Investigating the low-energy incomplete fusion in 12c+193ir system

Abstract

Heavy-ion (HI) nuclear reactions at low incident energies have fascinated nuclear physicists for several decades, and considerable theoretical and experimental studies have been undertaken to understand the underlying dynamics. The HI-induced nuclear reactions play a crucial role in understanding astrophysical processes, production of exotic nuclei, and formation of super-heavy elements by gaining insights into different processes [1,2]. The ongoing advancements in accelerator technology have opened up the possibility of accelerating heavy ions (with A > 4), creating new avenues for investigating the dynamics of interactions among heavy nuclei. A significant amount of information about nuclear properties, forces, decay characteristics, energy states of excited nuclei, etc., has been obtained by studying nuclear reactions. These studies are essential for understanding unexplained aspects of nuclear properties. HI reactions involve many nucleons, giving rise to various nuclear reaction processes depending upon the incident beam energy and the entrance channel parameters. At energies above the Coulomb barrier, the nuclear reactions exhibit two predominant modes: complete fusion (CF) and incomplete fusion (ICF). In CF, the driving input angular momentum ℓ falls below a critical threshold, ℓ < ℓcrit, and an effective potential energy curve exhibits a fusion pocket. In this configuration, the attractive nuclear potential dominates the combined effect of repulsive Coulomb and centrifugal potentials. Consequently, the incident projectile completely merges with the target nucleus, forming an excited composite system, thereby transferring the energy and angular momentum from the relative motion to the intrinsic degrees of freedom of the composite system from which light nuclear particles and/or characteristic γ-rays may be emitted [3,4]. In ICF, as the energy of the incident projectile increases, surpassing the critical threshold, ℓ > ℓcrit, the fusion pocket in the effective potential energy curve gradually disappears [5–8]. As a result, to maintain a sustainable input value ℓ, the incident projectile starts to break into fragments in the vicinity of the nuclear field of the target nucleus. In this scenario, one of the fragments fuses with the target nucleus. At the same time, the remaining part of the projectile, the spectator, moves almost along the beam direction, maintains nearly the beam velocity, and does not interfere with the ongoing reaction processes. The excited composite system formed due to the fusion of a fragment of the incident projectile may undergo de-excitation by the emission of light nuclear particles and/or characteristic γ-rays. However, this phenomenon of ICF was first documented over 60 years ago upon observing projectile break-up, resulting in the emission of rapid α-particles at forward angles in the intermediate energy HI (primarily 12C, 14N and 16O) reactions, since then, the term ICF or break-up fusion was adopted [9–11]. Through the analysis of experimental data, researchers have concluded that peripheral collisions create favorable conditions for ICF [12–14]. The ICF reactions in HIs represent one of the most profound rearrangements in nuclear many-body systems, making them an ideal tool for exploring high-spin and high-excitation energy states [15–18]. Several theoretical models, such as the Break-up fusion (BUF) model [19], Sum-rule model [7], Promptly emitted particles (PEPs) model [20], etc., have been proposed to elucidate ICF dynamics. Diaz-Torres et al. [21] recently proposed a three-dimensional classical model for low-energy break up fusion processes that can mimic ICF and CF cross-sections but is limited to light ion beams with low break-up threshold energy. While existing models qualitatively describe experimental data to some extent at energies > 10 MeV/nucleon in specific instances, they do not satisfactorily reproduce ICF data at low incident energies, i.e., 3–5 MeV/nucleon. The discrepancy between model predictions and ICF data at these energies has sparked increased interest in these processes. To address this, more precise data is needed to advance theoretical models and understand the dependencies of ICF probability on various entrance channel parameters such as projectile energy, driving angular momentum, the binding energy of the projectile, mass asymmetry of the interacting nuclei, projectile Qα value, Coulomb factor, projectile structure, and target deformation. Despite several existing studies, there is still a need for a comprehensive understanding of ICF dynamics, especially at low incident energies. Collecting extensive data on various projectile-target combinations will help refine nuclear reaction models. Considering these perspectives, the study of CF and ICF reaction dynamics below 7 MeV/nucleon remains an active area of investigation. Most experiments to date have focused on α–cluster structure projectiles such as 12C, 16O and 20Ne and non–α–cluster projectiles like 13C, 14N, 18O and 19F. This thesis investigates the onset of various reaction channels induced by α–cluster structured projectile. The experiments were conducted using the 12C+193Ir system, spanning energies of ≈ 5–7 MeV/nucleon using the 15UD Pelletron accelerator facility available at the Inter-University Accelerator Centre (IUAC), New Delhi, India. The thesis is organized into the following chapters: 1. Chapter- 1 of the thesis explores the growing interest in nuclear reactions induced by accelerating atomic ions with the mass number A > 4, known as HIs, incident on heavy targets at low incident energies, typically around 10 MeV/nucleon or less. It offers a brief description of nuclear reactions, followed by a description of the dynamics of HI fusion reactions. The features of the types of fusion involved in HI reactions, viz. CF and ICF are also provided. The literature survey and motivation of the present work are included at the end of the chapter. 2. Chapter- 2 delves into the details of the techniques employed for fabricating the thin target foils. In this thesis, we have reported the fabrication of thin 208Pb and 193Ir targets on Al backing using high-vacuum and ultra-high vacuum deposition techniques, respectively. Both targets were prepared with the motivation to study fusion excitation functions (EFs) [22], mass distribution of fission-like events [23], and forward recoil ranges in low-energy nuclear reactions. The characterization techniques used to measure target thickness, uniformity, and purity are briefly illustrated [24]. The latter part of this chapter concisely reviews the experimental setup and methodology per tinent to this research. The introduction to the stacked foil activation technique to measure the EFs and FRRs is described along with a brief of the General Purpose Scattering Cham ber (GPSC) in which irradiations have been carried out. It also discusses the post-irradiation analysis, such as the characterization of HPGe clover detectors, channel-by-channel identifica tion of evaporation residues (ERs), and the mathematical formulation used for the activation production cross-section measurements and associated uncertainties. 3. Chapter- 3 introduces the important features of computer codes employed for theoretical simulations. It discusses the theoretical formalism of fusion cross-sections, focusing on the statistical model code PACE4 [25,26] used to compare the experimental results obtained in the present work with theoretical predictions, including nuclear level densities and free parameters in the code. The level density parameter a can be obtained using the default option a = A/K MeV−1, where A is the mass number of the compound nucleus and K is a free adjustable parameter. The value of K may be adjusted to reproduce the experimental EFs. This code allows for a large number of events, up to 1,00,000, to obtain better statistical accuracy. The latter part of this chapter delves into the formulations used for data reduction meth ods. For a systematic understanding of fusion dynamics, the fusion cross-sections have been normalized to eliminate different geometric factors, such as radii, barrier height, and static effects arising from the potential between the interacting nuclei. The details about the Uni versal Fusion Function (UFF) [27,28] and Improved Fusion Function (IFF) [29] data reduction procedures have been provided, which are used to compare different projectile-target combi nations. 4. Chapter- 4 presents the EF measurements of a large number of reaction residues pop ulated in the interaction of the 12C with 193Ir viz. xn channels– 193Ir(12C,4n)201Bi and 193Ir(12C,5n)200Bi; pxn channels– 193Ir(12C,p3n)201Pb and 193Ir(12C,p4n)200Pb; αxn chan nels– 193Ir(12C,αn)200Tl, 193Ir(12C,α2n)199Tl and 193Ir(12C,α3n)198Tlg; and xαxn channels 193Ir(12C,2αn)196Aum via CF and/or ICF processes [30]. Experimental EFs for the 12C+193Ir system have been reported for the first time in the energy range of 5–7 MeV/nucleon (i.e., 64–84 MeV). The experimental results have been analyzed in the framework of the statistical model code PACE4, which only considers CF cross-sections of the ERs. The data analysis indicated that the measured cross-sections of the ERs populated via the emission of neutrons and/or proton, i.e., xn/pxn channels, were found to be in good agreement with the predictions of PACE4 for the level density parameter K = 13, which is a free parameter in the code. It indicates that xn/pxn channels are populated only through the CF process. However, a significant enhancement was observed in the measured cross-sections of all the α-emitting channels compared to PACE4 predictions for the same value of the free parameter. This enhancement has been attributed to the break-up fusion processes involved in populating these α-emitting channels besides the CF process. To have a better insight into the onset of ICF and how the structure of the projectile affects the ICF dynamics, the ICF strength function (FICF) has been deduced. From further analysis, it has been observed that FICF depends strongly on entrance channel parameters, such as the incident beam energy of the projectile, mass asymmetry (µm) of the interacting nuclei, Coulomb factor (ZPZT), and neutron skin thickness (tN). The probability of ICF has been observed to increase with beam energy. The value of FICF increases smoothly from ≈ 12% to 16%in this work. The observed increasing trend of ICF with incident energy indicates that the break-up probability of 12C projectile increases due to increasing input angular momentum. This may be because the angular momentum imparted into the system increases with incident energy, which leads to the flattening of the fusion pocket in the effective potential. To restore the fusion pocket and to provide sustainable input angular momenta to the system, the incident projectile 12C breaks up into its constituent α–clusters, i.e., 8Be+α or α+α+α. Depending on the input angular momentum conditions, one or a group of α–clusters may fuse with the target nucleus to form an incompletely fused composite (IFC) system. For comparison with other projectile-target pairs, the behavior of FICF has been studied for the projectile energy in terms of the effective relative velocity of collision (vrel) in line with the systematics proposed by Morgenstern et al. [31]. According to this systematics, the comparisons regarding the fraction of ICF with the other systems are drawn at a common and pivotal value of vrel = 0.053c, considered to be the lower limit for the onset of the ICF process. The FICF has been found to increase with vrel, and ICF is observed to contribute even well below vrel = 0.053c as well. The observed behavior of FICF suggests the increasing probability of ICF contributions from vrel ≈ 0.03c to 0.06c. A comparison of FICF for 12C+193Ir system with 13C, 16O and 18O projectiles on different targets displays higher ICF probability for 18O projectile systems. It has been found that the value of FICF increases with entrance channel mass asymmetry for 12C, 13C, 16O and 18O projectiles individually. Based on these observations, it can be inferred that the mass asymmetry systematics is valid only for individual projectile(s), and the projectile structure effect should be considered while interpreting the ICF data at low incident energies. It has been established that the mass asymmetry systematics alone can not explain ICF data obtained for different projectile-target combinations. Further, it has been observed that the probability of ICF is sensitive to the Coulomb factor (ZPZT). From the analysis, it has been noticed that the α–cluster structure projectiles (e.g., 12C and 16O) exhibit increasing ICF fraction trends and align on the same line, suggesting consistency in their behavior. However, non–α–cluster projectiles (13C and 18O) also show increasing trends in ICF, but separately for each projectile, contrary to recent findings [32]. Based on data analysis, it may be concluded that the structural characteristics of the projectile exert a substantial influence on ICF. Moreover, in low-energy HI reactions, ICF mainly onsets in non-central interactions, and hence neutron skin thickness (tN) may influence the probability of ICF. The fact is that the number of protons is found to be less than the number of neutrons in heavy-mass nuclei, and different combinations of protons and neutrons govern different potentials. The excess of neutrons in a nucleus forms a layer of neutrons above the nuclear surface– termed neutron skin. Neutron skin slightly reduces the Coulomb barrier due to the screening effect, which increases the attractive nuclear potential. To display the effect of neutron skin thickness on ICF, the value of FICF has been plotted as a function of neutron skin thickness, and it has been observed that the probability of ICF increases with neutron skin thickness for individual projectiles, indicating larger ICF probability for neutron-rich, heavy mass target nuclei. From the systematics, it has been found that the probability of ICF is higher for reactions involving 12C projectile than those involving 13C projectile, pointing towards the effect of Qα value of the projectile. The projectile with a more negative Qα value will have fewer ICF contributions, consistent with Qα value systematics. With a view to disentangle the CF and ICF reactions in the present work, the forward recoil range distribution of reaction residues viz., 200,199,198Tl (αn,α2n,α3n) and 196Au (2αn) populated in the interaction of 12C with 193Ir target have been measured at energy 83.99 MeV. A significant contribution from ICF reactions has been observed in almost all the α–emitting channels. It strongly reveals a transfer of partial momentum from the projectile to the target nucleus in the case of α–emitting channels associated with ICF reactions. The different partial LMT components correspond to the break-up of 12C with the target nucleus if 12C breaks up into 8Be+α. In the latter part of this chapter, the fusion cross-section data of the present system of 12C+193Ir has been reduced. It is necessary to eliminate differences that may arise due to the size and charge of the interacting nuclear entities. Reduction procedures to eliminate geometric and static effects suggest that the observed variation in the fusion data of the 12C+193Ir system is of a purely static origin in different potential barriers and radii. Analysis within the framework of UFF indicates that fusion is suppressed by ≈ 12% for the 12C+193Ir system. The suppression of experimental fusion functions concerning the UFF or the probability of ICF is estimated to be influenced by the α break-up threshold energy of the projectile. The projectile with a more negative Qα value is likely to give rise to less fusion suppression and vice-versa. The magnitude of suppression for the present system has been found to fall in line with the empirical relation obtained by Wang et al. [33] after a slight modification in the parameters. This observation further suggests that the break-up threshold energy affects the projectile break-up and, hence, the fusion cross-section. Moreover, the experimental fusion cross-section data for various systems, including the 12C+193Ir system, were plotted alongside the IFF. A suppression of 6% has been observed for 12C+193Ir system w.r.t. Classical Fusion Line (CFL). The reduced data points for different tightly bound projectile-target combinations closely align with the CFL, reflecting that nuclear structure properties have minimal influence at above-barrier energies. 5. Chapter- 5 summarizes the conclusions drawn from the research presented in this thesis and outlines future perspectives. In continuation of the work performed and included in this thesis, it is proposed to carry out velocity distribution measurement for 12C+193Ir system as it is a model-independent method for studying the ICF process to complement and/or verify the obtained results. We plan to propose more experiments with non–α–cluster projectiles because of the scarcity of ICF data for such projectiles. This initiative can help fill a crucial gap in our understanding of nuclear reactions. Particle-γ-coincidence and spin distribution measurements will be proposed for future experiments to get information about the involve ment of ℓ-values in the ICF process. For Fusion-Fission reaction dynamics, experiments will be conducted to measure distributions and neutron multiplicities in the in-beam experiments using fission and neutron array detectors available at the IUAC in the present energy range, and masses will get a better insight into the fission reaction dynamics; a detailed experimental analysis of 12C+208Pb and 12C+193Ir systems will be carried out.