Mass measurements towards doubly magic 78Ni: Hydrodynamics versus nuclear mass contribution in core-collapse supernovae

We report the ﬁrst high-precision mass measurements of the neutron-rich nuclei 74 , 75 Ni and the clearly identiﬁed ground state of 76 Cu, along with a more precise mass-excess value of 78 Cu, performed with the double Penning trap JYFLTRAP at the Ion Guide Isotope Separator On-Line (IGISOL) facility. These new results lead to a quantitative estimation of the quenching for the N = 50 neutron shell gap. The impact of this shell quenching on core-collapse supernova dynamics is speciﬁcally tested using a dedicated statistical equilibrium approach that allows a variation of the mass model independent of the other microphysical inputs. We conclude that the impact of nuclear masses is strong when implemented using a ﬁxed trajectory as in the previous studies, but the effect is substantially reduced when implemented self-consistently in the simulation.

We report the first high-precision mass measurements of the neutron-rich nuclei 74,75 Ni and the clearly identified ground state of 76 Cu, along with a more precise mass-excess value of 78 Cu, performed with the double Penning trap JYFLTRAP at the Ion Guide Isotope Separator On-Line (IGISOL) facility. These new results lead to a quantitative estimation of the quenching for the N = 50 neutron shell gap. The impact of this shell quenching on core-collapse supernova dynamics is specifically tested using a dedicated statistical equilibrium approach that allows a variation of the mass model independent of the other microphysical inputs. We conclude that the impact of nuclear masses is strong when implemented using a fixed trajectory as in the previous studies, but the effect is substantially reduced when implemented self-consistently in the simulation. Core-collapse supernovae (CCSN) represent the end point of stellar evolution for stars with masses greater than about 8-10 solar masses. Despite the enormous progress made in CCSN simulations in the last decades, several aspects still deserve clarification [1]. While many studies show the importance of the microphysics on the collapse dynamics (see, e.g. [1][2][3] for a review), the precise role of each microphysics input has not been fully pinpointed. This is because, due to the coupling of the microphysics with the hydrodynamics, quantifying the specific impact of each nuclear input is not trivial. However, the CCSN simulations of ref. [4] have shown that the uncertainties on the electron-capture rates on individual nuclei during infall induce stronger modifications on the mass of the inner core at bounce and the maximum of the neutrino luminosity peak than the other uncertainties of the collapse phase, namely the progenitor model, the equation of state, or the neutrino treatment. Those electron-capture rates depend on the nuclear structure details of the relevant nuclei which are still experimentally unconstrained, but a basic ingredient is given by the electron-capture Q-value, Q EC , which is solely determined by the nuclear masses. Previous studies [5,6]  shell closures with magic neutron N and proton numbers Z at (N = 50, Z = 28) and (N = 82, Z = 50), have been shown to be especially relevant both in CCSN and r-process calculations [5,[7][8][9][10][11][12][13][14][15], thus highlighting the need for new experimental data in those regions of the nuclear chart. The β-decay lifetime measurements of 78 Ni at NSCL [16] and at RIBF [17], the recent precise mass measurements of 77−79 Cu using the ISOLTRAP Penning trap at CERN [18] and the identification of the first 2 + state of 78 Ni at a rather large excitation energy at RIBF [19], suggest a weak quenching for the N = 50 shell gap at around Z = 28. However, due to the scarce experimental information in this exotic part of the Nuclide Chart, questions remain still open regarding the evolution of the N = 50 shell gap; the most important one being: to what extent is this shell closure preserved in case of the doubly magic nucleus 78 Ni?
In addition to the excitation energy of the first 2 + states and their corresponding reduced transition probabilities, another relevant parameter for this question is the evolution of the empirical two-neutron shell-gap energies 2n for different isotonic chains. In this Letter we report relevant new mass measurements along the nickel, copper and zinc isotopes. We present the first precise mass measurements of 74,75 Ni, extending the previous set of measurements done at the JYFLTRAP Penning trap for the nickel isotopes in [20]. New mass measurements of 76,77,78 Cu and 79 Zn isotopes, were also performed with the purpose of improving the mass precision. These newly measured values are then used to study systematics of the experimental 2n and are compared with the predictions of several theoretical mass models. Finally, using a dedicated extended nuclear statistical equilibrium formalism [10], incorporating a full nuclear distribution in the equation of state in a CCSN simulation, we have consistently studied the effect of the shell-gap quenching on the electron-capture rates in the corecollapse dynamics.
The mass measurements were carried out at the Ion-Guide Isotope Separator On-Line (IGISOL) facility in Jyväskylä [21], Finland. The studied neutron-rich isotopes were produced by induced fission, using a 35 MeV, 10 μA proton beam impinging on a 15 mg cm −2 -thick natural uranium target. The fission fragments were thermalized in a helium buffer gas and extracted from the gas cell dominantly in a singly-charged state. Following transport through a radio-frequency sextupole ion guide [22], the ions were accelerated to 30 keV and mass separated passing through a magnetic dipole with a mass resolving power of m/ m ≈ 500. The continuous beam was cooled and bunched in a radio-frequency quadrupole (RFQ) cooler buncher [23] prior to injection into the double Penning trap mass spectrometer JYFLTRAP [24]. The first trap was used for isobaric purification using the buffer-gas cooling technique [25]. The precision mass measurements were carried out in the second trap employing the time-of-flight ion-cyclotronresonance (TOF-ICR) technique [26]. The ion's cyclotron resonance frequency ν c = qB/(2πm), where q and m are the charge and the mass of the ion, and B the magnetic field strength, is determined by applying a quadrupolar excitation with a frequency ν r f near the expected cyclotron frequency ν c . When ν r f = ν c , the ions extracted from the trap have the shortest flight time to a micro-channel plate detector. A typical TOF-ICR resonance spectrum for 75 Ni + is presented in Fig. 1. A 200-ms quadrupolar excitation scheme was applied for 74 Ni and 79 Zn, 100-ms for 75 Ni and 77 Cu, and 1120-ms for 76 Cu. Ramsey's method of time-separated oscillatory fields [27,28] with an excitation pattern of 25-50-25 ms (On-Off-On) was used for 78 Cu. Cyclotron frequency measurements of the ions of interest were alternated with measurements of a stable reference ion with a well-known mass to determine the magnetic field strength at the time of the actual measurement. The cyclotron frequency ratio r between the studied singly-charged ref- respectively. It should be noted that electron binding energies for valence electrons are much smaller than statistical uncertainties and were negligible in the latter equation. The final frequency ratios and mass values were calculated as weighted means over typically 3-5 measurements. Systematic uncertainties related to the magnetic field fluctuations (8.18 × 10 −12 × t min −1 [30], where t represents the time between two reference measurements) and were quadratically added to the statistical uncertainties of the frequency ratios (∼ 2 − 20 × 10 −8 ).
The measured frequency ratios and the corresponding massexcess (ME) values are summarized in Table 1. The mass values of 74,75 Ni have been determined precisely for the first time.
Our experimental values are somehow higher than the extrapolations of the Atomic Mass Evaluation 2020 (AME2020) [29]: differences of 249(200) keV ( 74 Ni) and 184(201) keV ( 75 Ni). In fact, Ref. [32] reports on the mass of 74 Ni but this has not been considered in AME2020 due to the large error bar. Our measured value, which is 759(990) keV higher than the value in [32], provides a good reference point for the expected future measurements of more exotic species in this region via other methods, such as storage rings [33,34], Multi-Reflection Time-of-Flight Mass Spectrometry (MR-TOF-MS) [35,36] or Bρ-ToF [37,38]. Moreover, the new mass values of 74,75 Ni will improve the extrapolations toward 78 Ni in the forthcoming mass evaluations. Regarding 76 Cu, the two long-living states were resolved in the TOF-ICR spectra (see Fig. 1) and measured accordingly. In addition, we used the phase-imaging ion cyclotron resonance technique [39] to further identify the states based on their half-lives and to confirm their energy difference. The relatively large difference to the ISOLTRAP measurements [18,40] can be explained if mixtures of both states have been measured due to a lower resolution of the TOF-ICR technique in their work. Nevertheless, the new mass values of 77,78 Cu are in good agreement with the recent ISOLTRAP Penning trap and multi-reflection time-of-flight mass spectrometer mea- Table 1 List of nuclei and their properties (half-life T 1/2 , spin-parity I π based on Ref. [29]), as well as the measured frequency ratios r = ν ref /ν and mass-excess values "ME" for the ground states from this work in comparison with the literature values from the AME2020 [29]. '#' denotes a value based on extrapolations. The difference between the two mass-excess values (Diff. = ME lit -ME JYFL ) is also indicated. Singly-charged ions of 84 Kr (m = 83.911497727(4) u [29]) were used as a reference for all studied cases. The validity of these two properties will be discussed in a separate paper.
surements [18]. The precision for 78 Cu has been improved thanks to the Ramsey's method. Furthermore, the measured ground-state mass-excess value of 79 Zn agrees with the values reported from ISOLTRAP, -53435.1(3.9) keV [41] and JYFLTRAP, -53430.9(2.7) keV [42]. We have also determined the mass for the 1/2 + isomeric state 79m Zn. Our results on the isomers will be discussed in a separate paper. The recently published [43] ground-state mass values of 67 Fe and 69,70 Co obtained during the same experiment are also taken into account in the following analysis.
The new mass-excess values (see Table 1) were employed to investigate the evolution of the empirical two-neutron shell-gap energies 2n (N, Z ) = ME(N + 2, Z)+ME(N − 2, Z) − 2ME(N, Z) toward N = 50 and Z = 28. For Z = 28 and for N = 44 − 49, the 2n from the AME2020 [29] mass-excess values are significantly different from the 2n obtained with our measurements (in average 288 keV absolute difference): from -184 keV to +497 keV. In Fig. 2, eight new 2n values are presented and ten more obtained including extrapolated mass values from AME2020, thus extending the experimental 2n (N, Z ) trends far from stability. For the magic neutron number N = 50, the empirical two-neutron shell-gap energy is between ∼3-6 MeV for Z = 29 − 40, much higher than for the neighboring isotonic chains. The N = 50 empirical shell gap is weakly reinforced as Z = 28 is approached, in agreement with the recently observed doubly magic behavior of 78 Ni [18,19]. The empirical two-neutron shell-gap energies were compared to the predictions of several theoretical mass models conventionally used in astrophysical studies. The colored bands shown in Fig. 2 represent the range of shell-gap energies covered by the studied mass models. For comparison, we have indicated with solid and dashed lines the gaps predicted by the HFB-24 and DZ10 mass models, previously used in [4,8] to assess the influence of nuclear masses on the core collapse. Among the different mass models, HFB-24 is the only one coming from a microscopic energy density functional [44], which explains the complex non-smooth behavior shown in Fig. 2. It predicts a strong quenching for the N = 50 gap, extending up to 78 Ni. In the region close to Z = 28, the DZ10 mass model overestimates the neutron shell-gap energies for and above N=49 and underestimates them below N=49. The opposite behavior is observed for HFB-24. The strong shell gap predicted by the DZ10 model for N = 50 explains why nuclear statistical distributions are more peaked and persist around magic nuclei with respect to those predicted by HFB-24 for which the N = 50 closure is weaker. In addition, the trends of the empirical two-neutron shell-gap energies, especially for N = 50, are better reproduced by the HFB-24 mass model than DZ10. Interestingly, the shell-gap quenching observed for N = 50 -in good agreement with the predictions of the microscopic HFB-24 model -appears strongly reduced in 78 Ni, even if extrapolated values leading to non-negligible error bars are needed. We observe that the HFB-24 and DZ10 mass models differ considerably in the 2n predictions: for N = 50, Z = 28, the discrepancy amounts to 3.6 MeV. Therefore, the use of these two distinct mass models can address the question of the mass-model dependence in astrophysical scenarios like CCSN modeling. Note that results from another mass model (e.g. FRDM12 [46]) would thus lead to an intermediate conclusion.
Previous CCSN studies [5,6] have been performed considering typical (fixed) collapse trajectories, i.e. a predetermined set of densities (ρ), temperatures (T ), and electron fractions (Y e ). Here, we Fig. 3. Relative difference between the total electron-capture rate obtained using the distribution of the HFB-24 mass model compared to DZ10 as function of baryonic density obtained for a self-consistent (solid line) trajectory. The inset is adapted from [4], showing the most relevant nuclei for electron captures up to neutrino trapping using HFB-24 mass model and the self-consistent trajectory method. The black squares indicate the nuclei with our new mass results. The pink contour shows the nuclei for which the Q EC precision is improved thanks to our work. Their impact is well illustrated by the partial relative difference between the rates obtained with the two reference mass models and our experimental values for a fixed trajectory (dashed and dotted lines). See text for details. perform CCSN numerical simulation using the ACCEPT code (see [4,[50][51][52] for details). The latter is a spherically symmetric corecollapse code solving general relativistic hydrodynamics, with neutrinos treated in a simple leakage-type multi-group scheme (here, the trapping density has been fixed to 10 12 g cm −3 ). In order to assess the mass-model dependence, we use the perturbative method developed in [8] built upon the Lattimer & Swesty [53] equation of state, employing the DZ10 and HFB-24 mass models. Electron-capture rates are computed with the parametrization from [54]. Results are shown in Fig. 3, where the relative difference between the instantaneous electron-capture rates calculated with the DZ10 and HFB-24 mass models are plotted as a function of baryonic density during the collapse, using a self-consistent trajectory (solid line). Since DZ10 (HFB-24) does not allow (allows) for shell-gap quenching, the ordinate in Fig. 3 can be considered as a quantitative prediction of the impact of the quenching on the rates. To evaluate the impact of the newly measured masses, we have also calculated the partial relative difference between the sums of the rates of the nuclei in the pink contour Fig. 3, obtained with either the DZ10 (dashed line) or HFB-24 (dotted line) mass models and our new experimental masses, using a fixed trajectory. All the curves are very similar for ρ 5 ×10 10 g cm −3 , since nuclei are located around A ∼ 60 ( Z ∼ 28) where the shell gaps at Z = 28, N = 32 from DZ10 (1.79 MeV) and HFB-24 (1.49 MeV) models are not dramatically different. Therefore, the relative electron-capture rates differ less than 10% in this phase. In subsequent stages of the collapse, discrepancies arise, because the populated nuclei are located near, between, or even beyond the doubly magic nuclei 78 Ni and 132 Sn, for which the DZ10 and HFB-24 predictions differ. Comparing the dashed and dotted lines, we can notice that the rates obtained with HFB-24 show a much closer agreement with those calculated using the new experimental mass values, confirming that this model gives an adequate description of the masses (see Fig. 2), and has therefore to be preferred for nuclei without experimentally determined mass values. Conversely, if DZ10 is used, the rates can be overestimated up to a factor of 5. This clearly shows the importance of the newly measured mass values to assess the reliability of the theoretical models for astrophysical applications. The difference between the two models can be qualitatively understood from the fact that a strong N = 50 gap around 78 Ni, such as in DZ10, disfavors a strong neutronization, thus leading to an over-estimation of the production of nuclei with relatively high Q EC values. Such a strong N = 50 gap is excluded by our mass measurements. Our results for the fixed trajectory are qualitatively in good agreement with Refs. [5,6], suggesting a strong impact of the used mass model on the electron-capture rates. Surprisingly, this effect is reduced when a self-consistent treatment is done; indeed, the feedback effect is sufficiently strong to almost completely erase the effect of the mass model. Indeed, even if the HFB-24 mass model is still more efficient in neutronizing the medium during most of the time of the self-consistent trajectory (85 % of the neutronization process), in the last stage (> 6 × 10 11 g cm −3 ) when the total electron-capture rate is higher, the DZ10 electron-capture rate overcomes the HFB-24 rate during a short period (0.6 % of the neutronization process). It turns out that this is long enough to compensate the integrated effect of the HFB-24 mass model on the electron fraction at the neutrino trapping density, thus inducing only small differences on the CCSN properties at bounce. However, we have to underline that for a final word to be said, the individual electron-capture rates should be experimentally constrained. This requires, in addition to the masses ( Q EC values), a new generation of Total Absorption Spectrometers and the use of charge-exchange reactions setups with radioactive beams [55].
Ideally, experimentally measured mass values instead of theoretical mass models would be used for all relevant nuclei. The precision mass measurements of this work provide more precise Q EC values for around 12 key nuclei contributing the most to the total electron-capture rate during the core collapse (see the inset of Fig. 3). This is an important first step to provide accurate electron-capture rate calculations for CCSN simulations, however, more experiments are needed to fully base the simulations on experimental values.
In conclusion, using the JYFLTRAP double Penning trap the masses of the neutron-rich magic nuclei 74,75 Ni and the ground state of 76 Cu were precisely measured for the first time. In addition, we presented new mass measurements of 77,78 Cu and 79 Zn. The empirical two-neutron shell gaps obtained with our data suggest the preservation of the doubly magic nature of 78 Ni in agreement with the recent results obtained in [18,19]. These results will provide key reference points for expected future measurements of more exotic species in this region via new experimental methods [33][34][35][36][37][38], and allow more precise theoretical predictions e.g. for nuclear interactions in this region. Finally, it will impact AME predictions. By comparing the updated empirical two-neutron shellgap energies around N = 50 with theoretical predictions, we have shown that HFB-24 and DZ10 represent the two extremes of the studied mass models, and were therefore selected for systematic studies of the electron-capture rates during the core collapse of a massive star. The corresponding difference in the instantaneous electron-capture rates between the HFB-24 and DZ10 models, was investigated with a fixed and a self-consistent core-collapse supernova trajectory. We have shown that there is a strong feedback effect between the hydrodynamics and the microphysics, namely the equation of state and electron-capture rates, thus highlighting the need to perform numerical simulations to have a more realistic and quantitative evaluation of the impact of nuclear-physics data on astrophysical predictions. More details concerning the data analysis (e.g. identification and characterization of ground states and isomeric states when relevant) and the CCSN simulations results will be given in a forthcoming paper. Lastly, our new massexcess values will allow better electron-capture Q -value calculations of key nuclei for CCSN (see the inset of Fig. 3). Although the electron-capture rates for these key nuclei should be experimentally constrained to have a full control of the core collapse modeling [55], the Q -values are a basic ingredient in the rate calculation, meaning that our results constitute a first important step in this direction.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
Data will be made available on request.