THE ROLE OF FISSION IN NEUTRON STAR MERGERS AND ITS IMPACT ON THE r-PROCESS PEAKS

We utilize the extended nuclear network Winnet (Winteler et al. 2012) with more than 6000 isotopes up to Rg. Our sets of reaction rates utilized are based on masses from the FRDM (Möller et al. 1995), the ETFSI-Q with shell quenching (Aboussir et al. 1995; Pearson et al. 1996), both in combination with the statistical model calculations of Rauscher & Thielemann (2000) for $Z\leqslant 83$, and on the HFB-14 model (Goriely et al. 2008, 2009), respectively. Theoretical β-decay rates are taken from Möller et al. (2003), experimental data from the nuclear database NuDat2 (2009). The neutron capture rates on heavy nuclei ($Z\gt 83$) as well as the neutron-induced fission rates are from Panov et al. (2010), while the β-delayed fission rates are taken from Panov et al. (2005). In our calculations, we refer to the combined application of these basic sets of reaction rates as original. We also test the effect of very recent advances in β-decay half-life predictions by T. Marketin (2015, in preparation) and Panov et al. (2015).

We have performed r-process calculations for a neutron star merger scenario with two 1.4 ${{\rm{M}}}_{\odot }$ neutron stars (Korobkin et al. 2012; Rosswog et al. 2013). We use 30 representative fluid trajectories, covering all the conditions in the ejected matter and providing the temperature, density, and electron fraction within the ejected material up to a time of ${t}_{0}=13$ ms. We start our nucleosynthesis calculations after the ejecta have begun to expand and the temperature has dropped to 10 GK. For $t\gt {t}_{0}$ we extrapolate, using free uniform expansion for radius, density and temperature:

$$\begin{eqnarray}&&r(t)={r}_{0}+{{tv}}_{0},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\rho (t)={\rho }_{0}{\left(\displaystyle \frac{t}{{t}_{0}}\right)}^{-3},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&T(t)=T[S,\rho (t),{Y}_{{\rm{e}}}(t)],\end{eqnarray} \tag{ 3 }$$

with radius r, time t, velocity v, density ρ, temperature T, entropy S, and electron fraction Y_e of the fluid element. The index 0 denotes the values at t₀. The temperature is calculated at each timestep, using the equation of state of Timmes & Swesty (2000).

Our network accounts for heating due to nuclear reactions (Freiburghaus et al. 1999), using

$$\begin{eqnarray}&&{kT}\displaystyle \frac{{dS}}{{dt}}={\epsilon }_{\mathrm{th}}\dot{q}\end{eqnarray} \tag{ 4 }$$

to calculate the entropy increase caused by thermal heating, where $\dot{q}$ is the energy generated due to nuclear reactions. We choose a heating efficiency parameter of ${\epsilon }_{\mathrm{th}}=0.5$ (introduced in Metzger et al. 2010a), corresponding to about half of the β-decay energy being lost via neutrino emission. The efficiency for neutron captures and fission processes should be higher, as none of the released energy escapes. However, the energy release in neutron captures is small due to small neutron-capture Q-values along the r-process path (compared to large β-decay Q-values), and the abundances of heavy fissioning nuclei are small in comparison to the majority of nuclei in the r-process path. Thus, while the heating via β-decays dominates, the exact value of ${\epsilon }_{\mathrm{th}}$ is difficult to determine. In the case of extremely neutron-rich dynamic NSM ejecta, the final abundances are, however, quite insensitive to its value (Korobkin et al. 2012).

The fission fragment distribution depends on the nuclear structure of the fissioning nucleus as well as that of the fission products, e.g., the shell structure of nuclei far from stability. The fission products can be predicted statistically by assigning a probability to each possible fission channel. Rates for the various fission channels considered and the associated yield distributions are crucial for r-process studies in NSMs. In each fission reaction there is a possibility of several fission neutrons being emitted. While the number of fission neutrons has been measured to be 2–4 for experimentally studied nuclei, it is known to increase with mass number as heavy nuclei become more neutron-rich (Steinberg & Wilkins 1978). Additional neutrons can be emitted as the fission fragments decay toward the r-process path (Martínez-Pinedo et al. 2006).

For our NSM nucleosynthesis calculations we employ four different fission fragment distribution models: (a) Kodama & Takahashi (1975), (b) Panov et al. (2001), (c) Panov et al. (2008), and (d) ABLA07 (Kelic et al. 2008, 2009). The first one is a relatively simple parameterization that does not take into account the release of neutrons during the fission process. The second and third are parameterizations guided by experimental data. The number of released neutrons in Panov et al. (2008) has been estimated as a function of charge and mass number of the fissioning nucleus and can reach 10 per fragment for nuclei near the drip line. The ABLA07 model is based on a statistical model considering shell effects in the fragments from theoretical predictions and has been tested to provide an accurate description of known fission data, including the number of released neutrons (Gaimard & Schmidt 1991; Benlliure et al. 1998; Kelic et al. 2009). It also includes the reproduction of fragment distributions from extended heavy ion collision yields (Kelic et al. 2008), and therefore goes far beyond the areas in the nuclear chart where spontaneous, β-delayed, or neutron-induced fission yields are known experimentally. Further applications of recent fragment models (GEF and SPY) are also employed in Goriely (2015). However, these models have either been restricted so far to not very neutron-rich nuclei ($A/Z\lt 2.8$ and $N\lt 170$; GEF), or have not yet been the subject of the same severe tests as ABLA07 (both GEF and SPY).

Based on NSM simulations of Rosswog et al. (2013), we present a comparison of the abundance features resulting from utilizing the different fission fragment models in Section 3 (see also Eichler et al. 2013).

In the following section(s), containing results of our nucleosynthesis calculations, it will become apparent that not only the choice of a mass model and the treatment of fission are important for the final abundances. It also turns out that the neutrons released during fission and from highly neutron-rich fission products play an important role for the late r-process freeze-out and the final abundance distribution. One of the main features is related to the timing between neutron release in fission and from decay products and the final neutron captures, possibly occurring after the freeze-out from (n,γ)–(γ,n) equilibrium. The role of β-decays (especially of the heaviest nuclei) is essential for the speed to produce heavy (fissioning) nuclei, as well as the time duration for which fissioning nuclei still exist. There are experimental indications (Domingo-Pardo et al. 2013; Kurtukian-Nieto et al. 2014; Morales et al. 2014) that the half-lives of nuclei around N = 126 are shorter than predicted by the FRDM+QRPA approach (Möller et al. 2003). Several theoretical calculations based on an improved treatment of forbidden transitions suggest a similar behavior (Suzuki et al. 2012; Zhi et al. 2013). Caballero et al. (2014) have explored the impact on r-process calculations utilizing the half-live predictions of Borzov (2011). Faster β-decay rates for nuclei in the mass region $Z\gt 80$ are also supported by the recent theoretical work of Panov et al. (2015) and T. Marketin (2015, in preparation).

The effect of adopting different fission fragment distribution models, all in combination with the FRDM mass model for the r-process calculations, is illustrated in Figure 1. It shows final abundances of the NSM ejecta in the atomic mass range A = 110–210. Two of the fragment distributions (Kodama & Takahashi 1975; Panov et al. 2001) have already been used for NSM calculations before (Korobkin et al. 2012) (see also Bauswein et al. 2013, utilizing the latter of the two, but with fragment mass and charge asymmetry derived from the HFB-14 predictions; see Goriely et al. 2011), while the other two (Kelic et al. 2008; Panov et al. 2008) have been newly implemented for the present calculations. All our results are compared to the solar r-process abundance pattern (Sneden et al. 2008).

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For the fissioning nuclei produced in the present r-process simulations, our fission models mainly result in fission fragments in the mass range $100\leqslant A\leqslant 160$. Therefore, it is no surprise that the largest differences between the models are found around the second peak. The results obtained with the two Panov models (Figure 1(a)) show a drastic underproduction of the mass region beyond the second peak ($A\approx 140-170$) by a factor of 10 and more, due to the dominance of the symmetric fission channel and a large number of released neutrons. The Kodama & Takahashi model, in contrast, shows an overproduction of these nuclei and fails to produce a distinct second peak. The ABLA07 model (dashed line in Figure 1(b)) shows the best overall agreement with the solar r-process abundance pattern (for the chosen mass model FRDM), leading only to an underproduction of $A=140-170$ nuclei by a factor of about 3.

Figure 2 demonstrates the importance of fission in our calculations, indicating the fission rates from two fission modes (neutron-induced and β-delayed fission) at t = 1 s. It is obvious that the mass region with $Z=93-95$ and $N=180-186$ dominates. In Figure 2(c) we show the corresponding (combined) fragment production rates for ABLA07 in the nuclear chart. In Figure 3 (and the related caption) we also provide the fission fragment distributions as a function of A as well as the number of released neutrons, for ²⁷⁴Pu (Z = 94). Note that the model by Kodama & Takahashi (1975) does not lead to any neutron release and Panov et al. (2008) predicts the largest number of released neutrons. It can also be seen that the predicted fragments in the Panov et al. distributions do not extend beyond A = 140 and thus lead to the strongest underproduction in the mass range $A=140-170$. We will come back to the importance of this topic later, when we address the question of whether the release of neutrons from fission dominates over β-delayed neutron emission.

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Some of the deficiencies beyond the second peak can also be attributed to the FRDM mass model, which is known to predict rather low or even negative neutron separation energies for nuclei beyond the N = 82 shell closure around N = 90 ($A\sim 138$) (e.g., Meyer et al. 1992; Chen et al. 1995; Arcones & Martínez-Pinedo 2011). As a consequence, material is piled up in and slightly above the second peak, while the mass region beyond A = 140 is underproduced. This effect might be reduced when applying the new FRDM version which is not publicly available yet (Möller et al. 2012), see e.g., Kratz et al. (2014). Thus, in order to explore the full dependence on uncertainties due to the combination of mass models and fission fragment distributions, we also performed reference calculations, employing the ETFSI-Q mass model (Pearson et al. 1996) and the HFB-14 model (Goriely et al. 2008, 2009) for the set of fragment distributions Kodama & Takahashi 1975, Panov et al. 2008 and ABLA07 (Kelic et al. 2008). They show less or no underproduction for $A\gt 140$, even for the Panov et al. (2008) fragment distribution. The results are displayed in Figure 4.

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A comparison of all different mass models with the fragment distribution ABLA07 is shown in Figure 5. ETFSI-Q suffers from a sudden drop of the neutron separation energy for $A\approx 140$, causing the formation of a small peak around this mass number. The distinctive trough in the ETFSI-Q abundance distribution before the third peak was subject of a detailed discussion in Arcones & Martínez-Pinedo (2011). While the extent of the underproduction in the mass range 140–160 is due to a combination of the fission fragment distribution and the mass model used (see also Figure 4), the results for all mass models utilized here show a shift of the third peak to higher mass numbers by up to 5 units, which will be a topic of the following sections.

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While the position of the third peak is similar for all the mass models considered here, the abundance patterns around the second peak and the rare-earth peak show some diversity. For these mass regions, the final abundances are strongly influenced by fission close to the freeze-out and also possible final neutron captures thereafter. Therefore, different final abundance patterns can be an indicator of different fission progenitors. Figure 6 shows the predominant fission reactions at the time of freeze-out for the HFB-14 model. A comparison with Figure 2 reveals that for the HFB-14 model the fission close to freeze-out tends to happen at higher mass numbers (up to A = 300), while for the FRDM model the fission parent with the highest mass is found at A = 287. As a consequence, fragments with higher mass can be produced (Figure 6(c)). However, the bulk of the fragments lie between A = 125 and A = 155, very similar to the FRDM case. Therefore, the aforementioned shift of the second peak in the HFB model calculations cannot be due to the fission fragment distribution lacking fragments with mass numbers at the lower flank of the second peak. The main cause must be reactions occurring after fission, which will be discussed in the following section.

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In our NSM calculations, the third peak is shifted toward higher mass numbers compared to the solar values (Figures 1, 4, and 5), regardless of the nuclear mass model utilized in the present investigation. This phenomenon has appeared in various calculations of NSMs before (Freiburghaus et al. 1999; Metzger et al. 2010b; Roberts et al. 2011; Korobkin et al. 2012; Goriely et al. 2013). We find that the position of the third peak in the final abundances is strongly dependent on the characteristics of the conditions encountered during/after the r-process freeze-out that are characterized by a steep decline in neutron density and a fast increase in the timescales for neutron captures and photodissociations, leading to different stages (timescales): (1) freeze-out from an (n,γ)–(γ,n) equilibrium; (2) almost complete depletion of free neutrons (${Y}_{{\rm{n}}}/{Y}_{\mathrm{seed}}\leqslant 1$); and (3) the final abundance distribution. In the following, we use the term freeze-out in the context of definition (1).

Figure 7 shows a comparison of our abundances on the r-process path resulting from detailed nucleosynthesis calculations at t = 1 s for the FRDM mass model with those which would result from an (n,γ)–(γ,n) equilibrium in each isotopic chain (as first discussed by Seeger et al. 1965) for the temperature and neutron density at that time ($T=9.5\times {10}^{8}$ K, ${n}_{{\rm{n}}}=7.44\times {10}^{26}\;{\mathrm{cm}}^{-3}$). The plot displays the most abundant nuclei in each isotopic chain, i.e., those on the r-process path. The colors indicate the factor between the equilibrium abundances and the abundances in our calculation. The highest discrepancies can be observed around N = 100 and N = 140, but only few nuclei show a factor larger than 2. This leads to the conclusion that at this time the r-process still proceeds in (n,γ)–(γ,n) equilibrium with (n,γ) and (γ,n) timescales much shorter than β-decays, characteristic of a hot r-process.

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This changes at t = 1.34 s (see Figure 8), when the timescales for neutron capture and photodissociation become larger than the β-decay timescale. Here both reaction timescales become longer than β-decays, and also neutron capture wins against photodissociations. Note that the timescales of β-decay also become larger as the material moves closer to stability. As can be seen in Figure 8, there is a short period after the freeze-out where (n,γ) dominates over both (γ,n) and β-decay. Figure 9 shows the second and third peak abundances at r-process freeze-out and the final abundances for a representative trajectory for the FRDM, ETFSI-Q, and HFB-14 mass models. It is evident that the position of the third peak is still in line with the solar peak at freeze-out, but is shifted thereafter for all mass models. The position of the second peak behaves differently. For all mass models, the final abundances for $A\lt 120$ nuclei are higher than the abundances at freeze-out, because fission fragments with these mass numbers are still produced after freeze-out. Nevertheless for the HFB-14 model the (final) second peak seems shifted to higher mass numbers, similar to its position at freeze-out. This might indicate that, for the astrophysical conditions encountered here, this mass model leads to a path running too close to stability.

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The shift in the third peak as described above is a generic feature in our NSM calculations. It is caused by the continuous supply of neutrons from the fissioning of material above $A\simeq 240$. Figure 10 shows that after the freeze-out the release of neutrons from fission dominates over β-delayed neutrons.

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To further illustrate the importance of fission neutrons after the freeze-out, we have run several calculations with both FRDM and HFB-14 where we have switched off certain types of reactions after the freeze-out. (1) The dashed lines in Figure 11 (labeled "only decays") represent the cases where only decay reactions are allowed after the (n,γ)–(γ,n) freeze-out (without fission). In this artificially created scenario the only possibility for nuclei after the freeze-out is to decay to stability, without the option to fission or capture neutrons. In fact, a small shift of the third peak to lower-mass numbers can be observed during this phase (compare Figures 9 and 11), as β-delayed neutrons cause the average mass number to decrease. In addition, since fission is not allowed either, the second peak consists of just the material that was present there at freeze-out, but the composition is (slightly) modified due to the combined effects of β-decays and β-delayed neutrons. (2) If we also allow for fission in addition to the decay reactions (dotted-and-dashed lines in Figure 11), the second peak is nicely reproduced by fission fragments for both mass models and the third peak is still not affected. (3) However, a notable difference between the two mass models can be seen for the final abundance distribution also including final neutron captures (denoted as "original" in Figure 11), indicating that for HFB not only the position of the third peak is influenced by late neutron captures, but also the position of the second peak. On the other hand, the behavior is reversed for the mass region $140\lt A\lt 160$, where large deviations can be observed compared to the original calculation for FRDM, since in the original case neutron captures move material up to higher masses, creating the underproduction we have discussed in chapter 3.1. This indicates that when neutron captures and all other reactions are permitted after freeze-out (i.e., the original calculation), major changes in the abundance pattern can still occur. The third peak moves to higher masses for all mass models discussed here. In the HFB case, the second peak moves to the position it had at freeze-out, resembling abundance features resulting from an r-process path too close to stability for the astrophysical conditions encountered here.

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It can be seen in Figures 1 , 4, and 9 that the shift of the third peak is indeed related to the amount of released neutrons. The shift is smallest for the Kodama & Takahashi (1975) model, which does not assume any neutron emission during fission, and largest for the Panov et al. (2008) model, which assumes the largest amount of neutrons produced. It should be noted, however, that the differences are smaller than expected from the numbers of released neutrons, as in addition to the neutrons directly released during fission, those released from the neutron-rich fission fragments can also be important as they move back to the r-process path. These in turn depend on the fission yields used.

Since the position of the third peak does not coincide with the third peak of the solar abundance pattern, we explore under which conditions such a shift to larger mass numbers can be avoided. In a first test we artificially increase the temperature throughout the expansion by setting the heating efficiency parameter ${\epsilon }_{\mathrm{th}}=0.9$ instead of our default value of 0.5 (see Section 2). This change does not affect the final abundance distribution significantly, in particular the position of the third peak, because more vigorous heating simply prolongs the (n,γ)–(γ,n) equilibrium until the temperature drops to a similar value due to expansion. Therefore, the r-process freeze-out happens later, at a temperature that is comparable to the reference case (${\epsilon }_{\mathrm{th}}=0.5$). Our finding that the exact value of the heating efficiency parameter ${\epsilon }_{\mathrm{th}}$ does not greatly affect the final abundances, provided that it is above some threshold value, is in agreement with Korobkin et al. (2012).

We have further explored the effect of modified neutron capture rates. Slower rates could arise as the statistical model might not be applicable for small neutron separation energies S_n and not sufficiently high level densities in the compound nucleus. Faster rates could be attributed to the rising importance of direct capture contribution far from stability (Mathews et al. 1983; Rauscher 2011). We realized that artificially varying the neutron capture rates across the nuclear chart does not have an effect on the position of the third peak. However, some minor local effects on the final abundance distribution can be observed. Reduced rates slow down the reaction flux and as a consequence lead to a reduced underproduction of $140\lt A\lt 165$ and a slight overproduction of $180\lt A\lt 190$ nuclei, the former due to fission fragments, the latter caused by S_n predictions of the FRDM mass model. Accelerating the rates has an opposite, but still minor effect.

As the shift is related to the continuous supply of neutrons from fission of heavy nuclei, any mechanism that affects the timescale for this supply can potentially influence the position of the third r-process peak. As an example, we have artificially increased all the β-decay rates for nuclei with $Z\gt 80$ (which corresponds roughly to $A\gt 220$) by exploratory factors of 2.5 and 6, respectively. This change of rates has been motivated by recent calculations (T. Marketin 2015, in preparation; Panov et al. 2015). These latest predictions underline that especially the heavy nuclei with $Z\gt 80$ may have shorter half-lives by a factor of about 10. This is exactly the mass range tested in the present calculations. The results are shown in Figure 12 for the example of one trajectory with two nuclear mass models (FRDM and HFB). As a consequence of the increased β-decay rates, the reaction flux for the heavy nuclei is accelerated, which increases both the heating rate and the temperature at around $0.1\;{\rm{s}}$ in the calculation (Figures 12(a) and (c)). Additionally, the release of neutrons by fission of heavy nuclei is accelerated, providing neutrons before freeze-out (when the third r-process peak is still located close to solar values). The evolution after freeze-out proceeds faster and consequently the period of time where a combination of neutron captures and β-decays can move nuclei to higher mass numbers becomes shorter. As a consequence, the shift in the third r-process peak is reduced.

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We have also tested the effect of an overall increase of (experimentally unknown) β-decay rates by constant factors across the nuclear chart. In this case the effect discussed above vanishes again, as the matter flux feeding the abundance of fissioning nuclei continues on a faster pace and thus leads to an extended release of fission neutrons.

In summary, neutron capture after (n,γ)–(γ,n) freeze-out changes composition features that originate from classical r-process patterns related to an r-process path at a given neutron separation energy. This can be realized by combining the findings in Figures 9, 11, and 12, but is complicated by a complex interaction of freeze-out and final neutron captures, plus the feeding due to fission (combined with neutron release). Figure 9 demonstrates (for all mass models) that the third peak is shifted to higher masses during/after freeze-out, caused by the final neutron captures from neutrons which are released during fission of the heaviest nuclei in the final phases of nucleosynthesis (whereas the third peak is still located at the correct position in the last moments when (n,γ)–(γ,n)-equilibrium holds). This feature is underlined by the results of Figure 12, which show the effect of accelerating the β-decays of the heaviest nuclei ($Z\gt 80$), i.e., accelerating the feeding of fission parents, which causes fission (and the related neutron release) to occur at different phases (before/during/after) of the freeze-out. An early neutron release (coming with the fastest β-decays of heavy nuclei) still tends to permit (n,γ)–(γ,n)-equilibrium and reduces the effect of late neutron capture, although the effect is not sufficient to prevent the move of the third peak completely. We see a similar effect in the $A=140-160$ mass region for the FRDM mass model, slowing down the movement of matter to heavier nuclei and partially avoiding the trough which appears in the final abundance pattern for the original calculation with unchanged nuclear input. A more complex behavior causes the final abundance pattern of the second r-process peak with a complex interaction of fission feeding and final neutron processing. In Figure 11 we see that for the FRDM as well as the HFB mass model (when utilizing ABLA07) we have an almost perfect fragment distribution in order to reproduce the second r-process peak (see the entry "decays and fission" in Figures 11, 2(c), and 6(c)). However, the final ("original") distribution in the case of FRDM fits the second peak nicely, while for the HFB mass model the peak is shifted by several mass units. From Figure 9 it becomes clear that (not the overall abundance shape, but) the peak positions are in both cases close to the average peak position at (n,γ)–(γ,n) freeze-out. This seems to indicate that even in these final phases an r-process path is again established that is closer to stability for the HFB than for the FRDM mass model, leading to a peak shifted to higher masses (for the conditions obtained in the dynamical ejecta of NSM). This effect can only be avoided either by a change of the nuclear mass model or by different environment conditions.

Having shown the impact of a simple (and artificial) change in β-decay half-lives in the previous chapter, we now employ the newly calculated sets of half-lives of Panov et al. (2015) and T. Marketin (2015, in preparation). Both new sets predict shorter half-lives for the majority of neutron-rich nuclei in the nuclear chart compared to the previously used Möller et al. (2003) half-lives. However, there are some decisive differences. In Figure 13 we present a comparison of the new β-decay rates with the Möller et al. (2003) rates that we have used before. The Panov et al. (2015) set does not predict significantly faster rates far from stability, but in fact even noticeably slower rates (marked in blue) around N = 162 close to the neutron drip line. The faster rates (red) closer to stability only come into effect after freeze-out. The T. Marketin (2015, in preparation) calculations, on the other hand, predict faster rates for all nuclei on the r-process path beyond N = 126. The impact on the final abundances can be seen in Figure 14, where we present calculations performed using the T. Marketin (2015, in preparation) rates combined with both the FRDM and HFB-14 reaction sets as well as the Panov et al. (2015) rates together with the FRDM model. Note that the T. Marketin (2015, in preparation) rates have been calculated using a different mass model, so they are not fully consistent with either FRDM or HFB-14. The Panov et al. (2015) rates are based on FRDM, therefore we do not show a calculation with HFB-14.

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The T. Marketin (2015, in preparation) rates show a similar effect on the final abundances as our artificial study in Figure 12, broadening the low-mass flank of the third peak and increasing the abundances around the rare-earth peak. In fact, the broadening of the peak to lower mass numbers strongly improves the shape of the peak and (at least for the HFB-14 mass model) even a shift of the position to lower masses can be observed. The Panov et al. (2015) rates have a different effect. Here the β-decays are faster for nuclei with N = 126 along the r-process path (before the freeze-out). Therefore the reaction flux proceeds faster in this region before it is held up afterward at higher mass numbers, which means that less matter is accumulated in the peak. As a result, the height and shape of the third peak match the solar peak very well (Figure 14(c)). However, as the abundances of the nuclei in the peak are lower by roughly a factor of 2, each nucleus in the third peak can capture double the amount of neutrons and the effect of the third peak shift is increased. Furthermore, the Panov et al. (2015) rates show strong odd-even dependencies in the mass region $140\lt A\lt 170$ (Figure 13(b)), a quality which is reflected in the final abundances in this mass region.