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tokens: measured Eu is likely due to the current detection limit for Eu (Ishimaru et al. 2004 ). Overall, the result for case 1 (a mean delay of 0.1 Gyr in the lognormal term for NSMs) appears in qualitative agreement with those in Ishimaru et al. ( 2015 ) and Ojima et al. ( 2018 ) with a fixed delay of 0.1 Gyr (see Appendix A for additional tests). The top-right panel of Fig. 5 shows the result for case 2, in which the delay-time distribution of NSMs is ∝ t −1 . We find a slower increase of [Eu/Fe] with [Fe/H] and a smaller [Eu/Fe] at high [Fe/H] than those for case 1. This is due to an absence of the early (lognormal) component in the delay-time distribution. As a whole, however, the evolution of [Eu/Fe] including its scatter is similar between cases 1 and 2. The bottom-left panel of Fig. 5 shows the result for case 3, in which a CCSN-like, little delay time for NSMs is assumed (Fig. 1 ). We find that the evolution of [Eu/Fe] with [Fe/H] appears incompatible with the measured stellar abundance. The model predicts stars with [Fe/H] −3.5, at which few stars with measured Eu have been found. Note this cannot be attributed to the detection limit for Eu, because the predicted stars have high [Eu/Fe] (>0.5). It should also be noted that the reason cannot be the rarity of stars with [Fe/H] −3.5. The building blocks more massive than M * = 10 6 (orange curve in the bottom-left panel of Fig. 5 ), which generate the bulk of stars in the halo (the right-hand panel of Fig. 3 ), have already experienced NSM events (〈 N NSM 〉 > 1) at [Fe/H] −3.5. Moreover, the model does not predict stars with [Eu/Fe] 0 at [Fe/H] ∼ −3, at which a large number of stars with measured Eu exist (see also Section 4.4 and Appendix A ). The result for case 4 is shown in the bottom-right panel of Fig. 5 . The smaller SFE ( K in Table 1 ) results in the appearance of Eu at too low metallicity ([Fe/H] ∼ −4) to be compatible with the observation. However, the lowest metallicity at which Eu starts increasing depends on t min in the delay-time distribution of NSMs (equation ( 13 ); see Appendix A ). Another problem is that the contribution of SNe Ia starting at low metallicity inhibits the increase of Eu above [Eu/Fe] ∼ 0. It should be noted, however, that the yield of Eu from NSMs and their event rate, the product of which determines the average [Eu/Fe], are somewhat uncertain. Overall, therefore, our model is (at least marginally) compatible with the observational trend of [Eu/Fe] in the MW halo, regardless of the explored variations in the delay-time distributions (except for case 3). Note that a reduction of the NSM (or rare CCSN-like) event rate (or B in Section 2.2 ), which also reduces 〈 N NSM 〉, will enhance [Eu/Fe] at low metallicity in the low-mass building blocks with 〈 N NSM 〉 1. However, this will not substantially change the probabilistic distribution of stars on the [Eu/Fe]–[Fe/H] plane (colour scale in Fig. 5 ) as presented in Appendix A (Fig. A4 ) because of the resulting