the angular distributions using the radial distribution and the velocity distribution of the evaporation residues exiting the solenoid. The angular distributions are compared with existing direct measurements of evaporation residue angular distributions.

Channel coupling effects on the fusion excitation functions forSi28+Zr90,94in sub- and near-barrier regions

Fusion excitation functions and angular distributions of evaporation residues (ERs) have been measured for $^{28}\mathrm{Si}+^{90,94}\mathrm{Zr}$ systems around the Coulomb barrier using the recoil mass spectrometer, Heavy Ion Reaction Analyzer (HIRA). For both systems, the experimental fusion cross sections are strongly enhanced compared to the predictions of the one-dimensional barrier penetration model (1-d BPM) below the barrier. Coupled channels formalism has been employed to theoretically explain the observed sub-barrier fusion cross section enhancement. The enhancement could be explained by considering the coupling of the low-lying inelastic states of the projectile and target in the $^{28}\mathrm{Si}+^{90}\mathrm{Zr}$ system. In the sub-barrier region, the measured fusion cross sections for $^{28}\mathrm{Si}+^{94}\mathrm{Zr}$ turned out to be about an order of magnitude higher than the ones for the $^{28}\mathrm{Si}+^{90}\mathrm{Zr}$ system, which could not be explained by coupling to inelastic states alone. This observation indicates the importance of multinucleon transfer reaction channels with positive $Q$ values in the sub-barrier fusion cross section enhancement, because $^{90,94}\mathrm{Zr}$ are believed to have similar collective strengths. This implies that no strong isotopic dependence of fusion cross sections is expected as far as the couplings to collective inelastic states are concerned. In addition, the role of projectile and multiphonon couplings in the enhancement has been explored.

Temperature andn−pasymmetry dependencies of the level-density parameter in Ni+Mo fusion reactions

Properties of evaporation residues and the accompanying light particles have been measured in ${}^{60}\mathrm{Ni}{+}^{92,100}\mathrm{Mo}$ fusion reactions at bombarding energies from $E/A=5$ to 9 MeV. The data indicate that these reactions are essentially complete-fusion reactions with only a small amount of nonequilibrium emission at the highest bombarding energy studied. The measured kinetic-energy spectra of evaporated n, p, d, t, ${}^{3}\mathrm{He},$ and $\ensuremath{\alpha}$ particles are compared to statistical-model predictions. It is found that a constant excitation-energy independent level-density parameter is not able to reproduce these spectra over the compound-nucleus excitation-energy range from 90 to 250 MeV. The kinetic-energy spectra for all particles were fit using the level-density parametrization $a=A/(7+1.3\ifmmode\times\else\texttimes\fi{}U/A){\mathrm{MeV}}^{\ensuremath{-}1},$ where U is the thermal excitation energy. The Coulomb barriers for charged-particle emission were reduced from the standard values to reproduce the peak energy and multiplicity for $\ensuremath{\alpha}$ particles. Using these ingredients, the measured mass, velocity, and angular distributions of evaporation residues are also reproduced. The average Z and N of the evaporation residues deduced from the light-particle multiplicities are in agreement with the predicted location of the evaporation attractor line. A neutron-proton asymmetry dependence of the level-density parameter is shown to have potentially important consequences for the neutron or proton richness of the evaporation residues. However, no evidence for such an effect is found in the measured data; and from the experimental multiplicity ratio of ${t/}^{3}\mathrm{He}$ it was deduced that any such dependence in the excitation-energy regime $100<{E}^{*}<250\mathrm{MeV}$ is very small.

Investigation of the level density parameter using evaporativeα-particle spectra from the19F+181Tareaction

Light charged particles in coincidence with evaporation residues from the ${}^{19}\mathrm{F}{+}^{181}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{Ta}}}^{200}\mathrm{Pb}$ reaction have been studied at ${E}_{\mathrm{lab}}=121,$ 154, 179, and 195 MeV with the aim of determining, within the context of the statistical model, a possible dependence of the Fermi-gas level density parameter on the temperature/excitation energy of the emitting system. Angular distributions of evaporation residues and of fission fragments, along with fission fragment folding angle distributions, were also measured. A moderate excitation energy dependence of the level density parameter, as given by recent theoretical calculations, is consistent with the measured $\ensuremath{\alpha}$-particle spectral shapes. Although the spectra are reproduced best with a weakly varying level density parameter, a constant level density parameter of a=A/12 ${\mathrm{MeV}}^{\ensuremath{-}1}$ cannot be excluded.

Velocity spectra and angular distributions of evaporation residues from 32S +12C at 145 MeV.

Velocity spectra and angular and mass distributions for the evaporation residues of the $^{32}\mathrm{S}$${+}^{12}$C system at ${\mathit{E}}^{32}$S=145 MeV in the angular range 3\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}${\mathrm{\ensuremath{\vartheta}}}_{\mathit{L}}$\ensuremath{\le}12\ifmmode^\circ\else\textdegree\fi{} have been measured. In order to separate compound nucleus evaporation residues from other heavy reaction products, a kinematic analysis based on simple statistical assumptions relative to the velocity spectra was performed. The structures in the mass distribution are compared with the lilita code predictions. The fusion excitation function of the existing results is compared with theoretical models. The total reaction cross section has been extracted by means of the modified sum of differences method.

Velocity and angular distributions of evaporation residues from 32S-induced reactions.

Velocity distributions of mass-resolved evaporation residues from reactions of $^{32}\mathrm{S}$ with $^{12}\mathrm{C}$, $^{24}\mathrm{Mg}$, $^{27}\mathrm{Al}$, $^{28}\mathrm{Si}$, and $^{40}\mathrm{Ca}$ have been measured at bombarding energies of 194, 239, and 278 MeV using time-of-flight techniques. In all cases, the observed shifts in the velocity centroids relative to the values expected for complete fusion are consistent with a previously reported parametrization of a threshold for onset of incomplete fusion. Angular distributions were measured and total cross sections extracted for the $^{32}\mathrm{Mg}$ system at all three energies. A comparison with existing results for $^{32}\mathrm{Mg}$ at lower energies, and with other systems leading to the $^{56}\mathrm{Ni}$ compound nucleus, suggests two different types of compound-nuclear limitations to complete fusion at higher energies.

Velocity and angular distributions of evaporation residues from induced32 reactions

Velocity and angular distributions of evaporation residues from induced32 reactions

Fusion and Peripheral reactions ofC12+N14at energies up to 13 MeV/A

Angular and energy distributions have been measured for reaction products of the $^{14}\mathrm{N}$ + $^{12}\mathrm{C}$ system at nine bombarding energies in the energy range ${E}_{^{14}\mathrm{N}}=34.1 \mathrm{to} 178.1$ MeV. The fusion and direct reaction components for products from Li to Al have been determined. The experimental fusion cross sections and deduced critical angular momenta are discussed in terms of entrance channel models for compound nucleus formation and the rotating liquid drop model. Hauser-Feshbach calculations of the $Z$ distributions, energies, and angular distributions of evaporation residues are presented and compared to the data. The direct reaction yield has been analyzed with a diffraction model and is also compared with time-dependent Hartree-Fock calculations. The experimental total reaction cross section is in good agreement with optical model calculations.NUCLEAR REACTIONS $^{14}\mathrm{N}$ + $^{12}\mathrm{C}$, ${E}_{^{14}\mathrm{N}}=34.1 \mathrm{to} 178.1$ MeV, measured $\frac{{d}^{2}\ensuremath{\sigma}}{d\ensuremath{\Omega}\mathrm{dE}}$ for reaction products from $Z=3 \mathrm{to} 13$. Extracted ${\ensuremath{\sigma}}_{\mathrm{fusion}}$, ${\ensuremath{\sigma}}_{\mathrm{direct}}$, and ${\ensuremath{\sigma}}_{\mathrm{total}}$.

Mass, velocity, angular and charge-state distributions from the fusion ofS32andSn112

Evaporation residues from the fusion of $^{32}\mathrm{S}$ and $^{112}\mathrm{Sn}$ at ${E}_{^{32}\mathrm{S}}=160$ MeV were studied using an energy-mass spectrometer. The velocity selector of the energy-mass spectrometer was first utilized to measure summed fusion products as a function of velocity setting and reaction angle. In-flight mass separation of the fusion products with the energy-mass spectrometer identified masses 141, 140, and 139 from the evaporation of three to five nucleons from the $^{144}\mathrm{Dy}$ compound nucleus. Absolute cross-section measurements are compared to theoretical predictions of the statistical evaporation model. Velocity, angular and charge state distributions of evaporation residues are also compared to calculated values.NUCLEAR REACTIONS $^{32}\mathrm{S}$ + $^{112}\mathrm{Sn}$ fusion, $E=160$ MeV, $\ensuremath{\sigma}(v, \ensuremath{\theta})$. Compared mass, velocity and angular distributions of evaporation residues to statistical particle evaporation theory. Compared charge-state distribution of fusion products to semiempirical predictions.

Determination ofΓnΓfat 12 to 20 MeV Excitation from Evaporation-Residue Cross Sections

Angular distributions of evaporation residues from the (/sup 7/Li, ..cap alpha..) reaction on /sup 197/Au, /sup 232/Th, and /sup 236/U have been measured as a function of excitation energy in the compound nuclei /sup 200/Hg, /sup 235/Pa, and /sup 239/Np. Evaporation-residue probabilities P/sub ER/ = sigma (/sup 7/Li,..cap alpha..xn)/sigma (/sup 7/Li, ..cap alpha..) are obtained. These give the first microscopic information on GAMMA/sub n//GAMMA/sub f/ at 12 to 20 MeV excitation, which is independent of the compound-nucleus formation cross section. The results are compared with expectations based on previous systematic values of GAMMA/sub n//GAMMA/sub f/.