Extreme alpha-clustering in the 18O nucleus

The structure of the 18O nucleus at excitation energies above the alpha decay threshold was studied using 14C+alpha resonance elastic scattering. A number of states with large alpha reduced widths have been observed, indicating that the alpha-cluster degree of freedom plays an important role in this N not equal Z nucleus. However, the alpha-cluster structure of this nucleus is very different from the relatively simple pattern of strong alpha-cluster quasi-rotational bands in the neighboring 16O and 20Ne nuclei. A 0+ state with an alpha reduced width exceeding the single particle limit was identified at an excitation energy of 9.9+/-0.3 MeV. We discuss evidence that states of this kind are common in light nuclei and give possible explanations of this feature.

After the discovery of the neutron it was understood that α particles cannot exist in the bulk of a nucleus at normal nuclear density due to the need for antisymmetrization over all nucleons. Still, α clustering manifests itself in light 4N nuclei such as 8 Be, 12 C, 16 O, and 20 Ne through the existence of twin quasi-rotational bands of states with alternating parities and α-particle reduced widths which are close to the single particle limit (see recent review by M. Freer [1] and references therein).
There are different approaches that attempt to describe the shell model and the α-cluster structure of nuclei on an equal footing in order to shed light on the interplay between the α-cluster and single particle degrees of freedom [1]. Data on the nucleon decay of α-cluster states would be instrumental for such efforts. However, this data is practically absent due to the much higher nucleon decay thresholds in comparison with the thresholds for the α decay in the 4N nuclei. It is more promising to observe nucleon decay from the α-cluster states in N =Z nuclei where the nucleon and α-particle thresholds are close to each other. The study of non-self-conjugate nuclei has an advantage in that one can investigate α-cluster states in mirror systems and use the Coulomb shift to extract information on the relationship between the cluster and single particle degrees of freedom. Unfortunately, the data on the α-cluster structure of N =Z nuclei are generally very limited.
Current interest in the α-particle interaction with N =Z nuclei is also strongly motivated by astrophysics [2]. Even if astrophysical reactions involving helium do not proceed through the strong α-cluster states (because of high excitation energy), these states can provide α width to the states that are closer to the region of astrophysical interest through configuration mixing [3]. However, the study is complicated by experimental difficulties and the need for multi-channel analysis of many broad overlaping, interfering resonances. This is illustrated by the previous investigations of the α+ 14 C interaction. In the first [4] (and only) study of the resonances in the α+ 14 C elastic scattering, the experimental difficulties were minimized by using a solid (radioactive) 14 C target. However, only a few assignments for some strong and sharp resonances were made. Goldberg et al. [5] reanalyzed the data of [4] using a simplified version of the R-matrix theory. In the analysis approach used in [5] only the elastic scattering channel was considered explicitly, while influence of all other decay channels was parametrized through a Γ α /Γ total parameter for each resonance. They gave a few new assignments, but again many of them were tentative. The need for a more detailed investigation, better fit and new experimental data was pointed out in [5]. The β-delayed α spectrum of 18 N was measured in Refs. [6,7]. Due to the high selectivity of β decay only 1 − states were observed in the 18 O spectrum. Several broad 1 − states were identified in [7]. In this letter we report new measurements of α+ 14 C resonance elastic scattering made using the Thick Target Inverse Kinematics (TTIK) method [8]. This experimental approach provided good statistics and excitation functions which were remarkably free of any background. The data provided a basis for a successful analysis of the excitation functions using a complete multi-level, multi-channel Rmatrix approach [9]. As a result, we found that in 18 O there is a system of strong α-cluster states. Both α and nucleon reduced widths of these α-cluster states were de-termined from the multi-channel R-matrix fit. The main focus of our discussion in this letter is the surprising finding of a state with an α-particle width exceeding the single particle limit. We interpret this as evidence for extreme α-clustering and argue that existing experimental data on light 4N nuclei indicates that this is a common feature for nuclei in this mass range.
The experiment was carried out at the Florida State University John D. Fox Superconducting Accelerator Laboratory. The 25 MeV 14 C beam was produced by an FN Tandem Van-de-Graff accelerator and directed into the scattering chamber, which consisted of two compartments. The first compartment was under vacuum, the second was filled with 99.9% pure helium gas ( 4 He). The two compartments were separated with a 1.27 µm Havar foil. The intensity and quality (focusing and alignment) of the beam was monitored using elastic scattering off a gold target, placed in the middle of the vacuum compartment, and from the Havar foil (energy of the beam is less than the C+Co Coulomb barrier). The helium gas pressure in the second compartment was adjusted to stop the incoming beam before an array of Silicon detectors located at a distance of ∼40 cm from the Havar foil. Details of the method are given in [10].
The excitation functions for the 14 C+α elastic scattering covering the center-of-mass (c.m.) energy region of 2.0-4.5 MeV were measured at 20 different angles. The observed background was less than 1%. Conversion of the laboratory excitation functions into the c.m. was made on a bin-by-bin basis using a computer code which takes into account the relevant experimental conditions [11]. The accuracy of the absolute normalization of the cross section, performed by the monitor detector using elastic scattering of the 14 C beam off the Havar foil, is 15%. The uncertainty in the specific energy loss of 14 C in helium is responsible for a 20 keV uncertainty in the absolute calibration of the c.m. energy.
The analysis of the excitation functions was performed using a multi-level, multi-channel R-matrix approach [9]. The 14 C+α excitation functions measured in this experiment are continuous which excludes the possibility of missing a narrow resonance. The sensitivity of the data is demonstrated by the fact that even the 2 + state at 8.213 MeV (1.986 MeV c.m.), which has width of 1 keV, is still clearly visible in the 180 • excitation function (see inset in Fig. 1). In addition, data from previous measurements of the 14 C(α,α) [4] and 14 C(α,n) [12] excitation functions were used. The overall fit was very good with χ 2 /ν=1.64 for the c.m. energy range 2.65-4.45 MeV. The R-matrix fit to the 14 C(α,α) data is shown in Fig. 1. As can be expected most of the states also have substantial neutron widths, which are obtained through the (α,α) fit. We verified that the 14 C(α,n) total cross section from Ref. [12] is reproduced rather well by R-matrix calculations performed using the parameters from the 14 C(α,α) fit. One can notice that the R-matrix fit underestimates the experimental cross section at the lowest energies for angles far from 180 • . This is understood to be an effect of the finite dimensions of the beam spot. The fourth panel in Fig. 1 is 90 • data from [4]. The spectrum at 90 • in c.m. is only influenced by states with even angular momentum and positive parity. This is an important simplification and makes the spectrum at 90 • very valuable for the R-matrix analysis. Clearly, our data contains this information. However, for the purpose of a more clear representation of the data we used the spectrum of [4] at 90 • rather than construct the 90 • spectrum from several different detectors.
Twenty-four resonances were used to fit the data, some of them were previously known. Detailed discussion of the analysis procedure and notes on the properties of each state will be given in the follow up paper. Levels with large α-cluster reduced widths (θ 2 α > 0.1) are given in Table 1.
Five levels with dimensionless α reduced width greater than 0.1 have been observed in 18 O in the narrow excitation energy range between 9.1 and 9.9 MeV. Three of them have been suggested in previous publications [6,5,7]. The strong α-cluster state at 9.0 ± 0.2 MeV was first suggested in [6], where the 1 − spin parity assignment was made on the basis of population of this state in 18 N β decay. A more recent 18 N β decay experiment [7] confirmed the 1 − state at 9.16 MeV with a width of Γ = 420±200 keV. Our R-matrix fit requires a 1 − state at an excitation energy of 9.17±0.03 MeV in good agreement with [7]. The width of this state is lower in the present work (230±50 keV) but still within the error bars of [7]. Another 1 − state observed at 9.85±0.5 MeV in [7] with a width of 560±200 keV is in very good agreement with the results of this work. The 3 − at 9.39 MeV was previously suggested in [5] and has excellent agreement with the present results. The strong α-cluster 2 + state at 9.77 MeV is identified for the first time in this work.
The most surprising finding of this work was the observation of a very broad 0 + state at 9.90±0.3 MeV. Generally it is not easy to identify very broad resonances because they are disguised by interference with the sharp ones. This is especially true for the 0 + resonances. Nevertheless, existence of the broad α-cluster 0 + state in the spectrum of 18 O is certain. The effect of this state on the cross section is demonstrated in Fig. 2. The cross section is lowered dramatically due to the destructive interference of the 0 + state with Coulomb scattering. The Rutherford cross section and the Rutherford with the broad 0 + state at 9.90 MeV (3.7 MeV c.m.) are shown at two c.m. angles, 90 • and 180 • , in Fig. 2. Without this destructive interference it is not possible to reproduce the experimental data. As seen in the bottom panel of Fig. 1, the cross section calculated without the broad 0 + state is significantly larger than the experimental one. This is a clear indication of a 0 + resonance. All other resonances would not produce the right interference with the Rutherford scattering and could not be broad enough. One can follow the effect of the 0 + level at different angles in Fig. 1 and reach the same conclusion. We also considered the possibility of two narrower 0 + states instead of one. The decisive factor against it was that the characteristic interference pattern between two nearby 0 + states was not observed experimentally. The α particle reduced width amplitude of the 0 + state with channel radii of 5.2 and 6.5 fm are 1.38 and 0.66 MeV 1/2 , respectively. Formally, both values exceed the single-particle limit. Using a classical approach one can interpret this as evidence that the α particle resides at a large distance from the 14 C core.
A more detailed description of the observed 0 + state in 18 O can be given using the potential model approach. The parameters of this model were extracted starting from the potential model for 8 Be given in [13], which provides an accurate description of the s-wave α-α phase shift over a large energy range. First, this potential model was used to investigate the 16 O+α interaction by assuming the αcluster model [14] for the ground state of 16 O, properly modified [15] to include antisymmetry and the strong repulsion between nucleons. The strong interaction between the incoming α and the target "alphas" is obtained by folding the Buck interaction [13] with the target α-density in the ground state and produces a nuclear potential with several Pauli forbidden states. These are removed by adding a repulsive Gaussian potential in the relative α-16 O radial coordinate. The result is to produce a bound state for the ground state of 20 Ne and a broad 0 + state at 4 MeV in  Table 1. Levels with large α-reduced width in 18 O. Γtot, Γα and Γn are the total and partial α and neutron widths, respectively. θ 2 α = γ 2 α /γ 2 SP is the dimensionless reduced width for the α channel, where γ 2 SP =h 2 /µR 2 is the single particle limit, calculated at channel radius 5.2 fm. c.m. as observed in [16] with the same 0 + phase shift behavior. The corresponding density distribution for this 0 + resonance has an inner peak at 2 fm and an outer peak at 5 fm. The outer peak is at a separation distance beyond the sum of the charge radii of 4 He and 16 O and it contains most of the probability indicating that the broad 0 + resonance in 20 Ne appears to be a state with extreme α-clustering. The 18 O system was then investigated using the 20 Ne potential as a starting point but small changes in the strengths of the folded and repulsive potentials were used to reproduce the ground state of 18 O. This potential pro-duces a broad 0 + state at 3.5 MeV in c.m. The experimental s-wave resonance phase shift from the R-matrix fit (solid black curve in Fig. 2a) is reproduced rather well by such a potential (dash-dotted blue curve in Fig. 2a). The density distribution for the broad 0 + state in 18 O is similar to the one in 20 Ne. The outer peak is at 5.5 fm which is considerably larger than the sum of the charge radii for 4 He and 14 C and even larger than the 20 Ne outer peak radius. This latter result is presumably due to the larger Coulomb barrier in the 20 Ne system. Both systems appear to show well separated α-cluster configurations that correspond to extreme α-clustering.
Due to the large distance between the α cluster and the core, one can speculate that levels of this kind should be a general feature of the interaction between an α particle and a core nucleus which is independent of the specific structure of the core. If this is the case then resonances of this kind should be present in all nearby nuclei at excitation energies on the order of a few MeV above the α decay threshold. Indeed, a broad (3 MeV) 0 + level at an excitation energy of 10.3 MeV (∼3 MeV above the α threshold) appears in 12 C [17]. Recently, the parameters of this 0 + level were revised in measurements of the 3α decay of this level populated after β decay of 12 B or 12 N [18,19]. The new parameters, as given in [19], are an excitation energy of 10.73 MeV and a width of 1.72 MeV. However, there are still significant uncertainties in these values.
There is much more controversy related to a possible broad 0 + level in 16 O at ∼11.3 MeV excitation energy (∼4 MeV above the threshold) [20], since there are conflicting results for this state [21,22,23,24,25]. However, the most recent article presented clear evidence for broad 0 + strength at the excitation energy in question [26,27]. Finally, a broad 0 + level (Γ > 800 keV) at ∼4 MeV above the α decay threshold, was observed in 20 Ne [16]. This result has not been questioned since it was first reported.
One may refer to these states as "α-halo" states. This term was first suggested in [28] and has merit. Also, one should not link directly unbound α-halo resonances with bound neutron halo configurations found in some weakly bound neutron rich nuclei.
While the purely single α particle nature of these states is clear it is interesting to consider the possible quantum mechanical reasons behind the emergence of such pure configurations. The answer may be a "super-radiance" phenomenon (see for example [29]). Super-radiance emerges in the limit of strong coupling to the continuum (broad strongly overlaping resonances of the same spin-parity) and represents accumulation of the total summed α width from the unperturbed intrinsic states by one very broad (super-radiant) resonance. Since the centrifugal barrier is absent for ℓ = 0 states the condition of strong continuum coupling is more likely realized for the 0 + states than for the states of any other spin-parity.
In summary, we are only in the beginning phases of studying the α-cluster structure of light N =Z nuclei. Here we report a measurement of the 14 C+α elastic scattering excitation functions including a successful analysis using the complete R-matrix framework. We identified that the α-cluster states in 18 O have many surprising properties, foremost of which is the discovery of a broad, ℓ=0 state which we suggest may be present in other nuclei in this mass range. This conclusion is strengthened through comparison with previous results [16,17,18,19,20,26]. There is much work still ahead to prove this point. The discovery of the broad states in question within odd-even nuclei is an especially important and difficult task. Nevertheless, the possible influence that these broad low spin resonances may have on astrophysically important reaction rates along with the insight they can give into α clustering justifies these efforts.