Evaporation and fission decay of ${}^{158}\mathrm{Er}$ composite nuclei within the statistical model

Light charged particles emitted by the compound nucleus ${}^{158}\mathrm{Er}$ produced in the reaction ${}^{32}\mathrm{S}$ $(180 \mathrm{MeV})+{}^{126}\mathrm{Te}$, at the excitation energy $E_x=92$ MeV, have been measured at Laboratori Nazionali di Legnaro in coincidence with fission fragments and evaporation residues. The $4\pi$ detector array $8\pi \mathrm{LP}$ coupled to a system of parallel-plate avalanche counters to detect evaporation residues has been used. Data have been analyzed in the framework of the statistical model of evaporation with the code pace2_n11. This enlarged version of the code pace2 has been used to reproduce the large set of observables measured in the fusion-evaporation and fusion-fission channels along with experimental prescission neutron multiplicity and fission cross section taken from literature. It is found that the simultaneous reproduction of the prescission neutron, proton, and $\alpha$-particle multiplicities can be obtained with zero fission delay without dynamical effects. However, the same set of model input parameters does not allow us to reproduce proton and $\alpha$-particle multiplicities in the evaporation channel. Extensive calculations, with different sets of parameters, show the limits of the statistical model in reproducing the whole set of data. This work evidences the importance of measuring a large set of observables in order to obtain a reliable description of the decay of the compound nucleus, and in particular of the fission process.

Figure 1

Schematic of a coincident event: the LCP is detected by the Ball telescope number 25, and the ER by a sector of the annular parallel-plate avalanche counter (PPAC). The line connecting the target with the center of the PPAC sector at ${\theta }_{\mathrm{ER}}$ and the beam direction define the reaction plane. The direction of LCPs impinging on a Ball telescope is defined by the polar angle ${\theta }_{\mathrm{LCP}}$ and azimuthal angle ${\varphi }_{\mathrm{LCP}}$. Ring B (at ${\theta }_{\mathrm{LCP}}={137}^{\circ }$ with respect to the beam direction) is shown. It is made of 18 identical bitelescopes mounted at same polar angle and spanning all the possible azimuthal angles. There are seven rings in $8\pi \mathrm{LP}$, named from A to G, from backward to forward directions, respectively, each containing a replica of the same bitelescope.

Figure 2

(a) Proton and (b) $\alpha$-particle energy spectra measured with two $8\pi \mathrm{LP}$ Ball telescopes in coincidence with ERs in the PPAC. The spectra are normalized to 1 at the maximum.

Figure 3

(a) Proton and (b) $\alpha$-particle energy-integrated differential multiplicities measured in coincidence with ERs identified in the PPAC system as function of the $8\pi \mathrm{LP}$ Ball telescopes number. The polar angles ${\theta }_{\mathrm{LCP}}$ corresponding to the rings of the Ball are reported.

Figure 4

Folding angle distributions of binary fragments from fusion-fission channel (FF, dashed black line) and deep inelastic collisions (DIC, solid red line). Viola total kinetic energy systematics [50] and constraints of detector geometry in ring F ($\langle {\theta }_{\mathrm{lab}}\rangle ={61}^{\circ }$, $\mathrm{\Delta }{\theta }_{\mathrm{lab}}={17}^{\circ }$) were employed.

Figure 5

Fission excitation function for the reaction ${}^{32}\mathrm{S}+{}^{126}\mathrm{Te}$ (dots) (taken from Ref. [35]) compared with two pace2_n11 calculations: (a) combination [solid red (gray) line] and (e) combination (dashed green line). For more details, see the text and Table 2.

Figure 6

Proton energy spectrum measured in coincidence with ER in the PPAC (dots) and the simulations (lines) obtained with the parameter combinations in Table 2. The model combinations correspond to lines: (a) solid red (gray), (b) dashed blue, (c) dash-dotted olive, (d) solid cyan (light gray), (e) dotted green, and (f) short-dotted yellow. All the spectra are normalized to the maximum. For more details, see the text.

Figure 7

$\alpha$-particle energy spectrum measured in coincidence with ER in the PPAC (dots) and the simulations (lines) obtained with the parameter combinations in Table 2. The model combinations correspond to lines: (a) solid red (gray), (b) dashed blue, (c) dash-dotted olive, (d) solid cyan (light gray), (e) dotted green, and (f) short-dotted yellow. All the spectra are normalized to the maximum. For more details, see the text.

Figure 8

Proton energy-integrated differential multiplicities measured with the Ball telescopes in correlation with ERs detected with the PPAC system (dots) and the simulations (lines) obtained with the parameter combinations in Table 2. In panel (a), the solid red (gray), dashed blue and dash-dotted olive lines correspond to the (a), (b), and (c) combinations, respectively. In panel (b), the solid cyan (light gray), dotted green, and short-dotted yellow lines correspond to the (d), (e), and (f) combinations, respectively. In both panels, experimental (Exp) data are the same as in Fig. 3. Simulated data have been normalized to the maximum of the experimental data. See the text for more details.

Figure 9

$\alpha$-particle energy-integrated differential multiplicities measured with the Ball telescopes in correlation with ERs detected with the PPAC system (dots) and the simulations (lines) obtained with the parameter combinations in Table 2. In panel (a), the solid red (gray), dashed blue, and dash-dotted olive lines correspond to the (a), (b), and (c) combinations, respectively. In panel (b), the solid cyan (light gray), dotted green, and short-dotted yellow lines correspond to the (d), (e), and (f) combinations, respectively. In both panels, experimental (Exp) data are the same as in Fig. 3. Simulated data have been normalized to the maximum of the experimental data. See the text for more details.