Measurements of the fusion cross section at energies around the Coulomb barrier provide insight into the quantum many-body interaction and allow an exploration of the different mechanisms, such as breakup and transfer reactions, that define the structural properties of the fusion excitation function [1]. Phenomena like enhancement and hindrance of the cross section are currently being investigated using stable and radioactive beams. Such effects are crucial for understanding the fusion process which plays an important role in, for example, astrophysical environments [2]. Several studies have shown that for systems involving weakly-bound nuclei the breakup and transfer mechanisms cause hindrance of the total fusion cross section at energies above the Coulomb barrier and enhancement below it [3][4][5]. A systematic investigation of these effects on the fusion cross section can be performed using the coupled channels approach, see e.g. Refs. [2,[5][6][7] for reviews on this subject.
Many fusion systems can be reasonably reproduced by the coupled channels approach. However, different interpretations are needed in the case of light symmetric or near symmetric systems where oscillatory structures in the fusion excitation function at energies above the Coulomb barrier have been observed. These oscillations are prominent in the 12 C + 12 C, 16 O + 16 O, and 12 C + 16 O systems [8][9][10]. They have also been observed in 20 Ne + 20 Ne [11] and, recently, there is evidence of their existence in 28 Si + 28 Si [12]. Such features have been explained as due to a coupling effect of successive partial waves entering the fusion cross section as their centrifugal barriers are exceeded [11,13,14] or by using an effective model with an energy dependent barrier [15].
An interesting case for benchmarking our understanding of the fusion process is provided by the 17 O + 12 C system. The 17 O nucleus may be thought of as a 16 O core with a valence neutron in the d 5/2 orbital and is the mirror of the halo nucleus 17 F. The total fusion excitation function of the exotic 17 F + 12 C system has been shown to be smoothly varying within experimental error at energies above the Coulomb barrier [16,17], despite the underlying 16 O core and the known oscillations and resonances in the 16 O + 12 C system. Moreover, the fusion excitation function of the 17 O + 12 C system is of particular interest because of a discrepancy in the published data that occurs at the energy of a known resonance in the 16 O + 12 C system [18]. It therefore seems timely to revisit the 17 O + 12 C total fusion excitation function to attempt to resolve the apparent discrepancy between the published data sets.
In this work we present a measurement of the 12 C + 17 O total fusion excitation function for energies above the Coulomb barrier using a 17 O beam and the Encore active target detector at Florida State University (FSU). Previous data show a striking discrepancy marked by a sharp discontinuity between the data of Hertz et al. [19] and Eyal et al. [20] at around E c.m. = 14 MeV, see Fig. 1. Our experimental results span both data sets and show a large oscillation in the cross section that puts all data sets in agreement. This oscillation is comparable in size with the observed resonances in the even-even systems discussed above.
The experiment was performed at the John D. Fox accelerator laboratory at Florida State University (FSU). A 17 O beam was extracted from the SNICS ion source then accelerated by the tandem Van de Graaff and deliv- Encore is a multi-sampling ionization chamber (MU-SIC) type active target detector developed at FSU and has been successfully used to measure fusion cross sections of stable 16 O and 19 F [22] and radioactive 17 F beams on 12 C [16] using CH 4 as the counting gas. Encore has also been used to measure cross sections of the 18 O(α,p) and 18 O(α,n) reactions using helium as counting gas [22]. A similar MUSIC-type detector has been used to measure various other reactions at Argonne National Laboratory (ANL) [23][24][25][26]. A full description of Encore is given in Ref. [16].
For the present experiment Encore was filled with CH 4 as counting gas with the carbon of the methane furnishing the target. The gains in the detector were set such that reactions with the hydrogen in the methane were not observed. The 17 O beam passed through a 2.11 mg/cm 2 HAVAR window and a 3 cm "dead" layer of CH 4 gas before entering the active region of the detector. Encore measures energy losses of the beam and the reaction products in a segmented anode. The anode is segmented into 18 distinct strips allowing for an energy loss measurement in 18 different regions within the detector. Two different beam energies and gas pressures were employed. Firstly, a 65 MeV MeV with an average energy of 0.7 MeV deposited in each strip. Both energies were delivered to the detector at a rate of about 10,000 pps. These settings were chosen in order to resolve the discrepancy between the data sets of Refs. [20,21] and provide overlapping data points between ∼ 12 -16 MeV in the center of mass of the 17 O + 12 C system.
Total fusion events resulting in compound nucleus formation and evaporation residues (ERs) in Encore are identified within a strip by a characteristic ∆E "jump" and consequent signals relative to the Bragg curve of the beam as it passes through the detector. The detector is not sensitive to light particle evaporation coming from the ERs. A thorough description of the analysis procedure is given in Ref. [16]. These events are normalized by the number of beam events registered within the same strip. The absolute total fusion cross section is then determined by calculating the density of carbon 'targets' within the thickness of a strip (1.5 cm) in the detector. The reported error bars in the cross section measurements are statistical and are on average about ±8%. The energy values in each strip are assigned using an energy loss calculation for the beam in each strip of the detector performed with LISE++ [27]. The initial beam energy for a stable beam is set by the analyzing magnet in the accelerator beam line and it is confirmed after the entrance window by a silicon detector mounted at the back of Encore, used for tuning the beam without gas in the detector. The energy points are taken to be the values at the center of the strips. Error bars in the energy are given by the size of the strip.
The fusion cross sections measured in this experiment are plotted in Fig. 2 and listed in Table I. Our results show a large structure in the fusion excitation function of the 17 O + 12 C system around E c.m. = 13 -15 MeV, followed by one or two smaller structures between E c.m. = 14 -20 MeV. The overlapping data points from the two sets of measurements with different beam energies and gas pressures confirm these structures. As Fig. 2 shows, the new data reconcile the large differences between the previous measurements and all four existing data sets (the present measurement plus the data of Refs. [19][20][21]) agree within experimental errors where they overlap.
In order further to investigate these results, coupled reaction channel (CRC) calculations were carried out using the code fresco [28]. Couplings included inelastic excitation of the 4.44-MeV 2 + excited state of the 12 C, with the B(E2) taken from Raman et al. [29] and the nuclear deformation length, δ 2 = -1.40 fm, from Ref. [30]; inelastic excitation of the 0.87-MeV 1/2 + first excited state of 17 O, with the B(E2) taken from Ref. [31] and the δ 2 = 1.20 fm from Ref. [32]; and the 12 C( 17 O, 16 O) 13 C single-neutron transfer reaction. Excitation of the 6.13-MeV 3 -level of 16 O was also included in the exit partition, with the B(E3) taken from Ref. [33] and δ 3 = 1.71 fm from Ref. [32]. The various overlaps, together with the spectroscopic amplitudes used are listed in Table II. Note that due to the matching conditions and the relatively low incident energies involved single-neutron trans- fer leaving the 16 O in its 6.13-MeV 3 -level was only included for the transition to the 13 C 1/2 -ground state.
The real parts of the input optical model potentials were calculated within the double-folding framework with the M3Y nucleon-nucleon effective interaction [38] using the code dfpot [39]. The required 12 C, 17 O, 13 C, and 16 O nuclear matter densities were derived from the experimental charge densities of Refs. [40], [41], [42], and [43], respectively by unfolding the proton charge density and assuming that ρ Nuc = (1 + N/Z)ρ p . The imaginary parts of the optical potentials were of Woods-Saxon squared form, with depth W = 50 MeV, radius
t ) fm and diffuseness a W = 0.3 fm, effectively reproducing the incoming wave boundary condition [44]. In this model the total fusion cross section is defined as the sum of the absorption by the imaginary parts of the potentials in all channels and is thus the difference between the reaction cross section and the sum of the integrated cross sections for all channels included in the coupling scheme.
As can be seen in Fig. 2, the data for E c.m. < 13 MeV and > 20 MeV are reproduced quite well by the CRC calculation. However, the data fall below the theoretical curve at energies E c.m. = 13 -20 MeV and the structure at E c.m. = 14 MeV is not reproduced. Similar behavior was observed in the 13 C + 12 C system where the total fusion data also fall below the prediction of CRC calculations including the elastic and inelastic transfer couplings for energies E c.m. > 13 MeV [45], although the 13 C + 12 C data do not exhibit any marked oscillations. A possible explanation may lie in the structure measured by Taras et al. [18] in various exit channels of the 16 O + 12 C reaction in a similar energy region causing constructive and destructive interference resulting from a 16 O + n + 12 C type configuration. The large "elbow" at E c.m. = 14 MeV could thus be related to the well known oscillatory behavior of the fusion cross section in the 16 O + 12 C system [9]. To highlight this, Fig. 3 plots existing 16 O + 12 C total fusion data from Refs. [9,46] together with the present 17 O + 12 C measurement. A large resonance is observed in the 16 O data in the same energy region of E c.m. = 14 MeV as for 17 O. If the observed structure in the 17 O + 12 C total fusion excitation function is indeed linked to resonant-like behavior in the underlying 16 O + 12 C system then conventional CRC calculations would not be expected to be able to reproduce the data in the energy region concerned, since such effects cannot be included in the standard formalism.
The 17 O + 12 C total fusion cross section was measured with Encore, an active target detector that measures a large portion of the fusion excitation function using a single beam energy with absolute self-normalization and full angular coverage of evaporation residues, in order to resolve a long-standing discrepancy at around E c.m. ∼ 14 MeV where previous data differ by a large factor not explained by the experimental error bars. The measurement was performed using two sets of beam energy and gas pressure to map out the energy region E c.m. = 8. 7 -20.4 MeV with overlapping data between 12 -16 MeV, spanning all the existing data sets.
Our results show a large oscillatory-like structure, not previously observed, in the region of the discrepancy between the data of Refs. [20] and [21], reconciling the two data sets within their respective experimental errors. Similar behavior has been seen in the 16 Taking the above considerations into account, it seems likely that the newly observed structure in the 17 O + 12 C total fusion excitation function is linked to resonance-like features in the 16 O + 12 C total fusion data [9,46], suggesting the formation of a 16 O + n + 12 C type configuration.