Mass, total kinetic energy, and neutron multiplicity correlations in the binary fragmentation of ${}^{50}\text{Ti}+{}^{208}\text{Pb}$ at 294 MeV bombarding energy

The correlations between mass distributions of the binary fragments, total kinetic energy (TKE), and neutron multiplicity have been investigated for the reaction ${}^{50}\text{Ti}+{}^{208}\text{Pb}$ at 294 MeV bombarding energy. Although this reaction has been used to synthesize the Rf ($Z=104$) superheavy element, a complete study of its fragmentation dynamics is still not available in the literature. In this work, average neutron multiplicities were extracted as a function of different fragment mass splits and TKE windows. A weak increase of the prescission neutron multiplicity is observed going from asymmetric to symmetric mass splits. A fission delay time of $4.5\times {10}^{-20}$ s has been extracted for the symmetric fission. The neutron multiplicity extracted for the symmetric mass split was used to derive the average number of neutrons emitted in the spontaneous fission of ${}^{258}\text{Rf}$. The extrapolated value of $4.7\pm 1.4$ is found to be consistent with systematics of spontaneous and neutron-induced fission in heavy nuclei and with the results of previous works for superheavy nuclei with $Z=116$ and $Z=124$.

Figure 1

Two-dimensional plot of $V_{\parallel }/V_{CN}$ vs $V_{\perp }/V_{CN}$ distribution for the ${}^{50}\text{Ti}+{}^{208}\text{Pb}$ reaction at 294 MeV bombarding energy.

Figure 2

(a) Scatter plot of total kinetic energy vs fragment mass. The dashed line is the average TKE ($\langle \text{TKE}\rangle$) from the Viola systematics [20]. (b) Variation of the measured $\langle \text{TKE}\rangle$ with the fragment mass compared with the predicted values from Viola (dashed line) and Itkis systematics (solid line). The horizontal error bars indicate the width of the fragment mass cuts, while the vertical error bars indicate the uncertainty of the TKE centroid.

Figure 3

Mass-yield distribution for 294 MeV ${}^{50}\text{Ti}+{}^{208}\text{Pb}$ reaction: (a) total distribution, (b)–(d) mass yield for three different cuts in the TKE distribution. The average TKE increases from (b) to (c). The gray area indicates the Gaussian-like mass distribution from symmetric fission systematics. This distribution is normalized to the data at symmetric splitting for comparison. For details see the text.

Figure 4

Experimental (full circles) double differential neutron energy spectra at different angles with respect to the beam direction for the symmetric mass split $(\text{A}={\mathrm{A}}_{CN}/2\pm 20)$. Multisource fits to the data are also shown: solid curves correspond to the total neutron emission, dotted curves correspond to the prescission neutron emission, dot-dashed curves to postscission neutron from fragment F1 and dashed curves from fragment F2. The relative angles between the detected neutron and the two fragments are also indicated.

Figure 5

(a) Variation of ${\nu }_{\mathrm{tot}}$ with atomic number of composite nucleus in the excitation-energy range 64–74 MeV. Full diamonds are from Ref. [10], full down triangles from Ref. [27], and full circles from Ref. [28]. Open squares show the result of the present experiment. (b) Variation of ${\nu }_{\text{sf}}$ with atomic number of composite nucleus. Full diamonds are from Ref. [10], full up triangles from Ref. [9], the cross represents the ${}^{252}\text{Cf}$ spontaneous fission datum. Open squares show the result of the present experiment.

Figure 6

(a) The three cut applied in the TKE vs fragment mass plane for the study of the TKE dependence of the neutron multiplicity. (b) Total projection of TKE in the selected mass range together with the deduced prescission (open triangles), single fragment postscission (full circles), and total (full diamonds) neutron multiplicities plotted at the mean TKE of the gates in the fragment mass vs TKE plane shown in the upper panel.

Figure 7

Neck coordinate $\sigma$ versus elongation $s$ for dynamical trajectories calculated with the hicol code at different values of the orbital angular momentum $L$ for the ${}^{50}\text{Ti}+{}^{208}\text{Pb}$ system at 294 MeV bombarding energy.

Figure 8

Fission time as a function of the orbital angular momentum calculated with the hicol code [33] for the ${}^{50}\text{Ti}+{}^{208}\text{Pb}$ system at 294 MeV bombarding energy.

Figure 9

Variation of the average TKE as a function of fragment mass along with the predictions of hicol [33] (solid line) and Viola systematics [20] (dashed line).