Mechanisms Suppressing Superheavy Element Yields in Cold Fusion Reactions

Superheavy elements are formed in fusion reactions which are hindered by fast nonequilibrium processes. To quantify these, mass-angle distributions and cross sections have been measured, at beam energies from below-barrier to 25% above, for the reactions of ${}^{48}\mathrm{Ca}$, ${}^{50}\mathrm{Ti}$, and ${}^{54}\mathrm{Cr}$ with ${}^{208}\mathrm{Pb}$. Moving from ${}^{48}\mathrm{Ca}$ to ${}^{54}\mathrm{Cr}$ leads to a drastic fall in the symmetric fission yield, which is reflected in the measured mass-angle distribution by the presence of competing fast nonequilibrium deep inelastic and quasifission processes. These are responsible for reduction of the compound nucleus formation probablity $P_{CN}$ (as measured by the symmetric-peaked fission cross section), by a factor of 2.5 for ${}^{50}\mathrm{Ti}$ and 15 for ${}^{54}\mathrm{Cr}$ in comparison to ${}^{48}\mathrm{Ca}$. The energy dependence of $P_{\mathrm{CN}}$ indicates that cold fusion reactions (involving ${}^{208}\mathrm{Pb}$) are not driven by a diffusion process.

Figure 1

Mass angle distributions (MADs) and (below) projected mass ratio spectra within the red dashed gate in (a), for ${}^{48}\mathrm{Ca}$, ${}^{50}\mathrm{Ti}$, and ${}^{54}\mathrm{Cr}$ reactions with ${}^{208}\mathrm{Pb}$ at the values of $E/V_B$ indicated. The experimental cross sections have been multiplied by the factor given for each measurement in the projection panel for clarity in presenting the results. Blue curves are quasifission background (see text). ${}^{54}\mathrm{Cr}+{}^{204}\mathrm{Pb}$ data at $E/V_B$ 1.08 are shown by red symbols in (p).

Figure 2

Measured fissionlike cross sections (filled symbols) as a function of center-of-mass energy $E$, together with previous data (open symbols) [20, 38, 40, 41, 42]. Coupled channels calculations are shown by full lines. Dashed lines show these calculations scaled by the factor indicated.

Figure 3

Measured TKE as a function of mass ratio for ${}^{48}\mathrm{Ca}$, ${}^{50}\mathrm{Ti}$, and ${}^{54}\mathrm{Cr}$ at energies $E/V_B\sim 1.07$. The spectra are normalized by the indicated factor to give the same integrated counts. The angle cut ${\theta }_{\mathrm{c}.\mathrm{m}.}>135°$ results in the elastic scattering yields (elastic energies are indicated by the arrows) being small. The curves indicate the energies for fully damped events (see text). Typical regions for DIC, QF, and FF are marked.

Figure 4

Ratio of the symmetric-peaked fission yield (after subtraction of a quasifission background) to the capture cross sections, representing upper limits to $P_{\mathrm{CN}}$ (see text). Error bars include estimated background uncertainties [31]. Predictions of $P_{\mathrm{CN}}$ from Ref. [19], based on a diffusion model of fusion for reactions with ${}^{208}\mathrm{Pb}$, are also indicated with lines. Values of $P_{\mathrm{CN}}$ from [20] for ${}^{50}\mathrm{Ti}+{}^{208}\mathrm{Pb}$ are also shown.