Impact of nuclear $\beta$-decay rates on the $r$-process rare-earth peak abundances

The impact of $\beta$-decay rates of an individual nucleus on the $r$-process rare-earth peak abundances has been studied in different astrophysical scenarios. The variation in $\beta$-decay rates by a factor of 10 can produce large abundance uncertainties in the rare-earth mass region, while fission deposition can significantly reduce this uncertainty, which is not a suggested case by the current simulations of neutron-star mergers with moderately neutron-rich conditions where fission is less active. The most impactful nuclei include even-neutron-number ($N$) nuclei on the early $r$-process equilibrium path or $r$-process freeze-out path and nuclei with $N=100$, 102, and 104. It is found that the variations in the $\beta$-decay rate of nuclei located to the left and right sides of the $r$-process freeze-out path have significant different effects on rare-earth peak abundance.

Figure 1

Uncertainties in final abundances (shaded bands) corresponding to the sensitivity studies for increases and decreases in the $\beta$-decay rate by a factor of 10 for each nucleus in the $r$-process network for different scenarios. Darker shaded bands indicate the uncertainty in final abundances caused by changes in the $\beta$-decay rate of the ten nuclei with the highest sensitivity measure $F$. The cyan lines represent the baseline abundances, and the dots represent the solar $r$-process abundance pattern [40].

Figure 2

Sensitivity measures $F$ for $\beta$-decay sensitivity studies in four different scenarios. The region of measured $\beta$-decay rates from NUBASE 2020 [41] is overlaid with pink color and black squares are stable isotopes. The colored lines represent the $r$-process paths at different times, with the black line representing paths at the time of $r$-process freeze-out (defined as the neutron-to-seed ratio $R=1$), the olive line representing the early $r$-process paths before freeze-out, and the blue line nearest to the stable nuclei corresponding to the time when the rare-earth peak formation is completed with the timescale of neutron capture being approximately 2 to 3 times of the timescale of $\beta$ decay.

Figure 3

The effect of $\beta$-decay rate on the final rare-earth peak abundances for ${}^{157}\mathrm{I}$ (a) and ${}^{158}\mathrm{Ba}$ (b) in the hot1 scenario. The baseline curve is represented by a dashed green line, and the red and blue lines represent the final abundances corresponding to the ten times and one-tenth of the original $\beta$-decay rates of one specific nuclide in the $r$-process calculations, respectively.

Figure 4

Categories of nuclei with $F>350$ with two different effects on abundance distribution caused by $\beta$-decay rate variation. The nuclei in Category I are indicated by blue pentagram, while the rest nuclei are in Category II. Nuclei with increase of mass fraction in the rare-earth region $\mathrm{\Delta }X$ [defined in Eq. (4)] $>10\%$ are indicated by cyan hexagons. The colored lines represent the $r$-process paths at different times as in Fig. 2.