In-target rare nuclei production rates with EURISOL single-stage configuration

S. P. Chabod 1,2,1, N. Thiollière 1,3, J.-Ch. David 1, D. Ridikas 1, V. Blideanu 4, D. Doré 1, D. Ene 1

1 CEA Saclay, Irfu/SPhN, F-91191 Gif-sur-Yvette, France
2 present adress, LPSC, Université Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, 38000 Grenoble, France
3 present adress, SUBATECH, Université de Nantes, CNRS/IN2P3, Ecole des Mines de Nantes, 44000 Nantes, France
4 CEA Saclay, Irfu/SENAC, F-91191 Gif-sur-Yvette, France

Abstract
We conducted calculations of exotic nuclei production rates for 320 configurations of EURISOL (European Isotope Separation On-Line Radioactive Ion Beam Facility) direct spallation targets. The nuclei yields were evaluated using neutron generation-transport codes, completed with evolution calculations to account for nuclei decays and low energy neutron interactions. The yields were optimized for 11 selected elements (Li, Be, Ne, Mg, Ar, Ni, Ga, Kr, Sn, Hg, Fr) and 23 of their isotopes, as function of the target compositions and geometries as well as the incident proton beam energies. For the considered elements, we evaluated the yield distributions as functions of the charge and mass numbers using two different spallation models.

Key words: EURISOL, spallation target, nuclei yields, generation-transport code, spallation model
PACS: 29.25.Rm; 29.38.-c; 25.40.Sc


1. Context and objectives

To explore nuclear matter far from stability, European laboratories are collaborating on the design and operation of the next generation radioactive ion beam (RIB) facility, based on the on-line isotope separation method (ISOL). The project, called EURISOL, aims to provide nuclear physicists with exotic nuclei beams at least one hundred times more intense than those available today. To meet this objective, EURISOL network had consequently launched an ambitious design study within the framework of the 6th European research programme, in order to investigate the eligible technological options. The first guidelines are available now and are presented in Ref. [1]. The proposed driver accelerator is a megawatt linear superconducting proton machine, with incident energies around 1 GeV and a possibility to accelerate some light ions as projectiles (d or 3He). The EURISOL facility will use two different target configurations: (a) the single-stage (or direct) configuration, where a 100 kW proton beam is focalized on a thick target to produce RIB directly, (b) the two-stage configuration, where a MW proton beam is directed on a converter target to generate high neutron fluxes by spallation-evaporation processes. Exotic nuclei are then produced by fission reactions induced by the secondary neutrons on actinide targets surrounding the converter. Then, whichever the target type is, the radioactive nuclei will be extracted, ionized and post-accelerated to provide high intensity RIB to the experimental areas.
Within EURISOL Design Study (DS), we proposed to estimate and optimize the nuclei production rates for the direct target option. To achieve this objective, we performed calculations of the in-target nuclei yields for different configurations, by varying parameters such as the target composition and volume or the incident proton energy. The production rates were simulated using MCNPX generation-transport code, coupled with the CINDER 90 evolution programme. The methodology of our work is described in section 2 of this paper. In section 3, we present the distributions of the nuclei production rates obtained, as a function of the charge and mass numbers. In section 4, we conduct the yield optimizations for selected elements. Finally, we calculate in section 5 the isotopic distributions to estimate the individual secondary beams. The results obtained in this paper will be combined with extraction efficiencies to get the final beam intensities.


2. Methodology of the study

In the direct target configuration, exotic nuclei are produced by three distinct processes: a) the spallation reactions induced by the primary beam; b) the reactions induced by secondary particles. Among them, we can cite for instance the fission processes occurring in heavy targets or the (n, xn) reactions induced by secondary neutrons; c) the decay of radioactive parents. As a consequence, a correct estimate of the nuclei production rates require extensive simulations of the whole possible nuclear processes, using event generators, transport codes as well as evolution programmes.

2.1. Modelling parameters

To achieve a full picture of RIB predictions, we followed the recommendations of the EURISOL DS task 3 board [2, 3] for the production targets. We tested different types of materials (refractory and molten metals, oxides, carbides) and geometries. We accounted for the beam characteristics (beam power P and mean energy E), as these parameters directly govern the spallation processes (E dependent) and the nuclei production yields (E and P dependent). At the end, the multiplicity of the input parameters led us to test a huge number of target configurations. We decided to explore 320 different configurations of cylindrical targets (length L and radius R), whose characteristics are summarized in Table 1. 
First, we assumed that the EURISOL beam will present a gaussian profile, with its  defined as the full width at half maximum. In Table 1, the choice of the beam spot  = R/3 came from a previous study [3, 4] and has direct consequences. Indeed, as  cannot be smaller than 3 mm [3], the minimal target radius R must be equal to 9 mm in our study. We chose the other radii to successively increase the target volume by a factor 2 for a given length. Finally, we considered different increasing target lengths, until the stopping range was reached for each eligible material. 

Target material
Al2O3
SiC
Pb (molten)
Ta
UC3
 [g.cm-3]
2.0
3.2
11.4
12.5
2.418
R [mm]
9.0 – 12.7 – 18.0 – 25.5
L [cm]
50 – 75 – 
100 – 125
32 – 48 – 
64 – 80
9 – 18 – 
27 – 36
8 – 16 – 
24 – 32
40 – 60 – 
80 – 100
Beam particles
protons
P [kW]
100 
E [GeV]
0.5 – 1.0 – 1.5 – 2.0
 [mm]
R/3

Table 1: Parameters used in the calculations.

According to the ongoing EURISOL DS, the incident proton energy will remain close to the 1 GeV level. Thus, we selected in our simulations E values ranging from 0.5 to 2 GeV. As EURISOL targets are designed to stand up to 100 kW of the primary beam power, we fixed P to this maximal value, which corresponds to a 100 A beam of 1 GeV protons. Indeed, for a given energy E, the secondary nuclei yields are proportional to the beam intensity, and consequently to the beam power.

2.2. Calculation strategy

To estimate the exotic nuclei yields, we used two modelling tools: MCNPX and CINDER. The first one, the MCNPX 2.5.0 code [5], is based on Monte Carlo procedures. It computes the transport of light particles (n, p, d, t, 3He, , , etc.) and the production of secondary particles such as spallation and fission fragments. The code uses data libraries for low energetic neutrons (En < 20 MeV) and physical models for the other reactions. Note that the MCNPX outputs display the complete list of the reaction products obtained for all processes (all particles) at all energies except, however, reactions involving low energetic neutrons. Within EURISOL DS, MCNPX was extendedly benchmarked [6, 7] and it appeared that the precision of its predictions is highly sensitive to the quality of the models used to describe the spallation reactions. Taking into account this conclusion, we decided to use for our simulations two different cascade/de-excitation models available within MCNPX package: INCL4/ABLA [8, 9] and CEM2k [10]. Two of the most striking differences between these models are the presence of an explicit pre-equilibrium phase in CEM2k, whereas it is considered as non-necessary in INCL4. More, INCL4 is coupled to the fission part computed by PROFI included in ABLA, while the RAL fission model [11] is used when CEM2k is called. Note that, in order to manage statistical error and calculation time, we performed MCNPX simulations using 5.106 incident particles for each configuration mentioned in Table 1.
As mentioned, MCNPX does not display the production rates due to low energetic neutrons. We had consequently to reprocess the MCNPX outputs with CINDER’90, a standard material evolution program [12]. CINDER can indeed simulate the nuclear reactions (capture, fission, (n,xn), (n,p), (n,d), etc.) induced by neutrons below 25 MeV. Moreover, it can also account for the nuclei losses/creations through the natural decay processes. For each set of target parameters (see Table 1), we performed thus 4 MCNPX+CINDER simulation cycles: (a) two for the spallation models (CEM2k or INCL4/ABLA), (b) then, for each spallation model, two CINDER computations taking into account, or not, the reactions induced by the low energy secondary neutrons. For each CINDER run, we considered also evolution times ranging from 1 ms (instantaneous nuclei production rates) to 3 months (rough estimation of the impact of exotic nuclei finite lifetimes on their production rates, being at equilibrium with the decay rates). The combination of the MCNPX and CINDER codes allowed us to generate the list of the whole nuclei yields. Among these yields, we studied specifically the production rates of 11 nuclei of interest. 7 were given by the NUPECC board [13] (Be, Ar, Ni, Ga, Kr, Sn and Fr), and we added to this list 4 elements which could play a pre-eminent role in the experiments programmed within EURISOL collaboration (Li, Ne, Mg and Hg) [14]. Finally, for each of these elements, we examined different isotopes of interest (ex: for Z = 4, 11Be being a one-halo nucleus, or 12Be a two-halo nucleus).


3. Charge and mass distributions of the nuclei produced

In this section, we present the distributions of the nuclei yields produced inside EURISOL direct targets, as functions of their charge numbers Z and mass numbers A. The distributions were calculated for each target material retained in Table 1 using MCNPX simulations followed by CINDER runs (short evolution time: 1 ms), to account for the reactions due to the low energy neutron flux. We considered targets of identical radii (18 mm) and same masses (2 kg), for different spallation models and beam configurations. The graphics obtained are presented in Fig. 1. As usual, the shapes of the distributions are formed by successive parts from heavy to light charges and masses: (a) hedges located close to the charge and mass number of each target compound element, (b) decreasing evaporation slopes, (c) “spallation valleys”, progressively filled when the proton energies increase. These valleys correspond to the zone where the evaporation step of the excited target nucleus reaches either the fission process (for fissionable nuclei such as Ta, Pb and U) or another mechanism not fully understood today, namely multi-fragmentation or transition state of asymmetric splitting modes [15] for lighter nuclei. On Fig. 1, note that the quick falls of the production rates in the Z ≈ 87 and A ≈ 215 – 217 regions are not artefacts of the calculation. They result from the very short half-lives (~ s) of the corresponding isotopes, which rapidly decay by alpha radioactivity during the first millisecond of the CINDER temporal evolution.



Fig. 1: Charge and mass number distributions of the production rates per incident proton (atom/s/proton) for the secondary nuclei (R = 18 mm, M = 2 kg, spallation model = INCL4/ABLA, low energetic secondary neutron flux taken into account, CINDER evolution time = 1 ms).



Fig. 2: Impact of the low energetic secondary neutron flux on the charge and mass number distributions of the production rates per incident proton (atom/s/proton) inside Pb, Ta and UC3 targets (R = 18 mm, M = 2 kg, model = INCL4/ABLA, E = 2 GeV, CINDER evolution time = 1 ms).

Starting from the charge and mass number distributions (see Fig. 1), we determined in Table 2 the optimal target materials for the production of selected elements. We verified that these conclusions remain valid for calculations using both spallation models. Note that, if Z and A numbers are not reported in Table 2, it means that two or more materials are eligible. Concerning the 11 elements of interest, we observed that: (a) Fr nuclei can obviously only be produced using UC3 targets, (b) Hg isotopes can essentially be produced using Pb targets, (c) Kr and Sn isotopes can essentially be produced using UC3 targets, (d) Ar, Ni and Ga nuclei can be produced both with Pb or UC3 targets, (e) Ne and Mg nuclei can essentially be produced using Al2O3 or SiC targets, (f) Li and Be isotopes can essentially be produced using Al2O3, SiC or UC3 targets. For all these nuclei, tantalum targets seem to be not optimized. However, at this level it is important to recall that the results presented in this article concern the production of isotopes inside the EURISOL targets. To obtain the corresponding secondary beam intensities, the yields will have to be convoluted with the ion extraction and ionization efficiencies, estimates of which are in progress within Task 2, 3 and 11 of EURISOL DS [16]. Indeed, even if an exotic isotope is produced in high quantities, if its escape time from the target by diffusion/effusion processes reveals too long (due to excessive density or volume of the target material for example), its natural decay could prevent it to constitute a valuable radioactive beam [17 – 19]. The diffusion/effusion times can be calculated using the RIBO code [20]. 

Z
Best material

A
Best material
≈ 7
Al2O3

≈ 15
Al2O3
≈ 15
SiC

≈ 30
SiC
30 ≤ Z ≤ 55
UC3

160 ≤ A ≤ 180
Ta
65 ≤ Z ≤ 70
Ta

185 ≤ A ≤ 210
Pb
75 ≤ Z ≤ 80
Pb

A ≥ 215
UC3
Z ≥ 85
UC3




Table 2: Optimal target materials for the production of radioactive nuclei (R = 18 mm, M = 2 kg, P = 100 kW, spallation models = INCL4/ABLA and CEM2k, MCNPX 2.5.0 simulations followed by 1 ms CINDER’90 evolutions).



Fig. 3: INCL4/ABLA and CEM2k results for the charge and mass number distributions of the production rates per incident proton (atom/s/proton) for the secondary nuclei produced inside Al2O3 and UC3 targets (R = 18 mm, M = 2 kg, low energetic secondary neutron flux taken into account, CINDER evolution time = 1 ms)



Fig. 4: Charge and mass number distribution of the relative ratios between INCL4/ABLA and CEM2k production rates results (targets = Al2O3 and UC3, R = 18 mm, M = 2 kg, low energetic secondary neutron flux taken into account, CINDER evolution time = 1 ms).

We observe on Fig. 2 that the impact of the low energetic secondary neutron flux on the instantaneous production rates (MCNPX calculations followed by 1 ms CINDER evolutions) is almost negligible. Substantial differences appear only for nuclei very close to the target nuclei and for the fission region of uranium targets (especially in the range of fission product yields for 30 ≤ Z ≤ 60 and 80 ≤ A ≤ 160). We observe also, for instance, an increase in the 9Be production rate due to (n,) processes on 12C.
On Fig. 3 – 4, we show that the relative differences between INCL4/ABLA and CEM2k predictions can reach almost a factor 2 for some nuclei, thus leading to a 100 % modelling uncertainty on their corresponding yields (far more than statistical error for most isotopes). This problematic has been investigated during the benchmarks of several spallation models, including CEM2k and INCL4/ABLA codes, done within EURISOL framework [6, 7]. The predictions of these models were tested using experimental data, from ISOLDE [16, 21] and Dubna installations [22] particularly. At this occasion, it was demonstrated that the de-excitation model combined to CEM2k in MCNPX2.5.0 induces a high overestimation of the neutron rich/neutron deficient fission products formation, where INCL4/ABLA was doing much better. At the same time, INCL4/ABLA model is not perfect in other regions: it appeared that it overestimates the production of + particles and gives questionable results for light nuclei. As we will discover it in next section, these modelling specificities can play sometimes an important role in the prediction of the exotic nuclei production rates.


4. Optimization of the production rates of selected exotic nuclei

In this section, we aim to characterize the target configurations that maximize the in-target nuclei production rates of the 11 selected elements (see section 2) and some of their isotopes. To achieve this objective, we considered the targets and beam parameters described in Table 1, simulated with MCNPX 2.5.0. MCNPX calculations were followed by 1 ms CINDER’90 temporal evolutions in the low energetic secondary neutron flux. Finally, the results were plotted for different target lengths L, spallation models and proton energies E to visualise more easily the best configurations.
To conduct the optimization on the proton energy, we assume first that the acceleration cost due to an increase in E would be higher than the cost of an increase in the beam intensity. Thus, if two calculations result in equivalent nuclei yields at a given beam power, we must choose the lower energy configuration. Starting from this point, we divided in the graphics of this section the production rates  of the nuclei by the energy E. Indeed, the optimal proton energy for a given isotope appears consequently as the energy which maximises the /E ratio for a given power P.
To estimate the optimal lengths L and radii R of the targets, we have to remember that the exotic nuclei should still effuse and diffuse efficiently before they can be ionised and post-accelerated afterwards. As the extraction times inevitably increase with the target dimensions, excessive volumes V will induce important losses by radioactive decay and even prevent heavy elements from reaching the target surface. Thus, we must choose L and R values that represent reasonable compromises between significant boosts of the nuclei production rates and limited volume growths. In this article, we don’t show the numerous 3D contour graphics of the production rates obtained for each isotope as functions of the L and R parameters. These graphics can be retrieved in Ref. [23].

4.1. Lithium and Beryllium isotopes

With Fig. 5, we can note that, for both spallation models, the optimal configurations for 11Be (1n-halo nucleus) and 12Be (2n-halo n-magic nucleus) production are the L ≈ 50-75 cm length Al2O3 targets, irradiated with a 1 GeV proton beam. Concerning 7Be (neutron-deficient nucleus), the maximal production rates are obtained using the L ≈ 48 cm SiC targets irradiated with a 0.5 GeV proton beam, with a rather good agreement between CEM2k and INCL4/ABLA predictions. 
For 11Li (2n-halo n-magic nucleus), the optimal configuration is obtained with the L ≈ 75 cm length Al2O3 target irradiated with a 1 GeV proton beam. However, in this case, notable differences appear between the spallation models used. These discrepancies become especially high for the production of 9Li (neutron-rich nucleus), with the consequence that a determination of the optimal targets is almost impossible. As it was expected (see Fig. 1 and Table 2), the Pb, Ta and UC3 targets seem not efficient for producing these nuclei.

4.2. Neon isotopes

From Fig. 5 – 6, we notice anew high discrepancies between the model results for 25Ne (neutron-rich isotope). First, its production with UC3 targets is higher for CEM2k than for INCL4/ABLA. As this target opens also fission channel, we could discard CEM2k results remembering that gives non-reliable predictions for fission products far from stability. This conclusion is reinforced by the appearance of unexpected energy dependence in the CEM2k production rates: /E values increase by a factor 25 between targets irradiated with 0.5 and 2 GeV protons beams. Secondly, production through Al2O3 targets requires successive cascade/evaporations of 3 protons from {27Al+p} compound nucleus, altogether with a + formation. As INCL4/ABLA model tends to overestimate + production, its predictions are consequently to be considered with caution. Finally, the unique target that seems trustworthy for 25Ne production could be the SiC target, for which CEM2k and INCL4/ABLA simulations give rather close values (optimal configuration: L ≈ 32-48 cm with a 1 GeV proton beam). 
For 18Ne (n-magic neutron-deficient nucleus), the best configurations are the L ≈ 48-64 cm length SiC targets, irradiated with a 1 GeV proton beam. However, as for 25Ne case, notable differences are observed between different model outputs. Concerning 17Ne (2p-halo nucleus), it is again difficult to obtain a definitive conclusion. As observed for 25Ne isotopes, the CEM2k energy dependence on the production rates is unusual, which suggests using INCL4/ABLA simulations. The optimal configuration would thus be the L ≈ 48 cm length SiC target irradiated with a 1 GeV proton beam.

4.3. Magnesium and Argon isotopes

On Fig. 6, we observe that the optimal configurations for the formation of 20Mg (n-magic neutron-deficient isotope) are SiC targets with L  64 cm. However, the spallation models considered in this study lead to notable differences. In particular, the predictions using CEM2k show unexpected variations with energy of the production rates: as in the case of 25Ne, the distributions of /E factors with E are rather unexpected. Contrary, the INCL4/ABLA outputs are coherent for Al2O3 and SiC targets and could consequently be more reliable, giving  the optimal energy of protons around 1 GeV. 
For 30Mg (neutron-rich isotope), it is even more difficult to conclude. Indeed, the INCL4/ABLA models exhibit quasi-null values and therefore result in high statistical errors, whereas CEM2k is susceptible to overestimate notably the production rates. Situation is identical for the production of 46Ar (n-magic neutron-rich nucleus) from Pb or UC3 targets.

4.4. Nickel, Gallium, Krypton and Zinc isotopes

As it is shown on Fig. 6 – 8 for both spallation models, the production of 72Ni (p-magic), 81Ga (n-magic), 92Kr and 132Sn (double-magic) neutron-rich fission products is optimal for L ≈ 40 cm UC3 targets irradiated with a 0.5 GeV proton beam. Having in mind the last section 3 remark on the validity domain of CEM2k, we can deduce that this model will overestimate the yields values, whereas the best predictions will be obtained using INCL4/ABLA simulations. 
For 56Ni (double-magic), 63Ga, 74Kr and 107Sn isotopes, it is unfortunately impossible to obtain definitive conclusions. Indeed, INCL4/ABLA calculations exhibit quasi-null results and therefore with high statistical errors (less than 10 events are obtained despite of 5.106 incident protons), whereas CEM2k simulations lead to higher yield values. As 56Ni, 63Ga, 74Kr and 107Sn are all neutron-deficient fission products, we can suppose again that the CEM2k results would be overestimated. INCL4/ABLA results are certainly closer to reality, but would require more precise simulations involving huge computation times in order to obtain good statistical errors.





     
Fig. 5: Production rates per incident proton per GeV for 9, 11Li, 7, 11, 12Be and 17Ne (atom/s/proton/GeV) (R = 18 mm, spallation models = INCL4/ABLA and CEM2k, low energetic secondary neutron flux contribution taken into account, CINDER evolution time = 1 ms).





    

Fig. 6: Production rates per incident proton per GeV for 18, 25Ne, 20, 30Mg, 46Ar and 56Ni (atom/s/proton/GeV) (R = 18 mm, spallation models = INCL4/ABLA and CEM2k, low energetic secondary neutron flux contribution taken into account, CINDER evolution time = 1 ms).






Fig. 7: Production rates per incident proton per GeV for 72Ni, 63, 81Ga, 74, 92Kr and 107Sn (atom/s/proton/GeV) (R = 18 mm, spallation models = INCL4/ABLA and CEM2k, low energetic secondary neutron flux contribution taken into account, CINDER evolution time = 1 ms).





Fig. 8: Production rates per incident proton per GeV for 132Sn, 180, 206Hg and 205, 231Fr (atom/s/proton/GeV) (R = 18 mm, spallation models = INCL4/ABLA and CEM2k, low energetic secondary neutron flux contribution taken into account, CINDER evolution time = 1 ms).

4.5. Mercury isotopes

Using Fig. 1, we note that 80Hg elements are located in the UC3 “spallation valley”, therefore their production is favoured if lead target is employed. We observe that the optimal configuration for the production of 180Hg neutron-deficient nuclei is the L ≈ 27 cm length Pb target irradiated with a 1 GeV proton beam, whereas the best target for production of 206Hg (n-magic) neutron-rich isotopes is somewhat shorter: L ≈ 18 cm Pb target irradiated with a 0.5 GeV proton beam.




4.6. Francium isotopes

Due to its heavy charge number, 87Fr element can only be generated using uranium targets. Concerning the production of 205Fr (neutron-deficient isotope), we proved that both spallation models lead to an optimal L ≈ 40-60 cm uranium target irradiated with a 1 GeV proton beam. However, we noted that the production rates obtained using INCL4/ABLA and CEM2k differed by two orders of magnitude. For 231Fr (neutron-rich isotope), we notice that CEM2k leads to zero values of the production rates. Starting from 235U, 231Fr nuclei can be formed during spallation reactions involving 5 proton emission and the formation of a + pion. From 238U, 231Fr production can be achieved through {6 p + 2 n} or {5 p + 3 n + 1 +} emission from the compound {238U + p} nucleus. These complex reaction channels can explain the quasi-null production rates given by both spallation models. In addition, INCL4/ABLA results can be questioned if we remember that this model overestimates the formation of + particles.

In this section, we determined for a number of exotic nuclei far from stability which target configuration could be retained or discarded for their optimal production. As expected, our analysis was highly sensitive to the spallation models employed and therefore has required dedicated individual studies. For this reason, in the next section, we study the isotopic distributions of the 11 elements of interest in order to examine the “exoticism” of radioactive nuclei that EURISOL targets can produce and evaluate in more detail the reliability of predictions of the different spallation models within MCNPX.


5. Isotopic distribution of the elements of interest

The exotic nuclei studied in the previous sections will be extracted from EURISOL targets, ionised and post-accelerated in order to produce RIB. The isotopes accessible with these beams will be used to feed physical experiments studying the properties of nuclear structure, creation of super-heavy elements, etc. For all these studies, the full isotopic distribution of the given element will impact the quality and duration of the associated experimental programmes. To enlighten this problematic, we studied in this last section the isotopic distributions of the 11 elements of interest presented in section 2. As for previous sections, calculations were done using MCNPX 2.5.0 simulations, followed by 1 ms CINDER temporal evolutions, for targets of identical radii (18 mm) and masses (2 kg). Both INCL4/ABLA and CEM2k spallation models were considered in order to estimate the impact of the chosen physics models on the results.
From Fig. 9 we first notice that the isotopic distributions calculated with the CEM2k model for light nuclei (Mg and Ne) exhibit strong oscillations of the productions rates, whose minima and maxima appear for odd and even neutron numbers respectively. This behaviour could be explained by a strong nucleon pairing effect in CEM2k pre-equilibrium/evaporation step. For the INCL4/ABLA model, this effect can be observed for argon isotopes but vanishes quickly for heavier nuclei. More generally, INCL4/ABLA distributions remain rather smooth and preserve a regular form. On the opposite, CEM2k results are less regular and excessively flat. A good illustration of this unexpected (non-physical) behaviour can be observed for magnesium production, where the production rates remain constant for mass numbers ranging from 20 to 34. This effect remains important for heavier nuclei and confirms thus our remarks (see section 3) concerning CEM2k overestimation of the neutron rich/neutron deficient reaction product formation.





Fig. 9: Isotopic distribution of the production rates per incident proton (atom/s/proton) for Li, Be, Mg, Ne, Ar and Ni (R = 18 mm, M = 2 kg, spallation models = INCL4/ABLA and CEM2k, low energetic secondary neutron flux contribution taken into account, CINDER evolution time = 1 ms).





Fig. 10: Isotopic distribution of the production rates per incident proton (atom/s/proton) for Ga, Kr, Sn, Hg and Fr (R = 18 mm, M = 2 kg, spallation models = INCL4/ABLA and CEM2k, low energetic secondary neutron flux contribution taken into account, CINDER evolution time = 1 ms).

As the low energetic secondary neutron flux contribution must be taken into account, CINDER temporal evolutions (decay and transmutation in neutron fluxes) are necessary. Consequently, decrease in the isotopic yields for 215Fr, 216Fr or 217Fr (see Fig. 10) is for instance observed. Indeed, the half-lives of these nuclei are 0.09 s, 0.7 s and 22 s respectively and this suppression is simply due to the natural decay of the corresponding nuclei within 1 ms decay time, being the CINDER evolution time.
Finally, for both spallation models used in this study, we can observe on Fig. 9 – 10 (Ni, Ga, Kr, Sn) that an increase in the incident proton energy E involves a displacement of the distribution maxima towards lower neutron numbers. This effect is directly linked to the evaporation phase, which results in more excitation energy for higher incident E values and enhances consequently the nucleon emission, mainly neutrons as the light charged particle emission is suppressed due to the Coulomb barrier. For nuclei situated closer to the target elements (Hg for molten lead targets and Fr for UC3 targets), there is no important impact of the proton energy on the isotopic distributions forms, only on their absolute value. Finally, Hg distributions show a pronounced peak for A = 206, probably due to the double magic shell closure Z = 80 and N = 126.
To conclude this study, we sum up in Table 3 the maximal in-target nuclei yields expected to be produced within EURISOL direct targets for the isotopes considered in section 4. The evolution time is 1 ms, the proton energy 1 GeV, the beam power 100 kW and the target radii 18 mm.

Isotope
Optimal target(s)
for E = 1 GeV
Max. yield [atom/s]


INCL4/ABLA
CEM2k
9Li
Al2O3, SiC
2 1011
1012
11Li
Al
109
3 1010
7Be
SiC
1013
1013
11Be
Al
1011
4 1011
12Be
Al
2 1010
2 1011
17Ne
SiC
1010
3 109
18Ne
SiC
1012
7 1010
25Ne
Al, Pb
1010
3 109
20Mg
SiC
2 1011
2 1010
30Mg
Pb (?)
×
4 109
46Ar
UC3 (?)
×
2 1010
56Ni
Pb (?)
×
2 1010
72Ni
UC3
9 109
9 1010
63Ga
Pb, UC3
×
2 1010
81Ga
UC3
1010
1011
74Kr
Pb
×
1010
92Kr
UC3
9 1011
6 1011
107Sn
UC3
×
1010
132Sn
UC3
2 1011
3 1011
180Hg
Pb
1010
1010
206Hg
Pb
4 1011
1010
205Fr
UC3
×
9 1010

Table 3: In-target maximal nuclei yields (atom/s) expected within EURISOL direct targets (proton beam energy = 1 GeV, beam power = 100 kW, spallation models = INCL4/ABLA and CEM2k, target radii = 18 mm, low energetic secondary neutron flux contribution taken into account, CINDER evolution time = 1 ms). Note that E = 1 GeV is not always the best energy for maximizing the nuclei yields (see section 4 and Figs 5 – 8).

6. Conclusion

We calculated the in-target production rates of rare isotopes inside the EURISOL single-stage (direct) targets. Using particle generation-transport codes, we estimated the distributions of the nuclei yields, in terms of their charge and mass numbers, for 320 configurations of cylindrical targets. We determined then, for 11 elements of interest (Li, Be, Ne, Mg, Ar, Ni, Ga, Kr, Sn, Hg, Fr) and 23 of their isotopes far from stability, which target configuration can be retained or discarded to reach the highest production rates. The results presented in this paper will have to be coupled with the ion extraction and ionization efficiencies to complete the calculations of EURISOL RIB compositions.


Acknowledgement

We acknowledge the financial support of the EC under the FP6 “Research Infrastructure Action – Structuring the European Research Area” EURISOL DS Project; Contract No. 515768 RIDS; www.eurisol.org. The EC is not liable for any use that may be made of the information contained herein. We thank O. Bringer for his help in the programming part of this study.


References

[1]	EURISOL design study, available at: www.eurisol.org/site02/index.php
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