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Impact of New beta-decay Half-lives on r-process Nucleosynthesis

We investigate the effects of newly measured beta-decay half-lives on r-process nucleosynthesis. These new rates were determined by recent experiments at the radioactive isotope beam factory facility in the RIKEN Nishina Center. We adopt an r-process nucleosynthesis environment based on a magnetohydrodynamic supernova explosion model that includes strong magnetic fields and rapid rotation of the progenitor. A number of the new beta-decay rates are for nuclei on or near the r-process path, and hence they affect the nucleosynthesis yields and time scale of the r-process. The main effect of the newly measured beta-decay half-lives is an enhancement in the calculated abundance of isotopes with mass number A = 110 -- 120 relative to calculated abundances based upon beta-decay rates estimated with the finite-range droplet mass model. This effect slightly alleviates, but does not fully explain, the tendency of r-process models to underproduce isotopes with A = 110 -- 120 compared to the solar-system r-process abundances.

Introduction. Rapid neutron-capture (r)-process nucleosynthesis is responsible for the origin of approximately half of the elements heavier than iron and is the only means of producing the naturally occurring radioactive heavy actinide elements such as Th and U. In spite of more than a half century of study and observational progress [e.g., 1], however, the astrophysical sites for r-process nucleosynthesis have still not been unambiguously identified (for recent reviews see, e.g., [2,3]). Although many candidate sites have been proposed and supernovae appear to be well suited as the r-process site [4], up till now there has been no consensus as to the correct astrophysical model.
Notwithstanding the difficulties in finding a suitable astronomical environment, the physical conditions for the r-process are well constrained [5]. It is evident that the r-process occurs via a sequence of near equilibrium rapid neutron captures and photo-neutron emission reactions far on the neutron-rich side of stability. This equilibrium is established with a maximum abundance strongly peaked on one or two isotopes far from stability. The relative abundance of r-process elements is then determined by the relative β-decay rates along this r-process path., i.e., slower β-decay lifetimes result in higher abundances. At least part of the reason for the difficulty in finding the astrophysical site for the r-process stems from the fact that it lies so far from the region of stable isotopes where there is little experimental data on β-decay rates.
In this context, it is of particular interest that β-decay half-lives of 38 neutron-rich isotopes including 100 Kr, 103−105 Sr, 106−108 Y, 108−110 Zr, 111,112 Nb, 112−115 Mo, and 116,117 Tc have been measured [6] at the recently commissioned radioactive isotope beam factory (RIBF) facility at the RIKEN Nishina Center. A secondary beam, containing the neutron-rich nuclei of interest, was produced by inflight fission of a 345 MeV/nucleon 238 U beam in a Be target.
The nuclei in the secondary beam were identified on an event-by-event basis. Their atomic numbers were determined from the energy loss in an ionization chamber, and the charge to mass ratio was determined by combining the projectile time-of-flight and magnetic rigidity measurements. The nuclei were then implanted in a silicon-strip detector where the β-decay lifetimes could be measured. Most of the measured lifetimes are an improvement on existing measurements and a number of them [6] were measured for the first time.
Many of these isotopes are near or directly on the r-process path. As such, they are of particular interest as they determine the β-flow toward the important r-process peak at A = 130. Thus, they regulate the ability of models for the r-process to form heavier 2 elements [7]. It is of particular interest, therefore, to examine the impact of these new rates on r-process models.
The magnetohydrodynamic (MHD) supernova explosion model is of particular interest in the present study as it provides a good fit to the observed r-process abundances and avoids some of the problems [7, and references therein] associated with other paradigms such as the neutrino driven supernova wind scenario [8]. Robust r-process nucleosynthesis appears to be a natural consequence of MHD mechanisms for core-collapse supernova explosions involving strong magnetic fields and rapid rotation. These models are also consistent with the observed jets and asymmetry of core-collapse supernovae. The detailed hydrodynamic properties of the MHD supernova model and the input nuclear physics are described below.
Magnetohydrodynamic Models. The main features of the MHD supernova model employed here are described in Ref. [9] and need not be repeated here. However, we emphasize that although this calculation is performed in the context of a particular r-process paradigm, this model is selected because it matches the required conditions of the r-process environment (timescale, neutron density, temperature, entropy, electron fraction, etc.). Thus, the results presented here should be similar to those obtained from more generic r-process models [e.g.,

7].
We utilize the jet-like explosion (model 4 in [9]) based upon a two-dimensional magnetohydrodynamic simulation. The ejecta were evolved with 23 tracers to describe the evolution of thermodynamic state variables. These were then post-processed to obtain the nucleosynthesis yields. Figure 1 shows the evolution of entropy, measured in units of the Boltzmann constant k B , and electron fraction, Y e , after nuclear statistical equilibrium (NSE) is achieved for three representative tracer particles together with temperature and density.
Hydrodynamic quantities (e.g., entropy, temperature, and density, etc.) are obtained from the magnetohydrodynamic simulation, whereas the electron fractions are deduced from the nucleosynthesis calculation. We switch from the NSE abundances to a nucleosynthesis network calculation at T = 9 GK (∼ 0.78 MeV).
Nuclear Reaction Network. The nuclear reaction network utilized for the nucleosynthesis simulations has been described in detail elsewhere [9,10] and need not be described in more detail here. The network consists of more than 4000 isotopes, including neutrons, protons, and heavy isotopes with atomic number Z ≤ 100 (for detail, see Table 1 in Ref. [9]). We also consider possible reactions related to the r-process involving two-and three-body reactions or decay channels, and we include electron capture as well as positron capture and screening effects for all of the relevant charged particle reactions. Experimentally determined masses [11] and reaction rates are adopted if available. Otherwise, the theoretical predictions for nuclear masses, reaction rates, and β-decays are obtained from the finite-range droplet model (FRDM) [12].
In the present study, we perform r-process calculations based upon three different nuclear reaction networks as summarized in Table I where Q is the theoretical Q value (in MeV) obtained from the FRDM [12]. The motivation for these modified Q values is that they lead to a better fit to the observed β-decay lifetimes away from stability.
Results. The nucleosynthesis calculations have been performed for 23 tracer particles from the MHD supernova model (e.g. Figure 1) with the three different reaction networks b RIKEN : experimental data given in Ref. [6].
b Q + modified : defined in Eq. (1). Table I. In particular, the underproduction of isotopes near A = 120 becomes slightly less pronounced relative to predictions based upon the FRDM rates when the new measured rates are employed. Figure 2 illustrates the final abundances obtained from the three representative trajectories (A, B, and C) of Figure 1 and the three reaction networks employed. Note that as the A ∼ 130 r-process peak is approached, the new rates begin to make a difference in isotopes with A ∼ 90 -120. Figure 3 shows the final integrated abundance distribution from all of the trajectories.

listed in
These are compared to the solar system r-process abundance distribution [14]. Here the effect of new rates becomes more apparent. There has been a recurrent conundrum in the r-process models in that they tend to underproduce nuclei with A ∼ 120 [8]. One hope has been that the newly measured β-decay rates in this mass region might shift the β-flow equilibrium thereby filling in the low abundances near A ∼ 120. Here, however, we see on  the adopted MHD supernova model (jet model 4 in Ref. [9]). Red solid, green dotted, and blue dashed lines correspond to results from using the FRDM (standard), RIBF, and RIBF+ rates, respectively. Abundances of solar system r-elements [14] are represented by black dots with error bars.
a new light-element primary process (LEPP) [15]. Our results suggest that nucleosynthesis in the LEPP should also be sensitive to the nuclear physics uncertainty from β-decay rates in this region. Hence, further studies on both the nuclear physics and astrophysics of the synthesis of elements with A ∼ 110 − 120 are warranted.