Breakup mechanisms for 7 Li + 197 Au , 204 Pb systems at sub-barrier energies

Coincidence measurements of breakup fragments were carried out for the 7Li + 197Au and 204Pb systems at sub-barrier energies. The mechanisms triggering breakup, and time-scales of each process, were identified through the reaction Q-values and the relative energy of the breakup fragments. Binary breakup of 7Li were found to be predominantly triggered by nucleon transfer, with p-pickup leading to 8Be → α + α decay being the preferred breakup mode. From the time-scales of each process, the coincidence yields were separated into prompt and delayed components, allowing the identification of breakup process important in the suppression of complete fusion of 7Li at above-barrier energies.


Introduction
The discovery of halo nuclei [1,2] ushered in the development of radioactive ion beams (RIBs).This called for better understanding of the interactions of their cousins, the weakly-bound but stable nuclei.Such understanding is essential in relating the internal nuclear structure, e.g.nucleon clustering and low threshold for cluster-breakup [3][4][5][6], to the reaction outcomes, e.g.fusion, nucleon transfer, and breakup [7].Relating nuclear structure of weaklybound and unstable nuclei to nuclear reaction outcomes within a coherent framework has became an important goal in reaction theory.With 6,7 Li and 9 Be being more accessible, while offering similar characteristics (namely nucleon clustering and low breakup threshold), studying the former presents a great opportunity to understand and predict the behaviour of the much less accessible RIBs.
Complete fusion (CF) of the weakly-bound nuclei 6,7 Li and 9 Be with high-Z targets, at above-barrier energies, are consistently observed [8][9][10] to be lower than theoretical expectation.The low threshold energies for breakup of Li and Be are widely associated with this suppression of CF [8][9][10][11][12][13], with breakup described as cluster decay from unbound states independent of the mechanism that populates it [14][15][16][17][18][19][20].Qualitatively, coupling to channels leading to breakup was shown [21] to suppress CF at abovebarrier energies.More realistic modelling of the inter- play between breakup and CF requires the incorporation of the mechanisms for triggering breakup, the time-scales of breakup [22][23][24], and possible post-breakup capture of the fragments [7,25].To isolate breakup itself from the probability of fragment capture, sub-barrier coincidence measurements of breakup fragments of 7 Li with 197 Au and 204 Pb were performed.The mechanisms for breakup, and their time-scale, were identified through the reaction Q-values and the relative energy of the captured breakup fragments.

Experimental setup
Beams of 7 Li were provided by the 14UD electrostatic accelerator at the Australian National University.They were incident on a self-supporting 197 Au target, 150 µg cm −2 in thickness, and a 400 µg cm −2 thick 204 Pb target on a 20 µm cm −2 carbon backing.The beam energies and target combination are listed in Table 1, along with the centre-ofmass barrier energy V b of each reaction.Charged breakup fragments from the reaction were captured in coincidence using BALiN [27], a detector array consisting of four large area double-sided silicon strip detectors (DSSD) arranged in a lamp-shade configuration with apex angle 45 • .For the given detector thickness of 400 µm, only high-Z particles, α-particles, and low energy protons (<7.0 MeV), deuterons (<9.0 MeV) and tritons (<11.0MeV) would fully deposit their energies in the DSSDs.The detector array was placed at backward angles, covering scattering angles from 117 • to 167 • .The pixel identification characteristics of the DSSDs does not allow position location within the pixel.However, to simplify subsequent event reconstruction, a position was assumed by randomisation, taking a uniform distribution of the position within the physical boundaries of the pixel.

Mechanism for binary breakup
The Verification of the identities of the coincidence particles, and thus the reaction mechanism, requires the reconstruction of the three-body reaction Q-value.Consider a two-body collision with a projectile having initial and final kinetic energy E lab and E f , respectively.The ground-state Q-value, Q gg , for any collision can be written as where E f is the kinetic energy of the projectile-like nuclei, E ex,PL and E ex,TL are the excitation energies of the projectile-like and target-like nuclei respectively, and E rec is the recoil energy of the latter, all in the laboratory frame.
For binary breakup of the projectile-like nucleus, its excitation energy is shared by the kinetic energies E i of the fragments, E f + E ex,PL = E 1 + E 2 , and the reaction Qvalue can be determined from energy balance as where E lab is derived from E beam after correcting for energy lost in traversing the target.The recoil energy E rec and mass of the target-like nucleus is determined through conservation of momentum from the momenta and masses of the two detected fragments [24,28].Since the excitation energy E ex,TL of the target-like nucleus cannot be captured in our detector, the Q-spectra will show separate peaks for each state populated in the target-like nucleus.Shown in Fig. 1 are the reconstructed Q-spectra, not corrected for coincidence detection efficiency, for the reactions of 7 Li with 197 Au and 204 Pb.The spectra show that almost all the yield contributes to sharp peaks in Q, meaning the breakup is indeed almost exclusively binary, with identified breakup modes of α + α (green), α + t (blue), and α + d (magenta).The expected Q gg for respective breakup modes are indicated by dashed lines.
Direct breakup of 7 Li into α + t can be seen to be less probable than breakup triggered by nucleon transfer, e.g.n-stripping of 7 Li leading to 6 Li → α + d, and p-pickup resulting 8 Be → α + α.Peaks in the Q-spectra corresponding to α+α breakup show that the target-like products 196 Pt and 203 Tl are populated mostly in their excited states.For the n-stripping reaction of 7 Li with 204 Pb, the higher E beam allowed population of 205 Pb at up to ≈2.7 MeV excitation.
The Q-value spectra give no clue to the relative population between the ground-and excited-states of 8 Be and 6 Li.However, the energy E ex,PL of the excited states of the target-like nuclei appears in the kinetic energies E 1,2 of the breakup fragments, and have been shown [24] to be related to the time-scales of the process.

Time-scale of breakup and E rel
For binary breakup of the projectile-like nucleus on the outgoing trajectory, the relative energy E rel of the fragments is the sum Q BU + E ex,PL , where Q BU is the breakup Q-value.In terms of measured quantities where θ 12 is the angular separation between the fragments.For breakup close to the target nucleus, the breakup fragments particles will experience tidal effect [29] and E rel no longer depends solely on the breakup energetics.

Relating fragment relative energy to time-scale of breakup
Using the three-body three dimensional model PLATYPUS [30][31][32], an illustrative calculation of the 02004-p.2dependence of E rel on the projectile-target separation at which breakup occurs (R BU ) was performed for breakup of 6 Li from the 3 + (2.186 MeV) state.The distance R BU was uniformly sampled along the trajectory of the 6 Li projectile with energy E beam = 29.0MeV.The orientations of the α+d fragments at R BU , relative to the target nucleus, were also randomly sampled with an isotropic distribution.Shown in Fig. 2 is the result of this calculation.Since this is a classical calculation, the time of breakup T BU relative to that of the closest approach (T 0 ) could be exactly evaluated, and is also shown.For comparison, the one-dimensional experimental E rel spectra for α + d coincidences, from breakup of 6 Li on 205 Pb following n-stripping of 7 Li at E beam = 30.0MeV, is shown above in magenta.

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The variation of E rel as a function of R BU − R 0 is indicative of the dependence of the former on the latter.The wide spread of E rel from breakup before reaching R 0 is due to post-breakup acceleration of the fragments in the Coulomb field of the target nucleus.For breakup after the projectile-like nucleus has travelled past R 0 , E rel converges to ≈ 0.7 MeV, the energy available at breakup.The mapping of radius R BU to the breakup time T BU allows correlation of the time-scale for breakup to the measured E rel .Given that transfer occurs on time-scales of ∼ 10 −22 s [24], information on T BU allows the classification of breakup into prompt (T BU 10 −22 s), or delayed breakup.Prompt breakup results in breakup of the projectile or projectilelike nuclei in the entrance trajectory, and thus reduces the flux of intact nuclei available for fusion at the distance of closest approach R 0 .On the other hand, delayed breakup happens on the exit trajectory, in the asymptotic region.These nuclei have survived breakup at R 0 , and thus would have been able to participate in fusion if the beam energy was above the barrier.

Separation of prompt and delayed breakup
From the established relationship between the E rel spectrum and the time-scale of breakup (Fig. 2(a)), the experimental E rel spectra shown in Fig. 2(b−e) thus give information on the breakup time-scale, allowing a degree of separation between prompt and delayed breakup.For the direct 7 Li → α + t breakup, the broad distribution to high E rel shows its prompt nature, and would possibly play a role in the suppression of CF at above-barrier energies.For breakup at higher E beam , there is a slight peak at E rel ∼ 2.1 MeV, perhaps denoting a tiny fraction of breakup from the 7 2 − (4.65 MeV) state of 7 Li whose lifetime of ∼ 9 × 10 −21 s might just be long enough to see the projectile breakup in the asymptotic region.

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For transfer-triggered breakup, the breakup of 6 Li → α + d following n-stripping have mostly high concentration of events with E rel = 0.7 MeV.This indicates breakup in the asymptotic region, and would have little impact in the CF of 7 Li at above-barrier energies.As for the 8 Be → α + α breakup following p-pickup, the high intensity of events with E rel ≈ 0.1 MeV and broad tails comprising high E rel events follows qualitatively the behaviour of asymptotic and prompt breakup, respectively, as expected from the classical model (Fig. 2(a)).Even when the asymptotic (low E rel ) component is excluded, prompt α + α breakup is still the most probable binary breakup channel for 7 Li.This reaction channel would thus play a major role in the suppression of CF, at above-barrier energies, in 7 Li-induced reactions.

Conclusion
The measurements presented in this work carry the most complete information on breakup in the reactions of 7 Li with high-Z targets.Binary breakup of 7 Li projectile is found to be triggered predominantly by nucleon transfer, both n-stripping leading to the α+ d breakup of 6 Li, and ppickup triggering the 8 Be → α + α decay.The dominance of transfer-initiated breakup is a stark contrast to the expected α + triton cluster breakup of 7 Li.This will provide a major challenge for the quantum theory of low energy nuclear reactions.From the relative energy E rel of the binary breakup fragments, information on the breakup timescales allows the separation of prompt and asymptotic breakup components.By incorporating the breakup timescale into classical model calculations like PLATYPUS, more quantitative understanding of the breakup mechanism and its effects on fusion are expected.
a e-mail: huy.luong@anu.edu.aub Present address: Malmö University, Faculty of Technology and Society, 205 06 Malmö, Sweden c Present address: School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Perth, WA 6009, Australia d Present address: China Institute of Atomic Energy, Beijing 102413, P.R.China

Figure 1 .
Figure 1.Q-spectra determined for the reactions of 7 Li with 197 Au and 204 Pb at indicated energies.Identified breakup modes consist α + d (magenta) and α + α (green).Dashed lines indicate the expected Q gg for each breakup mode.Peaks in the Q-spectra indicate breakup following the population of excited states of the target-like nuclei.(Contribution from α + p are not plotted due ot their insignificant yield.)

Figure 2 .
Figure2.(a) Landscapes of the classically calculated E rel versus the nuclear separation (left axis) or time (right axis) at which breakup occurs, relative to the point of closest approach (R 0 , T 0 ), for6 Li → α + d breakup in the field of a 207 Pb nucleus.The spread in E rel arises from the different impact parameters and fragments orientations at the moment of breakup.Breakup prior to reflection, (T BU − T 0 ) < 0 results in higher E rel values than breakup after reflection (T BU − T 0 ) > 0. Impact parameters corresponding to angular momenta up to 49 were considered.(b−e) Experimental E rel spectra for identified α + α (green), α + t (blue), and α + d (magenta) breakup modes for the indicated reactions.These spectra have neither been corrected for events with incomplete energy deposition, nor for coincidence detection efficiency.

Table 1 .
Beam energies at which measurements were made for the reactions of6Li with indicated targets.E c.m. includes energy loss in the target.