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Probabilities of delayed processes for nuclei involved in the r-process
Delayed fission, along with induced and spontaneous fission, is responsible for the suppression of the production of superheavy elements both during the r-process and after its completion. Beta-decay strength functions are required for calculating delayed fission. In the present study, respective strength functions are calculated by relying on the theory of finite Fermi systems and by predominantly employing nuclear masses and fission barriers predicted by a generalized Thomas-Fermi model. The probabilities for delayed fission and for the emission of delayed neutrons are calculated for a number of isotopes. On the basis of calculations performed in order to determine the probabilities for delayed processes, it is shown that some of the delayed-fission probabilities calculated thus far were substantially overestimated. The application of these new results to calculating the r-process may change substantially both the r-process path and the yields of superheavy nuclei.
Chemical evolution of {sup 244}Pu in the solar vicinity and its implications for the properties of r-process production
Meteoritic abundances of r-process elements are analyzed to deduce the history of chemical enrichment by the r-process, from the beginning of disk formation to the present time in the solar vicinity. Our analysis combines the abundance information from short-lived radioactive nuclei such as {sup 244}Pu with the abundance information from stable r-process nuclei such as Eu. These two types of nuclei can be associated with one r-process event and an accumulation of events until the formation of the solar system, respectively. With the help of the observed local star formation (SF) history, we deduce the chemical evolution of {sup 244}Pu and obtain three main results: (i) the last r-process event occurred 130–140 Myr before the formation of the solar system; (ii) the present-day low {sup 244}Pu abundance as measured in deep-sea reservoirs results from the low recent SF rate compared to ∼4.5−5 Gyr ago; and (iii) there were ∼15 r-process events in the solar vicinity from the formation of the Galaxy to the time of solar system’s formation and ∼30 r-process events to the present time. Then, adopting the hypothesis that a neutron star (NS) merger is the r-process production site, we find that the ejected r-process elements are extensively spread out and mixed with interstellar matter, with a mass of ∼3.5×10{sup 6} M{sub ⊙}, which is about 100 times larger than that for supernova ejecta. In addition, the event frequency of r-process production is estimated to be 1 per ∼1400 core-collapse supernovae, which is identical to the frequency of NS mergers estimated from the analysis of stellar abundances.
Efficient method for estimation of fission fragment yields of $\textit{r}$-process nuclei
Background: More than half of all the elements heavier than iron are made by the rapid neutron capture process (or $\textit{r}$ process). For very-neutron-rich astrophysical conditions, such at those found in the tidal ejecta of neutron stars, nuclear fission determines the $\textit{r}$-process endpoint, and the fission-fragment yields shape the final abundances of 110 ≤ $\textit{A}$ ≤ 170 nuclei. The knowledge of fission-fragment yields of hundreds of nuclei inhabiting very-neutron-rich regions of the nuclear landscape is thus crucial for the modeling of heavy-element nucleosynthesis. Purpose: In this study, we propose a model for the fast calculation of fission-fragment yields based on the concept of shell-stabilized prefragments defined with help of the nucleonic localization functions. Methods: To generate realistic potential-energy surfaces and nucleonic localizations, we apply Skyrme density-functional theory. In this work, the distribution of the neck nucleons among the two prefragments is obtained by means of a statistical model. Results: We benchmark the method by studying the fission yields of 178 Pt, 240 Pu, 254 Cf, and 254,256,258 Fm and show that it satisfactorily explains the experimental data. We then make predictions for 254 Pu and 290 Fm as two representative cases of fissioning nuclei that are expected to significantly contribute during the $\textit{r}$-process nucleosynthesis occurring in neutron-star mergers. Conclusions: The proposed framework provides an efficient alternative to microscopic approaches based on the evolution of the system in a space of collective coordinates all the way to scission. It can be used to carry out global calculations of fission-fragment distributions across the $\textit{r}$-process region.
The r-process nucleosynthesis during the decompression of neutronised matter
The rapid neutron-capture process, or r-process, is known to be of fundamental importance for explaining the origin of approximately half of the A>60 stable nuclei observed in nature. In recent years nuclear astrophysicists have developed more and more sophisticated r-process models, eagerly trying to add new astrophysical or nuclear physics ingredients to explain the solar system composition in a satisfactory way.We show here that the decompression of the neutron star matter may provide suitable conditions for a robust r-processing. After decompression, the inner crust material gives rise to an abundance distribution for A>130 nuclei similar to the one observed in the solar system. Similarly, the outer crust if heated at a temperature of about 8 10{sup 9} K before decompression is made of exotic neutron-rich nuclei with a mass distribution close to the 80{<=}A{<=}130 solar one. During the decompression, the free neutrons (initially liberated by the high temperatures) are re-captured leading to a final pattern similar to the solar system distribution.
Measurement of the Mo 100 ( α , x n ) cross section at weak r -process energies
Here, the weak r process in neutrino-driven winds following a core-collapse supernova is thought to contribute to the cosmic abundances of the first r-process peak elements between Se and Ag. Sensitivity studies have found that the early nucleosynthesis in the weak r process is primarily driven by (α, xn) reactions due to the high temperatures, and that current nuclear physics uncertainties in the (α, xn) rates result in significant uncertainties of the calculated abundances. The weak r-process path proceeds several nuclei away from stability where (α, xn) reaction cross sections have not yet been measured. In this paper we report the 100 Mo (α, xn) cross section (between 8.9 and 13.2 MeV in the center of mass, corresponding to 3.5–6.8 GK) in inverse kinematics using the Multi-Sampling Ionization Chamber (MUSIC) detector at the Argonne Tandem Linac Accelerator System (ATLAS) facility. With this first measurement of the 100 Mo (α, xn) cross section, we have demonstrated the ability of MUSIC to measure (α, xn) cross sections for A up to 100, therefore paving the way for further measurements with radioactive beams at ATLAS or the Facility for Rare Isotope Beams.
Direct cross-section measurement of the weak r -process Sr 88 ( α , n ) Zr 91 reaction in ν -driven winds of core-collapse supernovae
About half of the heavy elements beyond iron are known to be produced by the rapid neutron capture process, known as the r process. However, the astrophysical site producing the r process is still uncertain. Chemical abundances observed in several cosmic sites indicate that different mechanisms should be at play. For instance, the abundances around silver measured in a subset of metal-poor stars indicate the presence of a weak r process. This process may be active in neutrino-driven winds of core collapse supernovae where (α,n) reactions dominate the synthesis of Ζ ≈ 40 elements in the expelled materials. Scarcely measured, the rates of (α,n) reactions are determined from statistical Hauser-Feshbach calculations with α-optical-model potentials, which are still poorly constrained. Further, the uncertainties of the (α,n) reaction rates therefore make a significant contribution to the uncertainties of the abundances determined from stellar modeling. In this work, the 88 Sr (α,n) 91 Zr reaction which impacts the weak r-process abundances has been probed at astrophysics energy for the first time; directly measuring the total cross sections at astrophysical energies of 8.37–13.09 MeV in the center of mass (3.8–7.5 GK). Two measurements were performed at ATLAS with the electrically segmented ionization chamber MUSIC, in inverse kinematics, while following the active target technique. The cross sections of this α-induced reaction on 88 Sr, located at the shell closure N = 50, have been found to be lower than expected, by a factor of 3, despite recent statistical calculations validated by measurements on neighboring nuclei. This result encourages more experimental investigations of (α,n) reactions, at Ν = 50 and towards the neutron-rich side, to further test the predictive power and reliability of such calculations.
Long gamma-ray burst as a production site of r-process elements
We simulated the r-process nucleosynthesis in and around a high entropy jet from a long gamma-ray burst (GRB). Our simulation is based on the collapsar scenario for long GRBs and on relativistic magnetohydrodynamic simulations (Harikae et al. 2009, 2010) including ray-tracing neutrino transport, which describe the development of the black hole accretion disk and the heating of the funnel region to produce a relativistic jet. The time evolution of the jet was then extended to later phase via axi-symmetric special relativistic hydrodynamic simulation to follow the temperature, entropy, electron fraction, and density evolution for representative test particles. The evolution of nuclear abundances from nucleons to heavy nuclei for representative test particle trajectories was solved in a large nuclear reaction network including more than 5000 isotopes. We show that a robust r-process successfully occurs within the collapsar jet outflow and that sufficient mass is ejected within the flow to account for the observed r-process abundance distribution along with the large dispersion in r-process elements observed in metal-poor halo stars.
Physical conditions for the r-process
Recent works show that the r-process can proceed by competition between neutron capture and {beta}-decay in low temperature environments (< 5 Multiplication-Sign 10{sup 8} K; cold r-process) where photo-disintegration plays no role. This is in contrast to the traditional picture of the r-process in high temperature environments ({approx} 1 Multiplication-Sign 10{sup 9} K; hot r-process) where the (n, {gamma})-({gamma}, n) equilibrium holds. In this study, we explore nucleosynthesis calculations based on a site-independent model to elucidate the physical conditions leading to cold and hot r-processes.
Emulation of the calculations of final r -process abundance patterns with a neural network
This work explores the construction of a fast emulator for the calculation of the final pattern of nucleosynthesis in the rapid neutron capture process (the r-process). An emulator is built using a feed-forward artificial neural network (ANN). We train the ANN with nuclear data and relative abundance patterns. We take as input the β-decay half-lives and the one-neutron separation energy of the nuclei in the rare-earth region. The output is the final isotopic abundance pattern. In this work, we focus on the nuclear data and abundance patterns in the rare-earth region to reduce the dimension of the input and output space. We show that the ANN can capture the effect of the changes in the nuclear physics inputs on the final r-process abundance pattern in the adopted astrophysical conditions. We employ the deep ensemble method to quantify the prediction uncertainty of the neural network emulator. The emulator achieves a speed-up by a factor of about 20 000 in obtaining a final abundance pattern in the rare-earth region. The emulator may be utilized in statistical analyses such as uncertainty quantification, inverse problems, and sensitivity analysis.
THE r-PROCESS IN METAL-POOR STARS AND BLACK HOLE FORMATION
Nucleosynthesis of heavy nuclei in metal-poor stars is generally thought to occur via the r-process because the r-process is a primary process that would have operated early in the Galaxy's history. This idea is strongly supported by the fact that the abundance pattern in many metal-poor stars matches well the inferred solar r-process abundance pattern in the mass range between the second and third r-process abundance peaks. Nevertheless, a significant number of metal-poor stars do not share this standard r-process template. In this Letter, we suggest that the nuclides observed in many of these stars are produced by the r-process, but that it is prevented from running to completion in more massive stars by collapse to black holes before the r-process is completed, creating a 'truncated r-process', or 'tr-process'. We find that the observed fraction of tr-process stars is qualitatively what one would expect from the initial mass function and that an apparent sharp truncation observed at around mass 160 could result from a combination of collapses to black holes and the difficulty of observing the higher mass rare-earth elements. We test the tr-process hypothesis with r-process calculations that are terminated before all r-process trajectories have been ejected. We find qualitative agreement between observation and theory when black hole collapse and observational realities are taken into account.
Steady flow approximations to the helium r-process
A steady flow approximation to the r-process is presented and used for numerical experiments with physical quantities to determine the sensitivity of the process to variations in those quantities. The effect of neutron capture cross sections along the capture path and of recently available improved beta decay rates on the r-process are discussed. The peaks in the observed r-process yield curve near mass numbers 80 and 130 are roughly characterized by a neutron number density of 10 to the 20th per cu/cm; the mean beta decay rates are about 10/s, and the freezing time is comparable to or less than 0.1 s. The peak near mass number 195 is roughly characterized by a neutron number density of 10 to the 21st/cm, the mean beta decay rates are about 100/s, and the freezing time is comparable to or less than 0.01 s. The flow path of the steady state r-process is sensitively dependent upon the neutron capture cross sections in the flow network and on the values of the beta decay rates.
( r r)-process production sites as inferred from Eu abundances in dwarf galaxies
Recent observations of r-process material in ultrafaint dwarf galaxies (UFDs) shed light on the sources of these elements. Strong upper limits on the Eu mass in some UFDs, combined with detections of much larger masses in a UFD, Reticulum II, and other dwarf galaxies, imply that Eu production is dominated by rare events, and that the minimal Eu mass observed in any UFD is approximately the amount of Eu mass produced per event. This is consistent with other independent observations in the Galaxy. We estimate, using a model-independent likelihood analysis, the rate and Eu (Fe) mass produced per r-process (Fe production) event in dwarf galaxies, including classical dwarfs and UFDs. The mass and rate of the Fe production events are consistent with the normal core-collapse supernova (CCSN) scenario. The Eu mass per event is 3×10{sup −5} M{sub ⊙}< m-tilde {sub Eu}<2×10{sup −4} M{sub ⊙}, corresponding to a total r-process mass per event of 6×10{sup −3} M{sub ⊙}< m-tilde {sub r-process}<4×10{sup −2} M{sub ⊙}. The rate of r-process events is 2.5 × 10{sup −4} < R {sub rp/SN} < 1.4 × 10{sup −3} as compared with the CCSN rate. These values are consistent with the total Eu mass observed in our own Galaxy, suggesting that the same mechanism is behind the production of r-process events in both dwarf galaxies and the Milky Way, and that it may be the dominant mechanism for production of r-process elements in the universe. The results are consistent with neutron star merger estimates but cannot rule out other rare core-collapse scenarios, provided that they produce significant amounts of r-process material per event.
The r-process nucleosynthesis in the various jet-like explosions of magnetorotational core-collapse supernovae
The r-process nucleosynthesis in core-collapse supernovae (CC-SNe) is studied, with a focus on the explosion scenario induced by rotation and strong magnetic fields. Nucleosynthesis calculations are conducted based on magneto-hydrodynamical explosion models with a wide range of parameters for initial rotation and magnetic fields. The explosion models are classified in two different types: prompt-magnetic-jet and delayed-magnetic-jet, for which the magnetic fields of proto-neutron stars (PNSs) during collapse and the core-bounce are strong and comparatively moderate, respectively. Following the hydrodynamical trajectories of each explosion model, we confirmed that r-processes successfully occur in the prompt-magnetic-jets, which produce heavy nuclei including actinides. On the other hand, the r-process in the delayed-magnetic-jet is suppressed, which synthesizes only nuclei up to the second peak (A∼130). Thus, the r-process in the delayed-magnetic-jets could explain only “weak r-process” patterns observed in metal-poor stars rather than the “main r-process,” represented by the solar abundances. Our results imply that CC-SNe are possible astronomical sources of heavy r-process elements if their magnetic fields are strong enough, while weaker magnetic explosions may produce “weak r-process” patterns (A≲130). We show the potential importance and necessity of magneto-rotational SNe for explaining the galactic chemical evolution, as well as abundances of r-process enhanced metal-poor stars. We also examine the effects of the remaining uncertainties in the nature of PNSs due to weak interactions that determine the final neutron-richness of ejecta. Additionally, we briefly discuss radioactive isotope yields in primary jets (e.g., {sup 56}Ni), with relation to several optical observation of SNe and relevant high-energy astronomical phenomena.
Neutron Star Mergers Might Not Be the Only Source of r -process Elements in the Milky Way
Probing the origin of r -process elements in the universe represents a multidisciplinary challenge. We review the observational evidence that probes the properties of r -process sites, and address them using galactic chemical evolution simulations, binary population synthesis models, and nucleosynthesis calculations. Our motivation is to define which astrophysical sites have significantly contributed to the total mass of r -process elements present in our Galaxy. We found discrepancies with the neutron star (NS–NS) merger scenario. When we assume that they are the only site, the decreasing trend of [Eu/Fe] at [Fe/H] > -1 in the disk of the Milky Way cannot be reproduced while accounting for the delay-time distribution (DTD) of coalescence times ( ∝t -1 ) derived from short gamma-ray bursts (GRBs) and population synthesis models. Steeper DTD functions ( ∝t -1.5 ) or power laws combined with a strong burst of mergers before the onset of supernovae (SNe) Ia can reproduce the [Eu/Fe] trend, but this scenario is inconsistent with the similar fraction of short GRBs and SNe Ia occurring in early-type galaxies, and it reduces the probability of detecting GW170817 in an early-type galaxy. One solution is to assume an additional production site of Eu that would be active in the early universe, but would fade away with increasing metallicity. If this is correct, this additional site could be responsible for roughly 50% of the Eu production in the early universe before the onset of SNe Ia. Rare classes of supernovae could be this additional r -process source, but hydrodynamic simulations still need to ensure the conditions for a robust r -process pattern.
Sensitivity studies for the main r process: β-decay rates
The pattern of isotopic abundances produced in rapid neutron capture, or r-process, nucleosynthesis is sensitive to the nuclear physics properties of thousands of unstable neutron-rich nuclear species that participate in the process. It has long been recognized that the some of the most influential pieces of nuclear data for r-process simulations are β-decay lifetimes. In light of experimental advances that have pushed measurement capabilities closer to the classic r-process path, we revisit the role of individual β-decay rates in the r process. We perform β-decay rate sensitivity studies for a main (A > 120) r process in a range of potential astrophysical scenarios. We study the influence of individual rates during (n, γ)-(γ, n) equilibrium and during the post-equilibrium phase where material moves back toward stability. We confirm the widely accepted view that the most important lifetimes are those of nuclei along the r-process path for each astrophysical scenario considered. However, we find in addition that individual β-decay rates continue to shape the final abundance pattern through the post-equilibrium phase, for as long as neutron capture competes with β decay. Many of the lifetimes important for this phase of the r process are within current or near future experimental reach.
Natal kicks and time delays in merging neutron star binaries: implications for r-process nucleosynthesis in ultra-faint dwarfs and in the Milky Way
Merging neutron star binaries are prime candidate sources for heavy r-process nucleosynthesis. The amount of heavy r-process material is consistent with the mass ejection and rates of mergers, and abundances of relic radioactive materials suggest that heavy r-process material is produced in rare events. Observations of possible macronovae provide further support for this model. Still, some concerns remain. One is the observation of heavy r-process elements in ultra-faint dwarf (UFD) galaxies. The escape velocities from UFDs are so small that the natal kicks, taking place at neutron stars’ birth, might eject such binaries from UFDs. Furthermore, the old stellar populations of UFDs require that r-process nucleosynthesis must have taken place very early on, while it may take several Gyr for compact binaries to merge. This last problem arises also within the Milky Way where heavy r-process materials have been observed in some low-metallicity stars. We show here that ≳0.5 of neutron star binaries form with a sufficiently small proper motion to remain bound even in a UFD. Furthermore, approximately 90% of double neutron stars with an initial separation of 10{sup 11} cm merge within 300 Myr and ≈15% merge in less than 100 Myr. This population of “rapid mergers” explains the appearance of heavy r-process material in both UFDs and in the early Milky Way.
RELATIVE CONTRIBUTIONS OF THE WEAK, MAIN, AND FISSION-RECYCLING r-PROCESS
There has been a persistent conundrum in attempts to model the nucleosynthesis of heavy elements by rapid neutron capture (the r-process). Although the locations of the abundance peaks near nuclear mass numbers 130 and 195 identify an environment of rapid neutron capture near closed nuclear shells, the abundances of elements just above and below those peaks are often underproduced by more than an order of magnitude in model calculations. At the same time, there is a debate in the literature as to what degree the r-process elements are produced in supernovae or the mergers of binary neutron stars. In this paper we propose a novel solution to both problems. We demonstrate that the underproduction of nuclides above and below the r-process peaks in main or weak r-process models (like magnetohydrodynamic jets or neutrino-driven winds in core-collapse supernovae) can be supplemented via fission fragment distributions from the recycling of material in a neutron-rich environment such as that encountered in neutron star mergers (NSMs). In this paradigm, the abundance peaks themselves are well reproduced by a moderately neutron-rich, main r-process environment such as that encountered in the magnetohydrodynamical jets in supernovae supplemented with a high-entropy, weakly neutron-rich environment such as that encountered in the neutrino-driven-wind model to produce the lighter r-process isotopes. Moreover, we show that the relative contributions to the r-process abundances in both the solar system and metal-poor stars from the weak, main, and fission-recycling environments required by this proposal are consistent with estimates of the relative Galactic event rates of core-collapse supernovae for the weak and main r-process and NSMs for the fission-recycling r-process.