Direct measurement of astrophysically important resonances in ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{Ca}$

Background: Classical novae are cataclysmic nuclear explosions occurring when a white dwarf in a binary system accretes hydrogen-rich material from its companion star. Novae are partially responsible for the galactic synthesis of a variety of nuclides up to the calcium ($A\sim 40$) region of the nuclear chart. Although the structure and dynamics of novae are thought to be relatively well understood, the predicted abundances of elements near the nucleosynthesis endpoint, in particular Ar and Ca, appear to sometimes be in disagreement with astronomical observations of the spectra of nova ejecta.

Purpose: One possible source of the discrepancies between model predictions and astronomical observations is nuclear reaction data. Most reaction rates near the nova endpoint are estimated only from statistical model calculations, which carry large uncertainties. For certain key reactions, these rate uncertainties translate into large uncertainties in nucleosynthesis predictions. In particular, the ${}^{38}\mathrm{K}\left(p,\gamma \right){}^{39}\mathrm{Ca}$ reaction has been identified as having a significant influence on Ar, K, and Ca production. In order to constrain the rate of this reaction, we have performed a direct measurement of the strengths of three candidate $\ell =0$ resonances within the Gamow window for nova burning, at $386\pm 10$ keV, $515\pm 10$ keV, and $689\pm 10$ keV.

Method: The experiment was performed in inverse kinematics using a beam of unstable ${}^{38}\mathrm{K}$ impinged on a windowless hydrogen gas target. The ${}^{39}\mathrm{Ca}$ recoils and prompt $\gamma$ rays from ${}^{38}\mathrm{K}\left(p,\gamma \right){}^{39}\mathrm{Ca}$ reactions were detected in coincidence using a recoil mass separator and a bismuth-germanate scintillator array, respectively.

Results: For the 689 keV resonance, we observed a clear recoil-$\gamma$ coincidence signal and extracted resonance strength and energy values of ${120}_{-30}^{+50}{(\mathrm{stat}.)}_{-60}^{+20}(\mathrm{sys}.)\mathrm{meV}$ and ${679}_{-1}^{+2}(\mathrm{stat}.)\pm 1(\mathrm{sys}.)\mathrm{keV}$, respectively. We also performed a singles analysis of the recoil data alone, extracting a resonance strength of $120\pm 20(\mathrm{stat}.)\pm 15(\mathrm{sys}.)$ meV, consistent with the coincidence result. For the 386 keV and 515 keV resonances, we extract $90\%$ confidence level upper limits of 2.54 meV and 18.4 meV, respectively.

Conclusions: We have established a new recommended ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{Ca}$ rate based on experimental information, which reduces overall uncertainties near the peak temperatures of nova burning by a factor of $\sim 250$. Using the rate obtained in this work in model calculations of the hottest oxygen-neon novae reduces overall uncertainties on Ar, K, and Ca synthesis to factors of 15 or less in all cases.

Figure 1

(a) Sample rate vs time curves measured in the NaI detector. The green filled circles correspond to a run where the beam rate was constant, while the blue filled squares correspond to a run where there were significant changes in the rate. The solid orange lines show the fit results used to extract the average beam intensities. (b) Average beam rate determined for each $\sim 1$ hour run taken during the experiment. The filled circles, rectangles, and triangles denote each run's beam energy, as indicated in the legend.

Figure 2

(a) MCP vs separator TOF for the $15.58$ MeV and $20.56$ MeV beam energies. The blue dotted and green dashed ovals represent the expected location of recoils for the $15.58$ MeV and $20.56$ MeV beam energies, respectively. (b) Profile likelihood curve for the $15.58$ MeV beam energy. (c) Profile likelihood curve for the $20.56$ MeV beam energy.

Figure 3

Summary of the coincidence analysis for the data taken with a beam energy of $27.17$ MeV. The individual descriptions of panels (a) through (f) are as follows: (a) Separator vs MCP TOF particle identification spectrum. The blue filled circles represent data collected with the radioactive ${}^{38}\mathrm{K}$ beam, while the single filled yellow triangle represents data collected with a ${}^{38}\mathrm{Ar}$ beam, for background characterization. The open ellipse outlines the expected recoil region. Projections onto the horizontal and vertical axes are also included (as the unshaded orange and green histograms). (b) Target density as a function of center-of-mass beam energy. The filled circles with error bars represent the data points and the solid line shows the fit to Eq. (7). (c) NLL contour plot, calculated by comparing simulated and measured BGO $z$ positions as explained in the text. The solid blue point shows the location of the global minimum. (d) Measured BGO $z$-position distribution for recoil events (filled circles), compared with the best-fit simulation result at $E_r=679$ keV and $\omega \gamma =120$ eV (solid orange lines). (e) Same as panel (d), but showing the measured energy of the most energetic $\gamma$-ray hit in the BGO array. (f) Total energy deposited in the IC vs energy loss in the third (most downstream) anode. The filled (blue) circles show the location of the ${}^{39}\mathrm{Ca}$ coincidence recoils observed with the ${}^{38}\mathrm{K}$ beam. The filled yellow triangle denotes the location of the event observed with a beam of pure ${}^{38}\mathrm{Ar}$. The greyscale map shows the location of all heavy-ion singles events observed with the $27.17$ MeV ${}^{38}\mathrm{K}$ beam. This distribution is dominated by leaky beam.

Figure 4

Summary of the singles resonance strength analysis for the $27.17$ MeV beam energy. In panels (a)–(c), the blue filled circles represent events already identified as recoils in the coincidence analysis, and the greyscale intensity maps represent all singles data. In panel (d), the open circles represent all singles data, and the various curves represent fits as indicated in the legend. The solid black lines in panels (a) and (c) represent diagonal axes onto which the two-dimensional data are projected for subsequent analysis. The dashed black lines in panel (b) represent the cut placed on the “RF-MCP Projection” parameter. The full significance of each plot is explained in the main text.

Figure 5

Updated ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{Ca}$ reaction rate across the temperature regime covered by classical novae, calculated assuming the rate is dominated by the three $\ell =0$ resonances studied in the present experiment. The contributions of the 386 and 515 keV resonances represent upper limits, while the “689 keV” resonance contribution represents our measured central value of 120 meV. Also shown is the statistical model rate of Ref. [9] (“ILIADIS”), along with its associated uncertainties (shaded region).

Figure 6

Summary of the sensitivity study results presented in Table 4. The various data points represent the logarithm of the ratio $X/X_{\mathrm{rec}}$, where $X_{\mathrm{rec}}$ is the predicted abundance of a given isotope taking the recommended ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{Ca}$ rate from Ref. [9], and $X$ is the predicted abundance of the same isotope taking the ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{Ca}$ rate to be at the upper or lower limit of various uncertainty bands. For the points on the left of the figure (labeled “ILI01”), $X$ is evaluated at the factor of 100 up / 0.01 down uncertainty limits given in Ref. [9]. For points on the right of the figure (labeled “Present”), $X$ is taken from the uncertainty band established in Ref. [11]. In all cases, up-turned triangles represent $X$ calculated at the upper limit of the uncertainty band and down-turned triangles represent $X$ at the lower limit. The various dashed, dotted, and dot-dashed lines represent abundance calculations for ${}^{38}\mathrm{Ar}$, ${}^{39}\mathrm{K}$, and ${}^{40}\mathrm{Ca}$ as indicated in the legend at the top of the figure. Panel (a) shows the results of the present nugrid sensitivity study, while panel (b) shows the results of the Iliadis et al. sensitivity study [8]. In panel (b), results from both the “S1” and “P2” nova models are displayed for ${}^{39}\mathrm{K}$. The filled green triangles connected by the dotted line represent results of the “S1” model, while the open triangles connected by solid lines represent the results of the “P2” model.