Key $^{19}$Ne states identified affecting $\gamma$-ray emission from $^{18}$F in novae

TL;DR

This study identifies key $^{19}$Ne nuclear states affecting $^{18}$F gamma-ray emission in novae, refining reaction rates and reducing uncertainties in nova gamma-ray detection predictions.

Contribution

First measurement of $^{19}$Ne states relevant to $^{18}$F destruction, providing more accurate reaction rates for nova models.

Findings

Identification of two long-sought $^{19}$Ne levels.

Reduction of reaction rate uncertainty by a factor of 1.5-17.

Decreased uncertainty in nova gamma-ray detection probability.

Abstract

Detection of nuclear-decay $\gamma$ rays provides a sensitive thermometer of nova nucleosynthesis. The most intense $\gamma$-ray flux is thought to be annihilation radiation from the $\beta^+$ decay of $^{18}$F, which is destroyed prior to decay by the $^{18}$F($p$,$\alpha$)$^{15}$O reaction. Estimates of $^{18}$F production had been uncertain, however, because key near-threshold levels in the compound nucleus, $^{19}$Ne, had yet to be identified. This Letter reports the first measurement of the $^{19}$F($^{3}$He,$t\gamma$)$^{19}$Ne reaction, in which the placement of two long-sought 3/2$^+$ levels is suggested via triton-$\gamma$-$\gamma$ coincidences. The precise determination of their resonance energies reduces the upper limit of the rate by a factor of $1.5-17$ at nova temperatures and reduces the average uncertainty on the nova detection probability by a factor of 2.1.

Figures

Tables

Table 1. Table 1: Resonance parameters used in the S-factor calculation. The widths were scaled within the energy uncertainty range for the reaction-rate calculation.

$E_x$ (keV)	$E_r$ (keV)	$J^{\pi }$	${\Gamma }_p$ (keV)	${\Gamma }_{\alpha }$ (keV)
6286(3)a	-124	1/2+	83.5c	11.6
6416(4)b	6	3/2-	4.7$\times {10}^{-50}$	0.5
6423(3)	13	3/2+	$\le$3.9$\times {10}^{-29}$	1.2
6439(3)a	29	1/2-	$\le$3.8$\times {10}^{-19}$	220
6441(3)	31	3/2+	$\le$8.4$\times {10}^{-18}$	1.3
6459(5)b	49	5/2-	8.4$\times {10}^{-14}$	5.5
6699(3)a	289	5/2+	2.4$\times {10}^{-5}$	1.2
6742(2)a	332	3/2-	2.22$\times {10}^{-3}$	5.2
7075(2)a	665	3/2+	15.2	23.8
7871(19)a	1461	1/2+	55	347

Full text

The outburst of energy that occurs once a white dwarf accretes a sufficient amount of material from a less-evolved companion star is called a classical nova. Novae are fairly common events in the Milky Way, with $\sim$50 estimated to occur per year Shafter (2017). While many unstable isotopes are created by novae during the hot carbon-nitrogen-oxygen cycles, few have been postulated to produce detectable $\gamma$ rays in the keV-MeV energy range José and Hernanz (2007). The largest $\gamma$-ray flux from novae is predicted to be from energies $\leq 511$ keV, due to the annihilation of positrons created from the $\beta^{+}$ decays of 13N and 18F Hernanz and José (2006). The main contributor to the flux of the annihilation $\gamma$ rays has been identified as 18F because its half-life ($t_{1/2}=109.77(5)$ min Tilley et al. (1995)) allows it to survive until the envelope of the explosion becomes transparent to $\gamma$ rays. Detection of this radiation would provide a test of nova models, which currently fail to reproduce observed properties such as the total ejected mass José and Shore (2008).

Reliable estimates of the sensitivity required for detection have been impossible to determine. This is because the destruction of 18F prior to its $\beta^{+}$ decay, which occurs primarily via the 18F($p$,$\alpha$)15O reaction, was not sufficiently known. The 18F($p$,$\alpha$)15O reaction-rate uncertainty at nova temperatures ($T=0.1-0.4$ GK) is attributed to the unknown energies of, and interference between $s$-wave ($J^{\pi}=1/2^{+},3/2^{+}$) resonances corresponding to states of the same spin in the compound nucleus, 19Ne Dufour and Descouvemont (2007); Beer et al. (2011). Precise determination of these resonances would greatly reduce the reaction-rate uncertainty.

Based on mirror symmetry, there should be two near-threshold 3/2+ states in 19Ne, corresponding to the 6497- and 6527-keV states in 19F Tilley et al. (1995). The cross section exhibits interference between these states and a broad 3/2+ resonance at $E_{cm}=665$ keV Bardayan et al. (2001). This interference is a dominant source of uncertainty in the reaction rate Beer et al. (2011); Laird et al. (2013); Bardayan et al. (2015) and strongly depends on the energies and proton widths of the “missing” 3/2+ 19Ne levels. A compilation by Nesaraja et al. Nesaraja et al. (2007) estimated the average energy shift from states in the mirror nucleus above 6400 keV to be $50\pm 30$ keV, though the actual shift for individual levels could be larger. This means the two 3/2+ states should have energies of $6447\pm 30$ keV and $6477\pm 30$ keV in 19Ne. Estimates of the reaction rate, including the uncertainties for these energy levels and their interference with the 665-keV state, results in the 18F($p$,$\alpha$)15O rate being uncertain by factors between 3 and 33 at temperatures of $0.1-0.25$ GK, the most important range for nova nucleosynthesis.

Because of their importance, a number of experiments have searched for the $J^{\pi}=3/2^{+}$ levels above the proton (18F+$p$) threshold ($S_{p}=6410$ keV) Utku et al. (1998); Adekola et al. (2011a); Laird et al. (2013); Parikh et al. (2015); Bardayan et al. (2015). Utku et al. Utku et al. (1998) showed the presence of potential resonances at 8 and 38 keV using the 19F(3He,$t$)19Ne reaction and explored a $3/2^{+}$ spin-parity assignment to both. Adekola et al. Adekola et al. (2011a) reconstructed neutron angular distributions from the 18F($d$,$n$)19Ne reaction but were only able to set upper limits on the strength of the 3/2+ levels. Laird et al. Laird et al. (2013) deconvolved the counts in a near-threshold triplet to conclude none seemed consistent with a $3/2^{+}$ assignment based on measured angular distributions. Kozub et al. Kozub et al. (2005) and de Séréville et al. de Séréville et al. (2005a, b) observed a strong 3/2+ level population in 18F($d$,$p$)19F measurements, but could not accurately estimate its placement in the mirror, 19Ne.

All previous measurements relied upon charged-particle spectroscopy and thus were limited by the energy resolution at which these particles could be detected. This Letter details the first detection of $\gamma$ rays from the de-excitation of these closely-spaced, near-threshold levels in 19Ne, instead of solely relying on charged-particle detection. This was not previously attempted due to the small $\gamma$-ray branching ratios ($10^{-3}$ Nesaraja et al. (2007)) expected for energy levels above the proton threshold.

To search for the 3/2+ states of interest, the 19F(3He,$t\gamma$)19Ne reaction was studied using GODDESS (Gammasphere ORRUBA Dual Detectors for Experimental Structure Studies) Ratkiewicz et al. (2013); Pain (2014); Pain et al. (2017) at Argonne National Laboratory. A beam of 30-MeV 3He from the ATLAS accelerator impinged on a 938-$\mu$g/cm2 CaF2 target with an average beam intensity of 2.5 pnA. The reaction tritons were measured over laboratory angles of $18^{\circ}-90^{\circ}$ in the silicon detector array ORRUBA (Oak Ridge Rutgers University Barrel Array) Pain et al. (2007), which was augmented by custom endcap silicon detector $\Delta E$-$E$ telescopes Pain et al. (2017). Coincident $\gamma$ rays were detected using the Compton-suppressed high-purity germanium detector array Gammasphere Lee (1990). A 0.5-mm thick aluminum plate, which was thin enough to transmit the tritons of interest, was mounted in front of the endcap telescopes to suppress the high rate of elastically-scattered 3He.

Calibrations of the Gammasphere detectors were performed with sources of 152Eu, 56Co, and 238Pu+13C, covering an energy range of 122 to 6128 keV. Systematic uncertainties in the $\gamma$-ray energy calibration ($\sim 0.3-2.0$ keV) were combined in quadrature with the statistical errors in the peak centroids to calculate the reported energy uncertainties.

The 19Ne energy levels reconstructed from the detected $\gamma$ rays were highly constrained by the gates placed on the data. With the exception of transitions directly to the ground state, triton-$\gamma$-$\gamma$ coincidences were used to identify the transitions. For levels that decayed through multiple $\gamma$-ray cascades, the excitation energies were determined by averaging the summed level energies for each individual $\gamma$-ray cascade, weighted by their uncertainty. In addition, much of the $\gamma$-ray background was removed by requiring a tight time coincidence between Gammasphere and ORRUBA, and the remaining random background was characterized by gating adjacent to the timing peak.

Above 1000 keV, only the 1508- and 4634-keV states have lifetimes long enough ($\tau\approx 1.7$ ps and $\tau>1.0$ ps, respectively Tan et al. (2005)) to allow the 19Ne to stop in the target before de-excitation. In all other cases, the 19Ne will still be travelling when $\gamma$ decay occurs, and therefore, the $\gamma$-ray spectra needed to be Doppler corrected. While small, values of $\beta$ ranged between 0.005 and 0.025 and were calculated on an event-by-event basis from the detected triton energy and angle. The sharpest $\gamma$-ray peaks were obtained assuming the recoil 19Ne ions lost no energy before decaying.

In total, 41 decays from 21 energy levels were identified Hall (2019), including seven decays from three near-threshold levels of astrophysical interest. Figure 1 displays the 19Ne level scheme, reconstructed from decays observed in the data, next to the 19F level scheme. Newly observed transitions from 19Ne states around 6400 keV and previously observed 19F transitions for their proposed mirrors are shown, with $\gamma$-ray energies and branching ratios appearing next to each arrow. Results from the near-threshold levels are highlighted in the following discussions.

A strong subthreshold state was found at 6289 keV by Adekola et al. Adekola et al. (2011a), which was later shown to be a doublet by Parikh et al. Parikh et al. (2015). Bardayan et al. Bardayan et al. (2015) determined the low-spin member to be 1/2+, while Laird et al. Laird et al. (2013) showed the other member has high spin. Two strong transitions were observed to the 4634- (13/2+) and 2794-keV (9/2+) levels, and averaging the summed cascade energies results in a best value of $E_{x}=6291.7\pm 0.9$ keV for the level energy. A comparison with the known 19F energy levels and associated $\gamma$ decays between 6000 and 7000 keV suggests the spin-parity of this state is 11/2+, making it the mirror of the $E_{x}(^{19}\mathrm{F})=6500$ keV level. No $\gamma$ decays from the 1/2+ state were observed in this work, which is not surprising, since none have been observed for the mirror state in 19F at $E_{x}=6255$ keV Tilley et al. (1995).

Above the proton threshold, the next grouping of levels shown to be populated by the 19F(3He,$t\gamma$)19Ne reaction Utku et al. (1998); Laird et al. (2013); Parikh et al. (2015) has been a source of debate due to their potentially important contributions to the reaction rate. The present data show transitions to the ground state (1/2+), 275-keV (1/2-) and 1508-keV (5/2-) states from an energy level at $6423\pm 3$ keV ($E_{cm}=13$ keV). Additionally, decays to the 238-keV (5/2+) and 1616-keV (3/2-) states were observed from a level with excitation energy $6441\pm 3$ keV ($E_{cm}=31$ keV). The average uncertainties on the $\gamma$-ray peak centroids and $\gamma$-ray energy calibration were $\approx$3 keV and $\approx$1 keV, respectively. Figure 2 shows the 19Ne excitation energy ($E_{x}$) spectrum generated from the detected reaction tritons and all five of the $\gamma$-ray peaks mentioned above. The low spins of the levels decayed to and previous discussion of the 6292-keV state contradict the assertion by Laird et al. Laird et al. (2013) that the 6440-keV state is the mirror of the $E_{x}=6500$-keV 19F state and has an 11/2+ spin-parity.

The most likely spin assignment for both the 6423- and 6441-keV states is 3/2+ based on the known levels and $\gamma$-ray transitions from the 19F mirror states. The 6497-keV state in 19F decays to the mirrors of the ground state, 238-, 275-, 1508-, and 1616-keV 19Ne states, whereas the 6527-keV state in 19F decays to the mirrors of the ground state, 275-, and 4603-keV 19Ne states Tilley et al. (1995). Two of three decays from the 6423-keV state have been previously observed from the $E_{x}(^{19}\mathrm{F})=6527$-keV level, whereas both decays from the 6441-keV state have been observed from the $E_{x}(^{19}\mathrm{F})=6497$-keV state. Therefore, mirror connections between the 6497-keV 19F and 6441-keV 19Ne states and between the 6527-keV 19F and 6423-keV 19Ne states are suggested. The only other possible spin-parity for these states consistent with the energy levels of the mirror and the multipolarity of the transitions is 7/2+. However, the decay scheme for the 7/2+ mirror is quite different than what was observed, and thus this seems unlikely. In any case, such a level would have limited importance to the 18F($p$,$\alpha$)15O rate because of the lack of interference with any broad resonance.

These two 3/2+ states near $E_{x}=6400$ keV would have been observable by Adekola et al. Adekola et al. (2011a) using the 18F($d$,$n$)19Ne reaction if the states were of sufficient strength and could be resolved from other states. Upper limits for the spectroscopic factor ($S_{p}\leq 0.028$) and proton width ($\Gamma_{p}\leq 2.35\times 10^{-15}$ keV) were set for a $3/2^{+}$ state in this excitation-energy region Adekola et al. (2011a, b). To be consistent, the following calculations assume most of the spectroscopic strength to be in one of the two 3/2+ states (which was observed in 18F($d$,$p$)19F measurements Kozub et al. (2005); de Séréville et al. (2005b)) and scale the widths with energy accordingly. The mirror assignments for the candidate $3/2^{+}$ states could be reversed, but this would not affect the results since the widths were determined in previous experiments and not derived from those states in 19F.

To assess the 18F($p$,$\alpha$)15O rate uncertainties due to interference between $s$-wave resonances, the R-Matrix code Azure2 Azuma et al. (2010) was used. The reaction rate is calculated from the astrophysical S-factor, which is the reaction cross section with the strong energy dependence due to the Coulomb barrier penetration removed. The S-factors calculated using Azure2 for various interference combinations are shown in Fig. 3. The R-Matrix channel radius used was 5.2 fm, and a 15-keV energy resolution was included in the calculation to directly compare with the available experimental data Bardayan et al. (2002); Beer et al. (2011); Bardayan et al. (2001); de Séréville et al. (2009). Table 1 shows the level energies and widths used in the calculation. Constructive and destructive interference between the known 1/2+ states and candidate 3/2+ states is denoted by the first and second set of parentheses, respectively. The majority of the S-factor uncertainty comes from the unknown interference sign of the 1/2+ states. Nonetheless, interference between the broad 3/2+ state at 665 keV and the two near-threshold 3/2+ states exacerbates this uncertainty.

The effect of the interference between the three 3/2+ states is better illustrated by calculating the rate using the range of excitation energies predicted for the 3/2+ states. The energies and widths of the near-threshold levels were varied within uncertainty to calculate the upper and lower limits of the 18F($p$,$\alpha$)15O reaction rate. This process was performed twice: first for the previous best estimates of $E_{x}=6447\pm 30$ keV and $E_{x}=6477\pm 30$ keV and then again using the newly-constrained values of $6423\pm 3$ keV and $6441\pm 3$ keV. Figure 4 shows the 18F($p$,$\alpha$)15O rate as a function of temperature, comparing the calculated upper and lower limits. Values for the rate calculated with proton widths less than the upper limit set by Adekola et al. Adekola et al. (2011a) fall within the rate bands.

Constraining the 3/2+ states to $6423\pm 3$ keV and $6441\pm 3$ keV reduces the reaction-rate uncertainty at $T=0.25$ GK to 0.96 cm3mol*-1s-1*, a reduction from the previous upper limit by a factor of 1.5, whereas at low temperatures ($T=0.1$ GK) the current uncertainty of $7.2\times 10^{-5}$ cm3mol*-1s-1* represents a reduction from the previous upper limit by a factor of 17. For comparison, the previously accepted rate bands calculated by Bardayan et al. Bardayan et al. (2015) are also included in Fig. 4. However, the calculated uncertainties in the rate considered only known levels and an assumed 3/2+ state at $E_{x}=6457$ keV based on the best available information at the time. In this study, this state was taken to have a spin-parity of 5/2- as reported by Laird et al. Laird et al. (2013).

Nova nucleosythesis calculations were performed using the Computational Infrastructure for Nuclear Astrophysics Smith et al. (2006) to investigate how the various reaction rates affect the final 18F abundance. The calculations were carried out assuming a nova explosion on a 1.0 solar mass CO white dwarf, as well as 1.15, 1.25, and 1.35 solar mass ONeMg white dwarfs. The final 18F abundance after the explosion was compared for each calculated rate shown in Fig. 4. Rates for the other nuclear reactions were taken from the REACLIB v2.0 library Cyburt et al. (2010). Isotopic abundances were tracked from 1H to 54Cr in radial zones (27 for CO, 23 for ONeMg) of varying temperature and density calculated from 1D hydrodynamic model calculations Starrfield et al. (1998). It was found that for increasing white dwarf masses, the final 18F abundance range was reduced by factors of 2.5, 2.6, 2.5, and 2.4, respectively. Therefore, the range of the maximum detection radius is decreased by a factor of 3.3 by constraining the energies of the 3/2+ states. This also reduces the average uncertainty on the nova detection probability, which is proportional to the volume of space that can be surveyed by a telescope with minimum $\gamma$-ray flux requirements, by a factor of 2.1.

To summarize, the unknown positions of 3/2+ states in 19Ne near the proton threshold were a significant source of uncertainty in the astrophysically-important 18F($p$,$\alpha$)15O reaction rate. The previous lack of knowledge regarding the energies of these states resulted in the rate being uncertain by factors of 3 to 33. To search for these levels, triton-$\gamma$-$\gamma$ coincidences from the 19F(3He,$t\gamma$)19Ne reaction were measured using GODDESS, and these data constitute the first published result from the GODDESS campaign. An 11/2+ state thought to be at 6440 keV Laird et al. (2013) was found subthreshold, and a mirror connection was made with the 6500-keV 19F level based on similar $\gamma$-decay patterns. Decays from levels at $6423\pm 3$ and $6441\pm 3$ keV to low-spin states provide the first evidence of the expected 3/2+ states, based on the known levels in the mirror nucleus, 19F. Constraining the level energies reduces the upper limit of the 18F($p$,$\alpha$)15O rate by a factor of 1.5 to 17. Nova nucleosynthesis calculations show the nova detection probability uncertainty is reduced a factor of 2.1 on average. While only upper limits for the flux of the annihilation radiation have been placed by the $\gamma$-ray telescope INTEGRAL (e.g. Siegert et al. Siegert et al. (2018)), the e-ASTROGAM project is planned to have a wide field of view and projected to be up to 100 times more sensitive than INTEGRAL De Angelis et al. (2018). Since much of the difficulty in detecting the annihilation radiation from novae is due to the maximum flux occurring prior to the visual maximum, future telescopes with a wide field of view and increased sensitivity will provide the best chance of observation.