Nuclear structure dependence of fusion hindrance in heavy element synthesis

The production of the heaviest elements in fusion-evaporation reactions is substantially limited by very low cross sections, as fusion cross sections (including fusion-fission) are greatly reduced by the competing quasifission mechanism. Using the Australian National University Heavy Ion Accelerator Facility and CUBE detector array, fission fragments from the ${}^{48}\mathrm{Ti}+{}^{204,208}\mathrm{Pb}$ and ${}^{50}\mathrm{Ti}+{}^{206,208}\mathrm{Pb}$ reactions have been measured, with the aim to investigate how the competition between quasifission and fusion-fission evolves with small changes in entrance-channel properties associated mainly with the nuclear structure. Analysis of mass-distribution widths of strongly mass-angle-correlated fission fragments within the framework of the compound-nucleus fission theory demonstrates significant differences in quasifission (and therefore fusion) probabilities among the four reactions. The impact of nuclear structure on fusion highlights the importance of future radioactive beams.

Figure 1

Measured distributions of mass ratios ($M_R$) and scattering angles in the center of mass (${\theta }_{\mathrm{c}.\mathrm{m}.}$) for the reactions ${}^{50}\mathrm{Ti}+{}^{206,208}\mathrm{Pb}$ and ${}^{48}\mathrm{Ti}+{}^{204,208}\mathrm{Pb}$. The distributions are labeled by the center-of-mass energy ($E_{\mathrm{c}.\mathrm{m}.}$, MeV), its ratio to interaction barrier ($E_{\mathrm{c}.\mathrm{m}.}/V_B$), and the excitation energy ($E^{*}=E_{\mathrm{c}.\mathrm{m}.}-Q$, MeV). The color palettes were chosen to highlight the region of fission fragments and its numerical levels corresponding to values of double differential cross sections are the same for plots shown by the horizontal axis and are given. Regions marked by dashed lines indicate an appearance of presumably-deep-inelastic reaction products.

Figure 2

Mass-ratio distributions of fragments within the range ${\theta }_{\mathrm{c}.\mathrm{m}.}={21}^{\circ }–{159}^{\circ }$. ${}^{50}\mathrm{Ti}$- and ${}^{48}\mathrm{Ti}$-induced reactions are marked by lined and shaded-lined histograms, respectively. Differential cross sections ($d\sigma /d{M}_R$) are normalized by total cross sections integrated over $M_R=0.35–0.65$ (marked by dashed lines) where fission is dominant. Excitation energies of the corresponding CN in MeV, ${\mathrm{E}}_{\mathrm{c}.\mathrm{m}.}/V_B$ and root-mean-square deviations (${\sigma }_{\mathrm{MR}}$) within $M_R=0.35–0.65$ are given.

Figure 3

(a) Calculated mean-squared angular momenta ($\langle J^2\rangle$, lines) and (b) experimental (symbols) and calculated (lines) widths for $\text{S}+\text{Pb}$ reactions. These data for $\text{S}+\text{Pb}$ were taken from Ref. [27]. (c) Calculated mean-squared angular momenta ($\langle J^2\rangle$) and (d) calculated widths for $\text{Ti}+\text{Pb}$ reactions. Legends of symbols and lines are given in panels (a)–(d). Experimental and simulated $M_R$ distributions of (e) the ${}^{34}\mathrm{S}+{}^{208}\mathrm{Pb}$ reaction at $E^{*}=52.2$ and (f) the ${}^{50}\mathrm{Ti}+{}^{208}\mathrm{Pb}$ reaction at $E^{*}=55.1\mathrm{MeV}$. The experimental ${\sigma }_{\mathrm{MR}}\left(\text{expt}\right)$ within the appropriate range of $M_R$ (shaded region) and the calculated widths ${\sigma }_{\mathrm{MR}}\left(\text{calc}\right)$ within the $M_R=0.25–0.75$ are given in both panels (e) and (f). rms-deviation of the simulated $M_R$ distribution within the $M_R=0.35–0.65$ (shaded region) is given in panel (f). See text for detail.

Figure 4

(a) Calculated and (b) measured rms widths $[{\sigma }_{\mathrm{MR}}\left(\text{calc}\right)$ and ${\sigma }_{\mathrm{MR}}\left(\text{expt}\right)]$ of the mass-ratio spectra between $M_R=0.35$ and 0.65. (c) The ratio of calculated and experimental rms widths, ${\sigma }_{\mathrm{MR}}\left(\text{expt}\right)/{\sigma }_{\mathrm{MR}}\left(\text{calc}\right)$. Legends of symbols and selected $M_R$ range and ${\theta }_{\mathrm{c}.\mathrm{m}.}$ for rms widths are given.