Proton-induced fission cross sections on ${}^{208}\mathrm{Pb}$ at high kinetic energies

Total fission cross sections of ${}^{208}\mathrm{Pb}$ induced by protons have been determined at $370A,500A$, and $650A$ MeV. The experiment was performed at GSI Darmstadt where the combined use of the inverse kinematics technique with an efficient detection setup allowed us to determine these cross sections with an uncertainty below $6\%$. This result was achieved by an accurate beam selection and registration of both fission fragments in coincidence which were also clearly distinguished from other reaction channels. These data solve existing discrepancies between previous measurements, providing new values for the Prokofiev systematics. The data also allow us to investigate the fission process at high excitation energies and small deformations. In particular, some fundamental questions about fission dynamics have been addressed, which are related to dissipative and transient time effects.

Figure 1

Top schematic view of the experimental setup used in this experiment. Sizes are not to scale.

Figure 2

Atomic-number histogram of the ions detected with the ionization chamber placed before the target for the reaction ${}^{208}\mathrm{Pb}\left(500A\mathrm{MeV}\right)+p$.

Figure 3

Position distributions of the beam ions in horizontal (solid histogram) and vertical direction (dotted histogram) as determined by the TPC for our measurement at $500A$ MeV.

Figure 4

Scatter plot of the energy-loss signals registered by the two gas volumes of the Twin MUSIC chamber for the reaction ${}^{208}\mathrm{Pb}\left(500A\mathrm{MeV}\right)+p$. Fission fragments are located inside the triangular window.

Figure 5

Reconstruction of the fission reaction vertex along the $Z$ coordinate using the tracking capabilities, taking the position of the multiwire proportional chamber as reference point. The long-dashed lines define the window of fission events taking place inside the hydrogen volume for the reaction ${}^{208}\mathrm{Pb}\left(500A\mathrm{MeV}\right)+p$.

Figure 6

Energy loss of the two fission fragments measured independently in the two parts of the Twin MUSIC plotted versus each other under the conditions shown in Figs. 2, 4, and 5.

Figure 7

Horizontal $(x$ coordinate) position of the fission fragments recorded by the MWPC chamber for the reaction ${}^{208}\mathrm{Pb}\left(500A\mathrm{MeV}\right)+p$. The two dashed vertical lines indicate the shadow due to the cathode in the center of the Twin MUSIC chamber. The full line is the result of a fit to the histogram.

Figure 8

Simulated efficiency for the detection of both fission fragments in the same section of the Twin MUSIC detector as a function of the misalignment distance between the beam and the central cathode of the detector for the three energies investigated in this work. The vertical lines represent the mean value of the measured misalignment for each energy.

Figure 9

Simulated geometrical efficiency due to the finite size of the helium pipe located between the target and the Twin MUSIC detector. The vertical line represents the pipe radius.

Figure 10

Total fission cross sections measured in the present work (full circles) as a function of the proton energy in comparison to previously measured data for the reactions $p+{}^{\mathrm{nat}}\mathrm{Pb}$ and ${}^{208}\mathrm{Pb}+p$. The dashed line is to guide the eye.

Figure 11

Comparison between Prokofiev's systematics for proton-induced fission on ${}^{208}\mathrm{Pb}$ (dashed line) and different measurements (symbols). The full line represents a fit of the new data using Prokofiev's equation.

Figure 12

Fission cross sections measured in this work (full circles) and in other experiments in comparison with a the dynamical description of fission based on a time-independent fission width given by Kramers (long-dashed line) and with calculations using incl4.6 + abla07 for different values of the reduced dissipation parameter.

Figure 13

Fission cross sections measured for neutron-induced reactions on ${}^{\mathrm{nat}}\mathrm{Pb}$ [80, 81]. The solid and dotted lines represent calculations using incl4.6 + abla07 with a reduced dissipation parameter of $\beta =4.5\times {10}^{21}$ ${\mathrm{s}}^{-1}$ for fission reactions induced by neutrons on ${}^{\mathrm{nat}}\mathrm{Pb}$ and ${}^{208}\mathrm{Pb}$, respectively.