Semiclassical and quantum mechanical analysis of $\alpha$-particle-induced reactions on praseodymium: A study relevant to precompound emission

Background: The study of precompound emission has attracted considerable attention for testing nuclear models in light-ion-induced reactions at relatively higher energies above 10 MeV/nucleon.

Purpose: Aiming to study the precompound emission and to develop systematics at low energies below 10 MeV/nucleon, where the compound emission process is likely to dominate, the excitation functions of the reaction residues produced in the interaction of $\alpha$ particles with ${}^{141}\mathrm{Pr}$ have been measured in the energy range $\approx 14$–40 MeV. Further, the measured data have been analyzed within the framework of both the semiclassical and quantum mechanical models.

Methods: The off-line $\gamma$-ray spectroscopy based stacked foil activation technique has been used to measure the excitation functions.

Results: The experimentally measured excitation functions have been compared with the theoretical predictions based on both the semiclassical model codes, viz., pace4, talys-1.9, act, and alice91, and the quantum mechanical model code exifon. The analysis of the data shows that the experimental excitation functions could be reproduced only when the contribution of precompound emission, simulated theoretically, is taken into account. Further, the precompound fraction, which gives the relative importance of precompound emission over compound nucleus emission, has been deduced and is found to be energy dependent.

Conclusions: Analysis of data indicates that in $\alpha$-induced reactions, the precompound emission plays an important role, even at the low incident energies, where the pure compound nucleus process is likely to dominate. The precompound fraction is found to strongly depend on the mass of the target nucleus and the excitation energy per surface nucleon of the composite system.

Figure 1

A typical $\gamma$-ray spectrum of a standard source ${}^{152}\mathrm{Eu}$ of known strength, recorded prior to actual experiment for $\alpha$-induced reactions ${}^{144}\mathrm{Pm}$ at source-detector distance (gap) 3 cm.

Figure 2

The curves for geometry-dependent efficiency with proper dead-time correction obtained from a standard source ${}^{152}\mathrm{Eu}$ of known strength at source-detector distance 3 cm.

Figure 3

The experimentally measured and theoretically calculated EFs for reaction ${}^{141}\mathrm{Pr}(\alpha ,n){}^{144}\mathrm{Pm}$ using code pace4. The effect of variation of parameter $\mathit{K}$ (=8, 9, and 10) on pace4 calculations is also shown in this figure. See text for details.

Figure 4

The experimentally measured and theoretically calculated EFs for reaction ${}^{141}\mathrm{Pr}(\alpha ,2n){}^{143}\mathrm{Pm}$ using code pace4. The effect of variation of parameter $\mathit{K}$ (=8, 9, and 10) on pace4 calculations is also shown in this figure.

Figure 5

The experimentally measured and theoretically calculated EFs for reaction ${}^{141}\mathrm{Pr}(\alpha ,n){}^{144}\mathrm{Pm}$ using code talys-1.9. See text for details.

Figure 6

The experimentally measured and theoretically calculated EFs for reaction ${}^{141}\mathrm{Pr}(\alpha ,2n){}^{143}\mathrm{Pm}$ using code talys-1.9. See text for details.

Figure 7

The experimentally measured and theoretically calculated EFs for reaction ${}^{141}\mathrm{Pr}(\alpha ,n){}^{144}\mathrm{Pm}$ using code act. The effect of variation of parameter $n_0$ (=4, 5, and 6) is shown in this figure. The best choice of parameters $n_0$ is discussed in text.

Figure 8

The experimentally measured and theoretically calculated EFs for reaction ${}^{141}\mathrm{Pr}(\alpha ,2n){}^{143}\mathrm{Pm}$ using code act. The effect of variation of parameter $n_0$ (=4, 5, and 6) is shown in this figure.

Figure 9

The experimentally measured and theoretically calculated EFs for reaction ${}^{141}\mathrm{Pr}(\alpha ,n){}^{144}\mathrm{Pm}$ using code alice91. The effect of variation of parameter $n_0$ (=4, 5, and 6) is shown in this figure. The details of the parameter $n_0$ are discussed in the text.

Figure 10

The experimentally measured and theoretically calculated EFs for reaction ${}^{141}\mathrm{Pr}(\alpha ,n){}^{144}\mathrm{Pm}$ using code alice91. The effect of variation of parameter cost is shown in this figure. See text for details.

Figure 11

The experimentally measured and theoretically calculated EFs for reaction ${}^{141}\mathrm{Pr}(\alpha ,2n){}^{143}\mathrm{Pm}$ using code alice91. The effect of variation of parameter initial exciton number $n_0$ is shown in this figure.

Figure 12

The experimentally measured and theoretically calculated EFs for reaction ${}^{141}\mathrm{Pr}(\alpha ,n){}^{144}\mathrm{Pm}$ using code exifon. The effect of variation of parameter $\mathrm{\Delta }$ on theoretical calculations is also shown.

Figure 13

The experimentally measured and theoretically calculated EFs for reaction ${}^{141}\mathrm{Pr}(\alpha ,2n){}^{143}\mathrm{Pm}$ using code exifon. The effect of variation of parameter $\mathrm{\Delta }$ on theoretical calculations is also shown in this figure.

Figure 14

The experimentally measured and theoretically calculated EFs for reactions ${}^{159}\mathrm{Tb}(\alpha ,n){}^{162}\mathrm{Ho}$ [74], ${}^{181}\mathrm{Ta}(\alpha ,n){}^{184}\mathrm{Re}$ [75, 76], ${}^{197}\mathrm{Au}(\alpha ,n){}^{200}\mathrm{Tl}$ [77], and ${}^{203}\mathrm{Tl}(\alpha ,n){}^{206}\mathrm{Bi}$ [78], respectively, using code pace4.

Figure 15

The deduced $f_{\mathrm{pe}}$ as a function of laboratory energy $({\mathit{E}}_{\mathrm{lab}})$, center-of-mass energy $({\mathit{E}}_{\mathrm{c}.\mathrm{m}.})$, excitation energy ${\mathit{E}}^{*}$, and excitation energy per surface nucleons ${\mathit{E}}_{\mathit{S}}$ for the reactions ${}^{141}\mathrm{Pr}(\alpha ,n){}^{144}\mathrm{Pm}$, ${}^{159}\mathrm{Tb}(\alpha ,n){}^{162}\mathrm{Ho}$, ${}^{181}\mathrm{Ta}(\alpha ,n){}^{184}\mathrm{Re}$, ${}^{197}\mathrm{Au}(\alpha ,n){}^{200}\mathrm{Tl}$, and ${}^{203}\mathrm{Tl}(\alpha ,n){}^{206}\mathrm{Bi}$, respectively.

Figure 16

Deduced precompound fraction ${\mathit{f}}_{\mathrm{pe}}$ of mass of the target nuclei as a function ${\mathit{E}}_{\mathit{S}}$.