Issue 
A&A
Volume 568, August 2014



Article Number  A97  
Number of page(s)  12  
Section  Numerical methods and codes  
DOI  https://doi.org/10.1051/00046361/201322887  
Published online  28 August 2014 
The rJava 2.0 code: nuclear physics
^{1} Department of Physics & AstronomyUniversity of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada
email: mkostka@ucalgary.ca
^{2} Department of Physics & Astronomy, California State University Long Beach, 1250 Bellflower Blvd., Long Beach, California 90840, USA
Received: 21 October 2013
Accepted: 16 February 2014
Aims. We present rJava 2.0, a nucleosynthesis code for open use that performs rprocess calculations, along with a suite of other analysis tools.
Methods. Equipped with a straightforward graphical user interface, rJava 2.0 is capable of simulating nuclear statistical equilibrium (NSE), calculating rprocess abundances for a wide range of input parameters and astrophysical environments, computing the mass fragmentation from neutroninduced fission and studying individual nucleosynthesis processes.
Results. In this paper we discuss enhancements to this version of rJava, especially the ability to solve the full reaction network. The sophisticated fission methodology incorporated in rJava 2.0 that includes three fission channels (betadelayed, neutroninduced, and spontaneous fission), along with computation of the mass fragmentation, is compared to the upper limit on mass fission approximation. The effects of including betadelayed neutron emission on rprocess yield is studied. The role of Coulomb interactions in NSE abundances is shown to be significant, supporting previous findings. A comparative analysis was undertaken during the development of rJava 2.0 whereby we reproduced the results found in the literature from three other rprocess codes. This code is capable of simulating the physical environment of the highentropy wind around a protoneutron star, the ejecta from a neutron star merger, or the relativistic ejecta from a quark nova. Likewise the users of rJava 2.0 are given the freedom to define a custom environment. This software provides a platform for comparing proposed rprocess sites.
Key words: nuclear reactions, nucleosynthesis, abundances
© ESO, 2014
1. Introduction
A key nucleosynthesis mechanism for producing heavy elements beyond the iron peak is rapid neutron capture or the rprocess (Burbidge et al. 1957; Cameron 1957). In spite of a large volume of observational data (Sneden et al. 2008), where the rprocess occurs remains an open question. Explosive, neutronrich environments provide the ideal conditions for rprocesses to occur. The predominant astrophysical sites being studied as possible locations for rprocess: the highentropy winds (HEW) from protoneutron stars (see Qian & Woosley 1996; Farouqi et al. 2010) and ejected matter from neutron star mergers (see Freiburghaus et al. 1999a; Goriely et al. 2011). However, both of these scenarios face significant hurdles that must be overcome. The long timescale for neutron star merger events (Faber & Rasio 2012) limits this scenario’s ability to explain the rprocess element enrichment of metalpoor stars (Sneden et al. 2003). HEW models have been shown to be very sensitive to the chosen physical conditions of the winds, and elaborate hydrodynamic models have yet to prove that the HEW scenario can provide the necessary environment for significant rprocess to occur (e.g. Hoffman et al. 2008; Janka et al. 2008; Roberts et al. 2010; Fischer et al. 2010; Wanajo et al. 2011). The theoretical quark nova has also been proposed as a potential rprocess site (Jaikumar et al. 2007). The explosive, neutronrich environment of a quark nova provides an intriguing avenue of study for astrophysical rprocess (Jaikumar et al. 2007). It is important to note that the observed nuclear abundance of rprocess elements in metalpoor stars (Sneden et al. 2003) and abundance data of certain radionuclides found in meteorites (Qian & Wasserburg 2008) point to the likelihood of multiple rprocess sites (Truran et al. 2002). Certainly there is much to be learned about the astrophysical rprocess and its necessary conditions. To help drive this study we have developed rJava (Charignon et al. 2011), which is a crossplatform, flexible rprocess code that is transparent and freely available for download by any interested party^{1}.
Fig. 1 Schematic representation of the functionality of rJava 2.0. See Table 1 for description of symbols. 

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The purpose of this article is to introduce the second version of rJava (rJava 2.0), discuss the new features that it contains, and display a selection of simulation results. Prior to delving into the details of rJava 2.0, it would be enlightening to briefly examine the capabilities and limitations of the first version of the code. As discussed in Charignon et al. (2011), our aim for rJava was to create an easytouse, crossplatform rprocess code that avoids the “blackbox” pitfalls that plague many scientific codes. To achieve this goal, rJava was developed with an intuitive graphical user interface (GUI) and we provide extensive documentation and user tutorials on our website. The first version of rJava was predicated upon the waiting point approximation (WPA), which assumes an equilibrium between neutron captures and photodissociations. The practical effect of using the WPA is that the relative abundance along isotopic chains depends only on neutron density (n_{n}), temperature (T), and neutron separation energy (S_{n}) (For more details see Charignon et al. 2011, Eq. (12)). Through the WPA, the number of coupled differential equations that must be solved is reduced from thousands to about a hundred (the number of isotopic chains in the reaction network), greatly reducing computational costs.
Using the WPA comes at the expense of generality, in that the assumption is only valid in hightemperature and neutron density environments (typically only considered for T_{9}> 2 ,where T_{9} is in units of 10^{9} K and n_{n}> 10^{20} cm^{3}). Within the context of the WPA rJava 1.0 provided users the ability to run rprocess simulations for a wide variety of scenarios, including neutron irradiation of static targets and the dynamic expansion of rprocess sites. A key feature of rJava that has been maintained through the release of the second version is the ability for users to easily make changes to nuclear inputs between simulation runs. Other flexibilities of rJava include the ability to specify the amount of heating from neutrinos and turn on/off the various processes and to choose the density profile of the expanding material.
This paper is organized as follows. Section 2 provides an overview of the advancements made in rJava 2.0 and discusses the default rates included with the code. The nuclear statistical equilibrium (NSE) module is discussed in Sect. 3. The new fission methodology is detailed in Sect. 4. The effect of βdelayed neutron emission is discusssed in Sect. 5. Section 6 compares the full reaction network calculation with the WPA approach. Comparative analysis between rJava 2.0 and other full reaction network codes is carried out in Sect. 7. Finally in Sect. 8 a summary is provided along with a look to future work on rJava.
Description of symbols.
2. Overview of rJava 2.0
There are major developments made to rJava since the original release in 2011. Most noteworthy is that rJava 2.0 is now capable of solving a full reaction network and is no longer solely reliant on the WPA. The latest release also contains a more accurate handling of fission, as well as the implementation of βdelayed neutron emission of up to three neutrons. Another expansion to rJava is the ability for the user to specify the astrophysical environment of the rprocess, which determines the methodology used to evolve the density and temperature. Furthermore, the nuclear statistical equilibrium (NSE) module has been expanded to include the effect of Coulomb screening. Finally any nuclear reaction can be turned on or off, which allows the user to investigate individual processes. An organizational chart displaying the functionality of rJava 2.0 can be seen in Fig. 1.
As seen in Fig. 1, rJava 2.0 contains several distinct modules. NSE, WPA network, and the full network constitute the research modules that are used by scientists to study the rprocess. Complementary components to rJava 2.0 are the teaching modules, aimed for use in the classroom at the graduate and undergraduate levels, these modules allow for investigating individual nucleosynthesis processes. The fission module calculates the mass fragmentation of neutroninduced fission. The user is able to choose the target nucleus (or nuclei), vary the incident neutron energy, and adjust four parameters related to the potential energy of the fragmentation channels (to be discussed in Sect. 4). The remaining teaching modules; βdecay, αdecay, photodisocciation, and neutron capture all act in similar manners. The user can specify an initial abundance of nuclei and then investigate how varying the rates affects the final abundances for different physical conditions.
2.1. Rates
The default rates and crosssections are based on the HartreeFockBogolubov 21 (HFB21) mass model (Samyn et al. 2002) as calculated by the reaction code talys (Goriely et al. 2008). The publicly available Maxwellianaveraged neutron capture crosssections and corresponding photodissociation rates are provided on a temperature grid that extends from 10^{6} K to 10^{10} K (Goriely et al. 2008). Because neutron capture crosssections and photodissociation rates can change by many orders of magnitude between temperature grid points, a simple cubic spline interpolation was insufficient. A unique interpolation method was developed that does not fall victim to the overshooting and correction of a normal cubic spline. To avoid adding uncertainty by extrapolating the photodissociation rates and neutron capture crosssections, the extremel values of the temperature grid provide the temperature bounds for the rprocess calculations in rJava 2.0.
The β^{−} decay halflives and probability of βdelayed neutron emission of up to three neutrons are considered in rJava 2.0 by making use of the calculations by Möller et al. (2003). For complete consistency, these rates should be calculated using the HFB21 mass model, however to our knowledge such a calculation has yet to be carried out. Alpha decay halflives are calculated based on an empirical formula dependent on the ejected alpha particle kinetic energy (Lang 1980). Figure 2 shows a schematic representation of all the processes that are incorporated in the full reaction network calculation.
Fig. 2 Reactions incorporated in the full reaction network calculation in rJava 2.0 are represented schematically for a given isotope (Z,A). These reactions: neutroncapture (n,γ), photodissociation (γ,n), βdecay, betadelayed neutron emission (βdn), αdecay, and fission. 

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Fig. 3 Fastest rate plotted given a temperature of 1 × 10^{9} K and a neutron density of 1 × 10^{30} cm^{3}. The contour lines indicate when the probability of βdelayed emission of n neutrons reaches 50%. The neutron drip line and the locations of the proton and neutron magic numbers are denoted with black solid lines. The location of the stable nuclei are denoted by the black squares. A color version of this figure is available in the online article. 

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Fig. 4 Same as Fig. 3 but with a temperature of 3 × 10^{9} K and a neutron density of 1 × 10^{20} cm^{3}. A color version of this figure is available in the online article. 

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Fig. 5 Same as Fig. 3 but with a temperature of 1 × 10^{9} K and a neutron density of 1 × 10^{20} cm^{3}. A color version of this figure is available in the online article. 

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Since rJava 2.0 makes use of temperaturedependent neutron capture crosssections, photodissociation rates and neutroninduced fission crosssections at any given temperature, and neutron density, the dominant transmutational process for each nuclei could be different. Figures 3–5 consider all available processes in rJava 2.0 and display the dominant process for each nuclei in our network at three different neutron density and temperature combinations; Fig. 3 – (), Fig. 5 – () and Fig. 4 – (). For the high neutron density, low temperature scenario shown in Fig. 3 neutron capture or neutroninduced fission are the dominant channels for most nuclei in the network. Photodissociation is the strongest rate only for the most neutronrich isotopes of each element. The waiting points at the N = 82, 126 and 184 closed shells can be seen as steps along the interface between neutron capture and photodissociation the latter being the dominant process. In the high temperature, low neutron density case displayed in Fig. 4 photodissociation becomes the most probable channel for the majority of nuclei in the network. αdecay dominates neutroninduced fission for some neutronpoor isotopes of heavy elements, in particular in a region around the N = 126 closed shell. For the low neutron density, low temperature example shown in Fig. 5βdecay is the dominant channel for a band of nuclei that stretches nearly the entire length of the network. Oddeven effects can be seen as along many isotopic chains βdecay and photodissociation alternate as the dominant process. The region in which αdecay dominates is similar to but more robust than the high temperature low neutron density case seen in Fig. 4. The fertile and fissile regime is dominated by neutroninduced fission except in a region in which spontaneous fission is the dominant decay channel. This region of spontaneous fission instability can also be seen in Fig. 4.
A fundamental tenet followed during the development of rJava 2.0 was to maximize the flexibility afforded to the user. To this end, built into the rJava 2.0 interface is a module dedicated to displaying and editing the nuclear parameters. The user of rJava 2.0 can modify any parameter (mass or βdecay rate for instance) in between simulation runs, without having to restart the program. This allows users of rJava 2.0 to quickly and easily test the effect of changing nuclear properties on rprocess abundances. The choice of Java as the language for developing our nucleosynthesis code was made to ensure that rJava 2.0 could be used across all platforms. Special attention was paid to designing a graphical user interface that is intuitive and easytouse.
2.2. Getting started with rJava 2.0
As discussed above, maximizing flexibility was paramount when developing rJava 2.0. This extends beyond the nuclear inputs and to the astrophysical parameters that govern how the temperature and density of the system evolve. With rJava 2.0 we endeavoured to create rprocess software that could be applied to any potential astrophysical rprocess site. For this purpose the user of rJava 2.0 can choose from a set of astrophysical sites which provide unique density evolutions and related input parameters. The choices for astrophysical sites are highentropy winds around a protoneutron star, and ejecta from a neutron star merger or the ejecta from a quark nova. The details of the specific physics implemented for each of the astrophysical sites will be discussed in a forthcoming paper. If one chooses to go beyond the aforementioned astrophysical sites, a custom density evolution can be selected. The user of rJava 2.0 is free to define any dynamical evolution for the density or choose a static rprocess site. For the remainder of this work we will consider custom density evolution equations.
With the nuclear and physical parameters chosen and before an rprocess simulation can be run the user must determine the initial abundances of the rprocess site. This is handled differently for the WPA and full network modules. When entering a WPA simulation, the user may specify the initial electron fraction (Y_{e}) and element, then based on this information and the initial temperature rJava 2.0 computes the starting neutron density (n_{n,0}) and isotopic abundances using MaxwellBoltzmann statistics. If the user chooses a full network simulation the initial mass fractions must be specified after which rJava 2.0 calculates the starting Y_{e,0} and n_{n,0} ensuring that baryon number and charge are conserved.
Once the initial condition are determined, the rprocess code follows the algorithm detailed in Fig. 6 and runs until the userspecified duration is met or one of the stopping criterion is satisfied. The minimum temperature stopping criterion is determined by the neutron capture and photodissociation temperature grid.
Fig. 6 Schematic representation of a single timestep in our full network code. { Y_{0}(Z_{1},A_{1}),Y_{0}(Z_{2},A_{2}),... } denotes the set of initial nuclei abundances, ρ_{0} is the initial mass density, ρ(t) defines the density evolution, T_{0} is the initial temperature, Y_{e,0} denotes the initial electron fraction, and n_{n,0} is the initial neutron density. First the neutron decay is computed before the reaction network is solved using the CrankNicholson algorithm. Next the fission contribution is calculated along with the new physical parameters. If the changes in abundance or n_{n} are too large, the timestep is reattempted with dt = 0.1dt. Adaptive timesteps are used to maximize dt. 

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3. Nuclear statistical equilibrium
This release of rJava includes a refinement to the NSE module whereby the user can now choose to include the effect of Coulomb screening. Under NSE the nuclei abundances are uniquely determined by three parameters; Y_{e}, mass density (ρ), and T. In the most conventional sense, when a system that follows MaxwellBoltzmann statistics is said to be in NSE the particle number density of nuclei i, which contains Z protons and N neutrons (where mass number A = Z + N) is given by (e.g. Pathria 1977) (1)where T represents the temperature of the system, k is Boltzmann’s constant, h Planck’s constant, and B_{i}, μ_{i}, g_{i} denote the binding energy, chemical potential, and statistical weight, respectively. When the Coulomb correction is applied, μ_{C,tot} is added in the exponential where (2)This correction to the chemical potential arises from the Coulomb contribution to the free energy, which becomes significant for heavier nuclei (μ_{C,p} is the Coulomb potential of a bare proton). Our methodology for calculating μ_{C}(Z,A) is similar to that of Goriely et al. (2011) and is given by (3)where f_{C}(Γ_{i}) is the Coulomb free energy per ion in units of kT. For a Coulomb liquid, f_{C}(Γ_{i}) can be expressed as (Haensel et al. 2007) (4)with A_{1} = −0.9070, A_{2} = 0.62954, A_{3} = 0.27710, B_{1} = 0.00456, B_{2} = 211.6, B_{3} = −0.0001, B_{4} = 0.00462. When a user chooses to include the Coulomb correction, rJava 2.0 will only do so if the Coulomb liquid approximation is valid, which is to say that the Coulomb coupling parameter, (5)where a_{i} is the ionsphere radius, is smaller than the melting value Γ_{m} = 175.0 ± 0.4 (Potekhin & Chabrier 2000).
Fig. 7 NSE abundance distribution subject to the following physical conditions: temperature of 1 × 10^{10} K, mass density of 2 × 10^{11} g cm^{3}, and electron fraction of 0.3. The red dashed line denotes a calculation that includes the effects of Coulomb interactions, while for the black solid line the Coulomb interactions were ignored. 

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The effect of including Coulomb screening can be seen in Fig. 7, which displays an overlay of two NSE abundances both considering the same temperature (T = 1 × 10^{10} K), mass density (ρ = 2 × 10^{11} g cm^{3}), and electron fraction (Y_{e} = 0.3), the only difference being whether Coulomb screening is included. Coulomb screening can allow for the formation of a significant number of heavier elements. As the example in Fig. 7 shows, with the Coulomb correction to the chemical potential included, a peak appears at approximately A = 124, which is absent in the case where Coulomb screening is ignored.
Since the rprocess requires an explosive astrophysical site, there is a likelihood that the material that will undergo rprocess will have begun in NSE (Goriely et al. 2011). To accommodate such rprocess scenarios, rJava 2.0 gives the user the option of running the NSE module and setting the resulting nuclei abundance as the initial abundance for an rprocess simulation. Currently under development is a charged particle reaction network module that will be incorporated in a future release of rJava.
4. Fission
The previous release of rJava instituted a simple maximum Z and A approach to fission. After the reaction network was solved, species with higher values of Z or A than the imposed limit were split into two smaller species (see Charignon et al. 2011, for more details). For rJava 2.0, the users are given the option of turning off fission, choosing the same cutoff approach as in the previous rJava release, or choosing a more realistic treatment that includes spontaneous, neutroninduced, and βdelayed fission. Spontaneous fission rates are computed using the logic presented by Kodama & Takahashi (1975), and the βdelayed fission probabilities were taken from Panov et al. (2005). Fission barrier heights and neutroninduced fission rates provided as defaults in rJava 2.0 are calculated by Goriely et al. (2009) based on the HFB14 mass model.
In rJava 2.0 for the full fission treatment, three mass fragmentation channels are considered and neutron evaporation is explicitly handled for each fission event. The probability that the fission will follow a symmetric scission or one of the two standard channels is determined by integrals over the level density up to the available energy at the saddle point (Benlliure et al. 1998; Schmidt & Jurado 2010). The first standard channel (SI) results in the heavier fission fragment containing 82 neutrons, and for the second standard channel (SII) the heavier fission fragment contains approximately 88 neutrons. The likelihood of the fission event following a particular standard channel is parameterized by the relative strength (CI and CII) and depth (δVI and δVII) of the corresponding valleys in the potential energy landscape at scission. For rJava 2.0 the strength and depth of the standard channel parameters are found through fitting observed fission fragmentation distributions for a range of nuclei between ^{232}Th and ^{248}Cm (Chadwick et al. 2006). The remaining fissile and fertile nuclei use the standard channel parameter values of ^{235}U as the default values, however these parameters can be adjusted using the fission module of rJava 2.0. The mass fragmentation distributions for ^{232}Th, ^{235}U, and ^{240}Pu are displayed in Fig. 8. For reference in Fig. 8, the results calculated using the fission module in rJava 2.0 are compared to the results of the GEF model (Schmidt & Jurado 2010), as well as observations (Chadwick et al. 2006).
Fig. 8 Top: fission fragment mass distribution resulting for neutroninduced fission of ^{232}Th by 1.5 MeV neutrons. Middle: fission fragment mass distribution resulting for neutroninduced fission of ^{235}U by 1.5 MeV neutrons. Bottom: fission fragment mass distribution resulting for neutroninduced fission of ^{240}Pu by 1.5 MeV neutrons. 

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Fig. 9 Comparison of the full fission methodology to the mass cutoff approach. Two different initial neutrontoseed ratios (top: Y_{n}/Y_{seed} ~ 137, bottom: Y_{n}/Y_{seed} ~ 186) are considered while all other parameters remain the same (see section 4 of text for details). In both panels the red dashed line denotes the final abundance of a simulation that used the mass cutoff approach, while the black solid line represents the full fission treatment. The relevant magic numbers are highlighted with a fine vertical black line. 

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Fig. 10 Overlay of the abundances after having allowed the system to decay back to stability (black solid line) and at the end of the rprocess (red dashed line) for the same two initial neutrontoseed ratios simulations shown in Fig. 9. Top: Y_{n}/Y_{seed} = 137. Bottom: Y_{n}/Y_{seed} = 186. The relevant magic numbers are highlighted with a fine vertical black line. 

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The result of the mass fragmentation calculation for each fissionable parent is that a probability distribution of potential daughter pairs is found. In rJava 2.0 the probability for each daughter species is multiplied by the parent fission rate and is incorporated as the daughter production rate in the network calculation.
A comparison of rprocess final abundance distributions for both the mass cutoff and full fission treatment can be seen in Fig. 9. For the cutoff fission methodology, a maximum mass of A = 272 was used, and each fissioning nuclei splits into two daughter species. The full fission treatment uses the three fission processes discussed above, as well as the fission fragmentation calculation. For each simulation displayed in Fig. 9, the same initial abundance of irongroup nuclei were used, starting from the same initial temperature of 1.0 × 10^{9} K. The initial mass density was 10^{11} g cm^{3} for each simulation run, which followed the same density profile, ρ(t) = ρ_{0}/ (1 + 1.5 t/τ)^{2} with an expansion timescale (τ) of 0.003 s. The only variation between simulation runs shown in the top and bottom panels of Fig. 9 is the neutrontoseed ratio (Y_{n}/Y_{seed}). For the top panel Y_{n}/Y_{seed} = 137 was used and the bottom panel displays the rprocess yield of a more neutronrich simulation run, which began with Y_{n}/Y_{seed} = 186. These two parameter sets were chosen to highlight the differences between the two fission methodologies.
In the smaller Y_{n}/Y_{seed} scenario, shown in the top panel of Fig. 9, the rprocess is just capable of breaking through the N = 184 magic number. In this case the full fission run has been able to cross over a region of instability at about A ~ 280 and has produced a small peak of superheavies at about A ~ 290. Aside from the small superheavy peak, the results of both the full fission and cutoff methodology are largely the same.
For the larger Y_{n}/Y_{seed} scenario seen in the bottom panel of Fig. 9, the fission cutoff approach overproduces nuclei at A ~ 130 by over ten times compared to the full fission treatment. This overproduction is due to the increased fission recycling caused by forcing all nuclei heavier than A ~ 272 to undergo fission. For this Y_{n}/Y_{seed}, the full fission simulation run produces a superheavy peak of the order of 10^{7}. The results of these simulation runs do not speak to the longterm stability of the superheavy nuclei produced but rather shows the large variation between the two fission methodologies at the point of neutron freezeout, which is to say that when the neutron to rprocess product ratio drops below one, (Y_{n}/Y_{r}< 1).
The final abundances once the systems are allowed to decay to stability can be seen in Fig. 10. Fission recycling gives rise to nearly all the nuclei abundances below A ~ 150 seen in both cases. The distribution of fission recycled nuclei is similar in both cases because fission is occurring from the same region. The shape of the fission contribution found using rJava 2.0 coincides with the findings of Petermann et al. (2008), who used the statistical code ALBA to calculate the fission yield for each fission event. For comparison, the abundances at the moment rprocess stops is included in Fig. 10 for both neutrontoseed simulation runs. The robust fission calculations included in rJava 2.0 provides an accurate assessment of the role of fission recycling in the rprocess.
Fig. 11 Effect of βdelayed neutron emission on nuclei abundance. The black line denoting an rprocess simulation that included βdelayed neutron emission, and for the red dashed line that process was omitted. The results plotted in this figure, as well as in Figs. 12 and 13, are from simulation runs that were identical with the exception of whether or not βdelayed neutron emission was included. Top: the nuclei abundances at the moment the neutrontoseed ratio drops below one. Bottom: the nuclei abundances after decay to stability. The relevant magic numbers are highlighted with a fine vertical black line. 

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5. Betadelayed neutron emission
To study the effects of βdelayed neutrons on the rprocess, we compare two simulation runs that are identical except for whether βdelayed neutron emission is included. The top panel of Fig. 11 displays a comparison of the abundance distributions at the end of the rprocess, which for this study was defined to be once the neutrontorprocess products ratio (Y_{n}/Y_{r}) drops below one. The emission of βdelayed neutrons acts to smooth out the variability in nuclei distribution compared to that of the case without βdelayed neutrons. The peak at A ~ 188 is shifted slightly heavier with the inclusion of βdelayed neutrons and also the abundance of nuclei with mass greater than A = 200 is increased. The lower panel of Fig. 11 shows the final nuclei abundance distribution once the systems are allowed to decay to stability. For the simulation that did not include βdelayed neutron emission, the nuclei abundance distribution below A ≃ 209 remains virtually unchanged from the time rprocess stops to that of stability. However, when βdelayed neutrons are included, the decay to stability causes further reduction in the variability of the abundance distribution, and a shifting of the peaks towards lower mass.
Fig. 12 Evolution of neutron density until the rprocess is terminated. The black line denotes an rprocess simulation that included βdelayed neutron emission, and for the red dashed line that process was omitted. 

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In Fig. 12 the evolution of neutron density during the rprocess is compared between the simulations with and without βdelayed neutron emission. The βdelayed neutrons act to keep the neutron density higher for longer then in the case in which βdelayed neutron emission was ignored. By bolstering the neutron density, βdelayed neutron emission allows the rprocess to proceed more readily to heavier elements, an effect that can can be seen in the top panel of Fig. 11.
The abundances of nuclei at the end of the rprocess plotted on the (N,Z) plane can be seen in Fig. 13 (top panel displays the case where βdelayed neutron emission was ignored and the bottom panel the case with its inclusion). For the simulation run that included βdelayed neutrons, the rprocess accesses a broader range (along lines of constant Z) of nuclei, reaching closer to the valley of stability. This broadening effect caused by βdelayed neutrons is most noticeable around the N = 82 and 126 closed shells. The ability of βdelayed neutron emission to allow for matter flow past the N = 126 closed shell can be seen in Fig. 13 as the breadth of populated nuclei and abundance in the region past N = 126 is increased in the case where βdelayed neutron emission is included.
6. Full reaction network
To expand beyond the WPA, reactions that stay within an isotopic chain, namely neutroncapture and photodissociation, must be included in the network calculation. This means that rather than solving a system of equations the size of which is determined by the number of isotopic chains (110) as in the WPA case, for the full network case an equation for every nuclei must be included (a total of 8055). The computational cost of this addition is significant since finding a solution to a reaction network scales as N^{3} where N is the number of coupled differential equations. However there are methods that can be invoked to mitigate this cost; we take advantage of the fact that each nuclei in the network is only coupled to another nuclei if there is an adjoining reaction (i.e. nuclei (Z,A) is coupled to both (Z+2, A+4) and (Z2, A4) via α decay). This is effectively utilizing the sparseness of the reaction rate matrix, which alleviates memory load issues and speeds up runtime. We solve the fully implicit network using the CrankNicholson method. The rate of thermonuclear energy released (or absorbed) is calculated using the methodology laid out by Hix & Meyer (2006).
Fig. 13 Nuclei abundances at the moment the neutrontoseed ratio drops below one plotted on the (N,Z) plane. Stable nuclei, the location of the proton and neutron closed shells, and the neutron drip line are included for reference. Top: simulation that did not include βdelayed neutron emission. Bottom: simulation including βdelayed neutron emission. 

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Figure 14 highlights the importance of the imposed stopping criteria on network calculations through a comparison of the results from the WPA to that of the full network. For the results plotted in both panels of Fig. 14, the same initial conditions and expansion profiles^{2} were chosen. The simulations considered begin from an iron seed with Y_{e,0} = 0.16, T_{0} = 4 × 10^{9} K, and ρ_{0} = 10^{10} g cm^{3}. In the top panel of Fig. 14, the calculations are stopped when the temperature falls below 2 × 10^{9} K, an imposed cutoff based on the work of Cowan et al. (1983). The nuclei distribution in the WPA simulation is peaked at A = 80 with lower abundances of nuclei up to A ~ 120 and then a precipitous drop in abundance for heavier nuclei. In the case where the full reaction network calculation was stopped once the temperature fell to 2 × 10^{9} K (displayed in the top panel of Fig. 14), there is good agreement to the WPA calculation. The shape of the nuclei abundance distribution is the same for both network calculations, with the full reaction network producing a slightly greater abundance of heavy nuclei. However, the results displayed in the top panel of Fig. 14 are not indicative of the full potential of the rprocess for this chosen environment, since as the temperature drops below the imposed minimum cutoff, the neutron density still remains high (n_{n} ~ 10^{30} cm^{3}). For the bottom panel of Fig. 14, the minimum temperature stopping criterion for the WPA was lowered to 10^{9} K, and for this case both the WPA and full reaction network calculations halt at neutron freezeout (Y_{n}/Y_{r} = 1). Once again both network calculations display similar nuclei abundance distributions. The results of the WPA reflect the (n,γ) ⇋ (γ,n) equilibrium, which is not as accurate as the full treatment. This is manifested as deeper troughs in nuclei abundance, especially around the A = 190 peak, and greater variability for the lower mass nuclei. The smoother distribution in the full reaction network results is also due to the inclusion of βdelayed neutron emission.
The users of rJava 2.0 are afforded the option of choosing the stopping criteria for rprocess calculations: minimum temperature and neutron density for the WPA network and Y_{n}/Y_{r} for both networks.
Fig. 14 Comparison of the simulation results from the WPA (red dashed line) with that of the full network (black solid line). Top: nuclei abundances when the temperature drops to 2 × 10^{9} K. Bottom: the nuclei abundances at neutron freezeout, see text for details of stopping criteria. The relevant magic numbers are highlighted with a fine vertical black line. 

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7. Test cases
As part of the testing phase of the development of rJava 2.0 we attempted to reproduce the results from three other full network rprocess codes; the Clemson University nucleosynthesis code (Jordan & Meyer 2004) which will furthermore be referred to as the Clemson code, and the Basel University nucleosynthesis code (Freiburghaus et al. 1999a), to be referred to as the Basel code and the nucleosynthesis code developed at Université Libre de Bruxelles (Goriely et al. 2011) which will be called the Bruxelles code for the remainder of this article. While a complete applestoapples comparison was not tenable, the results of our tests showed good agreement with each of the three codes studied.
7.1. Clemson nucleosynthesis code
For the Clemson code comparison seen in Fig. 15, we endeavoured to reproduce the results shown in Figs. 7 and 8 of Jaikumar et al. (2007). We found that the initial abundance was not very important for either case because the neutrontoseed ratio was high enough that any influence from the initial abundance was washed away by the rprocess. The top panel of Fig. 15 shows the results of a fast expansion rprocess site and the bottom panel a slow expansion (corresponding to Figs. 7 and 8 from Jaikumar et al. 2007, respectively). In the fast expansion case both rJava 2.0 and the Clemson code show that the rprocess is not capable of proceeding past the A = 130 magic number. In the slow expansion case, the environment remains favourable for the rprocess much longer, and the final abundance for both rJava 2.0 and the Clemson code contains peaks shifted to the heavy side of the A = 130 and A = 190 observed solar peaks. The differences between the final abundances from rJava 2.0 and the Clemson code seen in both cases can be credited to the fact that the two codes use different mass models (the Clemson code used the finite range droplet model and rJava 2.0 HFB21), which has been shown to affect the rprocess abundance yield (e.g. Farouqi et al. 2010).
Fig. 15 Top: comparison of the final abundances from rJava 2.0 (red dashed line) and the Clemson nucleosynthesis code (black solid line) for a fast expansion rprocess site. Bottom: a comparison of the final abundances from rJava 2.0 with two different initial neutrontoseed ratios (Y_{n}/Y_{seed} ~ 1100 denoted by the green dotted line, Y_{n}/Y_{seed} ~ 1300 by the red dashed line) and the Clemson nucleosynthesis code (black solid line) for a slow expansion rprocess site. The relevant magic numbers are highlighted with a fine vertical black line. 

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7.2. Basel nucleosynthesis code
To compare to an updated version of the Basel code, we pushed to reproduce the abundances shown in Fig. 10 of Farouqi et al. (2010), which considers the HFB17 mass model. As described there the rprocess network begins at the termination of the charged particle network, thus we used the abundance per mass number at the end of the chargedparticle network displayed in their Fig. 5 to determine our initial seed nuclei distribution for comparison. Having only the abundance per mass number information, we had to choose which nuclei to set each abundance to in order to build our initial seed nuclei. We made the assumption that the system is in (n,γ) ⇋ (γ,n) equilibrium at the beginning of the rprocess based on the initial conditions used in Farouqi et al. (2010) of T = 3 × 10^{9} K and n_{n} = 10^{27} cm^{3}. Then for abundance at each mass number plotted in Fig. 5 of their work, we set it to the isotope that most closely matched the predictions of the nuclear Saha equation. For each different entropy simulation that we ran, these abundances were uniformly scaled such that they produced the correct seed abundance as shown in Fig. 3 of Farouqi et al. (2010). The initial neutron abundance was then determined from the neutrontoseed ratio stated in their Table 5. The use of the same initial abundance distribution for each simulation run by rJava 2.0, which may not have been the case for their simulations, is the largest potential source of discrepancy in this comparative analysis.
Consistent with Farouqi et al. (2010), we used Y_{e} = 0.45 and started our simulations with an initial temperature of 3 × 10^{9} K. We followed the same constant entropy methodology described there to evolve temperature and density. In this scenario the temperature evolves adiabatically, and the entropy is assumed to be radiationdominated, which allows for the inference of the evolution of matter density. The time dependence of the temperature and matter density (ρ_{5} is in units of 10^{5} g cm^{3}) are thus governed by the following equations, where R_{0} = 130 km and v_{exp} = 7500 km s^{1}.
To maintain consistency with the Basel code, we terminated the rprocess once the neutrontoseed ratio dropped below one, and the abundances shown in Fig. 16 are after decay back to stability.
The top lefthand panel of Fig. 16, which displays the results of the S = 175 simulation runs, shows the best agreement between rJava 2.0 and the Basel code of all the cases tested. Both rJava 2.0 and the Basel code show a final nuclei abundance that predominantly ranges from 70 <A< 135. The results from each code displays a peak below the A = 130 magic number, however the Basel code peak is shifted heavier with respect to that of rJava 2.0.
Fig. 16 Comparison of rprocess abundance yields as calculated by rJava 2.0 (black solid line) and the Basel nucleosynthesis code (red dashed line). The relevant magic numbers are highlighted with a fine vertical black line. For each panel a different entropy was assumed, which changes the initial neutrontoseed ratio as well as the evolution of the density, see text for details. Topleft: simulation run assuming the entropy of the wind is S = 175. Topright: simulation run assuming the entropy of the wind is S = 195. Bottomleft: simulation run assuming the entropy of the wind is S = 236. Bottomright: simulation run assuming the entropy of the wind is S = 280. See text for details of initial conditions. 

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The S = 195 simulation results (displayed in the top righthand panel of Fig. 16) from the Basel code and rJava 2.0 are both dominated by a peak at the A = 130 magic number. The differences between the final abundances from the two codes for this entropy are consistent with differing initial abundances. That the results from rJava 2.0 display a more distinct peak at the A = 80 magic number is consistent with the simulation run of rJava 2.0 starting with more nuclei below the A = 80 magic number. This would lead to nuclei piling up at A = 80 for rJava 2.0, which would not be the case for the Basel code simulation run. The difference in initial abundance also has an effect on the heavy side of the final abundance distribution. With more nuclei initially between the A = 80 and A = 130 observed solar peaks, the rprocess simulation run of the Basel code is more capable of pushing through the A = 130 magic number to higher masses. As for the rJava 2.0 simulation, once the rprocess pushes through the A = 80 magic number, nuclei will pile up on the lightside of the A = 130 magic number. By the time the rprocess reaches the A = 130 peak in the rJava 2.0 run, the neutron density will have dropped too low to significantly push past the A = 130 magic number. The result of this is the increased production of nuclei on the lower mass side of the A = 130 peak for the rJava 2.0 simulation run with respect to that of the Basel code and a longer highmass tail in the Basel code simulation.
Similar to the S = 195 case, the presence of nuclei below the A = 80 magic in the S = 236 rJava 2.0 simulation (seen in the lowerleft panel of Fig. 16) leads to the final abundance containing nuclei around A = 80, which is not the case for the Basel code results. Once again this difference is consistent with different initial abundances for the two runs. Neglecting the relatively small abundance for 80 ≲ A ≲ 125 in the rJava 2.0 results, the final distributions of the S = 236 simulation runs for both codes are consistent with peaks around A = 80, 165, and 190. The A = 190 peak in the Basel code simulation is stronger and shifted towards heavier masses with respect to that of rJava 2.0, which can be attributed to fact that the rJava 2.0 simulation had more nuclei stuck below the A = 80 magic number.
The S = 280 simulation runs seen in the lower righthand panel of Fig. 16 shows the same basic features for both codes. The final nuclei abundance for both codes contains strong peaks at A = 130 and A = 195, with the rJava 2.0 results displaying stronger peaks. The increased abundance of Th and U at stability in the Basel code simulation run could be due to the initial abundance differences discussed for the S = 195 and S = 236 cases or due to different definitions of stability. For the rJava 2.0 simulations, the systems decayed for 13 Gyr or until the percent change in any nuclei abundance was less than 1 × 10^{15}.
7.3. Université Libre de Bruxelles nucleosynthesis code
For our comparison to the Bruxelles code we attempted to reproduce the abundances after the decompression displayed in Fig. 10 of Goriely et al. (2011). As discussed in Goriely et al. (2011), the initial abundances used for the rprocess simulation are important because in this scenario the initial neutrontoseed ratio is roughly 5, and the rprocess is only capable of shifting the abundances toward heavier nuclei without dramatically altering the relative shape of the abundance distribution. Goriely et al. (2011) provide the initial abundances used for the rprocess simulation, which are calculated under NSE with Coulomb interactions included. A comparison of the initial abundances of the Bruxelles code and rJava 2.0 can be seen in the top panel of Fig. 17. The peaks roughly centred at A = 80 and 125 as calculated by rJava 2.0 are higher than for the Bruxelles code, while the intermediatemass region is more abundant in the Bruxelles calculation. The NSE calculation performed by rJava 2.0 assumes MaxwellBoltzmann statistics, while the Bruxelles code used FermiDirac, which accounts for the differences in abundances. While the nuclear physics used in the Bruxelles code is the most similar to rJava 2.0 of all the codes studied, we had to implement an analytic approximation to the density evolution used by Goriely et al. (2011). To compare to the Bruxelles code, we chose the density profile shown in Eq. (8) (8)where a, b, and c are free parameters. A value of 3 × 10^{4} s was used for the expansion timescale (τ), which is consistent with the one used by Goriely et al. (2011).
Fig. 17 Top: initial abundances used for the comparison of rprocess simulations from rJava 2.0 and the Bruxelles nucleosynthesis code. The red dashed line denotes rJava 2.0 and the black solid line the Bruxelles code. Bottom: final abundances from rJava 2.0 considering two different density evolution profiles (red dashed line and green dotted line) compared to that of the Bruxelles code (black solid line). See text for details of simulations. The relevant magic numbers are highlighted with a fine vertical black line. 

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Fig. 18 Top: final (black solid line) and initial (red dashed line) abundances as calculated by rJava 2.0 for comparison to the Bruxelles code. Bottom: final (black solid line) and initial (red dashed line) abundances as calculated by the Bruxelles code. See text for details of simulations. The relevant magic numbers are highlighted with a fine vertical black line. 

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A comparison of two different sets of free parameters used in the density profile of rJava 2.0 to the final abundances of the Bruxelles code can be seen in the bottom panel of Fig. 17. As expected, the differences in initial abundances are carried through to the final nuclei abundances with rJava 2.0 displaying higher peaks at approximately A = 85 and 130 with the intermediate mass region more strongly produced in the Bruxelles code simulation. To show that in both codes the rprocess has the same effect on abundances in Fig. 18, the final and initial abundances are overplotted for each code. For both rJava 2.0 and the Bruxelles nucleosynthesis code the rprocess acts to shift the peaks towards heavier nuclei.
8. Summary and conclusions
This paper has discussed the nuclear physics incorporated in rJava 2.0; providing cuttingedge fission calculations, βdelayed neutron emission of up to three neutrons and neutron capture and photodissociation rates from one of the most sophisticated mass models (HFB21). Nevertheless, it is the ability to change any parameter quickly and easily that makes rJava 2.0 a powerful tool for studying nuclear astrophysics. rJava 2.0 is capable of solving a full rprocess reaction network containing over 8000 nuclei and can do so both accurately and efficiently, with a typical full reaction network simulation completed in minutes. The scientific aim of this release of rJava is to study rprocess nucleosynthesis in the expansion phase (T ≲ 3 × 10^{9} K, e.g. Howard et al. 1993) and NSE at high temperature (T ≳ 4 × 10^{9} K, e.g. Truran et al. 1966). We are currently developing a chargedparticle reaction network module that will be incorporated into a future version of rJava.
With a more realistic treatment of fission we have added to rJava 2.0 the ability to investigate the role of fission recycling in the rprocess. In the past by simply using the mass cutoff approach the mistake of going to too high of a neutron density was masked by the fact that fission recycling would not allow the rprocess to proceed beyond the cutoff. This presents in the rprocess abundance at neutron freezeout in two ways; an underproduction of superheavy nuclei and the overproduction of nuclei around the A = 130 magic number. With the fission methodology implemented here the superheavy regime (A> 270) can be studied using rJava 2.0. The preliminary study undertaken here supports the findings of Petermann et al. (2012), where superheavy nuclei (A ~ 290) can be formed by the rprocess. The superheavies subsequently decay in seconds.
The emission of βdelayed neutrons can act to maintain a sufficiently high neutron density to allow for the rprocess to reach heavier elements. The effect of βdelayed neutron emission is also significant during the decay to stability once the rprocess has stopped. They act to smooth out the nuclei distribution on the path to stability and shifts the abundances to lower masses. Their role may in some cases not be as direct as just stated. The βdelayed neutrons can alter the rprocess path, thereby accessing nuclei that would more readily capture neutrons and cause the neutron density to drop more rapidly than if they were ignored. This must be studied in more detail, and with rJava 2.0 the user can quickly and easily investigate the effect of βdelayed neutrons on rprocess abundances.
By performing a comparative study between rJava 2.0 and three other full network rprocess codes, we have found good agreement between the codes, however undertaking this analysis has highlighted the potential pitfalls of comparing the results from different codes. Factors such as choice of mass model, evolution methodology of physical parameters, code stopping criteria, and precision can contribute to variations in rprocess abundances that are artifacts of the nucleosynthesis code structure rather than of the physical scenarios being studied. This comparative analysis highlights the universality of rJava 2.0, which by allowing the user to customize both the nuclear and astrophysical parameters, is capable of reproducing the results of other nucleosynthesis codes.
The development of rJava 2.0 was done in a way that maximizes the flexibility of the software, allowing for the adjustment of any nuclear or physical property both quickly and easily. The choice of Java as the programming language allowed for including an easy to use GUI that is crossplatform compatible. Beyond its applicability to scientific study, the goal of rJava 2.0 was to make it accessible in a teaching capacity by ensuring it is easy to use and allowing for the investigation of individual processes.
In the followup paper to this work we will turn our attention to the astrophysical side of the rprocess that is well covered by rJava 2.0. Built into the interface of rJava 2.0 is the option of defining a custom density evolution or of selecting one of three proposed astrophysical rprocess sites: highentropy winds around protoneutron stars (example studies: Woosley & Hoffman 1992; Qian & Woosley 1996; Thompson et al. 2001; Farouqi et al. 2010), ejecta from neutron star mergers (Freiburghaus et al. 1999b; Goriely et al. 2011, and others), or ejecta from quark novae (Jaikumar et al. 2007). For each of the proposed astrophysical sites, rJava 2.0 consistently calculates the temperature and density evolution, the details of which will be discussed in this upcoming paper. By including the physics of different astrophysical sites in one piece of rprocess software, we have provided a common platform for comparing the rprocess abundances of different astrophysical sites.
rJava 1.0 and 2.0 can be downloaded from http://quarknova.ucalgary.ca
Acknowledgments
This work is supported by the Natural Sciences and Engineering Research Council of Canada. NK acknowledges support from the Killam Trusts.
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All Tables
All Figures
Fig. 1 Schematic representation of the functionality of rJava 2.0. See Table 1 for description of symbols. 

Open with DEXTER  
In the text 
Fig. 2 Reactions incorporated in the full reaction network calculation in rJava 2.0 are represented schematically for a given isotope (Z,A). These reactions: neutroncapture (n,γ), photodissociation (γ,n), βdecay, betadelayed neutron emission (βdn), αdecay, and fission. 

Open with DEXTER  
In the text 
Fig. 3 Fastest rate plotted given a temperature of 1 × 10^{9} K and a neutron density of 1 × 10^{30} cm^{3}. The contour lines indicate when the probability of βdelayed emission of n neutrons reaches 50%. The neutron drip line and the locations of the proton and neutron magic numbers are denoted with black solid lines. The location of the stable nuclei are denoted by the black squares. A color version of this figure is available in the online article. 

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In the text 
Fig. 4 Same as Fig. 3 but with a temperature of 3 × 10^{9} K and a neutron density of 1 × 10^{20} cm^{3}. A color version of this figure is available in the online article. 

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In the text 
Fig. 5 Same as Fig. 3 but with a temperature of 1 × 10^{9} K and a neutron density of 1 × 10^{20} cm^{3}. A color version of this figure is available in the online article. 

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In the text 
Fig. 6 Schematic representation of a single timestep in our full network code. { Y_{0}(Z_{1},A_{1}),Y_{0}(Z_{2},A_{2}),... } denotes the set of initial nuclei abundances, ρ_{0} is the initial mass density, ρ(t) defines the density evolution, T_{0} is the initial temperature, Y_{e,0} denotes the initial electron fraction, and n_{n,0} is the initial neutron density. First the neutron decay is computed before the reaction network is solved using the CrankNicholson algorithm. Next the fission contribution is calculated along with the new physical parameters. If the changes in abundance or n_{n} are too large, the timestep is reattempted with dt = 0.1dt. Adaptive timesteps are used to maximize dt. 

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In the text 
Fig. 7 NSE abundance distribution subject to the following physical conditions: temperature of 1 × 10^{10} K, mass density of 2 × 10^{11} g cm^{3}, and electron fraction of 0.3. The red dashed line denotes a calculation that includes the effects of Coulomb interactions, while for the black solid line the Coulomb interactions were ignored. 

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In the text 
Fig. 8 Top: fission fragment mass distribution resulting for neutroninduced fission of ^{232}Th by 1.5 MeV neutrons. Middle: fission fragment mass distribution resulting for neutroninduced fission of ^{235}U by 1.5 MeV neutrons. Bottom: fission fragment mass distribution resulting for neutroninduced fission of ^{240}Pu by 1.5 MeV neutrons. 

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In the text 
Fig. 9 Comparison of the full fission methodology to the mass cutoff approach. Two different initial neutrontoseed ratios (top: Y_{n}/Y_{seed} ~ 137, bottom: Y_{n}/Y_{seed} ~ 186) are considered while all other parameters remain the same (see section 4 of text for details). In both panels the red dashed line denotes the final abundance of a simulation that used the mass cutoff approach, while the black solid line represents the full fission treatment. The relevant magic numbers are highlighted with a fine vertical black line. 

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In the text 
Fig. 10 Overlay of the abundances after having allowed the system to decay back to stability (black solid line) and at the end of the rprocess (red dashed line) for the same two initial neutrontoseed ratios simulations shown in Fig. 9. Top: Y_{n}/Y_{seed} = 137. Bottom: Y_{n}/Y_{seed} = 186. The relevant magic numbers are highlighted with a fine vertical black line. 

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In the text 
Fig. 11 Effect of βdelayed neutron emission on nuclei abundance. The black line denoting an rprocess simulation that included βdelayed neutron emission, and for the red dashed line that process was omitted. The results plotted in this figure, as well as in Figs. 12 and 13, are from simulation runs that were identical with the exception of whether or not βdelayed neutron emission was included. Top: the nuclei abundances at the moment the neutrontoseed ratio drops below one. Bottom: the nuclei abundances after decay to stability. The relevant magic numbers are highlighted with a fine vertical black line. 

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In the text 
Fig. 12 Evolution of neutron density until the rprocess is terminated. The black line denotes an rprocess simulation that included βdelayed neutron emission, and for the red dashed line that process was omitted. 

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In the text 
Fig. 13 Nuclei abundances at the moment the neutrontoseed ratio drops below one plotted on the (N,Z) plane. Stable nuclei, the location of the proton and neutron closed shells, and the neutron drip line are included for reference. Top: simulation that did not include βdelayed neutron emission. Bottom: simulation including βdelayed neutron emission. 

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In the text 
Fig. 14 Comparison of the simulation results from the WPA (red dashed line) with that of the full network (black solid line). Top: nuclei abundances when the temperature drops to 2 × 10^{9} K. Bottom: the nuclei abundances at neutron freezeout, see text for details of stopping criteria. The relevant magic numbers are highlighted with a fine vertical black line. 

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In the text 
Fig. 15 Top: comparison of the final abundances from rJava 2.0 (red dashed line) and the Clemson nucleosynthesis code (black solid line) for a fast expansion rprocess site. Bottom: a comparison of the final abundances from rJava 2.0 with two different initial neutrontoseed ratios (Y_{n}/Y_{seed} ~ 1100 denoted by the green dotted line, Y_{n}/Y_{seed} ~ 1300 by the red dashed line) and the Clemson nucleosynthesis code (black solid line) for a slow expansion rprocess site. The relevant magic numbers are highlighted with a fine vertical black line. 

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In the text 
Fig. 16 Comparison of rprocess abundance yields as calculated by rJava 2.0 (black solid line) and the Basel nucleosynthesis code (red dashed line). The relevant magic numbers are highlighted with a fine vertical black line. For each panel a different entropy was assumed, which changes the initial neutrontoseed ratio as well as the evolution of the density, see text for details. Topleft: simulation run assuming the entropy of the wind is S = 175. Topright: simulation run assuming the entropy of the wind is S = 195. Bottomleft: simulation run assuming the entropy of the wind is S = 236. Bottomright: simulation run assuming the entropy of the wind is S = 280. See text for details of initial conditions. 

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In the text 
Fig. 17 Top: initial abundances used for the comparison of rprocess simulations from rJava 2.0 and the Bruxelles nucleosynthesis code. The red dashed line denotes rJava 2.0 and the black solid line the Bruxelles code. Bottom: final abundances from rJava 2.0 considering two different density evolution profiles (red dashed line and green dotted line) compared to that of the Bruxelles code (black solid line). See text for details of simulations. The relevant magic numbers are highlighted with a fine vertical black line. 

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In the text 
Fig. 18 Top: final (black solid line) and initial (red dashed line) abundances as calculated by rJava 2.0 for comparison to the Bruxelles code. Bottom: final (black solid line) and initial (red dashed line) abundances as calculated by the Bruxelles code. See text for details of simulations. The relevant magic numbers are highlighted with a fine vertical black line. 

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In the text 
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