Mass measurement of ${}^{51}\mathrm{Fe}$ for the determination of the ${}^{51}\mathrm{Fe}(p,\gamma ){}^{52}\mathrm{Co}$ reaction rate

Background: The ${}^{51}\mathrm{Fe}(p,\gamma ){}^{52}\mathrm{Co}$ reaction lies along the main rp-process path leading up to the ${}^{56}\mathrm{Ni}$ waiting point. The uncertainty in the reaction $Q$ value, which determines the equilibrium between the forward proton-capture and reverse photodisintegration ${}^{52}\mathrm{Co}(\gamma ,p){}^{51}\mathrm{Fe}$ reaction, contributes to considerable uncertainty in the reaction rate in the temperature range of interest for Type I x-ray bursts and thus to an $\approx 10\%$ uncertainty in burst ashes lighter than $A=56$.

Purpose: With a recent Penning trap mass measurement of ${}^{52}\mathrm{Co}$ reducing the uncertainty on its mass to 6.6 keV [Nesterenko et al., J. Phys. G 44, 065103 (2017)], the dominant source of uncertainty in the reaction $Q$ value is now the mass of ${}^{51}\mathrm{Fe}$, reported in the 2016 atomic mass evaluation to a precision of 9 keV [Wang et al., Chin. Phys. C 41, 030003 (2017)]. A new, high-precision Penning trap mass measurement of ${}^{51}\mathrm{Fe}$ was performed to allow the determination of an improved precision $Q$ value and thus new reaction rates.

Method: ${}^{51}\mathrm{Fe}$ was produced using projectile fragmentation at the Coupled Cyclotron Facility at the National Superconducting Cyclotron Laboratory, and separated using the A1900 fragment separator. The resulting secondary beam was then thermalized in the beam stopping area before a mass measurement was performed using the LEBIT 9.4T Penning trap mass spectrometer.

Results: The new mass excess, $\mathrm{ME}=-40189.2\left(1.6\right)$ keV, is sixfold more precise than the current AME value, and $1.6\sigma$ less negative. This value was used to calculate a new proton separation energy for ${}^{52}\mathrm{Co}$ of 1431(7) keV. New excitation levels were then calculated for ${}^{52}\mathrm{Co}$ using the nushellx code with the GXPF1A interaction, and a new reaction rate and burst ash composition was calculated.

Conclusions: With a new measured $Q$ value, the uncertainty on the ${}^{51}\mathrm{Fe}(p,\gamma )$ reaction rate is dominated by the poorly measured ${}^{52}\mathrm{Co}$ level structure. Reducing this uncertainty would allow a more precise rate calculation and a better determination of the mass abundances in the burst ashes.

Figure 1

A schematic diagram showing the major elements of the gas cell and LEBIT facility.

Figure 2

A sample 250-ms ${}^{51}\mathrm{Fe}^{+}$ time-of-flight traditional continuous cyclotron resonance (top) and 125-ms ${}^{51}\mathrm{Fe}^{+}$ time-of-flight Ramsey cyclotron resonance (bottom) used for the determination of the frequency ratio of ${\nu }_{\text{ref}}^{\text{int}}\left({\mathrm{CH}}_2{}^{37}\mathrm{Cl}^{+}\right)/{\nu }_c\left({}^{51}\mathrm{Fe}^{+}\right)$. The solid red curves represents a fit of the theoretical profile [16, 17].

Figure 3

Measured cyclotron frequency ratios $R={\nu }_{\text{ref}}^{\text{int}}\left({\mathrm{CH}}_2{}^{37}\mathrm{Cl}\right)/{\nu }_c\left({}^{51}\mathrm{Fe}\right)$ relative to the weighted average $\overline{R}$. The grey bar represents the $1\sigma$ uncertainty in $\overline{R}$.

Figure 4

Forward and reverse rates for the current recommended rate in reaclib (blue solid and dashed, respectively) and the new recommended rate (red dotted and dot-dashed, respectively). The pale red band represents the current 1-$\sigma$ uncertainty range in the reaction rate.

Figure 5

Fractional differences in abundance relative to the current Reaclib rate for the median (blue solid), $1\sigma$ up (green dashed), and $1\sigma$ down (red dot-dashed) of the new reaction rate distribution.