Energy calibration

Energy calibration of the DSSDs was carried out using two α sources (²³⁹Pu, ²⁴¹Am), and the α particles decayed from the products of the fusion reactions. Additionally, energy calibrations of the QSDs were performed by evaluating the deposited energies of the charged particles within the QSDs. This was achieved by subtracting the measured energy loss in the DSSDs from the expected particle energy, as determined by calculations using the reference for LISE++. In the experiment, the coordinate location of the DSSDs pixels was used to determine the scattering angle of the charged particles detected by the detectors. A typical energy-calibrated single spectrum for ⁷Li + ²⁰⁹Bi measured at E_beam = 40 MeV is presented in Fig. 4, which shows elastic scattering events at ~36 MeV. For reactions in normal kinematics that produce two nuclei in the final state, such as elastic scattering or transfer, the energy of a projectile-like nucleus decreases monotonically with θ. The α lines between 5 and 10 MeV, as shown in Fig. 4, with energies independent of the angle, originate from the evaporation residues formed following complete fusion (CF) and incomplete fusion (ICF).

Fig. 4Full-screen View

(Color online) Energy-calibrated single spectrum for ⁷Li + ²⁰⁹Bi measured at E_beam = 40 MeV and displayed across the angular coverage of No.0-3 telescope units

Removal of spurious events

According to the principle of DSSDs, we used the energy signal output from both sides of the DSSDs (marked E_loss1, E_loss2, respectively) to select the correct events. As shown in Fig. 5(a), considering the statistics of events and the proportion of accidental coincidences, we select the events with E_loss1 - E_loss2 distributed within the σ (~100 keV) widening range as correct events. The two-dimensional spectrum E_loss1 vs. E_loss2 after screening is shown in Fig. 5(b). During the experiment, a large number of particles hit the inter-strips of the DSSDs, leading to a non-negligible number of accidental coincidence events (~3%). The two-dimensional spectra of the particles depositing energy in adjacent strips of the same DSSD before and after screening based on (a) are illustrated in Figs. 5(c) and (d). In Fig. 5(c), inter-strip events mainly originate from α, p, d, t particles distributed on the different lines $y=-x+c$. These events were removed after energy screening of the DSSDs, as shown in Fig. 5(d).

Fig. 5Full-screen View

(Color online) Example of No.0-3 telescope unit to demonstrate accidental events removal from ⁷Li + ²⁰⁹Bi at E_beam = 40 MeV. (a) The single energy spectrum of the difference in energy loss between the two sides of DSSD. (b) The two-dimensional energy spectrum E_loss1 vs. E_loss2 of the two sides of DSSD after screening based on (a). (c)(d) Particle energy deposition on adjacent silicon strips in the same side of DSSD before and after screening based on (a)

Typical two-dimensional particle identification spectra obtained from the same telescope unit are shown in Fig. 6. Owing to the excellent energy resolution of the detectors and statistics, the different masses (A = 1–7) and charges (Z = 1–3) produced by the different reaction channels can be clearly identified. In particular, the ³He and ⁶He bands can be observed in the experimental data of ^6,7Li, which provides the possibility of observing new breakup modes. In Fig. 6(a), ⁷Li band can be observed. It is evident that ⁶Li picked up one neutron from the target; thus, 1n-pickup process induced by ⁶Li can occur. In Fig. 6(b), ⁶Li band can be observed. This is due to 1n-stripping of ⁷Li. The results show that 1n-stripping process is populated in the reactions of ⁷Li. The other light particles were analyzed in sections below.

Fig. 6Full-screen View

(Color online) Calibrated two-dimensional ΔE-E particle identification spectra by No.2 telescope unit which covers an angular range from 110° to 155°. (a) for ⁶Li + ²⁰⁹Bi at E_beam = 40 MeV, (b) for ⁷Li + ²⁰⁹Bi at E_beam = 40 MeV

Identification of breakup modes

During the breakup process, momentum conservation dictates that the total momentum of the fragments should remain zero in the center of mass frame of the projectile-like nucleus. Thus, fragments must travel in opposite directions in the center of the mass frame but may be emitted in any direction. As a result, we can filter out α particles from the breakup process, as shown in Fig. 7(a), from ⁶Li + ²⁰⁹Bi at E_beam = 40 MeV, when a continuous distribution of energies with maximum and minimum energies is given by $E_{\text{min,max}}=\frac{m_1}{m_1+m_2}\left(E_{\text{p}}+\frac{m_2}{m_1}{Q}_{\text{BU}}\pm 2\sqrt{\frac{m_2}{m_1}{Q}_{\text{BU}}{E}_{\text{p}}}\right)，$ (1) E_p is the projectile-like fragment energy prior to breakup, m_i is the mass of the breakup fragments, and Q_BU is the Q-value for the breakup process. Figure 7(b) shows the current particle multiplicity (the number of particles contained in a coincidence event). We can observe that inclusive elastic scattering or transfer events still account for the majority, and the rest are the two coincidence fragments we expected.

Fig. 7Full-screen View

(Color online) (a) Single energy spectrum of inclusive α from No.0-3 telescope units. (b) Particle multiplicity of the entire array. (c)(d) The two-dimensional energy spectrum of the direct breakup modes from ^6,7Li at E_beam = 40 MeV

The correlations between the kinetic energies of the coincident fragments from the direct breakup mode of ^6,7Li at E_beam = 40 MeV are presented in Figs. 7(c) and (d). The band-like structures are immediately obvious, which suggests that these events have originated from the true ⁶Li → α + d and ⁷Li → α + t breakup processes. Other breakup events from different modes can be extracted in the same manner.

Based on the extracted breakup events, two-body dynamics calculations can be used to reconstruct the breakup reaction Q value to further understand the breakup mechanism. The energy change (Q value) in the reaction can be determined by Eq. (2): $Q=E_1+E_2+E_{\text{rec}}-E_{\text{lab}}.$ (2) E₁, E₂ are the kinetic energies of the coincidence particles in the reactions. E_rec is the energy of the recoiling target-like nucleus determined by conservation of momentum in three body system. E_lab is the laboratory kinetic energy of the incident projectile (E_beam for energy loss in the target after correcting). The ground-state Q value (Q_gg), for any collision can be expressed by: $Q_{\text{gg}}=E_{\text{p}}+E_{\text{p,x}}+E_{\text{rec}}+E_{\text{t,x}}-E_{\text{lab}},$ (3) where E_p is the kinetic energy of projectile-like nuclei and E_p,x and E_t,x are the excitation energies of projectile-like nuclei and target-like nuclei, respectively. For binary breakup, E_p + E_p,x = E₁ + E₂. Therefore, the Q spectra provide more information for each state populated in the target-like nucleus (calculated using E_t,x = Q_gg - Q).

The reconstructed Q spectra of all the breakup modes in the reactions of ^6,7Li with ²⁰⁹Bi at E_beam = 30, 40 and 47 MeV are shown in Fig. 8. Vertical dashed lines indicate the expected Q_gg, which corresponds to the ground state of the target-like nucleus. In the reaction of ⁶Li, compared with the direct breakup mode (⁶Li → α + d), the breakup of ⁵Li into α + p after 1n-stripping seems to be the most dominant, as can also be verified in Refs. [23, 36, 37]. In addition, a new breakup mode, ⁷Li → α + t was observed for the first time by STARE with obvious Q value peaks, indicating the ground and excited states of ²⁰⁸Bi. We can observe that the relevance of the ⁷Li → α + t channel increases with beam energy. The discovery of ⁷Li → α + t breakup mode indicates that the 1n-pickup process cannot be ignored in the reaction of ⁶Li, which also provides an additional explanation for the origin of inclusive α particles [38, 39].

Fig. 8Full-screen View

(Color online) The Q value spectra determined for ^6,7Li + ²⁰⁹Bi at E_beam = 30, 40, 47 MeV including different breakup modes, the vertical dashed lines indicate the expected Q_gg for each breakup mode in reactions of ⁶Li and ⁷Li, respectively

For the reaction ⁷Li + ²⁰⁹Bi, the breakup triggered by a 1p-pickup is the most probable channel for ⁷Li. The breakup after the production of ⁸Be into two α particles produces multiple peaks in the Q value spectra, including the ground state and two excited states of ²⁰⁸Pb. However, when the target is replaced by a medium-mass nucleus, conclusions may be inconsistent. In the ⁷Li + ⁹³Nb system [40], α + t and α + d are dominant. When the beam energy was increased to 40, 47 MeV, despite a very high breakup threshold (~10 MeV), a significant number of ⁶He + p events were observed in ⁷Li + ²⁰⁹Bi system. The present exclusive measurement of ⁶He in coincidence with a proton that provides direct evidence of the ⁶He + p cluster configuration of ⁷Li is important for understanding the possible nuclear cluster structures of ⁷Li [41].

Prompt breakup vs. Reasonant breakup

In recent works [25, 36], the relative energy (E_rel) of breakup fragments has been reported to provide significant information on the breakup time-scale and to allow a classification of the breakup process into prompt breakup or resonant breakup, which can be expressed in terms of the measured energies and masses of the fragments, and the measured opening angle of the fragments within the laboratory frame (${\theta }_{\text{12}}$): $E_{\text{rel}}=\frac{m_2{E}_1+m_1{E}_2-2\sqrt{m_1{E}_1{m}_2{E}_2}\cos {\theta }_{12}}{m_1+m_2}.$ (4) As presented in Figs. 9(a) and (b), the E_rel distribution of ²⁰⁹Bi(⁶Li,⁶Li→α+d)²⁰⁹Bi and ²⁰⁹Bi(⁷Li,⁷Li→α+t)²⁰⁹Bi at E_beam = 40 MeV is peaking around at ~0.7 and ~2.1 MeV, which correspond to the resonant states of ⁶Li (3⁺, 2.186 MeV) and ⁷Li (7/2^-, 4.63 MeV), respectively. These peaks are associated with the breakup on the outgoing trajectory, which is not affected by the target-like Coulomb field and can be described as a resonant breakup. On the other hand, when the lifetime of the final state in the projectile-like nucleus is lower than the breakup scale (~10^-22 s), breakup will occur in the entrance channel close to the target-like nucleus (prompt breakup) with a smooth and continuous E_rel distribution as a consequence of the Coulomb interaction exerted by the target-like nucleus. To better identify the different breakup components experimentally, new insights were focused on the angular correlation spectra. As shown in Figs. 9(c) and (d), the expected correlation between β and ${\theta }_{\text{12}}$ for resonant breakup from ⁶Li → α + d and ⁷Li → α + t corresponds well to the red solid lines, which confirms the interpretation of these events breakup far from the target-like nucleus. β is the orientation of the relative velocity of the fragments with respect to the motion of their center of mass, as determined by Eq. (5). v_i and u_i are the velocities of each fragment in the laboratory and their center-of-mass frame, respectively. A schematic of the relationship between these variables is shown in the upper right corner of Fig. 9(d). For events arising from breakup near the target-like that correspond to the prompt breakup, the β vs. ${\theta }_{\text{12}}$ correlation is distorted owing the influence of Coulomb interaction on the fragment trajectories. The prompt and resonant breakup components can be distinguished well by the relative energy spectrum and angular correlation spectrum calculated using STRAE. $\sin \beta =\frac{v_1{v}_2\sin {\theta }_{12}}{\sqrt{v_2^2{u}_1^2+v_1^2{u}_2^2+2u_1{u}_2{v}_1{v}_2\cos {\theta }_{12}}}$ (5)

Fig. 9Full-screen View

(Color online) (a)(b) Distributions of the relative energy of the coincident breakup fragments in direct breakup modes induced by ^6,7Li + ²⁰⁹Bi at E_beam = 40 MeV. (c),(d) The β vs. θ₁₂ spectra of breakup pairs for ^6,7Li + ²⁰⁹Bi at E_beam = 40 MeV. Solid lines show the expected β vs. θ₁₂ correlation assuming resonant breakup from the long-lived 3⁺ resonant state in ⁶Li and 7/2^- resonant state in ⁷Li