Received 29 May 2015; accepted 25 October 2015; published 28 October 2015

ABSTRACT

The study of inelastic scattering and multi-nucleon transfer reactions was performed by bombarding a ⁹Be target with a ³He beam at the incident energy of 30 MeV. Angular distributions for ⁹Be(³He, ³He)⁹Be, ⁹Be(³He, ⁴He)⁸Be, ⁹Be(³He, ⁷Be)⁵He, ⁹Be(³He, ⁶Li)⁶Li and ⁹Be(³He, ⁷Li)⁵Li reaction channels were measured. Experimental angular distributions for the corresponding ground states (g.s.) were analyzed within the framework of the optical model, the coupled-channel approach and the distorted-wave Born approximation. Cross sections for channels leading to unbound ⁵He_g.s., ⁵Li_g.s. and ⁸Be systems were obtained from singles measurements where the relationship between the energy and the scattering angle of the observed stable ejectile was constrained by two-body kinematics. Information on the cluster structure of ⁹Be was obtained from the transfer channels. It was concluded that cluster transfer was an important mechanism in the investigated nuclear reaction channels. In the present work an attempt was made to estimate the relative strengths of the interesting (n + ⁸Be) and (α + ⁵He) cluster configurations in ⁹Be. The contributions of different exit channels have been determined confirming that the (α + ⁵He) configuration plays an important role. The configuration of ⁹Be consisting of two bound helium clusters (³He + ⁶He) is significantly suppressed, whereas the two-body configurations (n + ⁸Be) and (α + ⁵He) including unbound ⁸Be and ⁵He are found more probable.

Keywords:

Nuclear Reaction Mechanism, Cluster Structure, DWBA

1. Introduction

In recent years the study of light radioactive nuclei [1] [2] has intensified due to the significant progress made with radioactive beam facilities. It has led to a decrease of interest in the study of light stable nuclei such as ^6,7Li and ⁹Be. It has been shown that in light nuclei the nucleons tend to group into clusters, the relative motion of which defines to a large extent the properties of these nuclei. Consequently, the cluster structure of their ground as well as low-lying excited states became the focus of theoretical and experimental studies. For example, ⁶Li and ⁷Li nuclei are both well described by the two-body cluster models ((α + d) and (α + t), respectively).

Due to its Borromean structure, a special attention has been focused on the ⁹Be nucleus, which may break up directly to α + α + n or via one of two unstable intermediate nuclei: ⁸Be or ⁵He.

The breakup of ⁹Be via ⁸Be_g.s. has been measured for many of the low-lying excited states of ⁹Be [3] [4] . However, the breakup branching via the first-excited 2⁺ state of ⁸Be and via ⁵He remained uncertain.

The three-body configuration (α + α + n) of ⁹Be may be of a significant astrophysical interest. The short lifetimes of ⁸Be_g.s., the first-excited state of ⁸Be and ⁵He_g.s. suggest that the sequential capture of a neutron or an α particle is very unlikely. The formalism used to derive the (ααn) rate by Grigorenko et al. [5] also suggested that any broad intermediate resonances would have little effect on the (ααn) rate. However, according to another theoretical calculation [6] the stellar reaction rate for this reaction proceeding via the ⁵He_g.s. channel is significant for the formation of ⁹Be.

In the measurement [7] of the ⁹Be(⁷Li, ⁷Liα)αn reaction it was unambiguously established for the first time that the excited states of ⁹Be around 6.5 and 11.3 MeV decayed into the α + ⁵He channel.

In Ref. [8] , the structure of ⁹Be was discussed in the frame of isobaric analogue states of ⁹B. It was found that the decay of ⁹B had the dominant branch α + ⁵Li implying that “the corresponding mirror state in ⁹Be would be expected to decay through the mirror channel α + ⁵He, instead of through the n + ⁸Be(2⁺) channel. The mirror state of ⁹Be at 2.429 MeV is also reported to decay by α emission”. In this case it would decay to the unstable ground state of ⁵He producing the n + 2α final state. On the contrary, another experimental work claimed that this state decayed almost exclusively by n emission to the unstable first-excited state of ⁸Be.

The excited states of ⁹Be have been populated in various ways including among others β-decay [9] . Most experiments confirm that the 2.429 MeV state has a branching ratio to the ⁸Be_g.s. + n channel of only 7%, but could not determine whether the remaining strength is in the ⁸Be(2⁺) + n or the ⁵He + α channel. However, it was reported in Ref. [9] that the ratio 2:1 could be assigned to these channels, respectively.

The results of Refs. [3] - [5] [7] [8] along with the qualitative breakup data discussed above suggest the necessity of obtaining quantitative branching-ratio data for the low-lying states in the Borromean nucleus ⁹Be.

The present experiment was designed to study the breakup of ⁹Be in the attempt to determine the contribution of ⁵He + α and n + ⁸Be channels. Our data are based on inclusive measurements, whereas the experimental results of Refs. [3] [4] were obtained in exclusive measurements. The exclusive measurements require fully defined kinematics with complicated detector systems allowing the complete reconstruction and identification of the breakup event. The inclusive measurements, in spite of their simplicity, may also be useful in the study of clustering phenomena. For example, in our recent paper [10] the obtained large value of the deformation parameter might be considered as the confirmation of the cluster structure of the low-lying states of ⁹Be. However, the inclusive measurement did not allow us to give unambiguous preference to one of the possible configurations, e.g. (α + α + n) or (α + ⁵He).

Another purpose of the present study was the attempt to obtain some information about the cluster structure of ⁹Be and try to understand how the cluster structure influenced the nuclear reaction mechanism.

Indeed, Détraz et al. [11] [12] argued that multi-particle-multi-hole structures were expected to occur at rather low excitation energies in nuclei. Therefore, four-nucleon transfer reactions have been extensively studied. It is hoped that the major features of such reactions, in spite of the a priori complexity of such a transfer, may be understood assuming that the nucleons are transferred as a whole, i.e. strongly correlated in the cluster. The angular distributions of the ⁹Be(³He, ⁷Be)⁵He and ⁹Be(³He, ⁶Li)⁶Li reaction channels were scrupulously measured at the energy of 60 MeV for the transitions to the ground states of ⁵He and ⁶Li by Rudchik et al. [13] . The experimental data were analyzed using the coupled reaction channels (CRC) model including one- and two-step cluster transfer and cluster spectroscopic amplitudes calculated in the framework of the translation-invariant shell model. It was concluded that the cluster transfer was unimportant: in the ⁹Be(³He, ⁷Be)⁵He reaction channel the α-transfer dominated only at small angles while the transfer of two neutrons dominated at large angles. Nevertheless, the conclusion of Ref. [13] in general supports the idea of cluster transfer.

2. Experimental Procedure

The ³He + ⁹Be experiments were performed at the K130 Cyclotron facility of the Accelerator Laboratory of the Physics Department of Jyväskylä University and at the Nuclear Physics Institute (NPI), Řež, Czech Republic. The ³He beam energy was 30 MeV. The average beam current during the experiments was maintained at 10 nA. The self-supporting Be target was prepared from a 99% pure thin foil of beryllium. The target thickness was 12 μm. Peaks due to carbon and oxygen contaminations were not observed in the energy spectra.

To measure (in) elastically scattered ions four Si-Si(Li) telescopes each consisting of ΔE₀, ΔE and E_r detectors with thicknesses 10 μm, 100 μm and 3 mm, respectively, were used. Each telescope was mounted at the distance of 45 cm from the target. Particle identification was based on the measurements of energy loss ΔE and residual energy E_r (the so-called ΔE-E method). The telescopes were mounted on rotating supports, which allowed to obtain data from θ_lab = 18˚ to θ_lab = 107˚ in steps of 1˚ - 2˚. The overall energy resolution of the telescopes was ~200 keV. The two-dimensional plots energy loss ΔE vs. residual energy E_r and ΔE₀ vs. ΔE are shown in Figure 1(a) and Figure 1(b), respectively. The excellent energy resolutions of both ΔE and E_r detectors allowed unambiguous identification of A and Z of each product. The panel (a) is mainly related to the transfer from the projectile to the target, whereas the panel (b) is completely related to the transfer from the target to the projectile.

Figure 2 shows experimental spectra of the total deposited energy for the detected ⁴He, ⁷Be and ⁷Li, measured at θ_lab = 18˚ for the reaction ³He (30 MeV) + ⁹Be. The plotted total energies were calculated as the sum of the calibrated energy losses ΔE and the residual energy E_r. The ground and the most populated excited states of ⁸Be, ⁵He and ⁵Li in the reaction channels ⁹Be(³He, ⁴He)⁸Be, ⁹Be(³He, ⁷Be)⁵He and ⁹Be(³He, ⁷Li)⁵Li were unambiguously identified.

Since ⁸Be, ⁵He, and ⁵Li are unbound nuclei and decay into ⁴He + ⁴He, ⁴He + n and ⁴He + p, respectively, we calculated the positions in the measured spectra (Figure 2) of the maximum energies of ⁴He, ⁷Li and ⁷Be, assuming either two bodies or three bodies in the exit channels. Calculations were performed with the aid of the NRV server [14] . The solid arrows show the maximum values of the kinetic energies of the detected ⁴He, ⁷Be and ⁷Li, which correspond in the case of ⁴He, ⁷Be and ⁷Li, to the two-body character of the reaction in the exit channels: ⁹Be(³He, ⁴He)⁸Be, ⁹Be(³He, ⁷Be)⁵He and ⁹Be(³He, ⁷Li)⁵Li, respectively. The maximum values of the

kinetic energies in the case of three-body final states in the reaction channels ⁹Be(³He, ⁴He + ⁴He)⁴He, ⁹Be(³He, ⁷Be)⁴He + n and ⁹Be(³He, ⁷Li)⁴He + p are shown by the dashed arrows. As can be seen from Figure 2, the local maxima at the g.s. are close to the values corresponding to the two-body exit channels in all studied reaction channels. This indicates that the two-body reaction channels dominate leading to the unbound ⁸Be, ⁵He and ⁵Li in their ground states. Therefore, it may certainly be concluded that one-step multi-nucleon transfer is the main reaction mechanism leading to the binary exit channels.

The broad ground state of ⁵He in the spectrum is overlapping with the ground and first-excited states of ⁷Be, which explains why the peak is rather broad (FWHM ~1.5 MeV). In the case of ⁵Li (Figure 2(c)) the ground state in not really prominent showing a larger value of FWHM than in the case of ⁵He. It might indicate that ⁵Li is a more loosely bound nucleus than ⁵He due to the Coulomb repulsion of the additional proton from the α core.

3. Results

3.1. Elastic and Inelastic Scattering

The measured angular distributions for the reaction channels: (a) ³He + ⁹Be → ⁷Be + ⁵He (♦), ³He + ⁹Be → ⁷Li_g.s. + ⁵Li (□), ³He + ⁹Be → ⁶Li + ⁶Li_g.s. (▲), ³He + ⁹Be → ⁴He + ⁸Be_g.s. (Δ), ³He + ⁹Be → ⁶He + ⁶Be_g.s. (●); (b) ³He + ⁹Be → ⁴He + ⁸Be_g.s. (Δ), 3.0 MeV (■) and 16.6 MeV (_*) excited states of ⁸Be are shown in Figure 3.

First of all, one may notice that the cross section for the case of ⁷Be + ⁵He is much larger than for the other reaction channels shown in Figure 3.

The ⁷Be energy spectrum (Figure 2(b)) indicates the large probability of population of the ground state of the ⁵He nucleus in conjunction with the 3⁻ ground state and the 1/2⁻ first-excited (0.429 MeV) state of ⁷Be (unresolved in the present experiment). Therefore, the angular distribution for the ⁷Be + ⁵He (♦) channel corresponds to the ground state and the first-excited state of ⁷Be.

As it was mentioned, this exit channel of the reaction has the largest cross section among the channels shown in Figure 3(a). The calculated Q-values of the investigated channels are given in the inset of Figure 3(a). It may be seen that the behavior of the cross sections does not strictly follow the famous Q-reaction systematics. For instance, the measured differential cross section for the channel ⁴He + ⁸Be_g.s. with the maximum value of Q = +19 MeV is much less than for the channel ⁵He + ⁷Be (Q = −0.7 MeV). The lowest cross section was observed for ⁶He + ⁶Be_g.s. (Q = −9.7 MeV).

Figure 3(b) shows the angular distributions for the ⁴He + ⁸Be channel populating the g.s. as well as the 3.0 MeV and 16.6 MeV excited states. It seems that the high positive Q-value (19 MeV) for this channel allows to excite very high-lying levels in the unbound ⁸Be nucleus. It is clear that for this channel the cross section corresponding to the 16.6 MeV level dominates over the others.

In order to describe various reaction channels within the coupled-channel (CC) framework special attention was paid to the elastic scattering to obtain the optical model (OM) potentials. The OM potential was chosen

in the usual Woods-Saxon form V(r) = −V₀f(r, R_v, a_v) − iW₀f(r, R_w, a_w), where the function f (r, R, a) = (1 + e^(r−R)/a)⁻¹ and radii R_i = r_iA^1/3 depend on the mass of the heavier fragment A and the corresponding reduced radius r_i. In addition, a spin-orbit potential with a Woods-Saxon form has been used.

In the first step, the experimental data for the elastic scattering of ³He + ⁹Be were fitted. The obtained OM potential parameters are listed in Table 1 in comparison with the parameters of Ref. [13] . The results of fitting are shown in Figure 4 together with the experimental data.

The difference between the obtained parameters and those of Ref. [13] is probably due to the different projectile energies: our data were obtained at 30 MeV and the data of Ref. [13] were obtained at 60 MeV. For instance, the depths of the real and imaginary parts are smaller at the lower incident energy, whereas the radii are larger than those of Ref. [13] . Concerning the ⁹Be(³He, ⁵He)⁷Be reaction channel, the OM parameters of both sets do not reflect any possible peculiarities which might be expected due to the unbound nature of ⁵He_g.s. (for example, a larger radius of this unbound nucleus considered as the candidate for one-neutron halo structure).

In the second step of the data analysis, the cross section for the channel ⁹Be(³He, ⁴He)⁸Be_g.s. was fitted and the OM potential parameters for the exit channel ⁴He + ⁸Be were obtained. In the fitting process, the OM potential parameters for the elastic scattering of ³He + ⁹Be obtained in the first step were used.

In the third step, the cross section for the transfer reactions ⁹Be(³He, ⁷Be)⁵He was fitted and the OM potential parameters for the exit channel ⁷Be + ⁵He were obtained (Table 1). In the fitting process, the OM potential parameters for the elastic scattering of ³He + ⁹Be obtained in the first step were used. In the calculations of the total cross section both transition amplitudes corresponding to the alpha-transfer mechanism (⁹Be(³He, ⁷Be)⁵He channel) and the 2n-transfer mechanism (⁹Be(³He, ⁷Be)⁵He channel) have been taken into account. All calculations and fitting have been performed using the FRESCO code [15] in the framework of the CC method.

By fitting the experimental angular distributions the attempt was made to determine which reaction mechanisms are the most important for the measured distributions. The results are shown in Figure 5 for the following channels (a) ³He + ⁹Be → ⁴He + ⁸Be_g.s. (Δ), (b) ³He + ⁹Be → ⁷Be + ⁵He (♦) and (c) ³He + ⁹Be → ⁶Li + ⁶Li_g.s. (▲).

It is clear that in the case of ³He + ⁹Be → ⁷Be + ⁵He reaction channel the α-transfer (long-dashed curve) dominates at forward angles, whereas the transfer of the two neutrons (short-dashed curve) dominates at backward angles.

The fit for ³He + ⁹Be → ⁶Li + ⁶Li (solid curve) was obtained assuming t transfer from the target nucleus to the projectile. A good agreement between the experimental data and the calculations is observed. A similar situation may be expected for the case of ³He + ⁹Be → ⁷Li + ⁵Li where d transfer dominates. All the values of the spectroscopic amplitudes are taken from [13] .

As could be seen from Figure 5, the main processes describing the angular distributions of the exit channels ⁴He + ⁸Be_g.s., ⁷Be + ⁵He and ⁶Li + ⁶Li_g.s. are, respectively, the neutron, α and t transfer from the target nucleus to the projectile.

3.2. Cluster Transfer in ³He + ⁹Be Reaction

Due to the Borromean structure of ⁹Be the breakup of this nucleus may, in principle, proceed directly into two α particles plus a neutron or via one of the unstable intermediate nuclei: ⁸Be or ⁵He. The attempt was made to get some insights into (n + ⁸Be), (⁴He + ⁵He), (d + ⁷Li) and (t + ⁶Li) cluster configurations inside of ⁹Be and especially to estimate the relative strengths of the most interesting (n + ⁸Be) and (⁴He + ⁵He) cluster configurations in ⁹Be.

Most likely, the studied reaction channels result from the cluster transfer:

³He + ⁹Be → ³He + (n + ⁸Be) → (³He + n) + ⁸Be → ⁴He + ⁸Be → ⁴He + ⁴He + ⁴He

³He + ⁹Be → ³He + (α + ⁵He) → (³He + α) + ⁵He → ⁷Be + ⁵He → ⁷Be + ⁴He + n

³He + ⁹Be → ³He + (t + ⁶Li) → (³He + t) + ⁶Li → ⁶Li + ⁶Li

³He + ⁹Be → ³He + (d + ⁷Li) → (³He + d) + ⁷Li → ⁵Li + ⁷Li → ⁴He + p + ⁷Li

³He + ⁹Be → ³He + (³He + ⁶He) → (³He + ³He) + ⁶He → ⁶Be + ⁶He.

These reaction channels are of specific interest since they provide direct information on the cluster structure of the initial and final states.

Based on the angular distributions, one may get some information about the strengths of cluster configurations in ⁹Be. To obtain the contributions for the observed channels, the angular distributions were integrated over the solid angle. The values of the contributions were calculated as weighted integrals among the channels listed above. The obtained values are given in Table 2.

The ratio of (n + ⁸Be) to (α + ⁵He) is 2.7:1, which is close to the ratio 2:1 given in Ref. [9] and contradicts the conclusion that the contribution of the (α + ⁵He) configuration is negligible.

As for the conclusion of the more detailed experiments Refs. [3] [4] where measurements showed that the α + ⁵He channel was not important for their consideration of the low-lying excited states of ⁹Be, the discrepancy may be explained from the experimental point of view. Our data are based on inclusive measurements, whereas the experimental results of Refs. [3] [4] are based on exclusive measurements. The latter always requires fully defined kinematics allowing the complete reconstruction and identification of events. The values of the branching ratio given in Refs. [3] [4] were corrected by the geometrical detector efficiency obtained using a special simulating code.

Additionally, it should be noted that the values of the branching ratios given in Refs. [3] [4] are assigned especially to the excited states, whereas our values of the contributions are associated entirely with ⁹Be without assignment of the excited levels.

The direct triton pick-up process requires that ⁹Be has the (⁶Li + t) cluster configuration, which seems highly unlikely compared to the (α + α + n) configuration. Also, the interpretation of any (³He, ⁶Li) reaction in terms of triton pick-up requires that ⁶Li has the (³He + t) cluster configuration, which seems equally unlikely compared to the (α + d) configuration. It has been shown in Ref. [16] that for ⁶Li the (³He + t) configuration is only slightly less probable than the (α + d) configuration. Since such cluster configurations are not mutually exclusive, one cannot judge upon the relative importance of the (⁶Li + t) cluster configuration of ⁹Be without making careful cluster structure calculations. Indeed, the differential cross section for the ⁷Li in the outgoing channel is higher than for the channel leading to ⁶Li.

4. Conclusions

The angular distributions of the ⁹Be(³He, ³He)⁹Be, ⁹Be(³He, ⁷Be)⁵He, ⁹Be(³He, ⁷Li)⁵Li, ⁹Be(³He, ⁶He)⁶Be and ⁹Be(³He, ⁶Li)⁶Li reaction channels were measured and described within the framework of the optical model, the coupled-channel approach and the distorted-wave Born approximation.

The performed analysis of the experimental data shows that the potential parameters are quite sensitive to the exit channel and hence to the cluster structure of the populated states, which allows to make general observations and conclusions regarding the internal structure of the target and exit channel nuclei.

The experimental data for ³He + ⁹Be elastic scattering were fitted. The fitting parameters were obtained and compared with the results of the previous measurements. Then, the cross sections for the transfer reactions ⁹Be(³He, ⁴He)⁸Be_g.s. and ⁹Be(³He, ⁷Be)⁵He were fitted.

The experiment was designed to study the breakup of ⁹Be in the attempt to determine the contribution of the n + ⁸Be and α + ⁵He channels in the inclusive measurements. The ratio 2.7:1 may be assigned to the contributions of these two channels, respectively. The determined contributions confirm that the ⁵He + α breakup channel plays an important role. The inclusive experimental method used has the advantage of its experimental simplicity in comparison with the exclusive one.

Acknowledgements

We would like to thank the JYFL Accelerator Laboratory and NPI (Řež) for giving us the opportunity to perform this study as well as the cyclotron staff of both institutes for the excellent beam quality. This work was

supported in part by the Russian Foundation for Basic Research (project numbers: 13-02-00533 and 14-02- 91053), the CANAM (IPN ASCR) and by the grants to JINR (Dubna) from the Czech Republic, the Republic of Poland and the mobility grant from the Academy of Finland.

Cite this paper

S. M.Lukyanov,M. N.Harakeh,M. A.Naumenko,YiXu,W. H.Trzaska,V.Burjan,V.Kroha,J.Mrazek,V.Glagolev,Ŝ.Piskoř,E. I.Voskoboynik,S. V.Khlebnikov,Yu. E.Penionzhkevich,N. K.Skobelev,Yu. G.Sobolev,G. P.Tyurin,K.Kuterbekov,Yu.Tuleushev, (2015) Some Insights into Cluster Structure of ⁹Be from ³He + ⁹Be Reaction. World Journal of Nuclear Science and Technology,05,265-273. doi: 10.4236/wjnst.2015.54026

References