Constraining the level density using fission of lead projectiles

The nuclear level density is one of the main ingredients for the statistical description of the fission process. In this work, we propose to constrain the description of this parameter by using fission reactions induced by protons and light ions on ${}^{208}\text{Pb}$ at high kinetic energies. The experiment was performed at GSI (Darmstadt), where the combined use of the inverse kinematics technique with an efficient detection setup allowed us to measure the atomic number of the two fission fragments in coincidence. This measurement permitted us to obtain with high precision the partial fission cross sections and the width of the charge distribution as a function of the atomic number of the fissioning system. These data and others previously measured, covering a large range in fissility, are compared to state-of-the-art calculations. The results reveal that total and partial fission cross sections cannot unambiguously constrain the level density at ground-state and saddle-point deformations and additional observables, such as the width of the charge distribution of the final fission fragments, are required.

Figure 1

(a) Comparison of the fission cross sections for the reaction ${}^{208}\text{Pb}+p$ as a function of the bombarding energy with different model calculations (lines). The data are taken from Refs. [13, 48, 49, 50, 51, 52]. (b) Same as panel (a) but for the the reaction ${}^{\text{nat}}\text{Pb}+n$. The data are taken from Refs. [53, 54].

Figure 2

Proton-induced fission cross sections of different nuclei obtained from Refs. [12, 13, 77] at 500 MeV as a function of the fissility. The lines indicate different model calculations. In the inset we show the ratio $a_{\text{sd}}/a_{\text{g.s.}}$ obtained by our model calculations as a function of the fissility.

Figure 3

Fission cross section of the reaction ${}^{208}\text{Pb}+p$ at 500A MeV as a function of the atomic number of the fissioning nuclei (open circles). The lines represent different model calculations.

Figure 4

(a) Width of the atomic-number distribution of the final fission fragments measured in spallation and fragmentation reactions of ${}^{208}\text{Pb}$ as a function of the atomic number of the fissioning nuclei for different entrance channels and projectile energies. (b) Same as panel (a) but for the data of the reaction ${}^{208}\text{Pb}\left(500A\text{MeV}\right)+{}^{27}\mathrm{Al}$ (open triangles) and ${}^{208}\text{Pb}\left(500A\text{MeV}\right)+p$ (open circles). The lines represent different model calculations.