Unified description of the fission probability for highly excited nuclei

Figures & data

Figure 1. Schematic of the high-energy fission model of the de-excitation process together with the INC process. Open circles represent the fission chances that determine whether fission occurs in accordance with the fission probability $P$. In this example, fission occurs after emitting three neutrons by evaporation. For simplicity, charged-particle evaporation is omitted.

Table 1. Fitting parameters $c_{k,\mathrm{\ell }}$

	$\mathrm{\ell }=1$	$\mathrm{\ell }=2$	$\mathrm{\ell }=3$
$k=1$	$505.94$	$17.049$	$-185.15$
$k=2$	$11.134$	$-0.1468$	$-0.4187$
$k=3$	$-23.999$	$0.7867$	$-1.210$
$k=4$	$-1.1188$	$0.0352$	–

Figure 2. Total fission probability for ${ }^{209}$Bi($p,x$), ${ }^{208}$Pb($p,x$), ${ }^{197}$Au($p,x$), ${ }^{181}$Ta($p,x$),and ${ }^{165}$Ho($p,x$) reactions as a function of incident proton energy, calculated with Prokofiev’s fission cross-section systematics and Pearlstein–Niita’s non-elastic cross-section systematics.

Figure 3. Relationship between the mean excitation energy after the INC process and incident proton energy for proton-induced reactions for ${ }^{208}$Pb and ${ }^{165}$Ho. Data points and lines indicate the calculation results of INCL4.6 and Equation (7)(7) $E_p=0.141\times ⟨E{⟩}^{\alpha },$(7) , respectively.

Figure 4. Relationship between the mean reduced $Z$ and $A$ numbers ($⟨\mathrm{\Delta }Z⟩$, $⟨\mathrm{\Delta }A⟩$) and the mean excitation energy $⟨E⟩$ after the INC process for proton-induced reactions for ${ }^{209}$Bi, ${ }^{208}$Pb, ${ }^{197}$Au, ${ }^{181}$Ta, and ${ }^{165}$Ho. Data points and lines indicate the calculation results of INCL4.6 and Equations (10)(10) $⟨\mathrm{\Delta }Z⟩=0.0216⟨E⟩-1.037,$(10) and (11(11) $⟨\mathrm{\Delta }A⟩=0.0457⟨E⟩-1.049,$(11) ), respectively.

Figure 5. Fission probability $P$ for the corresponding mean of ($Z_t$, $A_t$) for ${ }^{209}$Bi, ${ }^{208}$Pb, ${ }^{197}$Au, ${ }^{181}$Ta, and ${ }^{165}$Ho as a function of excitation energy.

Figure 6. Proton-induced fission cross-sections of ${ }^{209}$Bi, ${ }^{208}$Pb, ${ }^{197}$Au, ${ }^{181}$Ta, and ${ }^{165}$Ho, as compared with experimental data from Refs [40–60].

Figure 7. Neutron-induced fission cross-sections of ${ }^{209}$Bi, ${ }^{208}$Pb, ${ }^{\mathrm{n}\mathrm{a}\mathrm{t}}$Pb, ${ }^{197}$Au, and ${ }^{181}$Ta, as compared with experimental data from Refs [62–65].

Figure 8. Deuteron-induced fission cross section of ${ }^{209}$Bi and ${ }^{208}$Pb, compared with experimental data from Refs [42,66–68].

Figure 9. Fission cross-section ratios between proton- and neutron-induced fissions for ${ }^{209}$Bi, ${ }^{208}$Pb, ${ }^{197}$Au, and ${ }^{181}$Ta targets calculated with the modified model, as compared with experimental data from [62,69].

Figure 10. Neutron-induced fission cross section ratio between ${ }^{\mathrm{n}\mathrm{a}\mathrm{t}}$Pb and ${ }^{209}$Bi, as compared with experimental data from Ref [62].

Figure 11. Mass distribution for $p$ + ${ }^{208}$Pb (1000$A$ MeV), $p$ + ${ }^{197}$Au (800$A$ MeV), and $p$ + ${ }^{208}$Pb (500$A$ MeV) reactions, as compared with experimental data from Refs [49,52,70].

Figure 12. $⟨N⟩/Z$ distribution as a function of $Z$ number for $p$ + ${ }^{208}$Pb (1000$A$ MeV), $p$ + ${ }^{197}$Au (800$A$ MeV), and $p$ + ${ }^{208}$Pb (500$A$ MeV) reactions.

Figure 13. $⟨N⟩/Z$ distribution as a function of $Z$ number for $p$ + ${ }^{208}$Pb (1000$A$ MeV), $p$ + ${ }^{197}$Au (800$A$ MeV), and $p$ + ${ }^{208}$Pb (500$A$ MeV) reactions.

Figure 14. Reduced ${\chi }^2$ values as a function of $\eta$ for $p$ + ${ }^{208}$Pb (1000$A$ MeV), $p$ + ${ }^{197}$Au (800$A$ MeV), and $p$ + ${ }^{208}$Pb (500$A$ MeV) reactions. The values are scaled so that the minimum values of the fitting functions are normalized to unity.

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