Transient and quasistationary dissipative effects in the fission flux across the barrier in $1A$ GeV ${}^{238}\mathrm{U}$ on deuterium reactions

Isotopic cross sections of all projectile residues with $Z$ above 23 produced in collisions induced by ${}^{238}\mathrm{U}$ at $1A$ GeV on deuterium have been measured. The isotopic distributions reflect the role of evaporation and fission in the formation process of these nuclei. The comparison of the measured cross sections with Monte Carlo deexcitation codes including an analytical description of the dynamics of fission shows the sensitivity of the data to nuclear dissipation. Moreover, the large excitation-energy range covered in this experiment together with the high accuracy of the measured cross sections allowed to clearly separate and quantify the role of transient and quasistationary dissipative effects in the fission-decay width.

Figure 1

Two-dimensional cluster plot of all nuclei produced as projectile residues with a cross section larger than 100 μb in the reaction ${}^{238}\mathrm{U}+{}^2\mathrm{H}$ at $1A$ GeV presented on top of the chart of the nuclides. The color scale represents the production cross section, the black squares correspond to stable isotopes, and the lines indicate the limit of the known nuclides.

Figure 2

Isobaric distributions of projectile residues produced in reactions induced by ${}^{238}\mathrm{U}$($1A$ GeV) (black dots) and ${}^{208}\mathrm{Pb}$($1A$ GeV) (grey/red dots) [35] on deuterium as a function of the mass loss of the final residues ($\Delta A$) with respect to the projectile. In the bottom panel, the mass loss of the final residue is normalized to the initial mass number of the projectile to the power of 2/3. In (a) the isobaric distribution of residues produced in the reaction ${}^{208}\mathrm{Pb}$($1A$ GeV) on deuterium is compared to model calculations performed with the Isabel intranuclear cascade code [36] coupled to the ABLA evaporation code [37, 40] with a dynamical description of fission according to Ref. [10] (solid line) and a purely statistical description of fission (dashed line). In (b) both sets of data are compared to calculations where fission has been suppressed (solid line ${}^{238}\mathrm{U}$($1A$ GeV) + ${}^2\mathrm{H}$ and dashed line ${}^{208}\mathrm{Pb}$($1A$ GeV) + ${}^2\mathrm{H}$).

Figure 3

Excitation energy of the initial prefragments as a function of the mass loss of the final residue with respect to the projectile for the reaction ${}^{238}\mathrm{U}$ ($1A$ GeV) + ${}^2\mathrm{H}$.

Figure 4

Measured isobaric distribution of evaporation residues produced in the reaction ${}^{238}\mathrm{U}$($1A$ GeV) + ${}^2\mathrm{H}$ (dots), compared with different calculations performed with the Isabel intranuclear cascade code coupled to the ABLA evaporation code. The dotted line represents a calculation using a purely statistical description of fission and deformation-dependent level-density parameters. The calculation represented by the dashed line includes the Kramers factor in the fission width with $\beta =2\times {10}^{21}$ ${\text{s}}^{-1}$ and the solid line represents a calculation with not only the Kramers factor but also the time dependence of the fission width. Both calculations use deformation-dependent level-density parameters. Finally, the dashed-dotted line corresponds to a calculation using a purely statistical description of fission with no deformation-dependent level-density parameters ($a_f/$$a_n=1$).

Figure 5

Isobaric distribution of evaporation residues produced in the reaction ${}^{238}\mathrm{U}+{}^2\mathrm{H}$ at $1A$ GeV (dots). In the left panel, the data are compared to calculations using different values of β: $1\times {10}^{21}{\mathrm{s}}^{-1}$ (dashed line), $2\times {10}^{21}{\mathrm{s}}^{-1}$ (solid line), $3\times {10}^{21}{\mathrm{s}}^{-1}$ (dotted line) and $5\times {10}^{21}{\mathrm{s}}^{-1}$ (dashed-dotted line), in all these calculations the time dependence of the fission width follows the analytical solution of the Fokker-Planck equation. In the right panel, we compare calculations with $\beta =2\times {10}^{21}{\mathrm{s}}^{-1}$, but different time dependences of the fission width: an exponential in-growth function (dotted line), a step function (dashed line) and the analytical solution of the Fokker-Planck equation (solid line).