Fusion of neutron-rich oxygen nuclei

Measurement of the fusion excitation function for 18O + 12C and 19O + 12C is described. The fusion cross-section is extracted through the direct measurement of evaporation residues resulting from the fusion process. At near barrier energies, the single additional neutron present in 19O results in an enhancement in the fusion cross-section by a factor of over three as compared to 18O.


Introduction
Measuring the fusion excitation function for an isotopic chain of projectile nuclei presents an unique opportunity to examine the character of neutron-rich matter. For a given element, with increasing neutron number the neutron density distribution usually extends further out while the proton distribution remains largely unaffected. Hence, the repulsive Coulomb potential is largely unchanged while the attractive nuclear potential changes. As fusion at near barrier energies is sensitive to the interplay between the repulsive Coulomb and attractive nuclear potentials, the comparison of the fusion excitation function for isotopically related projectiles provides a sensitive probe of the change in the attractive nuclear potential. This change in the attractive potential can be related to changes in both the structure and dynamics of the neutron density distribution as the number of neutrons increases. Presented in Fig. 1 are the neutron density distributions for oxygen isotopes calculated within the context of a relativistic mean field theory [1,2]. As expected, with increasing neutron number the tail of the density distribution extends further out. It is perhaps surprising however that the tail of the neutron density distribution for 22 O is so close to that of the drip-line nucleus 24 O. This observation is particularly noteworthy as beams of 20,21 O are presently available at GANIL and a beam of 22 O is anticipated in the near future. In this paper, we describe the first step towards the systematic measurement of the fusion excitation functions of the oxygen isotopes namely fusion in 18 O+ 12 C and 19 O+ 12 C.
An extended neutron distribution could impact fusion both through its static spatial extent as well as through its dynamics (e.g. polarization effects). The influence of the static contribution can be estimated by using a onedimensional barrier penetration model such as the Sao-EPJ Web of Conferences 163, 00013 (2017) DOI: 10.1051/epjconf/201716300013 FUSION17 Paulo model [3]. For the density distributions presented in Fig. 1, we have calculated the relative fusion crosssections for several oxygen isotopes and present the results in Fig. 2. Evident in the figure is the fact that at all energies as the neutron-richness increases the fusion cross-section increases. At energies well above the barrier (E c.m. ∼ 8 MeV) this enhancement is relatively constant and can be considered geometric. Near and below the barrier however, the enhancement increases rapidly with decreasing incident energy. In this energy domain the enhancement reflects the increased importance of the nuclear potential due to the neutron-skin. It should be emphasized that as this is a purely static calculation, the inclusion of fusion dynamics could result in an enhancement larger than that depicted in Fig. 2.
In order to measure the fusion excitation function for 18 O + 12 C and 19 O + 12 C two separate experiments were performed at the John D. Fox accelerator laboratory at Florida State University. In the initial experiment we measured the fusion excitation function for 18 O + 12 C, extending the measured cross-section down to the sub 1 mb level, a factor of 30 lower than previously measured. Having established the technique, we subsequently measured the fusion excitation function for 19 O + 12 C. The experimental details of both measurements are summarized below.

Experimental setup
The experimental setup for this experiment consisted of two ExB microchannel plate detectors and two annular silicon detectors as depicted in Fig. 3. The beam first passes through a ExB microchannel plate detector, designated MCP US , situated approximately 1.3m upstream of the target position. For each ion traversing this detector a fast timing signal is generated. The beam subsequently encounters a second ExB microchannel plate detector, designated MCP TGT . The 100 µg/cm 2 thick carbon foil of MCP TGT is dual function. Not only does it serve as a secondary emission for the detector, but it also serves as the target for the experiment. The coincidence of these two ExB MCP detectors with the appropriate time-of-flight provided the incident beam count. The typical intensity of the 18 O beam incident on the target was ∼2x10 5 ions/s.

Measuring the fusion products
Fusion of a 18 O nucleus in the beam together with a 12 C nucleus in the target foil results in the production of an excited 30 Si nucleus. For collisions near the Coulomb barrier the excitation of the fusion product is relatively modest, E * ≈ 35 MeV. De-excitation of this fusion product by evaporation of a few neutrons, protons, and α particles results in an evaporation residue (ER). Statistical model calculations [4] indicate that for a 30 Si compound nucleus, the nuclei 29 Si, 28 Si, 28 Al, 27 Al, and 25 Mg account for the bulk of the ERs. Emission of the light particles deflects the ER from the beam direction allowing their detection and identification in two annular silicon detectors, designated T2 and T3, that are situated downstream of the MCP TGT . These detectors subtend the angular range 3.5 • < θ lab < 25 • allowing detection of the majority of the ERs produced [5]. By measuring the time-of-flight of particles between the MCP TGT detector and the silicon detectors [6] together with the energy deposit in the Si detector, evaporation residues are distinguished from scattered beam, as well as emitted light particles. By utilizing the measured energy deposit and time-of-flight, the mass of the ion can be calculated providing clear separation of ERs from the incident beam [7].

Fusion excitation function for 18 O + 12 C
The fusion cross-section is extracted by summing the total number of evaporation residues observed. Comparison of this yield with the number of incident 18 O ions while accounting for the target thickness and the geometric efficiency of the experimental setup yields the absolute fusion cross-section [7]. The measured excitation function is displayed in Fig. 4a together with previously published results [9][10][11]. Vertical error bars on the new data reflect both the statistical uncertainties as well as a 2% systematic error associated with the analysis. Horizontal error bars represent the uncertainty in whether the fusion occurs at the front or back of the target foil. While prior measurements using the direct measurement of evaporation residues only measured the fusion cross-section down to the 25 mb level [9], in this work the fusion cross-section is measured down to the 820 µb level, a factor of approximately 30 lower in cross-section. In the energy region where the present data overlaps with published data, overall agreement of the cross-sections is good, close to the statistical uncertainties. This overall agreement indicates both that our approach in extracting the fusion crosssection is sound and that there are no significant uncertainties in the values of the target thickness or detector efficiency. Closer comparison of the present dataset with the data of Ref. [9] indicates that the presently measured cross-sections are approximately 3-5% lower for E c.m. ≥ 10 MeV. This is within the statistical uncertainties of the data reported by Eyal et al. In addition, the present data are higher in their statistical quality.
We have compared the experimental fusion excitation function with the predictions of a microscopic model. Over the past several years, the density constrained TDHF (DC-TDHF) method for calculating heavy-ion potentials [12] has been employed to calculate heavy-ion fusion cross-sections with remarkable success [13,14]. While most applications have been for systems involving heavy nuclei, recently the theory was used to study above and below barrier fusion cross-sections for lighter systems, specifically for reactions involving various isotopes of O+O and O+C [15,16]. One general characteristic of TDHF and DC-TDHF calculations for light systems is that the fusion cross-section at energies well above the barrier are usually overestimated [17,18], whereas an excellent agreement is found for sub-barrier cross-sections [15]. neling probability for the experimental data as compared to the theoretical calculations. This enhanced tunneling probability can be associated with a narrower, lower barrier. The underlying reason that the barrier determined from the experimental data is weaker than in the model is presently unclear.

Producing and Chararacterizing a 19 O beam
A beam of 18 O ions at an energy of 80.7 MeV was used to bombard a deuterium gas cell at a pressure of 350 torr to produce the 19 O beam. To increase the gas density, the gas cell was cooled to a temperature of 77 K. Ions of 19 O produced via a (d,p) reaction were separated from the incident beam by the electromagnetic spectrometer RESO-LUT [20]. Despite the rejection of most of the unreacted beam by RESOLUT, the beam exiting the spectrometer consisted of both 19 O and 18 O ions. It was therefore necessary to identify each ion incident on the target. By accomplishing this it was possible to simultaneously measure the fusion excitation function for 18 O + 12 C and 19 O + 12 C which provided an important consistency check. Comparison of the 18 O + 12 C with the prior high statistics measurement of 18 O + 12 C demonstrated that there were no systematic differences between the two measurements. This dual measurement thus provided confidence that any observed fusion enhancement was a robust signal.

Experimental setup
Although the experimental setup for the 19 O beam was largely the same as in the prior experiment, a few changes were made to handle the radioactive beam. In order to identify beam particles, the energy deposit (∆E) and timeof-flight (TOF) of each particle was measured prior to the target. After exiting RESOLUT particles traversed a thin foil (0.5 µm thick aluminized mylar) which served as the electron emission foil for an MCP detector. Approximately 3.5 m downstream of this thin foil the oxygen ions passed through a compact ionization detector (CID) depositing an energy, ∆E. CID served two roles: to help identify the ion as well as to reduce its energy. While the production of 19 O is favored at higher energies, the measurement of the fusion cross-section at near barrier energies requires reducing the energy of the radioactive ion after its production. To perform the excitation function measurement, the energy of the incident beam was decreased by adjusting the gas pressure in CID. Upon exiting CID the ions were incident on a 105 µg/cm 2 carbon foil. This carbon foil, as in the prior experiment, served both as a secondary electron emission foil for the target microchannel plate detector (MCP TGT ) and as the target for the fusion experiment [8]. To measure the energy distribution of 19 O and 18 O ions incident on the target, a surface barrier, silicon detector was periodically inserted into the beam path just prior to the target.
The timing signals from both microchannel plate detectors together with the energy deposit in the ionization chamber allowed identification of ions in the beam through measurement of the ∆E-TOF. Ions of 19 Figure 5. Comparison of the measured cross-section for 18 O + 12 C and 19 O + 12 C. The cross-sections for the 18 O reaction have been scaled by a factor of two for clarity.

Fusion excitation function for 19 O + 12 C
The same general trend is observed for both of the excitation functions depicted in Fig. 5a. With decreasing incident energy the cross-section decreases as expected for a barrier controlled process. At essentially all energies measured the 19 O data exhibits a larger fusion cross-section as compared to the 18 O data.  18 O + 12 C 7.66 ± 0.10 7.39 ± 0.11 2.90 ± 0.18 19 O + 12 C 7.73 ± 0.72 8.10 ± 0.47 6.38 ± 1.00 To quantitatively examine the differences in the two excitation functions we have fit the excitation functions with the Wong formalism of penetration of an inverted parabolic barrier [19]. The fit of the high resolution 18 O data is indicated as the solid black line in Fig. 5a. The solid red curve in Fig. 5a depicts the fit of the 19 Table 1. Since the charge density distribution is essentially unchanged, it is unsurprising that the barrier height, V C , remains essentially the same for both of the reactions examined. Moreover, as expected with increasing neutron number an increase in R C is observed. This increase in the radius can be viewed by calculating the quantity R C /A 1/3 where A is the mass number of the compound nucleus. This quantity has a value of 2.38 for the 18 O induced reaction, while it is 2.58 for the 19 O induced reaction. The most significant change in the fit parameters is a substantial increase in the magnitude of ω for the 19 O case corresponding to a narrower barrier, reflecting an increase in the attractive nuclear potential.
Depicted in Fig. 5b as the solid (red) line is the dependence of the measured ratio of σ( 19 O)/σ( 18 O) on E c.m. . At energies well above the barrier σ( 19 O)/σ( 18 O) is essentially flat at a value of ≈ 1.2. As one approaches the barrier it rapidly increases to a value of approximately 3.5. Hence, the addition of a single additional neutron in 19 O as compared to 18 O results in a dramatic enhancement in the fusion cross-section at sub-barrier energies.

Summary
We have measured the fusion excitation functions for 18 O + 12 C and 19 O + 12 C using low intensity beams. Comparison of these excitation functions indicates a significant enhancement at near barrier energies for the neutron-rich projectile. The addition of a single neutron increases the fusion cross-section by more than a factor of three at the lowest energy measured. This enhancement may reflect the increased role of neutron transfer or coupling to collective degrees of freedom. These measurements represent the first step in the measurement of the fusion excitation function for an isotopic chain of oxygen nuclei. Acquiring a systematic, high quality dataset of this type, coupled with microscopic calculations of the fusion process has considerable promise in elucidating the nature of neutron-rich nuclear matter.

Acknowledgements
The support of the staff at Florida State University's John D. Fox accelerator in providing the 18