Systematic study of pre-equilibrium emission at low energies in ${}^{12}\mathrm{C}$- and ${}^{16}\mathrm{O}$-induced reactions

Background: The role of pre-equilibrium emission within the heavy-ion fusion process has not been fully characterized. An accurate description of this process is important for understanding the formation of the compound nucleus in fusion reactions.

Purpose: We develop a systematic description, based on experimental measurements, of the strength of the pre-equilibrium process in heavy-ion fusion reactions.

Method: With a view to study pre-equilibrium emission process, the excitation functions for some neutron emission channels occurring in the fusion of ${}^{12}\mathrm{C}$ with ${}^{128}\mathrm{Te}$ and ${}^{169}\mathrm{Tm}$, and of ${}^{16}\mathrm{O}$ with ${}^{159}\mathrm{Tb},{}^{169}\mathrm{Tm}$, and ${}^{181}\mathrm{Ta}$, respectively, have been measured at incident energies from near the Coulomb barrier to $\approx 7$ MeV/nucleon. The off-line $\gamma$-ray spectrometry–based activation technique has been used for the measurements of excitation functions. The measured excitation functions have been compared with theoretical predictions based on pure statistical model code pace4 and Geometry Dependent Hybrid (GDH)-based code alice-91. The strength of pre-equilibrium emission has also determined from comparison of the experimental excitation functions and the pace4 calculations.

Results: The measured excitation functions are satisfactorily reproduced by the pace4 calculations in the energy region up to the peak position. However, at relatively higher energies, the enhancement of experimental cross sections in the tail portion of excitation functions as compared to the theoretical predictions of code pace4 has been observed. The observed deviation may be attributed to the pre-equilibrium emission of particles during the thermalization of the compound nucleus. Further, alice-91 calculations which include PE emission satisfactorily reproduce the experimental data even at higher energies, indicating the significant contribution of pre-equilibrium emissions.

Conclusions: Analysis of data clearly indicates that pre-equilibrium emission is an important reaction mechanism even at low projectile energies where the compound nucleus reaction mechanism dominates, and pre-equilibrium fraction ‘$P_{FR}$ strongly depends on excitation energy available for surface nucleons in composite systems above the Coulomb barrier and the mass of the composite system.

Figure 1

The experimentally measured and theoretically calculated EFs for reaction ${}^{169}\mathrm{Tm}{{(}^{12}\text{C,3}n)}^{178}\mathrm{Re}$ using Monte Carlo–based code pace4. The measured cross sections for the residues ${}^{178}\mathrm{Re}$ by Chakrabarty et al. [12] are also shown for comparison.

Figure 2

The experimentally measured and theoretically calculated EFs for reactions ${}^{128}\mathrm{Te}{{(}^{12}\text{C,3}n)}^{137}\mathrm{Ce},{}^{159}\mathrm{Tb}{{(}^{16}\text{O,3}n)}^{172}\mathrm{Ta},{}^{169}\mathrm{Tm}{{(}^{16}\text{O,3}n)}^{182}\mathrm{Ir}$, and ${}^{181}\mathrm{Ta}{{(}^{16}\text{O,3}n)}^{194}\mathrm{Tl}$ using Monte Carlo–based code pace4. The parameters used in this calculations are discussed in the text.

Figure 3

The experimentally measured and theoretically calculated EFs for reaction ${}^{169}\mathrm{Tm}{{(}^{12}\text{C,3}n)}^{178}\mathrm{Re}$ using code alice-91. The effects of variation of parameter $K=10$, 12, 14, and 16, respectively, in alice-91 calculations are shown and are discussed in the text. The measured cross sections for the residues ${}^{178}\mathrm{Re}$ by Chakrabarty et al. [12] are also shown for comparison.

Figure 4

The experimentally measured and theoretically calculated EFs for reaction ${}^{169}\mathrm{Tm}{{(}^{12}\text{C,3}n)}^{178}\mathrm{Re}$ using code alice-91. The effects of rotational energy $E_{rot}$ in alice-91 calculations are shown in this figure and discussed in the text. The measured cross sections for the residues ${}^{178}\mathrm{Re}$ by Chakrabarty et al. [12] are also shown for comparison.

Figure 5

The experimentally measured and theoretically calculated EFs for reaction ${}^{169}\mathrm{Tm}{{(}^{12}\text{C,3}n)}^{178}\mathrm{Re}$ using code alice-91. The effects of different values of mean free multiplier $\mathrm{COST}=0$ and $\mathrm{COST}=2$ in alice-91 calculations are shown in this figure and discussed in the text. The measured cross sections for the residues ${}^{178}\mathrm{Re}$ by Chakrabarty et al. [12] are also shown for comparison.

Figure 6

The experimentally measured and theoretically calculated EFs for reactions ${}^{128}\mathrm{Te}{{(}^{12}\text{C,3}n)}^{137}\mathrm{Ce},{}^{159}\mathrm{Tb}{{(}^{16}\text{O,3}n)}^{172}\mathrm{Ta},{}^{169}\mathrm{Tm}{{(}^{16}\text{O,3}n)}^{182}\text{Ir,}$ and ${}^{181}\mathrm{Ta}{{(}^{16}\text{O,3}n)}^{194}\mathrm{Tl}$ using code alice-91. The parameters used in this calculations are discussed in the text.

Figure 7

(a) Variation PE fraction $P_{FR}$ as a function of excitation energy $E^{*}$ of composite system, (b) variation PE fraction $P_{FR}$ as a function of excitation energy $E^{*}$ per nucleon $A$, (c) variation PE fraction $P_{FR}$ as a function of excitation energy per nucleon $A$ at the surface of the composite system, i.e., $E/A^{2/3}$, and (d) variation PE fraction $P_{FR}$ as a function of excitation energy in excess of the Coulomb barrier nucleon $A$ at the surface of the composite system, i.e., $\left(E^{*}–E_{CB}\right)/A^{2/3}$. The solid rectangle, down triangle, circle, up triangle, and stars represent the data for the $3n$ channel in ${}^{12}\mathrm{C}+{}^{128}\mathrm{Te},{}^{12}\mathrm{C}+{}^{169}\mathrm{Tm},{}^{16}\mathrm{O}+{}^{159}\mathrm{Tb}$ ${}^{16}\mathrm{O}+{}^{169}\mathrm{Tm}$, and ${}^{16}\mathrm{O}+{}^{181}\mathrm{Ta}$ systems, respectively

Figure 8

The variation of $P_{FR}$ with the mass number of residual nucleus at 0.5 MeV excitation energy excess of the Coulomb barrier nucleon $A$ at the surface of the composite system, i.e., $\left(E^{*}–E_{CB}\right)/A^{2/3}$.