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,
3He)
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
8Be consisting of two bound helium clusters (
5He +
6He) is significantly suppressed, whereas the two-body configurations (n +
8Be) and (α +
5He) including unbound
8Be and
5He are found more probable.
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 8Beg.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 8Beg.s., the first-excited state of 8Be and 5Heg.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 5Heg.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 8Beg.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 Er 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 Er (the so-called ΔE-E method). The telescopes were mounted on rotating supports, which allowed to obtain data from θlab = 18˚ to θlab = 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 Er and ΔE0 vs. ΔE are shown in Figure 1(a) and Figure 1(b), respectively. The excellent energy resolutions of both ΔE and Er 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 θlab = 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 Er. 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
Particle identification plots for the products of the <sup>3</sup>He (30 MeV) + <sup>9</sup>Be reaction: (a) p, d, t and <sup>3,4</sup>He; (b) <sup>6</sup>He, <sup>6,7</sup>Li and <sup>7,9</sup>Be. ΔE is the energy loss and E<sub>r</sub> is the residual energy. The loci for the products are indicated.
Spectra of the total deposited energy for the detected <sup>4</sup>He (a), <sup>7</sup>Be (b) and <sup>7</sup>Li (c), measured at θ<sub>lab</sub> = 18˚ for the reaction <sup>3</sup>He (30 MeV) + <sup>9</sup>Be
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. Results3.1. Elastic and Inelastic Scattering
The measured angular distributions for the reaction channels: (a) 3He + 9Be → 7Be + 5He (♦), 3He + 9Be → 7Lig.s. + 5Li (□), 3He + 9Be → 6Li + 6Lig.s. (▲), 3He + 9Be → 4He + 8Beg.s. (Δ), 3He + 9Be → 6He + 6Beg.s. (●); (b) 3He + 9Be → 4He + 8Beg.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 + 8Beg.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 + 6Beg.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, Rv, av) − iW0f(r, Rw, aw), where the function f (r, R, a) = (1 + e(r−R)/a)−1 and radii Ri = riA1/3 depend on the mass of the heavier fragment A and the corresponding reduced radius ri. 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 5Heg.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)8Beg.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 + 8Beg.s. (Δ), (b) 3He + 9Be → 7Be + 5He (♦) and (c) 3He + 9Be → 6Li + 6Lig.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 + 8Beg.s., 7Be + 5He and 6Li + 6Lig.s. are, respectively, the neutron, α and t transfer from the target nucleus to the projectile.
The ratio of the measured elastic scattering cross section to the Rutherford cross section for <sup>3</sup>He (30 MeV) + <sup>9</sup>Be at the incident energy 30 MeV in comparison with the OM fit
OM potential parameters used within the optical model and the CC approach for the reaction <sup>3</sup>He (30 MeV) + <sup>9</sup>Be in comparison with the parameters of Ref. [<xref ref-type="bibr" rid="scirp.60664-ref13">13</xref>]
Reaction channel
V0 [MeV]
rv [fm]
av [fm]
W0 [MeV]
rw [fm]
aw [fm]
Vso [MeV]
rso [fm]
aso [fm]
3He + 9Be
108.5
1.123
0.54
15.69
1.15
0.855
13.63
1.83
0.4
3He + 9Be [13]
143.4
1.02
1.10
38.3
1.405
1.17
α + 8Be
90.98
1.382
0.404
12.36
1.01
0.4
α + 8Be [13]
143.4
1.024
1.35
38.3
2.539
1.67
5He + 7Be
60.88
1.25
0.65
2.8
1.25
0.65
8.93
1.28
0.65
5He + 7Be [13]
122.5
0.9768
0.61
51.71
0.914
1.178
6Li + 6Li
110.95
1.307
0.621
2.48
1.25
0.65
1.05
1.25
0.65
6Li + 6Li [13]
122.5
0.979
0.905
51.71
0.914
1.178
3.2. Cluster Transfer in <sup>3</sup>He + <sup>9</sup>Be 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:
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 angular distributions for (a) <sup>3</sup>He + <sup>9</sup>Be → <sup>4</sup>He + <sup>8</sup>Be<sub>g.s.</sub> (Δ), (b) <sup>3</sup>He + <sup>9</sup>Be → <sup>5</sup>He + <sup>7</sup>Be (♦) and (c) <sup>3</sup>He + <sup>9</sup>Be → <sup>6</sup>Li + <sup>6</sup>Li<sub>g.s.</sub> (▲). Results of the optical-model and the coupled- channel calculations are shown by lines (see text).
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)8Beg.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
Contribution of the observed exit channels and the corresponding cluster configurations in the <sup>9</sup>Be nucleus
Exit channel
9Be cluster configuration
Contribution (%)
4He + 8Be
(n + 8Be)
68.7 ± 10
5He + 7Be
(α + 5He)
25.1 ± 5
6Li + 6Lig.s.
(t + 6Li)
3.3 ± 2
5Li + 7Lig.s.
(d + 7Li)
2.7 ± 2
6Be + 6Heg.s.
(3He + 6He)
0.2 ± 0.7
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
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