Unraveling the reaction mechanism for large alpha production and incomplete fusion in reactions involving weakly bound stable nuclei

The origin of the large α particle production and incomplete fusion in reactions involving weakly-bound α+x cluster nuclei still remains unresolved. While the (two-step) process of breakup followed by capture of the “free” complementary fragment (x) is widely believed to be responsible, a few recent studies suggest the dominant role of (direct) cluster stripping. To achieve an unambiguous experimental discrimination between these two processes, a coincidence measurement between the outgoing α particles and γ rays from the heavy residues has been performed for the 7Li(α+triton)+93Nb system. Proper choice of kinematical conditions allowed for the first time a significant population of the region accessible only to the direct triton stripping process and not to breakup followed by the capture of the “free” triton (from the three-body continuum). This result, also supported by a cluster-transfer calculation, clearly establishes the dominance of the direct cluster-stripping mechanism in the large alpha production. Clustering is a general phenomenon observed over a wide range of physical scales and in diverse fields such as the aggregation of galaxies in the universe or the existence of gene clusters in complex biological systems. In nuclear physics, the enormous pairing stability in fermionic quantum systems leads to a large binding energy for the α particle and consequently α clustering is very prevalent in atomic nuclei [1]. While the α decay of radioactive nuclei was long ago adduced as direct evidence that α particles formed constituents of heavier nuclei [2], the origin and consequences of α clustering in nuclei remain the subject of intense research due to its importance in fundamental nuclear physics as well as other areas [3]. In many light nuclei, α clustering is responsible for the weak binding of α + x cluster configurations. A large α-particle yield compared to that of the complementary fragment (x) is observed in nuclear reactions involving such nuclei, e.g., 6,7Li and 7,9Be, indicating that it cannot arise solely due to simple breakup of the weakly-bound projectile in the field of the target Email address: sanat@barc.gov.in (S. K. Pandit) nucleus. Capture/transfer of the complementary fragment/cluster, also sometimes referred to as incomplete fusion (ICF), has also been observed with similar magnitudes in these reactions. Further, the measured large α production and ICF cross sections are commensurate with an observed suppression of the complete fusion (CF) process, suggesting a common origin. However, it is still debated whether the former process influences the multi-dimensional quantum tunneling of fusion in a coherent or incoherent way [4, 5]. The mechanisms responsible for the large α-particle production, ICF and fusion suppression remain unclear and the subject of current interest [6, 7, 8, 9, 10, 11, 12, 13]. Unraveling the reaction mechanisms in systems involving nuclei with clustering and weak binding, common features of many light radioactive ion beams (RIBs), is important not only from its fundamental aspect, but also as a promising tool in other areas including nuclear astrophysics [14, 15, 16] and nuclear energy applications [17, 18]. Incomplete fusion can arise due to either direct stripping of a cluster from a bound state of the projectile or fusion of one of the “free” fragments after breakup of Preprint submitted to Physics Letter B October 5, 2021 ar X iv :2 11 0. 01 02 1v 1 [ nu cl -e x] 3 O ct 2 02 1 the projectile, i.e. so-called breakup-fusion [10, 19, 20, 21, 22]. Experimentally, it is challenging to distinguish between these two mechanisms as both lead to the same final products with similar energy and angular distributions. Although a clear experimental identification of the underlying mechanism could not be achieved in earlier coincidence measurements, e.g. [10, 19, 20, 21], a dominant role of breakup-fusion was suggested by comparing the results with calculations based on a semiclassical model [10, 23] or otherwise [19]. In a recent study, a few exclusive events (<1% of the total α yields) could be identified as arising from direct stripping only and comparing the inclusive energy-angle distribution with simulations, it was concluded that direct stripping plays a dominant role in ICF [6]. Thus, a model independent experimental demonstration of the ICF mechanism is still missing. Significant theoretical effort has been invested in understanding the mechanism of the large α-particle production and ICF cross sections [8, 7, 9, 24, 25, 23, 26, 27, 28]. Recently, using a non elastic breakup model, the cluster-stripping process was shown to be the dominant mechanism for ICF [8, 7]. In other studies, fusion of the breakup fragments was considered to be the main ICF mechanism [9, 10, 24, 23]. Calculations assuming both cluster stripping [8, 7] and breakupfusion [9, 10, 24, 23] mechanisms have successfully reproduced experimental inclusive α yields and/or fusion data to a similar extent. Further, it has also been suggested that breakup-fusion and transfer to the continuum of the target are equivalent [9, 25]. It is therefore essential to have experimental data populating the bound states and the continuum with comparable magnitude to discriminate between the two widely different mechanisms. As depicted in Fig. 1, while the outgoing α particle has access to the reaction Q value in the case of direct stripping, the triton fusion (second step) Q value can not be shared with the α particle (produced in the first step) in the two-step breakup-fusion process. A suitable choice of experimental conditions could therefore allow a region which is exclusively populated by only one of these processes to be studied. This letter reports a measurement of particle-γ coincidences for the 7Li+93Nb system to identify the mechanisms responsible for the origin of the large α-particle production and ICF by exploiting the kinematical conditions illustrated in Fig. 1. Experimental observations are compared with Monte-Carlo simulations and quantum mechanical calculations based on the distorted-wave Born approximation (DWBA) for breakup and cluster transfer, respectively. The inclusive and exclusive measurements of α parFigure 1: Illustration of (a) direct cluster transfer and (b) breakup followed by fusion of one of the cluster fragments for a 7Li(α+ t)+target reaction. ticles were carried out using the 7Li beam from the BARC-TIFR Pelletron-Linac facility, Mumbai, in two separate experiments. Targets were self-supporting 93Nb foils of thickness ∼ 1.6 mg/cm2. A beam energy of 24 MeV (1.2VB) was chosen for both measurements to optimize the kinematical conditions and cross section. In the exclusive measurement, prompt γ-ray transitions were detected using the Indian National Gamma Array (INGA) [29], consisting of 18 Compton suppressed high purity germanium (HPGe) clover detectors. Three Si surface barrier telescopes (thicknesses ∆E ∼ 15-30 μm, E ∼ 300-5000 μm) were kept at 35◦, 45◦ and 70◦ for the detection of α particles around the grazing angle. One Si surface barrier detector (thickness ∼ 300 μm) was fixed at 20◦ to monitor Rutherford scattering for absolute normalization purposes. The time stamped data were collected using a digital data acquisition system with a sampling rate of 100 MHz [29]. Efficiency and energy calibration of the clover detectors were carried out using standard calibrated 152Eu and 133Ba γ-ray sources. In the inclusive measurement, angular distributions of α particles and elastically scattered 7Li were measured with three Si surface-barrier detector telescopes (thicknesses: ∆E ∼ 20-50 μm, E ∼ 450-1000 μm) mounted on a movable arm inside the scattering chamber. A typical energy correlation spectrum of prompt γ rays versus outgoing α particles, detected at an angle of 35◦, is shown in Fig. 2(a). Photo-peaks corresponding to the residues (94−96Mo) formed after triton capture (t+93Nb→ 96Mo) are identified and labeled on the projected spectrum in the same figure. Other possible sources of 94−96Mo residues are compound nuclear evaporation (αxn), d-stripping: 93Nb(7Li,5He)95Mo, and p-stripping: 93Nb(7Li,6He∗)94Mo reaction channels. In case of p-stripping, the ejectile (6He) has to be left in an excited state above its 2n emission threshold (975 keV) in order to give an α particle in coincidence with a characteristic γ-rays of 94Mo. As can be seen, γ transitions from 96Mo are mixed with intense transitions from 94Mo and 95Mo. However, after