Mean-square Angular Momentum Research Articles

Study of isotopic chain capture

Isotopic dependences of the capture cross section and the mean and mean-square angular momenta of a captured system in the 16O, 48Ca + 196,200,204,208Pb and 16O + 152,154Sm reactions are investigated using the quantum diffusion approach. The obtained results are in good agreement with the existing experimental data.

Study of Isotopic Effects in Capture Process

Recently, many experimental and theoretical efforts have been devoted to the investigation of fusion, fission, and capture processes at sub-barrier energies [1–4]. Measurements of excitation functions down to the extreme sub-barrier energies are important for studying the long range behavior of the nucleus–nucleus interaction. The experimental data obtained are also of interest for solving astrophysical problems related to nuclear synthesis. The main objective of the present work is to study the isotopic dependencies of the capture cross section and the mean-square angular momentum in the reactions 48Ca + 144,150,154Sm and 40Ca + 154Sm. The quantum diffusion approach [3, 4] is employed. The collisions of nuclei are treated in terms of a single dynamic collective coordinate, the relative distance between the colliding nuclei. Our approach takes into consideration the fluctuation and dissipation effects in collisions of heavy ions that model the coupling with various channels [3, 4]. The deformation and neutron transfer effects are taken into account through the dependence of the nucleus–nucleus potential on the deformations and orientations of interacting deformed nuclei.

Isotopic trends of capture cross section and mean-square angular momentum of the captured system

Within the quantum diffusion approach, the isotopic dependencies of capture cross section and mean-square angular momentum are studied in the reactions ${}^{4}$He, ${}^{16}$O, ${}^{36}$S, ${}^{48}$Ca $+$ ${}^{196,200,204,208}$Pb and ${}^{16}$O $+$ ${}^{70,72,74,76}$Ge. The results are in a reasonable agreement with existing experimental data.

Sub-barrier capture with quantum diffusion approach: Actinide-based reactions

With the quantum diffusion approach the behavior of capture cross sections and mean-square angular momenta of captured systems are revealed in the reactions with deformed nuclei at subbarrier energies. The calculated results are in a good agreement with existing experimental data. With decreasing bombarding energy under the barrier the external turning point of the nucleusnucleus potential leaves the region of short-range nuclear interaction and action of friction. Because of this change of the regime of interaction, an unexpected enhancement of the capture cross section is expected at bombarding energies far below the Coulomb barrier. This effect is shown its worth in the dependence of mean-square angular momentum of captured system on the bombarding energy. From the comparison of calculated and experimental capture cross sections, the importance of quasifission near the entrance channel is shown for the actinide-based reactions leading to superheavy nuclei.

Peculiarities of sub-barrier reactions with heavy ions

With the quantum diffusion approach the behavior of capture cross sections and mean-square angular momenta of captured systems are revealed in the reactions with deformed and spherical nuclei at sub-barrier energies. The calculated results are in a good agreement with existing experimental data. With decreasing bombarding energy under the barrier the external turning point of the nucleus-nucleus potential leaves the region of short-range nuclear interaction and action of friction. Because of this change of the regime of interaction, an unexpected enhancement of the capture cross section is expected at bombarding energies far below the Coulomb barrier. This effect is shown its worth in the dependence of mean-square angular momentum of captured system on the bombarding energy. From the comparison of calculated capture cross sections and experimental capture (fusion) cross sections, the importance of quasifission near the entrance channel is shown for the actinide-based reactions and reactions with medium-heavy nuclei at sub-barrier energies.

Sub-barrier capture with quantum diffusion approach

With the quantum diffusion approach the behavior of capture cross sections and mean-square angular momenta of captured systems are revealed in the reactions with deformed and spherical nuclei at sub-barrier energies. With decreasing bombarding energy under the barrier the external turning point of the nucleus-nucleus potential leaves the region of short-range nuclear interaction and action of friction. Because of this change of the regime of interaction, an unexpected enhancement of the capture cross section is found at bombarding energies far below the Coulomb barrier. This effect is shown its worth in the dependence of mean-square angular momentum on the bombarding energy. From the comparison of calculated capture cross sections and experimental capture or fusion cross sections the importance of quasifission near the entrance channel is demonstrated for the actinidebased reactions and reactions with medium-heavy nuclei at extreme sub-barrier energies.

Preequilibrium fission for low angular momentum

We have compared the fragment anisotropies of 11B + 237Np and 16O + 232Th which both populate the same fissioning system 248Cf. The data clearly show the evidence of the entrance-channel dependence of fission-fragment anisotropies. A new version of the preequilibrium fission model is put forward. In the framework of this model, the discrepancy between the experimental mean-square angular momentum 〈 J 2〉 exp. and the prediction of the coupled-channels model, 〈 J 2〉 theory is reasonably removed.

Signature of non-compound-nucleus fission at sub-barrier energies.

We have extracted the experimental ${\mathit{J}}_{\mathrm{eff}}$ values from fission fragment angular distributions for the systems of $^{16}\mathrm{O}$${+}^{232}$Th, $^{19}\mathrm{F}$${+}^{232}$Th, and $^{16}\mathrm{O}$${+}^{238}$U at near- and sub-barrier energies. The ${\mathit{J}}_{0}$/${\mathit{J}}_{\mathrm{eff}}$ values for the cases of the above reactions and the heavy-ion reactions with projectiles heavier than A=24 show same systematic trend when plotted as a function of mean-square angular momentum of the fissioning nucleus. This observation leads us to the conjecture that the systematic trend of ${\mathit{J}}_{0}$/${\mathit{J}}_{\mathrm{eff}}$ bears the signature of non-compound-nucleus fission for the heavy-ion reactions with lighter projectiles at near- and sub-barrier energies.

Angular-Momentum Distributions of Residual Nuclei in Compound-Nuclear Reactions

A classical vector model is used to determine the changes which occur in the distribution functions for the angular momentum of nuclei when particles and photons are evaporated from these nuclei. Closed-form expressions are derived for angular-momentum distributions after a sequence of evaporations. It is found that at higher excitations one must expect the average angular momentum of a nucleus to decrease by a relatively small amount per evaporation. The mean-square angular momentum will increase or decrease depending on the ratio of the nuclear angular momentum to the equipartition value appropriate to the nuclear excitation. General expressions are given for the angular distributions of the evaporations. Some of the difficulties of applying statistical models to emissions at low excitation energies are briefly discussed.

Fragment Anisotropies in Neutron-, Deuteron-, and Alpha-Particle-Induced Fission

Fragment anisotropies have been measured from fission of several compound nuclei each formed by two different projectile-target combinations: ${\mathrm{U}}^{234}$ by $n$+${\mathrm{U}}^{233}$ and $\ensuremath{\alpha}$+${\mathrm{Th}}^{230}$, ${\mathrm{U}}^{236}$ by $n$+${\mathrm{U}}^{235}$ and $\ensuremath{\alpha}$+${\mathrm{Th}}^{232}$, ${\mathrm{Np}}^{238}$ by $n$+${\mathrm{Np}}^{237}$ and $d$+${\mathrm{U}}^{236}$, ${\mathrm{Pu}}^{239}$ by $d$+${\mathrm{Np}}^{237}$ and $\ensuremath{\alpha}$+${\mathrm{U}}^{235}$, and ${\mathrm{Pu}}^{240}$ by $n$+${\mathrm{Pu}}^{239}$ and $\ensuremath{\alpha}$+${\mathrm{U}}^{236}$. These measurements extended over an energy range of approximately 12- to 25-MeV excitation energy of the compound nucleus. Transmission coefficients were calculated to estimate the mean-square orbital angular momentum ${〈{l}^{2}〉}_{\mathrm{av}}$ of the fissioning nuclei required for the theory of fragment angular distributions. At the higher energies attained in the present experiment, uncertainties in ${〈{l}^{2}〉}_{\mathrm{av}}$ introduced by Coulomb-barrier penetration effects were small, and it was therefore possible to make comparisons between measurements and theory which indicate that the distortion of the compound nucleus at the saddle-point configuration before fission is independent of the total angular momentum and the identity of the bombarding particle. At the lower energies, where the Coulomb parameter $\ensuremath{\eta}=\frac{{Z}_{1}{Z}_{2}{e}^{2}}{\ensuremath{\hbar}v}$ is roughly 15, this comparison has shown that calculations of transmission coefficients for alpha particles give values of ${〈{l}^{2}〉}_{\mathrm{av}}$ in agreement with the data only if careful attention is given to the effects of barrier penetration. At the lowest energies, comparisons of data from ${\mathrm{U}}^{236}$ and ${\mathrm{Pu}}^{240}$ indicate that the effect of target spin on fission anisotropy is small. Additional angular distributions from neutroninduced fission of ${\mathrm{Th}}^{232}$, ${\mathrm{U}}^{233,\phantom{\rule{0ex}{0ex}}234,\phantom{\rule{0ex}{0ex}}235,\phantom{\rule{0ex}{0ex}}236,\phantom{\rule{0ex}{0ex}}238}$, ${\mathrm{Np}}^{237}$, and ${\mathrm{Pu}}^{239}$ and anisotropies of alpha-particle-induced fission of ${\mathrm{U}}^{233,\phantom{\rule{0ex}{0ex}}235,\phantom{\rule{0ex}{0ex}}238}$ are also reported.