Clustering in non-self-conjugate nuclei 10Be and 18O

Clustering phenomena in 10Be and 18O were studied by means of resonance elastic scattering of α-particles on 6He and 14C. Excitation functions for α+6He and α+14C were measured and detailed R-matrix analyses of the excitation functions was performed. We compare the experimental results with the predictions of modern theoretical approaches and discuss properties of cluster rotational bands.


Introduction.
Clustering is known to play an important role in the structure of light N = Z, even-even nuclei. A number of known structure peculiarities in nuclei, such as 8 Be, 12 C, 16 O, and 20 Ne, are associated with clustering (see recent review [1] and Refs. therein).
It has been proven to be more difficult to study clustering phenomena in non-self-conjugate, N = Z nuclei. Clustering might manifest itself in a much more complex way in these nuclei. This is because the "extra" nucleons introduce additional degrees of freedom which may modify, create, enhance or destroy cluster structures. In addition to that there are difficulties with the experimental studies, which require a more complicated analysis due to the presence of lowlying nucleon decay channels and higher level density. On the other hand, the investigation of clustering phenomena in non-self conjugate, N = Z nuclei seems very promising. "Valence" nucleons may be responsible for exotic, molecular-type structures [2]. Also, nucleon and α-decay thresholds are typically close in these nuclei, which allows more direct exploration of the interplay between the single nucleon and cluster degrees of freedom by measuring the corresponding partial widths and correlations. We studied the cluster structure of non-self conjugate nuclei 10 Be and 18 O by measuring the excitation functions for α+ 6 He and α+ 14 C resonance elastic scattering. Figure 1. Identification of 6 He+α elastic scattering events in ANASEN. Part (a) shows the particle ID plot with energy deposited in the silicon array on the x-axis and energy loss measured by proportional counters in the y-axis. Part (b) is the energy -scattering angle correlation plot for α-particles. Bananas that correspond to the kinematics for 6 He+α and α+α elastic scattering are labeled.
rotational band based on the 0 + 2 state (0 + at 6.17 MeV, 2 + at 7.54 MeV and 4 + at 10.15 MeV). The cluster structure of 10 Be has been studied in many experiments (see [7,8,9,10,11] and Refs. therein) but our knowledge is still incomplete. S α factors are still unknown for the 0 + and 2 + states at 6.17 MeV and 7.54 MeV (although, results of Ref. [12] indicate unusually large α-strength that far exceeds a single particle limit for the 2 + state while the α-strength was measured to be close to the single particle limit for the corresponding isobaric analog resonance in 10 B [14]). The spin-parity assignment for the state at 10.15 MeV was controversial at the time when this project started, with 3 − and 4 + conflicting assignments [10,11]. Existence of the next, 6 + member of this band was predicted in [6] based on SU(3) algebraic model, but never observed experimentally. Confirmation of the 4 + spin-parity assignment and search for the 6 + member of the α:nn:α rotational band in the excitation function for 6 He+α elastic scattering were the main goals of the project. The excitation function for 6 He+α resonance elastic scattering in the excitation energy range 9.5 to 13.4 MeV was reported recently in [15]. We present new experimental data, which extends the previously measured 6 He+α excitation function to higher excitation energies, up to 15.4 MeV. These measurements were part of the commissioning run for new active target detector ANASEN.
Measurements were performed at the John D. Fox Superconducting Linear Accelerator Laboratory at Florida State University. The 6 He beam was produced by the in-flight rare isotope beam facility RESOLUT with intensity of about 10 5 pps. The new active target detector -Array for Nuclear Astrophysics and Structure with Exotic Nuclei (ANASEN) -was used to perform the measurements. ANASEN is a gas filled detector, which has an array of position sensitive silicon detectors that surrounds the beam axis and a cylindrical array of position sensitive proportional counters. The recoils that emerge from the place of interaction go through the proportional counter first. The location and energy loss in the active gas volume are measured. If the second hit is recorded by the silicon detector then the track of the recoil can be reconstructed using position information provided by the proportional counter and the silicon array. Particle identification is performed using energy loss in the active gas volume and the total energy measured by the silicon array (see Fig. 1(a)). The 6 He+α elastic scattering events can be identified using the energy-angle kinematic dependence reconstructed from the tracks of the recoils, as shown in Fig. 1(b). The excitation function for 6 He+α resonance elastic scattering in the energy range between 2.2 and 8 MeV in c.m.s. (9.7 and 15.5 MeV excitation energy in 10 Be) measured near 90 • in c.m. is shown in Fig. 2. Obvious features of this excitation function is a peak at 2.75 MeV (10.16(2) MeV excitation energy in 10 Be) and a small peak near 5.9 MeV (13.4 MeV excitation energy). The first peak corresponds to the state that was first observed in [7] and [8]. The 3 − spin-parity was assigned to it in [10]. However, this was contradicted by [11] where the 6 He+α angular distribution at 2.75 MeV energy in c.m. showed a maximum at 90 degrees, indicating positive parity. The 4 + spin-parity assignment was made for the state in [11]. This spin-parity assignment was confirmed recently in [15], where the excitation function for 6 He+α was measured in the energy range from 2.4 to 6 MeV in c.m. The excitation function shown in Fig. 2 is similar to that measured in [15], but the higher energy data obtained in this work allowed us to see that there is also another peak at 5.9 MeV, with the cross section sharply decreasing toward higher energies.
The angular distribution for 6 He+α elastic scattering at 2.72 MeV in c.m is shown in Fig.  3. The R-matrix fit with the 4 + state at 2.79 MeV reproduces the corresponding angular distribution rather well. No other spin-parity assignment can produce a fit of comparable quality. We confirm the 4 + spin-parity assignment for this state that was first made in [11] and later confirmed in [15]. The partial α width for the 10.16 MeV state determined from Rmatrix fit exceeds the single-particle limit for the purely α-cluster state and we agree with the conclusions made in [11,15] that this is indeed a highly clustered 4 + state, that may belong to the α:nn:α rotational band. The peak at 5.9 MeV in the 6 He+α excitation function (Fig. 2) is very intriguing. It appears that this structure corresponds to a positive parity high spin state because it is most prominent near 90 • in the limited angular range (70-130 • ) measured in this work. A definitive spin-parity assignment is handicapped by what appears to be direct ("potential") scattering that dominates angular distribution at this energy (around 6 MeV in c.m.). Model R-matrix calculations indicate that the shape and width of the resonance may correspond to a highly clustered 6 + state that predominantly decays by α emission to the ground and 2 + first excited states in 6 He. However, more analysis and/or new experimental data at angles close to 180 • may be necessary to confirm or rule out the existence of this state. If confirmed, this state would be a strong candidate as the next, 6 + member of the α:nn:α rotational band in 10 Be.

Search for inversion doublet quasi-rotational bands in 18 O
One of the most striking manifestations of α-clustering in light nuclei is the appearance of a sequence of highly clustered states that form rotational bands of alternate parities. The positive parity α-cluster rotational band is found at a lower energy and the corresponding negative parity band is shifted up by several MeV toward higher excitation energies. These bands are called inversion doublets and have been conclusively identified in 16 O and 20 Ne (see [1] and references therein). There have been numerous attempts to find the members of the inversion doublet rotational bands in 18 O that correspond to an 14 C(g.s.)+α configuration ( [16] e.g.), in analogy to the well known rotational bands in 16 O and 20 Ne. In spite of significant effort, the assignment of the band members remains controversial. The identification of states that can be considered as the members of the inversion doublet rotational bands in 18 O using excitation function for 14 C+α elastic scattering is the main focus of the discussion below. The excitation function for 14 C+α elastic scattering was measured in the broad excitation energy and angular range using the Thick Target Inverse Kinematics (TTIK) technique [17]. The experiment was performed at Florida State University, John D. Fox Superconducting Linear Accelerator facility. The Thick Target Inverse Kinematics (TTIK) technique allows one to measure a large range of excitation energies without the need to change the initial energy of the beam, making the experiment more efficient and less time consuming. A 42 MeV 14 C beam and 99.9% pure helium gas ( 4 He) were used.
The 180 • excitation function for 14 C+α elastic scattering measured in this experiment is shown in Fig. 4. A detailed R-matrix analysis was performed and spectroscopic information on 54 states in 18 O in the broad excitation energy range from 8 to 15 MeV were extracted. A complete description of the results of this experiment is given in [18]. Here we only consider those aspects of 18 O structure that are related to the inversion doublet α-cluster quasi-rotational bands. Selected states in 18 O that were observed in this experiment and are relevant for the discussion below are listed in Table 1.
Assignments of the 14 C g.s. +α rotational bands have been suggested in many experimental works ( [19,20,16] e.g.). The states 0 + (3.63 MeV), 2 + (5.24 MeV), 4 + (7.11 MeV) and 6 + (11.69 MeV) have been considered as members of the positive parity rotational band, which resembles the 20 Ne g.s. rotational band. (In [19] the 4 + state at 10.29 MeV was suggested as a member of this rotational band instead of the 4 + at 7.11 MeV, however our results indicate that this state has only moderate α-strength (Table 1).) An 8 + state at 17.6 MeV and 18.06 MeV was suggested by [20] and [16] respectively as the fifth member of this rotational band. Only the 6 + state at 11.7 MeV is within the energy range measured in this work and we confirm that this is a clustered state with α-strength θ 2 α =0.23. The α-strength is defined in a standard way as the dimensionless reduced α-width, θ 2 α , that is the ratio between the α reduced width and the single particle limit θ 2 α =γ 2 α /(h 2 /(µR 2 )), where R=5.2 fm and µ is a reduced mass. However, there exists the second strong 6 + state at 12.58 MeV (θ 2 α = 0.38). This forces us to conclude that clustering in 18 O is more complicated and cannot be described by a single pair of inversion doublet rotational bands. This is also supported by the data on the cluster states with negative parity.  The location of the band head and identification of the other members of the negative parity inversion doublet, α-cluster, quasi-rotational band in 18 O is a subject that has a rich history and has been discussed in many theoretical and experimental papers (see [16] and ref. therein). The 1 − state at 8.035 MeV was proposed as the band head for this band in recent work of W. von Oertzen, at el. [16] (the same suggestion was made in [21]). Our result rules out this state as a member of the 0 − band due to its small dimensionless reduced α-width (θ 2 = 0.02). In fact, none of the states identified in [16] as members of the negative parity inversion doublet (1 − (8.04 MeV), 3 − (9.7 MeV ), 5 − (13.6 MeV), 7 − (18.63 MeV)) can belong to this band (except maybe a 7 − state that lies beyond the energy region studied in this work). The 3 − state at 9.7 MeV has θ 2 α of only 0.04 (an order of magnitude less than the 3 − at 9.3 MeV) and the 5 − state at 13.6 MeV is not observed at all in this work, which rules out the assignment made in [16]. We observed the highly clustered 1 − and 3 − states at 9.19 MeV and 9.35 MeV with θ 2 α 0.2 and 0.48 respectively and it is tempting to identify them as the members of the inversion doublet band. However, as in the case of positive parity band, we observed a 1 − state at 9.76 MeV with θ 2 α =0.46, which makes the situation complicated. There is also another strong 3 − state (θ 2 α = 0.18) at excitation energy of 8.28 MeV. It is 1 MeV below the most clustered 3 − state at 9.35 MeV (θ 2 =0.48). There is no dominant 5 − α-cluster state in the spectrum. Instead, there are several 5 − states with substantial α-strength spread out over a 3 MeV energy interval between 11.5 and 15 MeV. Their combined α-strengths add up to 0.8. The experimental data presented here reveal that there is a strong splitting of α-strength between several states of the same spin-parity and it is not possible to identify a single, dominant α-cluster rotational band of either positive or negative parity. This is contrary to some theoretical predictions [22,23] and suggestions made in previous experimental studies ( [19,20,21,16] e.g.).

Summary
The cluster structure of non-self-conjugate nuclei 10 Be and 18 O were studied using the αparticle resonance elastic scattering approach. The excitation functions for 6 He+α and 14 C+α were measured and R-matrix analyses were performed to extract parameters for the observed resonances. We confirmed the 4 + spin-parity assignment for the 10.16 MeV state in 10 Be and observed a peak in the 6 He+α excitation function at 15.9 MeV near 90 • in c.m. This may be due to positive parity high spin state. It is possible that this is the next, 6 + member of the α:nn:α rotational band but more data, especially at angle close to 180 • in c.m. may be needed to confirm. Detailed spectroscopic information on 54 states in 18 O in the energy range between 8 and 15 MeV have been obtained in this work. The main conclusion is that unlike for N = Z, 16 O and 20 Ne nuclei, the α-strength is spread between several states for each spin-parity and it is not possible to define an inversion doublet rotational bands in the same sense as for 16 O and 20 Ne nuclei. This conclusion is in contradiction to some theoretical predictions [22,23] and suggestions made in previous experimental studies ( [19,20,21,16] e.g.).