Probing cluster structures through sub-barrier transfer reactions

Multinucleon transfer probabilities and excitation energy distributions have been measured in 16,18O, 19F + 208Pb at energies between 90% 100% of the Coulomb barrier. A strong 2p2n enhancement is observed for all reactions, though most spectacularly in the 18O induced reaction. Results are interpreted in terms of the Semiclassical model, which seems to suggest α-cluster transfer in all studied systems. The relation to cluster-states in the projectile is discussed, with the experimental results consistent with previous structure studies. Dissipation of energy in the collisions of 18O is compared between different reaction modes, with cluster transfer associated with dissipation over a large number of internal states. Cluster transfer is shown to be a long range dissipation mechanism, which will inform the development of future models to treat these dynamic processes in reactions.


Introduction
The propensity of nucleons within the nuclear medium to coalesce into alpha-particles has been known since the earliest days of nuclear physics.Alpha-decay, in which the Helium nucleus emerges preformed from the parent nuclide was one of the first discoveries in the field.In fact, some of the initial models of nuclear structure (prior to the discovery of the neutron) posited the alpha particle as the basic building block of the nucleus [1].Such models quickly fell out of favour with the formulation of the liquid drop and shell model of the nucleus, which were better able to predict nuclear properties.However, in recent years cluster models have seen a renaissance, due to their ability to predict certain peculiar spectral properties of some light nuclei.
A classic example of a cluster is the first excited 0 + state in 12 C, known as the Hoyle state [2]; a resonance state of three alpha particles that decays only very rarely to stable 12 C, and is the sole production mechanism of this isotope, that is essential to all life on earth.Whilst many studies have examined the properties of cluster resonance states in α-conjugate nuclei (those that are even-even with N = Z), more recently cluster states have been identified in nonconjugate nuclei, with this phenomena seen to be particularly important in neutron-rich nuclei that have become accessible with the advent of radioactive ion beam facilities.The influence of such structures on reaction dynamics remains mostly unexplored.Coupled channels models have been very successful at reproducing fusion cross sections in the near-barrier region a e-mail: dominic.rafferty@anu.edu.au[3], but there are discrepancies both above and far below where cross sections are hindered relative to the predictions [4,5].At above barrier energies this has been attributed to dissipative processes that occur during the very violent impact between the ions.Past experiments have shown that dissipation remains important even at subbarrier energies, so may also have some bearing on the hindrance effects seen in this energy region.Cluster transfer is a possible long-range dissipation mechanism [6], since the cluster states that might be expected to participate are predicted to be radially diffuse [7].In this work multi-nucleon transfer probabilities and excitation energy distributions in 16,18 O, 19 F + 208 Pb spanning the well-below to above barrier energy regions have been measured.The chosen projectiles have been previously identified to exhibit clustering properties in the context of structure studies [8].How multi-nucleon transfer varies between the projectiles and how the prominence of different channels evolves as a function of the internuclear separation, as well as how energy is dissipated between the reaction partners has been studied.

Experiment
An experiment was performed at the Heavy Ion Accelerator facility at the ANU in June 2013, in which a 208 Pb target was bombarded with 16  The detector used in this experiment was a simple Frischgrid ionization chamber, coupled to a Silicon detector [9].
As ions enter the detector, their energy loss in the gas (ΔE) is recorded together with their residual energy on reaching the Silicon detector (E Si ).Together these allow a separation of the reaction products in mass and Z.

Analysis
To identify reaction products, the unique locus of each species must be determined from the ΔE − E Si spectrum, a typical example of which is shown in Fig. 2

Results
The measured transfer probabilities have been interpreted in terms of the Semiclassical model [10].In this approach, the probability of each mode has the form: Where r min is the distance of closest approach, and α is related to the binding energy of the transfered nucleons.α can be calculated or extracted from transfer probability data, by fitting the exponential slope of the probabilities outside the barrier radius-for the systems studied, this involves fitting the data beyond r min ≥ 13.2 fm.At the subbarrier energies studied, it is assumed that the trajectories are purely Coulomb enabling a calculation of r min using: where p and t denote projectile and target respectively.In this simple model of independent sequential transfer, the probability for transfer of N nucleons is a simple product of probabilities: Red curves indicate the resulting fitted components, which are attributed to yields of the expected isotopes, in this case 12,13,14 C. Vertical dashed lines show the gate limits as determined by the intersections between adjacent fitted peaks.
More realistic transfer probabilities can be calculated with advanced microscopic models [11,12].In this section transfer probabilities as a function of r min and an example of the extracted excitation energy spectra are shown.

Transfer Probabilties
4.1.1 16O + 208 Pb : Fig. 3 Single proton transfer is shown to be dominant over the energy range considered.The semiclassical prediction for 2p transfer is shown as the red dashed line in this figure.This is the square of a fit to the 1p data beyond 13.2 fm, where the loss of flux to fusion does not disturb the exponential slope α.As shown, the two prominent ΔZ = 2 modes shown in the figure are strongly enhanced relative to this prediction.Also interesting is the increasing equiv-  cluster structure.This is fully consistent with such a dominance of 2p2n over other transfer modes.

19 F + 208
Pb : Fig. 5 Single proton transfer is strongest here over the whole energy range.2p is shown to be very weak, falling in fact lower than the Semiclassical prediction.ΔZ = 2 transfer is dominated by the 2p2n mode.A strong population of events with ΔZ = -3, with a significant yield of 14 C at all energies is observed.The 3p2n is most significant, and is equivalent in magnitude to 2p2n at higher energies.This channel falls off quickly however, whilst the 2p2n decays in proportion to 1p with increasing distance.Previous studies of this reaction at energies closer to the barrier [16] found similar results, and interpreted this behaviour as evidence of clustering in 19 F, and in particular that the strong enhancement of 3p2n transfer was indicative of a direct (non-sequential) transfer of p + α.Here it is shown that this enhancement seems to disappear at larger internuclear separations.The strong 2p2n mode, on the other hand, seems to maintain the enhancement down to the deep sub-barrier region.

Energy Dissipation
The reaction Q-value is reconstructed on an event-byevent basis, from which the excitation energy can be derived.The Q-value can be determined from: Where the subscript notation is in standard reaction form 1(2,3)4, with E denoting energies and A atomic masses.The excitation energy is then obtained from the difference between this value and the ground state Q-value for the reaction mode in question Q g.g : In Fig. 6 shown is the recorded E x spectra for the 1p and 2p2n transfer modes in 18 O + 208 Pb.Since the target is so much heavier, with a much higher level density than the light projectiles, the target-like fragment is expected to absorb most of the excitation energy in the transfer process.Observed in Fig. 6 is that whilst the transfer of a single proton shows a detailed structure most concentrated at low E x , the transfer of 2p2n (α) is associated with a strong broad distribution of energy extending up to higher E x distributions, reaching ∼ 10 MeV even at the lowest energy.

Conclusions
It has been demonstrated that there are vastly different transfer reactions between the 16,18 O, 19 F + 208 Pb.These effects are likely related to cluster structures that can be found in the projectiles.The very strong 2p2n transfer mode in 18 O + 208 Pb is consistent with previous investigations into clustering in 18 O. 16O, despite being an α-conjugate nucleus, displays comparatively weak 2p2n transfer, though it appears to grow in relation to 2p with internuclear separation. 19F also displays a strong 2p2n mode, that can be attributed to cluster transfer on the basis of the very weak 2p mode.Excitation energy distributions involving the transfer of multiple nucleons are typically broad and featureless, and it has been shown how in 18 O + 208 Pb the transfer of an αparticle led to high excitation energies, well above the particle emission thresholds in the target-like fragment, even well below the barrier.While omitted here for brevity, 16 O and 19 F-induced reactions show similar behaviour.This is a potential mechanism through which energy dissipation can occur at long separations.It is the goal of this project to establish the systematics of how this differs among light to medium mass projectiles, at energies near to far below the Coulomb barrier.A modified version of the coupled channels code CCFULL [17] is in development to incorporate dissipation into this framework in an attempt to understand the effect of dissipation on fusion cross sections.
(a).The red line in the figure shows the locus of 12 C, mapped by tracing the distribution of inelastically scattered 12 C from a thick tantalum target.Projecting the ΔE − E Si spectrum in ΔE allows for a separation of the products within the gated region shown in Fig. 2 by mass.A typical mass separation spectrum is shown in Fig. 2(b), where the products are rebinned according to their relative ΔE compared to a product for which the locus in the ΔE − E spectrum is well known.

Figure 2 .
Figure 2. (Colour online) (a) ΔE − E Si plot obtained in the reaction16 O + 208 Pb at 0.98V B .The red line shows the12 C locus from which the relative energy loss (ΔE rel ) spectrum is calculated.The ΔE rel spectrum is determined from events within the dashed contour.(b) Resulting ΔE rel spectrum.Black dashed curve shows the multiple Gaussian function fitted to the distribution.Red curves indicate the resulting fitted components, which are attributed to yields of the expected isotopes, in this case12,13,14 C. Vertical dashed lines show the gate limits as determined by the intersections between adjacent fitted peaks.

Figure 5 .
Figure 5. Transfer probabilities in 19 F + 208 Pb.Blue dashed line shows a fit to the 1p data in the range r min > 13.2 fm.Red and green dashed lines are the square and cube respectively of the fitted 1p function, corresponding to the prediction of the semiclassical model (equation 2).
O,18O, and19F beams, at energies from 100% to 90% of the Coulomb barrier V B .The experimental setup is shown in Fig 1.The light projectilelike fragments were detected at 160.6 o , with yields normalized to elastic scattering events in two forward angle monitor detectors to obtain absolute transfer probabilities.
[13]sfer probabilities in16O + 208 Pb.Full symbols are the measurements reported from the June 2013 experiment.Empty symbols are those measured in a previous experiment[13]with a lower mass resolution.Blue dashed line shows a fit to the 1p data in the range r min > 13.2 fm.Red dashed line shows the square of the fitted function, representing the prediction of the Semiclassical model for sequential transfer (see equation 2). Figure 4. Transfer probabilities in 18 O + 208 Pb.Blue dashed line shows a fit to the 1p data in the range r min > 13.2 fm.
[8,14,15]wn is the fit of 1p data, but the semiclassical predictions (e.g.P 2p = (P 1p )2) for all other significant transfer modes in this case are not visible within the range of the figure.Previous experiments have demonstrated a rich cluster structure in 18 O[8,14,15], with α resonant states found over a wide excitation range and attributed to a 14 C + α Figure 6.Excitation energy distribution of 1p and 2p2n modes in 18 O + 208 Pb as it varies with bombarding energy, given in units of the Coulomb barrier energy V B .