Microscopic study of deformation and orientation effects in heavy-ion reactions above the Coulomb barrier using the Boltzmann-Uehling-Uhlenbeck model

Background: The understanding of the impact of initial deformation and collision orientation on quasifission and fusion-fission reactions remains incomplete.

Purpose: This paper aims to explore how the orientation of deformed nuclei influences quasifission and fusion-fission reactions around $1.2V_B$, employing a microdynamical method in systems with diverse shapes, namely ${}^{24}\mathrm{Mg}+{}^{178}\mathrm{Hf}, {}^{34}\mathrm{S}+{}^{168}\mathrm{Er}$, and ${}^{48}\mathrm{Ti}+{}^{154}\mathrm{Sm}$.

Method: Utilizing the Boltzmann-Uehling-Uhlenbeck model, this paper investigates quasifission and fusion-fission reactions. The model elucidates microdynamic processes and microscopic observables through the definition of the window and event-by-event simulations.

Results: The findings reveal that the orientation of deformed nuclei significantly influences the nucleus-nucleus interaction potential, thereby impacting the competition between quasifission and fusion-fission reactions. Particularly, the orientation of the deformed target nucleus emerges as the primary factor affecting this competition. Notably, a higher proportion of fusion-fission events is observed when the target nucleus is in the belly orientation compared to the tip orientation. The paper also observes that the configuration of the dinuclear system contributes to fluctuations and dissipation. Collisions with different orientations result in distinct dinuclear system configurations, with belly-oriented collisions leading to larger fluctuations between events, while tip-oriented collisions exhibit smaller fluctuations.

Conclusions: Considering diverse orientations of nuclei with distinct initial deformations, this paper concludes that the orientation of the target nucleus is the key factor influencing quasifission and fusion-fission reactions around $1.2V_B$.

Figure 1

(a) The setting of coordinate axes during the dynamical evolution of the dinuclear system involved. (b) The variation of the $I(\theta ,t)$ value as a function of the cosine value of the rotation angle of the coordinate axes. (c) The linear density distribution along the collision principal inertia axis.

Figure 2

The time range computed for the BUU model and gemini$++$ model.

Figure 3

The initial shape of nuclei for the three collision systems. The ${}^{34}\mathrm{S}$ nucleus is oblate. The ${}^{48}\mathrm{Ti}$ nucleus is spherical, while other nuclei are all prolate.

Figure 4

Mass distributions of BUU $+$ gemini$++$ calculations (QF $+$ FF) of model (red line) and experimental data (circles) for (a) ${}^{24}\mathrm{Mg}+{}^{178}\mathrm{Hf}$, (b) ${}^{34}\mathrm{S}+{}^{168}\mathrm{Er}$, and (c) ${}^{48}\mathrm{Ti}+{}^{154}\mathrm{Sm}$ at around $1.2V_B$. The incident energy ($E_{\mathrm{lab}}$) and the excitation energy of ${}^{202}\mathrm{Po}$ (the compound nucleus synthesized from the three systems) for each system are indicated. The experimental data and $E_{\mathrm{lab}}$ are from [42], and the BUU model calculates the excitation energy. The $x$ axis corresponds to the mass ratio $M_R=\frac{m}{m1+m2}$, where $\mathit{m}$ denotes the fragment mass number, and $m_1$ and $m_2$ represent the mass numbers of the projectile and target nuclei.

Figure 5

The dynamic and static nucleus-nucleus (NN) interaction curves for the ${}^{48}\mathrm{Ti}+{}^{154}\mathrm{Sm}$ system, where the dynamic NN interactions calculation is the average result of simulating 30 events at an incident energy of $E_{\mathrm{lab}}=235$ MeV. The calculations in the figure are performed for central collisions. $V$ represents the NN interaction, and $R$ represents the center-of-mass distance between the two nuclei. The solid red lines represent the static NN interaction for the target nuclei in the belly orientation, while the solid red circle-dotted lines represent the dynamic one for the target in belly orientation. The dashed black lines represent the static curve for the target in tip orientation, and the solid red square-dotted lines represent the dynamic curve for the target in tip orientation.

Figure 6

The proportion of quasifission (QF) reaction and fusion-fission (FF) reaction for ${}^{24}\mathrm{Mg}+{}^{178}\mathrm{Hf}, {}^{34}\mathrm{S}+{}^{168}\mathrm{Er}$, and ${}^{48}\mathrm{Ti}+{}^{154}\mathrm{Sm}$ systems in central collision at near Coulomb barrier energy. The initial deformation and orientation for projectile and target nuclei are indicated.

Figure 7

Mass distributions of quasifission (QF) fragments in (a) ${}^{24}\mathrm{Mg}+{}^{178}\mathrm{Hf}$, (b) ${}^{34}\mathrm{S}+{}^{168}\mathrm{Er}$, and (c) ${}^{48}\mathrm{Ti}+{}^{154}\mathrm{Sm}$ in central collisions at the near-Coulomb barrier with different orientations.

Figure 8

The relationship between the center-of-mass distance $R_{12}$ of two nuclei and the linear density ${\rho }_L$ at the window for sph.-tip collisions (black hollow circles) and sph.-belly collisions (red solid circles) in the ${}^{48}\mathrm{Ti}+{}^{154}\mathrm{Sm}$ system at $E_{\mathrm{lab}}=235$ MeV as a function of reaction evolution time.

Figure 9

The mass-angle distributions of quasifission (QF) fragments for central collisions in different orientations of the ${}^{34}\mathrm{S}+{}^{168}\mathrm{Er}$ system at $E_{\mathrm{lab}}=174$ MeV.

Figure 10

The the spatial distribution of the ${}^{34}\mathrm{S}+{}^{168}\mathrm{Er}$ system at different reaction times and orientations in central collisions with an incident energy of $E_{\mathrm{lab}}=174$ MeV.