Charged-particle branching ratios above the neutron threshold in $^{19}$F: constraining $^{15}$N production in core-collapse supernovae

Spatially-correlated overabundances of $^{15}$N and $^{18}$O observed in some low-density graphite meteoritic grains have been connected to nucleosynthesis taking place in the helium-burning shell during core-collapse supernovae. Two of the reactions which have been identified as important to the final abundances of $^{15}$N and $^{18}$O are $^{18}$F($n,\alpha$)$^{15}$N and $^{18}$F($n,p$)$^{18}$O. The relative strengths of the $^{18}$F($n,\alpha$)$^{15}$N and $^{18}$F($n,p$)$^{18}$O reactions depend on the relative $\alpha_0$ and $p_0$ decays from states above the neutron threshold in $^{19}$F in addition to other properties. Experimental data on the charged-particle decays from these highly excited states are lacking or inconsistent. Two experiments were performed using proton inelastic scattering from LiF targets and magnetic spectrographs. The first experiment used the high-resolution Q3D spectrograph at Munich to constrain properties of levels in $^{19}$F. A second experiment using the Orsay Split-Pole spectrograph and an array of silicon detectors was performed in order to measure the charged-particle decays of neutron-unbound levels in $^{19}$F. A number of levels in $^{19}$F have been identified along with their corresponding charged-particle decays. The first state above the neutron threshold which has an observed proton-decay branch to the ground state of $^{18}$O lies 68 keV above the neutron threshold while the $\alpha$-particle decays from the neutron-unbound levels are generally observed to be much stronger than the proton decays. Neutron-unbound levels in $^{19}$F are observed to decay predominantly by $\alpha$-particle emission, supporting the role of $^{18}$F($n,\alpha$)$^{15}$N in the production of $^{15}$N in the helium-burning shell of supernovae. Improved resonant-scattering reaction data are required in order to be able to determine the reaction rates accurately.

At the end of hydrogen burning, some 14 N is left as a result of the operation of the CNO cycles. This 14 N is converted into 18 F through the 14 N(α, γ) 18 F reaction. Under normal pre-supernova conditions, during which the mass fraction of neutrons is very low, this 18 F undergoes β + decays into 18 O. During the supernova explosion the 18 O(α, n) 21 Ne reaction begins to operate, supplying neutrons which can react with 18 F, resulting in 18 F(n, α) 15 N and 18 F(n, p) 18 O reactions. The temperatures in the helium-rich zone reach peak post-shock temperatures of 0.4 − 0.7 GK, corresponding to a range of thermal energies of kT = 35 − 60 keV. The reaction rates depend on the properties of states within a few kT of the neutron threshold, corresponding to approximately E cm < 200 keV in the present case.
The recommendation of the sensitivity study of Bojazi and Meyer [2] is that the focus of future evaluations of the 18 F+n reaction rates should attempt to de-arXiv:2007.03965v3 [nucl-ex] 16 Jul 2020 scribe the competition between the proton and α-particle exit channels . This is particularly important because of the interplay between the two reactions: greater proton production from 18 F(n, p) 18 O produces 15 N via the 18 F(n, p) 18 O(p, α) 15 N reaction chain whilst also destroying it via proton absorption in the 15 N(p, α) 12 C reaction. An increased production of 15 N through the 18 F(n, α) 15 N reaction also results in a decreased destruction of 15 N through the 15 N(p, α) 12 C reaction enabled by the protons produced in the competing 18 F(n, p) 18 O reaction. After the supernova shockwave has passed the remaining 18 F will decay into 18 O.
Presently the 18 F(n, α) 15 N and 18 F(n, p) 18 O reaction rates are based on Hauser-Feshbach calculations [3,4]. However, the level density at the neutron threshold in the compound nucleus 19 F (S n = 10.432 MeV) may not be high enough for statistical models to be used with a great deal of confidence. Additional factors also lead one to conclude that statistical models may be inappropriate for computing the 18 F+n reaction rates: the nucleus 20 Ne is known to be strongly deformed with strong αcluster structures [5], and these structures persist into the neighbouring 19 Ne and 19 F nuclei [6,7]. This nonstatistical clustering behaviour is not well described by statistical models [8]. Therefore, experimental values of the resonance properties above the neutron threshold in 19 F are necessary in order to constrain the astrophysical reaction rates.
Direct measurements of neutron-induced reactions on 18 F are made functionally impossible by the difficulty of fashioning either neutrons or 18 F into targets. In the absence of direct measurements, the reaction rates can instead be determined if the properties of the resonances in 19 F above the neutron threshold are known. Some data on neutron-unbound levels in 19 F are available but better constraints particularly on the charged-particle branching ratios are required.
In this paper, we report two experimental studies of excited states in 19 F using in one experiment the Munich Q3D spectrograph, and using in the other experiment the Orsay Enge Split-Pole magnetic spectrograph coupled with an array of silicon detectors. These experiments yield information on the energies and, for resonances for which the widths of the states are larger than the experimental resolution, total widths of the excited levels. The Orsay experiment provides additional information on the relative strength of the charged-particle p 0 and α 0 decay branches, giving qualitative support to the hypothesis of Bojazi and Meyer [2] that 15 N is produced from the 18 F(n, α) 15 N reaction in helium-burning shell in core-collapse supernovae. However, it is not yet possible to provide calculated rates for the 18 F(n, p) 18 O and 18 F(n, α) 15 N reactions as information on the neutron widths, and the spins and parities of a number of states in 19 F is not available.  [11] etc.; these direct reactions tend to have much poorer energy resolution than the resonance reactions and it is sometimes difficult to firmly identify which states populated in the direct reactions correspond to those observed in resonance reactions. For that reason, the present discussion of existing nuclear data is confined to those data resulting from resonance reactions. A compilation of available nuclear data may be found in Table  I. Important aspects of the previous studies are briefly introduced below.
The reactions using 15 N+α have been performed with a gas target filled with purified 15 N gas [19,20]. An experiment measuring the yields of the 15 N(α, γ) 19 F, 15 N(α, α γ) 15 N and 15 N(α, pγ) 18 O reactions by detection of the associated γ rays was performed at Oxford in the 1970s [20]. In the experiment of Ref. [20], nine resonances were reported to be observed in either the 15 N(α, α γ) 15 N or the 15 N(α, pγ) 18 O channels.
Subsequently, a measurement of the elastic resonant scattering reaction 15 N(α, α) 15 N was performed at the same facility [19]. Only two levels in the region-of-interest were observed in this measurement, at 10.088 and 10.411 MeV. Both of these levels correspond to narrow states in this region.
The resonance reactions involving 18 O+p have been performed with alumina targets enriched in 18 O [14,15] or thin gas targets [13,18]. Two of the older studies of 18 O+p reactions, those of Carlson et al. [13] and Gorodetzky et al. [14,15] use the then-current value for the proton threshold of 19 F, a value which is around 30 keV lower than the present, more accurate value [17]. This results in the excitation energies of levels determined in those experiments being around 30 keV below the correct value. The excitation-energy values listed in Table  I are re-calculated from the available data in Refs. [13][14][15]18] using updated mass measurements [17]. The uncertainties in the excitation energies are also recalculated -in these cases, they are dominated by the uncertainties in the proton bombarding energies. No information as to the systematic or statistical nature of the uncertainties of the proton bombarding energies in Refs. [13][14][15]18] are available. This is unfortunate: it is possible that the systematic uncertainties on the proton bombarding energies may be correlated and that the relative uncertainties in the bombarding energies is smaller.
We note that the level observed at E x = 10.162(3) MeV has a width of Γ = 31 keV according to Ref. [12]. However, the corresponding level in Sellin et al. has a width of Γ = 3.3 keV [18] which, if assumed to be the width in the laboratory frame, gives Γ cm = 3.1 keV, a  [12]). Energy levels which likely correspond to the levels listed in ENSDF [12] are listed in the column corresponding to that measurement. The excitation energies from Carlson et al. [13], Gorodetzky et al. [14,15] and Beard et al. [16] are recalculated using the proton energies listed in those papers and recent mass values [17]. The uncertainties are also recalculated, and are dominated by the uncertainties in the proton bombarding energies. Sellin et al. [18] and Hesmondhalgh et al. [19] do not report uncertainties on the proton and α-particle bombarding energies respectively for observed resonances meaning that uncertainties on the excitation energies may not be given. The excitation energies from the 15 N+α → γ study of Symons et al. [20] are taken directly from that paper. Partial widths are taken from various sources with the references given in each case.
See the note in the text about the width of this state. 10.187(8) 10.212 (7) 10.231 ( (7) 10.615 10.614(2) Γ = 9 keV [14,15], T = 3/2 10.676 (9) factor of ten smaller than the width quoted in Ref. [12]. We assume that the width quoted in Ref. [12] is a typographical error. The use of the 18 O(p, n) 18 F reaction to generate the medical radioisotope 18 F and as a neutron source means that it has been studied in great detail using both activation techniques [21] and direct measurement of the neutron flux [16,[22][23][24]. The study of Beard et al. [16] provides probably the most complete spectroscopy of the 18 O(p, n) 18 F reaction in the region of the neutron threshold. However, care must be taken when considering the excitation energies determined therein. If modern mass measurements [17] are used instead of mass excesses from the compilation in 1960 which is referenced by Beard et al. [25], the excitation energies of the states measured by Beard et al. are observed to shift by a little less than 2 keV. Bearing this in mind, the excitation energies in Table I have been re-calculated from the proton energies observed by Beard et al.. The uncertainties in the excitation energies are also recalculated -in these cases, they are dominated by the uncertainties in the proton bombarding energies.
Both the limitation and advantage of resonance reactions is that they are selective in the entrance channel of the populated resonances. Therefore, if the partial width in the entrance channel to a state using a particular reaction is relatively weak the state may drop below the limit-of-detection. A related effect can be observed comparing the study of Sellin et al. [18] with those of Gorodetzky et al. [14,15] or Carlson et al. [13]: the number of levels observed in the latter two experiments far exceeds the number of those claimed in the former. Careful visual inspection of the spectra of Sellin et al. [18] would suggest that some of the states claimed by Gorodetzky and Carlson are, in fact, observed in that experiment but are not treated as such.
In contrast, proton inelastic-scattering reactions at the energies used in the experiments described in this paper are not selective [26][27][28][29]. Therefore, unlike the previous resonance-reaction experimental studies of 19 F, we should populate most or all of the states present. Using high-resolution, unselective reactions has been used successfully in past experimental studies to help to clarify discrepancies between more selective reaction mechanisms (see, e.g. our previous experimental study of 26 Mg [30] and references therein).

III. MUNICH Q3D
A. Experiment A 16-MeV beam of protons was incident upon a target nominally comprising 40 µg/cm 2 of LiF deposited on a 20-µg/cm 2 natural carbon foil. Scattered protons were momentum-analysed in the Munich Q3D magnetic spectrograph [31]. The slits at the entrance of the spectrograph were set to 4 mm by 24.5 mm to optimise the energy resolution and to minimise the aberration from contaminating species.
The focal plane consisted of two gas proportional detectors backed by a plastic scintillator. The second proportional detector provides information on the focalplane position of the detected particle. Particles were identified using the energy losses in the proportional detectors and the remaining energy deposited in the plastic scintillator.
Data were also taken using a 28 SiO 2 target (nominally 40 µg/cm 2 on 5 µg/cm 2 carbon) for the purpose both of calibration and quantification of the 16 O background [32], and a natural carbon foil (nominally 55 µg/cm 2 ) to characterise the background resulting from the 12 C backing of the LiF target.
Data were taken for all targets at 25, 35, 40 and 50 degrees, with two overlapping field settings centred at E x = 10.2 and 10.5 MeV used to probe the astrophysically important region in 19 F.

B. Data Analysis
Protons were selected considering the energy losses in both of the proportional detectors and the residual energy detected in the plastic scintillator. The focal plane was calibrated in magnetic rigidity (Bρ) at each angle and for each field setting using well-known states in 28 Si.
The background from 12 C was scaled according to the measured charge and the nominal target thicknesses. This was found to under-predict the observed strength of the 9.62-MeV J π = 3 − state of 12 C in the present experiment. Additional scaling factors were introduced to ensure that the normalisation of the 12 C background was correct for both the LiF and 28 SiO 2 targets. This discrepancy is likely due to the nominal thickness of the carbon backing on the targets being inaccurate, potentially due to build-up of carbon residue on the target foil. The carbon background was then subtracted from the experimental spectra. Even following this background subtraction, a significant background is observed in the spectra taken with the LiF target. This background is not present in the spectra taken with the 28 SiO 2 target [33]. The background likely results from scattering from lithium present within the target and is not instrumental in nature.
The location of the contaminating E x = 10.356-MeV state of 16 O (Γ = 26 keV) was determined by using the 28 SiO 2 target. In this case, the spectrum -including any overlapping 28 Si states -was fitted with a linear combination of one exponentially tailed Gaussian function for the 16 O state, and one exponentially tailed Gaussian function for each 28 Si state. This allowed the location and shape of the 16 O state to be described. The contribution of the 16 O state to the LiF focal-plane spectrum was then included using the same function as used to fit the 16 O component of the 28 SiO 2 spectrum with a scaling factor to account for the different areal densities of 16 O in the LiF and 28 SiO 2 targets.
The resulting 19 F excitation-energy spectra were fitted using a combination of Voigt and exponentially tailed Gaussian functions [34]. The exponentially tailed Gaussian functions were used to describe the slight asymmetry in the Q3D response. The experimental energy resolution, corresponding to the width parameter of the Gaussian function or Gaussian component of the Voigt function, was constrained by the narrow peaks in the spectrum. Both the energy resolution (around 8 keV FWHM) and the exponential tail parameter (around 1 keV) were considered identical for all states in each individual fit.
Example spectra along with the resulting fits to the data from two different field settings and two different angles are shown in Figures 1 and 2. The centroids of observed states are shown by vertical lines. Individual contributions from states are also included in the figures, see the captions for details.

C. Results
The parameters of the levels extracted from the Munich data are given in Table II. The uncertainties on the excitation energies of the levels is purely statistical, and is taken from the weighted average of the excitation energies determined at each angle: where the E x,i are the excitation energies at each angle and the σ Ex,i are the associated statistical uncertainties in the excitation energies. The standard deviation in this case is given by: A complete uncertainty budget is given in Table III. When comparing the differences in the excitation energies determined in the present experiment from those from previous experimental studies, we find that the deviations observed are within the experimental uncertainties. However, this may merely reflect the dominance of systematic uncertainties in previous experimental studies.
The angular uncertainty is assumed to originate in the read-off of the angle setting for the Q3D, which is in gradations of 0.1°. However, the calibration is performed assuming scattering at a particular angle to calculate the proton rigidities. Therefore, the effect of the angular uncertainty on the excitation-energy uncertainty is relatively small, and is caused by the differing kinematic shifts of the 19 F(p, p ) and 28 Si(p, p ) reactions.
The calibration uncertainty is determined by propagating the uncertainties extracted on each of the parameters of the quadratic conversion from the focal-plane position to magnetic rigidity and thence to excitation energy. This contribution to the uncertainty budget does not include possible energy-loss or target-thickness effects on the calibration, which are accounted for separately.
The target-thickness and energy-loss contributions to the uncertainty are both assumed here as fractional contributions relative to the nominal thickness. The fractional contribution of the target thicknesses was taken from the scaling that had to be applied to the 12 C background in order to match the experimental data. As the targets are extremely thin, the energy loss for the protons through the foils is typically between 1 and 2.5 keV, and the corresponding uncertainties introduced by the target thickness or the energy losses are negligible.
The effects of field variations were determined in the same manner as described in Ref. [30] -two isolated narrow states at E x = 10.088 and E x = 10.616 MeV were fitted for sections of different runs and the shifts in the peak positions were measured. Shifts of a little less than 1 keV were observed. The shifts were within the fitting uncertainties for the excitation energies.

D. Discussion
Most of the levels observed in the present experiment have a corresponding observed level from the resonant reactions listed in Table I. For completeness, we discuss cases where the correspondence between levels listed in the ENSDF [12] and those observed in the present experiment is unclear, or where the status of a state is uncertain.
Some states listed in Table I at E x = 10.469 and 10.5656 MEV are not used in the fitting of the Q3D data. This could be because these states are not populated in the present reaction, which is unlikely given the non-selective nature of the (p, p ) reaction at low energies, or because these states in fact are spurious and correspond to other known states which have been reported in different reactions. The lack of reporting of sources of correlated systematic errors in some of the previous resonance-scattering measurements makes this possibility hard to discount.  Table  II. The two different fields correspond to different strengths of the magnetic fields of the Q3D to centre two different excitation energies on the focal plane of the spectrograph.  In the 18 O(p, α) 15 N experiments of Gorodetzky [14,15] and Carlson [13], a broad (Γ ∼ 60 keV) state was observed at E x = 10.426 (10) MeV. This state has typically been omitted in compilations of the levels of 19 F [12].
In order to ascertain whether this state is real we performed the analysis with and without the state included. No significant improvement was observed in the quality of the fits to the spectra for the Munich Q3D measurement. However, this state was found to be necessary to describe the α 0 coincidence spectrum (see Section IV B) and so it was included in the fits of the Q3D with pa-TABLE II. Energy levels determined from the Munich Q3D experiment. The index of the state is given for ease of reference during the discussion in the text. A 'narrow' state is one which was fitted with an exponentially tailed Gaussian function and not a Voigt function. Where possible, a suggested correspondence has been made between levels observed in the present experiment and those from previous experimental studies as summarised in Table I. All excitation-energy uncertainties from the present experiment reported in this table are purely statistical. The origin and magnitude of possible systematic errors is described in text.

State Index
Ex rameters of E x = 10.420(10) MeV and Γ = 90 keV. The Q3D data are not able to provide significant constraints for the properties of this state since the state is broad and there is a continuum background. The only previously observed level at around this excitation energy is the broad (Γ ∼ 60 keV) state at E x = 10.426 MeV discussed above. As both the excitation energy and width of these states are so different, it is unlikely that these states are the same. We conclude that this is a previously unobserved state in 19 F. A state at E x = 10.521 (7) MeV was observed in Refs. [14,15,20]. The resonance observed in the 18 O(p, α) 15 N study of Gorodetzky et al. [14,15] is extremely weak which may explain why this state was not observed in the 18 O+p measurement of Carlson et al. [13] or Sellin et al. [18]. No width is quoted for this state in those reference.
It is not clear if the state observed in the present experiment corresponds to those observed in previous measurements.  [14,15] at E x = 10.580(4) MeV with Γ = 22(3) keV [35] or Γ = 18 keV [14,15]. In the present experiment, there is a state observed at this excitation energy but with a width of Γ = 11(2) keV, significantly smaller than the width in the ENSDF database [12].
The width in the ENSDF database comes from a study of the 18 O(p, n) 18 F, 18 O(p, p γ) 18 O and 18 O(p, α 1,2 γ) 15 N reactions by Prosser et al. [35]. The widths observed in that measurement are typically much higher than the widths observed in the measurement of Beard et al. [16] and it is plausible that the widths in Ref. [35] are systematically overestimated. For this reason, we conclude that the resonance observed in Prosser et al. is the same as the resonance observed in the present measurement, and has a width of Γ = 11(2) keV.

21: The 10.676-MeV state
The state at E x = 10.676(1) MeV is not listed in current nuclear data compilations [12]. This state may correspond to the resonance observed at E p = 2831 (9) keV (E x = 10.676(9) MeV) in the 18 O(p, α 0 ) 15 N study of Gorodetzky et al. [14,15]. In Carlson et al. [13], only one resonance is observed (E p = 2824(8) keV) compared to the two in Gorodetzky et al. at E p = 2815(9) and 2831(9) keV. It is possible that the resonance listed in Carlson is the unresolved strength of the two resonances observed by Gorodetzky et al. [14,15].

A. Experiment
A beam of 15-MeV protons was incident upon a target comprising 84 µg/cm 2 of LiF deposited on a 32-µg/cm 2thick 12 C foil. Scattered protons were momentumanalysed in an Enge Split-Pole magnetic spectrometer. The aperture of the spectrometer covered 1.3 msr and was placed at θ lab = 30 • and 40 • . Data were taken at two angles so that contaminants could be identified but coincidence data with the silicon detectors (see below) were only taken at θ lab = 40 • . The focal plane consisted of a position-sensitive gas detector backed by a gas proportional detector and a plastic scintillator. Focal-plane particle identification was accomplished using the energy deposition in the gas proportional detector and the focalplane position.
An array of 6 silicon detectors ('W1' design from Micron Semiconductor Ltd. [36]) was placed within the scattering chamber of the spectrometer. The spectrometers were placed at backward angles at around 110 mm (detectors 1-4) or 90 mm (detectors 5 and 6) from the target. Detectors 1 and 2 covered 110 < θ < 125 degrees, detectors 3 and 4 covered 135 < θ < 165 degrees, and detectors 5 and 6 covered 110 < θ < 150 degrees. Detectors 1-4 were placed to the right of the beam and detectors 5 and 6 to the left. Charged-particle decays resulting from inelastic scattering reactions were detected in the silicon array. The signals from the silicon detectors were amplified in Mesytech STM-16 preamplifier modules, the signals were then transmitted to Mesytech STM-16 leadingedge discriminator modules which gave a shaped output energy signal and an ECL timing signal. Energy signals were recorded for strips on the junction and Ohmic sides of each detector. Timing signals were recorded for junction sides only.
The trigger for the experiment was a coincidence between the gas proportional detector and the plastic scintillator at the focal plane of the Enge spectrometer. The shaping time of the STM-16 amplifiers was set so that the silicon energy signal fell after the trigger from the focal plane-detectors. The timing window of the Caen V1190A time-to-digital converters was set so that it included the timing signals from the silicon detectors which precede the trigger from the spectrometer focal plane.

B. Data Analysis
Inelastically scattered protons detected at the focal plane were selected using the energy deposited in the gas proportional detector and the focal-plane position. The focal-plane spectrum was then converted to magnetic rigidity, Bρ, using a magnetic field which was logged during the experiment, correcting any variations in the focal-plane position caused by shifts in the magnetic field. The calibration of the focal plane is made by considering the energies of known levels in 19 F as determined from the experiment performed using the Munich Q3D.
Silicon hits were accepted if the energy deposited in the front and back of a detector was within 80 keV, and the time between the silicon and focal-plane events fell within a given kinematic locus. Two-dimensional matrices of the missing energy against the excitation energy were constructed for valid silicon events, assuming a particular reaction channel. The missing energy is the deficit between the known initial energy and the sum of the final energies of the reaction products, requiring an assumption about the kinematics of the reaction. For a reaction of beam a on target A resulting in the ejectile b and heavy recoil B which subsequently decays into light fragment c and heavy fragment C, the missing energy M is: where T i (m i is the kinetic energy (mass) of the ith particle. T a , the kinetic energy of the beam, is defined by the accelerator, T b is measured in the Split-Pole, T c is measured in the silicon detectors and T C is calculated under the requirement that the 4-momentum is conserved. The identification of different reaction channels and reactions from target contaminants is simpler using the missing energy. An example of two of these twodimensional matrices assuming α-particle and proton decays from states in 19 F are shown in Figure 3. Decay channels from 19 F states with the correct kinematic reconstruction appear as horizontal loci. Other reaction channels and target contaminants have sloped loci. Gates can then be placed on the loci corresponding to different reaction channels.
The α 0 locus is very clean. This is because of the low α-particle threshold in 19 F: the α-particles decaying from states in the excitation-energy range populated in the proton-scattering reaction are much higher in energy than those from reaction channels resulting from contaminating nuclei. The p 0 channel is, however, embedded in a region with a number of contaminating channels. The effect of these channels may be reduced/removed using tighter timing gates for detector 1 to 4; an example of this is shown in Figure 4. For detectors 5 and 6, which are closer to the target, this is not possible and the background is instead included in the fit of the data. This background is determined by the linear interpolation of the backgrounds found with gates on the missing energy. The generated inelastic proton spectra in coincidence with α 0 and p 0 as well as the inclusive (singles) spectrum are shown in Figure 5.
The parameters (E x , Γ) of states determined from the Munich Q3D data were used to fix the relevant fitting parameters for the Orsay Split-Pole data with the exception of the E x = 10.420(10)-MeV broad state. The parameters for this state were determined from the combined α 0 spectrum as it provides the cleanest signal from the broad state; the width of this state is estimated to be Γ = 105 (30) keV with the continuum background again making estimation of the parameters of this resonance difficult. The exclusive spectra were fitted using a combination of Gaussian and Voigt functions. The experimental resolution (16 keV FWHM) was fixed using narrow states in the p 0 decay locus.
In the case of the p 0 decay data (Figure 3, right panel), there is an overlapping locus resulting from other reaction channels. To account for this background in the fitting of the data, the background is described by a Gaussian function. The centroid and width of the background component are determined by generating the coincidence spectra gating above and below the p 0 -decay locus in the missing energy vs excitation energy plots. The centroids and widths of the background function are then deter-mined by linear interpolation of the centroids and widths of the background components generated from the off-p 0decay loci.
Branching ratios of excited states were determined by comparing the yields of state in the coincidence spectra to the yields of states in the inclusive spectrum. To account for anisotropy in the decays, the yields per detector were calculated using the GEANT4 simulation for isotropic decays and decays with an angular correlation function following W (θ) = 1 + P 2 (cos(θ)) and W (θ) = 1 + P 2 (cos(θ)) + P 4 (cos(θ)) where P 2 and P 4 are the second-and fourth-order Legendre polynomials, respectively.
The yields for each state were then calculated assuming that the angular correlation function is: where the A i are real coefficients found by minimising the χ-squared function: where the X i are the experimental per-detector yields and the Y i are the calculated per-detector yields. The σ i are the uncertainties on each datum. The total yield is extracted from the integration of the angular correlation function. The procedure to extract the yields was tested with a simulated dataset using the angular correlation function extracted for one of the observed states. The yields per detector and the total yield used in the simulation were successfully reproduced showing that the method used to extract the yields is robust.
Due to the high level of background in the inclusive spectrum from the Orsay measurement, the absolute branching ratios cannot be extracted. Instead we report relative p 0 /α 0 branching ratios in Table IV. For many states, no p 0 decay is observed above background. For these cases, we estimate what the smallest yield would have been for the state to have been observed, and this yield is used to compute the upper limit for the ratio of the branching ratios. The probability distribution for an observable peak above the background is calculated using the Feldman-Cousins method [38] using the implementation in the ROOT data-analysis framework [39]. The probability distribution function for the ratio of the p 0 and α 0 decays is then calculated by Monte-Carlo sampling of the probability distribution functions for the p 0 and α 0 decays; the probability distribution function for the α 0 decay is assumed to follow a log-normal distribution. The resulting numerically determined 84% percentiles are reported in Table IV.  Table IV also includes the ratio of the p 0 and α 0 partial widths determined from the 18 O+p data of Sellin et al. FIG. 3. 2D matrices of the excitation energy (abscissa) against missing energy (ordinate) for DSSSD detectors 1 and 2 covering the same angular range. The black points are experimental data and the red points are the results of the GEANT4 simulations using the NPTool package [37] being processed through the same analysis. The plot on the left (right) shows the missing energy computed assuming the kinematics of the 19 TABLE IV. Ratio of the proton to the α-particle branching ratio for states above the neutron threshold in 19 F, and for states below the neutron threshold which were also measured in the 18 [18]. There is moderate agreement between the present results and those of Sellin et al. [18] though direct comparison is hindered by the lack of uncertainties reported in those results.

C. Discussion
Due to the considerable uncertainty in the absolute branching ratios resulting from the high background in the singles spectrum from the Orsay Split-Pole, it is not possible to calculate the 18 F(n, α) 15 N and 18 F(n, p) 18 O reaction rates with reasonable uncertainties. The neutron widths or branching ratios are not available, and while a Monte-Carlo approach of reasonable values for the widths is possible, the resulting uncertainty in the reaction rates is extremely high. Instead, we limit the discussion to qualitatively considering the relative strengths of the α-particle and proton decay modes from the states above the neutron threshold in 19 F. It is clear from Figure 5 that the α-particle decay branch is significantly stronger than the proton decay branch. In fact, above the neutron threshold, the only states observed to have proton decay branches are at E x = 10.500 and 10.616 MeV. This result is in partial agreement with the 18 O+p data of Carlson who observed two states strongly in the 18 O(p, p) 18 O reaction (indices 21 and 24 in that work) at proton bombarding energies corresponding to E x = 10.500 and E x = 10.616 MeV.
The dominance of α-particle emission over proton  4. (Top) Energy of the particle detected in the silicon detector (abscissa) against the time difference between the focal-plane event and the particle detected in the silicon detector (ordinate). The additional timing gate on the proton events is also shown. This spectrum was generated using events from detectors 1 and 2 with a gate on Ex between 10. emission supports the hypothesis of Bojazi and Meyer [2] that the 18 F(n, α) 15 N reaction is a significant source of 15 N in core-collapse supernovae, and the cause of the enriched hotspots observed in presolar grains [1]. Remaining 18 F will decay into 18 O following the shockwave.

V. CONCLUSIONS
The 19 F(p, p ) 19 F reaction has been studied using the Q3D magnetic spectrograph at Munich, and the Orsay SplitPole. Excited states above the neutron threshold in 19 F were observed, along with charged-particle decays from those states. The α-particle decay of the states above the neutron threshold is generally stronger than the proton decay, supporting the calculations of Bojazi and Meyer [2] who suggested that the 18 F(n, α) 15 N reaction could produce 15 N in the helium-burning layer of core-collapse supernovae. This, in turn, can explain the spatially correlated over-abundances of 15 N and 18 O observed in some meteoritic grains in the Orgueil meteorite [1].
Calculations of the 18 F(n, p) 18 O and 18 F(n, α) 15 N reaction rates are not presently possible due to the lack of information about the neutron widths. Time-reversed measurements, i.e. the 15 N(α, n) 18 F and 18 O(p, n) 18 F reactions, would provide the required information and should be the focus of future experimental studies.