Gamma-Ray Spectra of \(R\)-Process Nuclei
October 09, 2025
Abstract
The radioactive decay of unstable nuclei created in the rapid neutron capture process release a large amount of \(\gamma\)-rays. When the ejecta is optically thick, these \(\gamma\)-rays may contribute to an associated kilonova. Once transparent, prominent spectral features will be directly observable in current and future \(\gamma\)-ray detectors. In this work, we study and compare the \(\gamma\)-ray spectra of a limited, weak, strong, and extended \(r\)-process across a broad timescale, identifying the nuclei which significantly contribute. We discuss these findings in the context of observability, noting that there are several practical challenges to connecting observed signatures to specific nuclei. However, if these challenges can be overcome, direct observation of \(\gamma\)-rays from \(r\)-process sites can provide insight into the fundamental physics underpinning the \(r\)-process.
1 Introduction↩︎
It has long been inferred from solar abundance data (see e.g. [1], [2]) that the majority of elements heavier than iron were created by a combination of two different mechanisms: the slow (\(s\)) and rapid (\(r\)) neutron capture processes. However, while it is clear that the \(r\)-process is a significant component of galactic chemical evolution, the site(s) where the \(r\)-process occurs and their relative significance are much less certain. The \(r\)-process occurs in extreme environments with large numbers of free neutrons and involves capture on neutron-rich isotopes far from stability. There are several proposed sites of the \(r\)-process, including core-collapse supernovae ([3]–[10]), compact object mergers ([6], [11]–[19]), collapsars ([20]–[22]), and magnetars ([23], [24]).
There have been observational hints of the \(r\)-process at some sites—notably, the multimessenger observations of GW170817 [25], as well as the magnetar giant flare SGR 1806-20 [26] and the long-duration gamma-ray bursts GRB211211A and GRB230307A [27]. Due to the extreme conditions present in these environments, as well as limited experimental data for many neutron-rich isotopes far from stability where the r-process occurs, it is difficult to directly link observational data to specific physics. For example, the observed kilonova associated with GW170817—in particular, its peak in the near-infrared and optical—was widely interpreted as evidence that NSMs undergo a strong \(r\)-process ([28]–[34]). This conclusion stems from the argument that the production of lanthanides (which have high opacity) results in a kilonova which peaks in the infrared (e.g., [35], [36]), while a weaker \(r\)-process would produce a kilonova which peaks in the blue and optical bands (e.g., [37]–[39]). While this interpretation has merit, the multi-physics required in the associated kilonova modeling is challenging, and a large number of poorly understood parameters can have significant impact on the resultant light curve (see e.g., [40]–[44]), suggesting that there are other interpretations of the observational data. For example, [45] and [46] found that different ejecta velocity assumptions can lead to late-time features that mimic the suggested contributions from lanthanides. [27] modeled the kilonova of a long-duration GRB associated with a weak \(r\)-process (no lanthanides) and found consistency with the observed near-infrared and optical peaks observed in GRB211211A and GRB230307A.
While the challenges associated with the modeling of kilonova make it very difficult to disentangle and understand the detailed physics of the \(r\)-process from kilonova light curves, there may also be more direct observational signatures. The large number of \(\beta\)-decays associated with \(r\)-process nucleosynthesis generate an enormous amount of emitted particles, including \(\gamma\)-rays. These \(\gamma\)-rays will initially be opaque to observations, and are a significant contributor to the aforementioned kilonova. However, in the days and weeks after the event, as the opacity lowers, specific strong spectral emission lines may be directly observable. Because of the numerous long-lived nuclei which are synthesized, some emission lines are potentially observable for hundreds of thousands of years in remnants. The observation of prominent \(\gamma\)-rays have been of interest to the astrophysical community outside the \(r\)-process: the \(\gamma\)-rays from decays of \(^{44}\)Ti and \(^{56}\)Ni have been informative to the detonation mechanism of core-collapse supernovae [47]–[49], and the observations of the 1.8 MeV line from \(^{26}\)Al have informed both star formation and nucleosynthetic activity in our galaxy [50]–[52]. The potential of \(\gamma\)-ray observations from \(r\)-process sites have also been explored. [53] calculated the \(\gamma\)-ray signal from kilonova ejecta and found it would be observable to \(\sim\)3-10 Mpc with current detectors. [54] expanded on this work by modeling \(\gamma\)-ray transport, identifying specific spectral lines which may be observable, and also examined kilonova remnants in detail. [55] studied \(\gamma\)-rays from the \(r\)-process in supernova, identifying several potential spectral lines. [56] studied neutron star merger remnants in detail, and proposed line diagnostics to infer the initial electron fraction of the ejecta. [57] highlighted the potential signal of \(^{208}\)Tl resulting from the decays of long-lived actinides at both prompt (\(\sim\) days) and longer (\(~\sim\) years) timescales, and [58] highlighted that the prompt emission spectrum from the fission of actinides could produce a significant amount of MeV \(\gamma\)-rays. In general, these studies have found that \(\gamma\)-rays from \(r\)-process nucleosynthesis may be observable in current and/or next generation detectors at galactic scales, highlighting the importance for these signatures to be studied in detail.
While the physics associated with the direct observation of strong spectral lines is more straightforward than kilonova modeling, it is still nontrivial for a multitude of reasons. Spectral lines will broaden due to the expansion of the ejecta, softening the magnitude of the spectral peaks. Transport of the emitted \(\gamma\)-rays through the medium may cause significant redistribution of energy, especially at earlier times when the opacity is higher. There may be other significant sources of \(\gamma\)-rays at the site which must be compared to the potential \(r\)-process emission. The consequences of this are that the specific spectral features which are observable are dependent on both the choice of astrophysical site and the details of the physics which comprise the model, and therefore, studies of \(\gamma\)-ray observability are very specific to the scenario which is considered.
In this work, we take a different approach than the above works. Rather than considering the observability of \(\gamma\)-rays, we narrow our focus, characterizing the nuclei which significantly contribute to the \(\gamma\)-ray emission spectra across a representative set of \(r\)-process scenarios. Our goal is to be comprehensive, considering these contributions across a broad timescale. In this manner, our results are independent of the \(r\)-process site considered, and while not all of the spectral features we discuss may be observable at all sites, spectral features which are observed by current and future \(\gamma\)-ray detectors may be identified and matched with the relevant nuclei to infer the nature of the \(r\)-process which may have occurred.
We organize our paper as follows: In \(\S\ref{sec:sec:method}\), we detail our methodology for calculating the \(\gamma\)-spectra. In \(\S\ref{sec:sec:spectra}\), we present our main results and compare the spectra for the different types of \(r\)-process, highlighting the most significant spectral features. In \(\S\ref{sec:sec:discuss}\), we qualitatively discuss our results in the context of observability, highlighting several important lessons learned. We summarize and conclude in \(\S\ref{sec:sec:conclude}\).
2 Methodology↩︎
To calculate the \(\gamma\)-ray spectra, we follow the approach of [59], which combines detailed spectra calculations for the \(\beta\)-decay of individual nuclei with a nuclear reaction network which calculates the number of nuclei of each species which decay as a function of time. The total \(\gamma\)-ray emission spectra \(S^{\gamma}(E,t)\) can be factorized as: \[\label{eq:spectra} S^{\gamma}(E,t)= \sum_{^A_ZX} F_{^A_ZX}(t) S^{\gamma}_{^A_ZX}(E)\tag{1}\] where \(S^{\gamma}_{^A_ZX}(E)\) is the \(\gamma\)-ray emission of the nucleus \({^A_ZX}\) per unit decay as a function of energy (number per unit energy per decay), and \(F_{^A_ZX}(t)\) is the \(\beta\)-decay reaction flow as a function of time (decays per second per unit mass), and the sum is over every nucleus which decays in the network. We discuss the calculation of these two quantities individually below.
2.1 Spectra of Individual Nuclei↩︎
For each nuclei which \(\beta\)-decays, we use the \(\gamma\)-ray and x-ray spectra of ENDF/B-VIII.0 [60] if available. If there is no available \(\beta\)-decay spectra for a specific nucleus, we use the tabulated results of [61], which provide theoretical \(\beta\)-decay emission spectra for neutron-rich nuclei, including \(\gamma\)-rays, electrons, neutrinos, and neutrons. We additionally include the \(\gamma\)-ray and x-ray spectra for \(\alpha\)-decay if available in ENDF. While we do not have theoretical \(\alpha\)-decay spectra, we do not anticipate that this will be a large contribution, as \(\alpha\)-decays primarily transition to the ground state in the daughter nucleus. Any nuclei which \(\alpha\)-decays but does not have a measured spectra is far from stability, and therefore short-lived enough that it should decay before the relevant timescales for potential direct observation (\(\sim\) hours or longer).
The fission of nuclei will introduce an additional prompt source of \(\gamma\)-rays. It is generally challenging to compute the prompt fission emission spectra for a nucleus. As a stand-in, for all fissioning nuclei, we will use the prompt fission emission spectra calculated from CGMF [62] for \(^{252}\)Cf. This emission spectra is shown in Fig. 1 as compared to the experimental measurements of [63] and [64]. For a detailed discussion of the impact of fission on the \(\gamma\)-ray spectra, see [58].
![Figure 1: Prompt fission spectra of ^{252}Cf from the CGMF code as compared to the experimental results of [63] and [64]. In each case, the experimental spectra shown are the ones obtained from the LaBr_{3} detector.](figs/PromptSpectra.png "fig:")
For the rest of the text, when we refer to the \(\gamma\)-ray spectra, we are referring to the combined photon spectra, including \(\gamma\)-rays (de-excitation of the nucleus), x-rays (de-excitation of the electrons), and the photons promptly emitted by fissioning nuclei.
2.2 Nuclear Reaction Flow↩︎
We simulate nucleosynthesis with version 1.6.0 of the Portable Routines for Integrated nucleoSynthesis Modeling (PRISM) reaction network [65]. The nuclear input to PRISM is based on the 2012 version of the Finite Range Droplet Model [66], [67]. Radiative capture rates are calculated with the CoH\(_3\) statistical Hauser–Feshbach code [68], [69]. \(\beta\)-decay rates, including delayed neutron emission, are calculated assuming statistical de-excitation from excited states [70], [71]. The remaining reaction rates (e.g. alpha decay and other less substantive reaction types for the \(r\)-process) are obtained from the REACLIB database [72]. Nuclear fission is handled as in [73].
We are interested in understanding the differences in \(\gamma\)-ray spectra which may result from different \(r\)-process scenarios, as well as the most significant spectral features of each scenario. The primary cause of these differences is the strength of the \(r\)-process which occurs. In a stronger \(r\)-process, higher mass nuclei are produced, which allows for the additional contributions from the unique signatures of the associated \(\beta\)-decays. In addition, there are relatively less lower mass nuclei which \(\beta\)-decay, which suppresses their associated signatures. We use the temporal evolution of temperature and density of trajectory (b) from [22]. This trajectory is obtained through modeling the cocoon of a \(\gamma\)-ray burst, which has been suggested to be a site of the \(r\)-process due to photo-hadronic interactions in the jet head. The cocoon is modeled with the density profile of: \[\rho(t) = \rho_0 \left( 1 + \frac{t}{\tau_1} + \left(\frac{t}{\tau_2}\right)^\xi \right)^{-1} \;,\] where \(\xi\) = 2, \(\tau_1\), \(\tau_2\) are characteristic timescales, for which we use \(\tau_1 = \tau_2 = 3.5 \times 10^{-2}\) s, and \(\rho_0\) is the initial density, for which we use \(3.2 \times 10^4\) g/cm\(^3\). The temperature is assumed to evolve as an adiabatic gas: \[\label{eqn:tempfromrho} T(t) = T_0 \left( \frac{\rho(t)}{\rho_0} \right)^{\gamma-1} \;,\tag{2}\] where \(\gamma=4/3\) (radiation dominated), and we take \(T_0 = 2\) GK. Our choice of trajectory, specifically the unique early-time behavior as compared to more conventional trajectories, does not have a significant impact on the observability of \(\gamma\)-rays, which are primarily determined by the final abundance pattern which is produced.
With this trajectory, we vary the initial electron fraction to control the strength of the \(r\)-process which occurs, adopting values of \(Y_e\) = 0.4, 0.25, 0.175, and 0.034 for Simulation A, B, C, and D, respectively. These scenarios produce abundance patterns which are characteristic of: a limited \(r\)-process which does not produce the first peak, a weak \(r\)-process which consists of primarily the first peak, a strong \(r\)-process which produces the first and second peaks, and an extended \(r\)-process which produces all three peaks, including an extensive amount of actinides. Fig. 2 shows the final abundance patterns of these scenarios.
While these scenarios are representative of the different strengths of the \(r\)-process which can occur, the inherent uncertainties in modeling the \(r\)-process as well as the differences in trajectories from different \(r\)-process sites make it possible to generate generally similar abundance patterns to the ones presented here, but with significant differences in the abundances of individual mass numbers. The effect of these differences is that individual spectral features could be boosted or suppressed by a significant factor in a different scenario. Therefore, in an effort to make our results more generally applicable, we also discuss the nuclei which have significant but subdominant contributions, as in a different scenario, these contributions may be more dominant.
3 Gamma-Ray Spectra↩︎
We consider the \(\gamma\)-ray spectra for each of our simulations at 8 representative timescales: 6 hours, 1 day, 1 week, 1 month, 1 year, 50 years, 1000 years, and 50,000 years. For each simulation at each of these times, we calculate the associated \(\gamma\)-ray spectra and perform a spectral decomposition, identifying the nuclei which significantly contribute to the spectral features. We focus on the energy region E \(>\) 0.1 MeV, as the lower energy region generally has contributions from a larger number of nuclei, less prominent spectral features, and an increased likelihood of background sources which lower the observability. Figs. 3 and 4 show these spectral decompositions at each of the 8 timescales for the regions 0.1 \(<\) E \(<\) 1 MeV and E \(>\) 1 MeV, respectively.
We have tabulated each nuclei shown in Figs. 3 or 4 in Table [tab:gammaray], along with the nuclei which drive the timescale at which they appear, the simulations they appear in, and the specific spectral lines which contribute significantly to the overall spectra. Bolded spectral lines indicates spectral features of notable prominence in at least one simulation.
3.1 Comparison of Spectral Profiles↩︎
In Figs. 5 and 6, we compare the \(\gamma\)-ray emission profiles at each representative timescale for the energy for the regions 0.1 \(<\) E \(<\) 1 MeV and E \(>\) 1 MeV, respectively. Below, we highlight the most significant features of each simulation at each timescale.
At 6 hours, there are a large number of nuclei contributing to the spectra for all simulations, and all simulations are relatively comparable in the lower energy region (\(\lessapprox\) 3 MeV). Due to the lower number of nuclei contributing, Sim A and B have the most prominent spectral lines, with strong contributions (particularly for Sim B) from \(^{73}\)Ga, \(^{77}\)Ge, \(^{78}\)Ge, and \(^{78}\)As. Sim C and D have several prominent lines from \(^{128}\)Sb and \(^{129}\)Sb at different characteristic energies; however, their overall magnitude is somewhat less than the extremely strong features of Sim B. In Sim D, these lines are somewhat less prominent; however, there are a few additional spectral lines from \(^{184}\)Hf and \(^{117}\)In.
The higher energy region (\(\gtrapprox\) 3 MeV) is characteristically very different from the lower energy region. There are only a few spectral features in Sim A, B, and C from \(^{56}\)Mn, \(^{84}\)Br, and \(^{88}\)Rb. Sim D also has a prominent contribution from \(^{142}\)La, as well as significant background from fissioning nuclei, predominantly \(^{254}\)Cf, \(^{267}\)Rf, and \(^{273}\)Rf, as well as several nuclei (\(^{86}\)Br, \(^{88}\)Br , \(^{92}\)Rb) which are fission byproducts. These fission byproducts have very short lifetimes (\(\sim\) seconds to minutes) but can appear on very long timescales due to the long lifetime of the fissioning nucleus.
At one day, the lower energy region of Sim A and B is already mostly composed of only a few nuclei: \(^{72}\)Zn, \(^{72}\)Ga, and \(^{77}\)Ge, though the prominence of these features is significantly less for Sim A. The most prominent spectral features of Sim C: \(^{127}\)Sb, \(^{128}\)Sb, \(^{129}\)Sb, \(^{131}\)I, and \(^{132}\)Te are the most significant spectral features across all nuclei. Once again, Sim D has a much stronger background from the large number of decaying nuclei, and thus the spectral lines are much less prominent. Sim D additionally includes higher energy lines from \(^{24}\)Na and \(^{208}\)Tl. The higher energy region (\(\gtrapprox\) 3 MeV) is similar to the 6 hour case, though the prominence of Sim A, B, and C are significantly lower relative to Sim D.
By one week, the prominence of Sim A and B are greatly diminished, with only a few strong spectral lines able to compete with the much more significant features of Sims C and D. The nuclei driving these features are \(^{47}\)Sc, \(^{47}\)Sc, \(^{59}\)Fe, \(^{72}\)Zn, and \(^{78}\)As. The higher energy region of both Sim A and B (\(\gtrapprox\) 1.5 MeV) is completely dominated by \(^{72}\)Ga.
In contrast, the spectra of Sim C and D are still significant. The spectra of Sim C is predominantly composed of \(^{125}\)Sn, \(^{127}\)Sb, and \(^{132}\)I, with strong spectral lines from \(^{131}\)I and \(^{132}\)Te. Although the spectra of Sim D is similar in overall prominence, it is composed of many more decaying nuclei, including significant contributions from the heavy elements. The most prominent spectral features of Sim D are from \(^{131}\)I, \(^{132}\)Te ,\(^{140}\)La, and \(^{208}\)Tl. At this point, the dominant fission comes from \(^{254}\)Cf, whose importance was shown in [74].
At one month, the \(\gamma\)-ray spectra from Sim D has surpassed all but the strongest features from Sims A, B, and C. These include \(^{47}\)Sc, \(^{59}\)Fe, \(^{103}\)Rh, \(^{125}\)Sn, and \(^{127}\)Sb. Sim C has additional contributions from \(^{140}\)La and \(^{156}\)Eu in the higher energy region (\(\sim\) 1.5-3 MeV). The prompt emission spectra from fissioning of \(^{254}\)Cf is so strong in Sim D that nearly every spectral feature is reduced in prominence, though the majority of the above mentioned spectral features are still present in Sim D.
By 1 year, there are only a few nuclei which contribute to the spectra of Sim A and B, and even their contributions are not as significant as those in Sim C and D. The most notable nuclei include \(^{42}\)K, \(^{59}\)Fe, \(^{106}\)Rh, \(^{95}\)Zr, and \(^{95}\)Nb. Sim C still has several nuclei which produce strong spectral features, in particular, \(^{125}\)Sb, but also including \(^{123}\)Sn , \(^{144}\)Ce , \(^{144}\)Pr, \(^{155}\)Eu, and \(^{188}\)Re. Sim D is still washed out by the prompt fission spectra–the lower prominence of \(^{254}\)Cf (with a half-life of 60 days) is compensated not only by the lower overall spectra, but also by the increasing prominence of \(^{252}\)Cf. Many of the spectral features prominent in Sim C are still prominent in Sim D, though relatively less so.
By 50 years, there are only a few remaining significant features for Sim A, B, and C: \(^{42}\)K, \(^{84}\)Kr, \(^{125}\)Sb, \(^{126}\)Sb, \(^{155}\)Eu, \(^{194}\)Ir, and \(^{208}\)Tl, which has re-emerged due to its production from the alpha decay of the long-lived \(^{228}\)Ra. Sim D is no longer as washed out by the prompt fission spectra, which is now dominantly produced from \(^{250}\)Cm, \(^{262}\)Fm, and \(^{265}\)No. There are a large number of spectral features in the lower energies (\(\lessapprox\) 3 MeV), primarily generated either directly from the \(\alpha\)-decay of long-lived nuclei (e.g. \(^{251}\)Cf), or nuclei which are produced from the \(\alpha\)-decay chains of these long-lived nuclei (e.g. \(^{214}\)Bi).
By 1000 years, the only significant feature of Sim A and B is the two strong spectral lines of \(^{60}\)Co. Sim C has strong contributions from \(^{126}\)Sb, even surpassing Sim D for its most prominent spectral features due to the higher abundance of A=126. For Sim D, the high energy spectra (\(\gtrapprox\) 1 MeV) is dominantly produced by the prompt fission of \(^{250}\)Cm, as well as the contributions of \(^{214}\)Bi. However, the lower energy spectra is still quite diverse, with contributions from many nuclei, most prominently \(^{214}\)Pb, \(^{239}\)Np, \(^{246}\)Am, and \(^{249}\)Cf.
By 50,000 years, the long lifetime of \(^{60}\)Fe (2.62 Myr) has allowed the spectral lines of \(^{60}\)Co in Sim A and B to grow in prominence, surpassing the spectra of Sim C and D. Sim C is almost completely composed of the spectral emission of \(^{126}\)Sb. Sim D is similar to its emission profile at 1000 years, though its overall prominence relative to Sims A, B, and C is diminished. At this point, prompt fission emission is dominantly \(^{248}\)Cm and \(^{250}\)Cm, and the relative prominence of the other spectral features are diminished, though we still see contributions from \(^{126}\)Sb, \(^{209}\)Tl, \(^{214}\)Pb, \(^{214}\)Bi, \(^{246}\)Pu, \(^{246}\)Am, and \(^{250}\)Bk.
3.2 Integrated Spectra↩︎
In Fig. 7, we compare the integrated spectra (E \(>\) 0.1 MeV) for each of our simulations as a function of time, as well as show the spectral decomposition of each of these integrated spectra. We note that each simulation has a different characteristic shape, but the overall magnitude of the \(\gamma\)-ray spectra is comparable for the first \(\sim\) year. After that, there is a general divergence, with Sim C and D having many more longer-lived nuclei and thus a larger spectra than Sim A and B. The characteristic bumps in each spectra can be easily matched to the corresponding nuclei which dominates the spectra. For example, the bump around 50 years for Sim A which causes the spectra of Sim A to be significantly larger than Sim B is due to the higher amount of \(\boldsymbol{^{42}{K}}\), which decays on a 32.9 year timescale due to the lifetime of its parent, \(^{42}\)Ar.
4 Discussion↩︎
Our results above not only provide a detailed accounting of the spectral contributions in different \(r\)-process scenarios, but they also highlight several important details which are crucial for the process of connecting observational signals to \(r\)-process physics.
First, \(\gamma\)-rays will undergo doppler broadening due to the expansion of the ejecta. This effect can be especially significant at early times when the ejecta may be significantly relativistic. This makes it more difficult to identify spectral features, especially when combined with the large number of nuclei which contribute \(\gamma\)-ray signals and the other factors discussed below.
Second, the most observable spectral contributions are not necessarily the dominant spectral contributions for a nucleus, because the strength of a spectral line must be considered relative to the background. For example, the decay of \(^{144}\)Pr produces (among other lines) a 696.5 keV line 1.34% of the time and a 2186 keV line 0.69% of the time. The 2186 keV line is prominently above background in Sim C, while the 696.5 keV line is completely superseded by the much more prominent lines emitted by \(^{125}\)Sb and \(^{95}\)Zr.
Third, prominent spectral lines which have been referenced in the literature are not necessarily the most prominent sources of \(\gamma\)-rays at that line energy. For example, the 1384 keV line produced by \(^{92}\)Sr has been noted as a potential \(\gamma\)-ray signature in multiple works [26], [54]. In practice, this line is very close to the 1369 keV line of \(^{24}\)Na and the 1374 keV line of \(^{78}\)As. In Sim A and B, \(^{78}\)As is dominant, in Sim C, \(^{92}\)Sr, and in Sim D, \(^{24}\)Na. Taken with the possible spectral broadening, this makes the determination of the source of an observed \(\sim\) 1370 keV peak a challenge.
Fourth, the spectral lines which are prominent may change significantly based on the detailed physics of the \(r\)-process that occurs. The prominence of a particular spectral line is mostly tied to the relative production of the corresponding mass number (though things are much more involved for the actinide reagion). Different proposed \(r\)-process sites impart different conditions, and when combined with the inherent uncertainties, the detailed production pattern for different characteristic \(r\)-process types is not well-understood. This adds to the challenge of identifying nuclei responsible for significant spectral features, as these features could be the result of a nuclei which is dominant in the \(r\)-process which occurred observationally, but subdominant in the \(r\)-process model which is used. However, if nuclei can be confidently identified through detailed observational modeling and spectral analysis, then much can be learned about the \(r\)-process.
Many of the nuclei with significant spectral features also have long-lived nuclear isomers. These isomers may be significantly populated, affecting the timescale of \(\beta\)-decay, and may also directly \(\beta\)-decay, producing a different \(\gamma\)-ray spectra. Both of these will change the observability of spectral features. Understanding which isomers are populated requires detailed understanding of the overall nuclear structure, as transitions through all possible nuclear states (not just the isomers) must be considered (see e.g. [75]). One nucleus significantly affected is \(^{128}\)Sb, which has an isomer with excitation energy 43.9 keV [76] with \(\beta\)-decay lifetime 10.8 minutes (ground state lifetime is 9 hours), but we also expect that there will be many other affected nuclei.
For very strong \(r\)-processes, the large amount of uncertainty in the nuclear data in the very high mass region creates additional uncertainty in the resultant spectra. The extended \(r\)-process (Sim D) produces a significant amount of high mass material (A\(>\)250). In this region it is generally possible for nuclei to decay via \(\alpha\), \(\beta^-\), \(\beta^+\), and fission, with the exact branchings for an individual nucleus not well measured. The lifetimes of these nuclei (and thus the timescale which their children emit \(\gamma\)-rays) are also poorly understood. As a consequence, the prominence of spectra from nuclei in the decay chain of these heavy mass nuclei is uncertain. As a prime example of this, \(^{250}\)Cm has a lifetime of \(\sim\) 8300 years. with uncertain decay branching, estimated at 8% \(\beta^{-}\), 18% \(\alpha\), and 74% fission. All three decay modes contribute significant spectral features: the prompt fission spectra of \(^{250}\)Cm dominates the fission spectra from \(\sim\) 50 to \(\sim\) 50,000 years, \(^{250}\)Bk has spectral lines at 989 and 1032 keV, and both\(^{246}\)Am and its child \(^{246}\)Pu have spectral lines between 100 and 200 keV. With a different branching ratio, the relative prominence of these spectral features could be significantly affected.
There is also much uncertainty surrounding the details of fissioning nuclei. For extended \(r\)-processes, the strength of the prompt fission spectra is competitive with the spectral features of \(\beta\)-decay at higher energies. However, the prompt fission spectra that is used for all nuclei is a reference curve based on the fission of \(^{252}\)Cf. In addition, fission produces short-lived nuclei with strong \(\gamma\)-ray lines, such as \(^{97}\)Y. The strength of these spectral lines is mediated by the probability that the given nucleus fissions into a fragment with the correct A value. Taken in concert with the uncertainties in the prompt fission spectra, it is unclear if the spectral features of these short-lived nuclei will be observable above the prompt fission background.
5 Conclusion↩︎
We have analyzed the \(\gamma\)-ray emission from the decay of \(r\)-process nuclei across a broad timescale for 4 different characteristic \(r\)-process
types: a limited, weak, strong, and extended \(r\)-process. For each of these profiles, we have identified the nuclei which are responsible for significant spectral features, which we have tabulated in Table [tab:gammaray]. We find that a large number of nuclei are capable of producing prominent spectral lines. The relative prominence of these lines can be influenced by a variety
of factors, including the strength of \(r\)-process, the site which the \(r\)-process occurs at (which affects the detailed abundance pattern), and uncertainties in both the nuclear data
input and the \(\gamma\)-ray emission spectra, especially in the actinide and super-heavy region. In addition, spectral broadening and the contributions from other background sources of \(\gamma\)-rays at the site will make it challenging to identify with certainty the nuclei responsible for spectral features from the plethora of possible emission lines at a given energy. These factors emphasize the importance
of detailed modeling of both the \(\gamma\)-ray emission spectra and the environment in which the \(r\)-process occurs. However, if these spectral features can be identified, much can be
learned about nature of the \(r\)-process. With the increase in observations of \(r\)-process \(\gamma\)-rays from next-generation \(\gamma\)-ray observatories, the provided reference tables will aid in the identification of the nuclear species responsible for observed spectral features and enable us to learn about the nature of the \(r\)-process which has occurred.
LANL is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001). Research presented in this article was supported by the Laboratory Directed Research and
Development program of Los Alamos National Laboratory under project numbers 20230052ER and 20240004DR.
LcLccc \(^{24}\)Na & 14.96 hr & & & A , B , C , D & 1369 , 2754 , 3866
\(^{28}\)Al & 2.245 min & \(^{28}\)Mg & 20.92 hr & D & 1779
\(^{38}\)S & 170.3 min & & & A , D & 1941
\(^{38}\)Cl & 37.23 min & \(^{38}\)S & 170.3 min & A , B & 3810 , 3936
\(^{41}\)Ar & 109.6 min & & & A , B & 1294
\(^{42}\)K & 12.36 hr & \(^{42}\)Ar & 32.9 yr & A , B , C , D & 312.6 , 692.0 , 899.7 , 1021 , 1525 ,
1921 , 2424
\(^{43}\)K & 22.3 hr & & & A & 372.8 , 396.9 , 593.4 , 617.5 , 1022
\(^{44}\)K & 22.13 min & & & A , B & 3661 , 4409 , 4866 , 5162
\(^{47}\)Ca & 4.536 day & & & A , B & 489.2 , 530.6 , 767.1 , 807.9 ,1297
\(^{47}\)Sc & 3.349 day & \(^{47}\)Ca & 4.536 day & A , B , C , D & 159.4
\(^{56}\)Mn & 2.579 hr & & & A , B & 846.8 , 1811 , 2113 , 2523 , 2658 , 2960 , 3370
\(^{59}\)Fe & 44.49 day & & & A , B & 142.7 , 192.3 , 334.8 , 382.0 , 1099 , 1292 , 1482
\(^{60}\)Co & 1925 day & \(^{60}\)Fe & 2.62 Myr & A , B , C & 347.1 , 826.1 ,1173 , 1332 , 2159
\(^{65}\)Ni & 2.518 hr & & & A , B & 366.3 , 1116 , 1482
\(^{66}\)Cu & 5.120 min & \(^{66}\)Ni & 54.6 hr & A , B & 1039
\(^{67}\)Cu & 61.83 hr & & & A , B , C & 184.6 , 300.2 , 393.5
\(^{72}\)Zn & 46.5 hr & & & A , B , C & 102.8 , 112.1 , 144.7 , 191.5
\(^{72}\)Ga & 14.10 hr & \(^{72}\)Zn& 46.5 hr& A , B , C & 336.7 , 381.7 , [600 - 3500]
\(^{73}\)Ga & 4.86 hr & & & A , B & 297.3 , 325.7
\(^{75}\)Ge & 82.78 min & & & A , B & 198.6 , 264.6
\(^{77}\)Ge & 11.21 hr & & & A , B , C , D & 211.0 , 215.5 , 264.5 , [350 - 2500]
\(^{77}\)As & 38.79 hr & & & A , B , C & 239.0 , 249.8 , 281.6 ,520.7
\(^{78}\)Ge&88.0 min & & & A , B , C , D & 277.3 , 293.9
\(^{78}\)As &90.7 min & \(^{78}\)Ge & 88.0 min & A , B , C , D & 174.2 , 354.3 , [450 - 3100]
\(^{84}\)Br & 31.76 min & & & B , C & 3235 , 3266 , 3928 , 4085
\(^{85}\)Kr& 10.74 yr & & & B , C , D & 514.0
\(^{86}\)Br & 55.1 s & & & C , D & 5406 , 5518 , 6212
\(^{87}\)Kr & 76.3 min & & & B , C & 402.6 , 2555 , 2558 , 3235 , 3266 , 3309 , 3705
\(^{88}\)Br & 16.34 s & & & C , D & 3932, 4148 , 4563 , 6999
\(^{88}\)Kr & 2.825 hr & & & B , C , D & 122.3 ,166.0 , 196.3 , 2196 , 2392
\(^{88}\)Rb & 17.77 min & \(^{88}\)Kr & 2.825 hr &B , C , D & 1836 , 3010 , 3218 , 3486 , 4742
\(^{90}\)Rb & 158 s & & & C , D & 4136 , 4366
\(^{90}\)Y & 64.05 hr & \(^{90}\)Sr & 28.91 yr & B , C & 1761
\(^{91}\)Sr & 9.65 hr & & & B , C , D & 118.5 , 652.3 , 652.9 , 749.8 ,1024
\(^{91}\)Y & 58.51 day & & & B , C , D & 1205
\(^{92}\)Rb & 4.48 s & & & C , D & [5000 - 6100]
\(^{92}\)Sr & 2.61 hr & & & C , D & 1384
\(^{92}\)Y & 3.54 hr & \(^{92}\)Sr & 2.61 hr & B , C & 1405 , 3264 , 3371
\(^{93}\)Y & 10.18 hr & & & C &266.9 , 1918 , 2191
\(^{95}\)Zr & 64.03 day & & & B , C , D& 724.2 , 756.7
\(^{95}\)Nb & 34.99 day & \(^{95}\)Zr & 64.03 day & B , C , D & 204.1 , 765.8
\(^{97}\)Y & 3.75 s & & & C , D & 3288 , 3401
\(^{97}\)Nb & 72.1 min & \(^{97}\)Zr & 16.75 hr & B & 657.9
\(^{98}\)Sr & 0.653 s & & & D & 119.4
\(^{98}\)Y & 0.548 s & & & C , D & 4399 , 4452 , 4492
\(^{99}\)Mo & 65.92 hr & & & B , C , D &142.7 , 181.1 , 739.5
\(^{103}\)Ru & 39.25 day & & & B , C , D & 497.1
\(^{105}\)Ru & 4.439 hr & & & C & 724.2
\(^{105}\)Rh & 35.34 hr & & & B , C & 306.3 , 319.2
\(^{106}\)Rh & 30.07 s & \(^{106}\)Ru & 371.8 day & B , C , D & 511.9 , 621.9 , 873.5 , [1000 -
3400]
\(^{111}\)Ag &7.45 day & & & B , C , D & 245.4 , 342.1
\(^{112}\)Ag & 3.130 hr & \(^{112}\)Pd & 21.04 hr & B , C , D & 617.5 ,1614 , 2106 , 2507
\(^{113}\)Ag &5.37 hr & & & C & 298.6
\(^{116}\)Pd & 11.8 s & & & D & 114.7
\(^{117}\)Cd & 2.49 hr & & & D & 273.3 ,1577
\(^{117}\)In & 43.2 min & \(^{117}\)Cd & 2.49 hr & C , D & 158.6 , 552.9
\(^{123}\)Sn & 129.2 day & & & B , C , D& 160.3 , 1030 , 1089
\(^{125}\)Sn & 9.64 day & & & B , C , D& 332.1 , 822.5 , 915.6 ,
& & & & &1067 , 1089 , 1420 , 1806 , 2002 , 2276
\(^{125}\)Sb & 2.759 yr & & & B , C , D & [100 - 700]
\(^{126}\)Sb & 12.35 day & \(^{126}\)Sn & 218,000 yr & B , C , D & 414.7 , [550 - 1000]
& & & & & 1064 , 1191 , 1213 , 1290 , 1477 , 1589
\(^{127}\)Sn & 2.10 hr & & & B , C , D & [100 - 1000], 1093 , 1096 , 1114 , [1500 - 2900]
\(^{127}\)Sb & 3.85 day & & & B , C , D & 154.3 , [250 - 900] ,1142 , 1290
\(^{127}\)Te & 9.35 hr & \(^{127}\)Sb & 3.85 day & B , C & 417.9
\(^{128}\)In & 0.84 s & & & D & 1169 , 3520 , 4298
\(^{128}\)Sn & 59.07 min & & & C , D & 152.7 , 482.3
\(^{128}\)Sb & 9.05 hr & & & B , C , D & 118.4 , 152.6 , 314.1 , [525-1800]
\(^{129}\)Sb & 4.366 hr & & & C , D & 359.2 , 544.6 , 813.0 , 915.0 , 966.8 , 1738 , [1000 - 2100]
\(^{129}\)Te & 69.6 min & \(^{129}\)Sb & 4.366 hr & C , D & 459.6
\(^{130}\)Sb & 39.5 min & & & C , D & 182.3 , 330.9 , 793.4
\(^{131}\)I & 8.025 day & & & B , C , D & 284.3 , 364.5 , 637.0 , 722.9
\(^{132}\)Te & 3.204 day & & & C , D & 111.8 , 116.3 , 228.2
\(^{132}\)I & 2.295 hr & \(^{132}\)Te & 3.204 day & C , D& 522.7 , 630.2 , 667.7 , 772.6 , 954.6 , [1000 - 2700]
\(^{134}\)I & 52.5 min & \(^{134}\)Te & 41.8 min & D & 847 , 884 , 1073 , 1136 , 1455 , 1614 , 1741 , 1807
\(^{135}\)I & 6.58 hr & & & C , D & 1132 , 1260 , 1458 , 1678 , 1791
\(^{138}\)Cs & 32.5 min & & & D & 1436
\(^{140}\)Ba& 12.75 day & & & C , D & 162.7 , 304.8 , 537.3
\(^{140}\)La& 1.679 day & \(^{140}\)Ba &12.75 day & C , D & 328.8 , 487.0 , 815.8 , 1596 , 2521
\(^{141}\)Ce& 32.50 day & & & C , D & 145.4
\(^{142}\)La& 91.1 min & & & C , D & 641.3 , [2900 - 3900]
\(^{143}\)Ce& 33.04 hr & & & D & 293.3
\(^{144}\)Ce& 284.9 day & & & C , D & 133.5
\(^{144}\)Pr& 17.28 min & \(^{144}\)Ce & 284.9 day & C , D & 696.5 , 1489 , 2186
\(^{147}\)Nd & 11.03 day & & & D & 531.0
\(^{149}\)Nd & 1.726 hr & & & C & 114.3
\(^{151}\)Pm & 28.40 hr & & & C & 104.8
\(^{153}\)Sm & 46.28 hr & & & C , D & 103.2
\(^{155}\)Eu & 4.753 yr & & & C , D & 105.3
\(^{156}\)Sm & 9.4 hr & & & C , D & 165.8 , 204.0
\(^{156}\)Eu & 15.19 day & & & C , D & 811.8 , [1050 - 1275] , [1875 - 2200]
\(^{157}\)Eu & 15.18 hr & & & D & 370.5 , 410.7
\(^{167}\)Ho & 2.98 hr & & & D & 346.5
\(^{171}\)Er & 7.516 hr & & & D & 295.9 , 308.3
\(^{172}\)Er & 49.3 hr & & & C , D & 407.3 , 610.1
\(^{172}\)Tm & 63.6 hr & \(^{172}\)Er & 49.3 hr & C , D & 1094 , 1387 , 1466 , 1530 , 1608
\(^{173}\)Tm & 8.24 hr & & & D & 398.9
\(^{175}\)Yb & 4.185 day & & & C , D & 396.3
\(^{181}\)Hf & 42.39 day & & & C , D & 133.0 , 345.9 , 482.2
\(^{182}\)Ta & 114.74 day & \(^{182}\)Hf & 8.90 Myr & D & 1121 , 1189 , 1221
\(^{183}\)Ta &5.1 day & & & C , D&133.0 , 346.0 , 482.2
\(^{184}\)Hf & 4.12 hr & & & C , D & 139.1 , 344.9
\(^{184}\)Ta & 8.7 hr & & & C , D & 111.2 , 215.3 , 252.9 , 414.0 , 1110 , 1174
\(^{187}\)W & 23.80 hr & & & C , D & 134.2
\(^{188}\)W & 69.78 day & & & C , D & 290.7
\(^{188}\)Re & 17.006 hr & \(^{188}\)W & 69.78 day & C , D & 155.0 , 1308 , 1457 , 1610
\(^{189}\)Re & 24.3 hr & & & D & 216.7 , 219.4
\(^{193}\)Os & 29.73 hr & \(^{[1]}\) & & C , D & 138.9
\(^{194}\)Ir & 19.18 hr & \(^{194}\)Os & 6.0 yr & C , D & 293.5 , 328.5 , 622.7 , 645.2 , 938.7 , [1175 - 1625]
\(^{195}\)Ir & 2.29 hr & & & C , D & 129.7
\(^{197}\)Pt & 19.89 hr & & & D & 197.6
\(^{199}\)Au & 3.139 day & & & D & 158.4
\(^{200}\)Au & 48.4 min & \(^{200}\)Pt & 12.6 hr & D &1225 , 1263
\(^{203}\)Hg & 46.61 day & & & C , D & 279.2
\(^{207}\)Tl & 4.77 min & \(^{231}\)Pa & 32,570 yr & C , D & 897.8
\(^{208}\)Tl\(^{[2]}\) & 3.053 min & \(^{212}\)Pb & 10.62 hr & C , D & 277.4 , 510.8 , 583.2 ,
860.6, 2615
& & \(^{224}\)Ra & 3.6316 day & &
& & \(^{228}\)Th & 1.912 yr & &
& & \(^{228}\)Ra & 5.75 yr & &
\(^{209}\)Tl\(^{[3]}\) & 2.162 min & \(^{225}\)Ra & 14.9 day & D & 117.2 , 465.1 ,
1567
& & \(^{229}\)Th & 7880 yr & &
\(^{210}\)Tl\(^{[4]}\) & 1.30 min & \(^{226}\)Ra & 1600 yr & D & [1000 - 2400]
\(^{211}\)Pb & 36.1 min & \(^{223}\)Ra & 11.43 day& C , D & 404.9 , 427.1
& & \(^{227}\)Th & 18.70 day & &
& & \(^{227}\)Ac & 21.77 yr& &
& & \(^{231}\)Pa & 32,570 yr& &
\(^{212}\)Pb & 10.62 hr & \(^{224}\)Ra & 3.6316 day & C , D & 238.6 , 300.1
& & \(^{228}\)Th & 1.912 yr & &
& & \(^{228}\)Ra & 5.75 yr & &
\(^{212}\)Bi &60.55 min & \(^{232}\)U& 68.9 yr& D & 727.3
\(^{213}\)Bi & 45.59 min & \(^{225}\)Ra & 14.9 day & C , D & 440.5
& & \(^{229}\)Th & 7880 yr & &
& & \(^{233}\)U & 159,190 yr & &
\(^{214}\)Pb & 27.06 min & \(^{222}\)Rn & 3.822 day & C , D & 242.0 , 295.2 , 351.9
& & \(^{226}\)Ra & 1600 yr & &
& & \(^{230}\)Th & 75,584 yr & &
\(^{214}\)Bi & 19.71 min & \(^{226}\)Ra & 1600 yr & C , D & 386.8 , 388.9 , 609.3 , 768.4 , 934.1 , [1000 -
3300]
& & \(^{230}\)Th & 75,584 yr & &
\(^{219}\)Rn\(^{[5]}\) & 3.96 s & \(^{227}\)Ac & 21.77 yr & C , D & 271.2 , 401.8
& & \(^{231}\)Pa & 32,570 yr & &
\(^{221}\)Fr\(^{[5]}\) & 22.00 min & \(^{225}\)Ac & 9.920 day & C , D & 134.6 , 204.9 , 234.8
& & \(^{225}\)Ra & 14.9 day & &
& & \(^{229}\)Th & 7880 yr & &
\(^{222}\)Rn\(^{[5]}\) & 3.822 day & \(^{226}\)Ra & 1,600 yr & C , D & 510.0
\(^{223}\)Ra\(^{[5]}\) & 11.43 day & \(^{227}\)Ac & 21.77 yr & C , D & 144.2 , 154.2
& & \(^{231}\)Pa & 32,570 yr & &
\(^{224}\)Fr & 3.33 min & \(^{224}\)Rn & 107 min & D & 131.6
\(^{226}\)Ra\(^{[5]}\) & 1600 yr & \(^{230}\)Th & 75,584 yr & C , D & 186.2
\(^{227}\)Th\(^{[5]}\) & 18.68 day & \(^{227}\)Ac & 21.77 yr & C , D & 210.6 , 236.0 ,
256.2 , 286.1 , 289.6 , 300.0 , 304.5
& & \(^{231}\)Pa & 32,570 yr & &
\(^{228}\)Ac & 6.15 hr & \(^{228}\)Ra & 5.75 yr& C , D & [100 - 2000]
\(^{229}\)Th\(^{[5]}\) & 7880 yr & & & C , D & 137.0 , 193.5
\(^{233}\)Pa & 26.975 day & \(^{237}\)Np & 2.14 Myr & C , D & 311.9 , 340.5
\(^{234}\)Pa & 6.70 hr & \(^{234}\)Th & 24.10 day & D & 131.3 , 152.7 , 226.5 , 227.3 , 293.8 , 369.5
& & & & & 568.9 , 569.5 , [700-2000]
\(^{237}\)U & 6.752 day & & & D & 101.1\(^{[6]}\) , [113.3 - 117.9] \(^{[6]}\) ,
208.0
\(^{239}\)Np &2.356 day & \(^{243}\)Am & 7364 yr & D & 106.1 , 209.8 , 228.2 , 277.6
\(^{240}\)Np & 61.9 min & \(^{240}\)U & 14.1 hr & D & 103.7 \(^{[6]}\) , [116.2-120.7]\(^{[6]}\) , 152.7 ,
& & & & & 175.4 , 193.3 , 566.3 , 973.9
\(^{245}\)Cm\(^{[5]}\) & 8243 yr & & & C , D &103.7 , [116.2-121.0]\(^{[6]}\) , 133.1 , 175.0
\(^{246}\)Pu & 10.84 day & \(^{250}\)Cm\(^{[7]}\)& 8300 yr & D & 102.0\(^{[6]}\) , 106.5\(^{[6]}\) , [119.2 - 123.8]\(^{[6]}\) , 180.0 , 223.8
\(^{246}\)Am & 39 min & \(^{250}\)Cm\(^{[7]}\) & 8300 yr & D & 127.4 , 153.5 , 205 , 679.2 ,
756.0
\(^{247}\)Am & 23.0 min & \(^{247}\)Pu & 2.27 day & D & 104.6\(^{[6]}\) , 109.3\(^{[6]}\) , 285.0
\(^{248}\)Cm & 348,000 yr & & & D & Prompt Fission
\(^{249}\)Cf\(^{[5]}\) & 351 yr & & & C , D & 252.8 , 333.3 , 388.2
\(^{250}\)Bk & 3.212 hr & \(^{250}\)Cm\(^{[7]}\) & 8300 yr & D & 890.0 , 989.1 ,
1032
\(^{250}\)Cm\(^{[7]}\) & 8300 yr & & & D & Prompt Fission
\(^{251}\)Cf\(^{[5]}\) & 898 yr & & & C , D & 104.6\(^{[6]}\) , 109.3 \(^{[6]}\) , [122.3-127.4]\(^{[6]}\) , 177.5 , 227.4
\(^{252}\)Cf & 2.647 yr & & & D & Prompt Fission
\(^{254}\)Cf & 60.5 day & & & D & Prompt Fission
\(^{257}\)Fm\(^{[5]}\) & 100.5 day & & & D & 109.9\(^{[6]}\) , 115.1\(^{[6]}\) ,
[128.6-134.0]\(^{[6]}\)
\(^{258}\)Cf & 2145 yr \(^{[8]}\) & & & D & Prompt Fission
\(^{262}\)Fm & 39.85 yr\(^{[8]}\) & & & D & Prompt Fission
\(^{265}\)No & 118.4 yr\(^{[8]}\) & & & D & Prompt Fission
\(^{267}\)Rf & 60.5 day & \(^{267}\)Lr& 1.9 day\(^{[8]}\) & D & Prompt Fission
\(^{273}\)Rf & 2.269 hr\(^{[8]}\) & & & D & Prompt Fission
6 Full Version of Figs. 3 and 4↩︎
