Production of a 15C radioactive ion beam based on 18O(n,α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha$\end{document})

In the context of the SPIRAL2 radioactive beam facility the production rate of the neutron-rich 15C nucleus by 18O(n,α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha$\end{document}) has been investigated. In a water target of 20 cm3, enriched in 18O and placed behind the neutron converter, a rate of a few 1010 nuclei per second can be reached with 1mA of 40MeV deuterons. A 18O(n,α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha$\end{document}) cross-section based on the activation method is proposed. It is intermediate between the highest and lowest evaluations available to date.


Introduction
The SPIRAL2 project at GANIL, Caen, France, is designed to extend the range of nuclear physics experiments, especially to neutron-rich and very heavy nuclei [1,2]. The first stage of SPIRAL2 is a high-intensity linear driver able to produce, among other applications, beams of energetic neutrons by stopping deuteron beams in the so-called converter target. The Neutrons-for-Science (NFS) program for neutron experiments [3] is starting.
The most ambitious project is certainly the production of beams of neutron-rich fission products, based on fission of natural uranium with fast neutrons. As a complement, production schemes of nuclei lighter than fission products have been evaluated. That study has been carried out in the frame of the FP7 program of the European Commission and resulted in a PhD [4]. One of the nuclei investigated as a candidate for a post-accelerated beam has been 15 C. The only suitable reaction seemed to be 18 O(n, α) 15 C. Neutron production with a deuteron beam of 40 MeV has been measured [5]. The flux of neutrons above 4 MeV is about 0.7% per deuteron in a target close enough to intercept neutrons emitted up to 30 degrees from the beam axis. This converts to 4.3 · 10 13 neutrons/s a e-mail: tomasz.malkiewicz@csc.fi b e-mail: wladyslaw.h.trzaska@jyu.fi (corresponding author) for a 1 mA deuteron current. However, technical aspects of the envisaged ISOL-based concept were not encouraging. The natural abundance of 18 O of only 0.2% requires a high degree of enrichment. The cost is hardly compatible with a high-temperature solid oxyde target which necessarily deteriorates and needs to be replaced. In addition, efficient release of 15 C (t 1/2 = 2.45 s) from such a target is a priori problematic. These considerations let the 15 C beam project to be, at least, postponed.
An alternative appeared yet during informal discussions among some of the authors of this work. Water enriched in 18 O is commercially available. One major use of it is to be bombarded by protons to generate the 18 F positron source for Proton-Electron-Tomography, e.g. ref. [6] that is used e.g. for clinical imaging of cancer and of some neurological diseases. A water target at room temperature should be suitable for extracting carbon. The native 15 C would combine with oxygen in suspension and quickly leave the liquid as CO 2 bubbles.
When a possible solution to two major technical challenges was found, it became interesting to test the production of 15 C experimentally. There apparently do not exist experimental cross-section data, though the National Nuclear Data Center [7] lists evaluations based on models in the ENDF data library. The cross-sections shown for 18 O(n, α) 15 C span a wide range in amplitude. A single measurement of production rate of 15 C with a 40 MeV deuteron beam was the primary goal of this work. Yet, Fig. 1. Schematic layout of the experiment, not on scale. The neutrons generated in the converter target activate either the foils used to measure the neutron spectrum or react with 18 O in the water target to produce 15 C. For a detailed description, see ref. [9].
there was an opportunity to obtain a rough estimate of the 18 O(n, α) 15 C cross-section by measuring the energy distribution and flux of the neutrons impinging on the target. In this work, four combinations of beam energies and targets enabled a rough experimental cross-section to be determined for the first time.

Experimental procedure
The present work consisted of irradiating a neutronconverter thick target with deuterons from the K-130 cyclotron at the JYFL laboratory to produce fast neutrons, and irradiate a target containing water enriched in 18 O. The neutron spectra were determined by the activation method applied in our former papers, see e.g. ref. [8] and references therein. The production of 15 C was obtained via its radioactivity. A 5297.8 keV γ-ray is emitted with a probability of 63.2% per decay (all nuclear data, unless quoted, have been taken from the ENSDF library in NNDC). The 2.45 s half-life of 15 C requires a fast transport system to carry the irradiated target to a well-shielded location for counting under lower background than in the cave where it has been irradiated. Such a system had been built for a measurement of production rates of fission products in a uranium target [9]. A schematic layout of the experiment is shown in fig. 1. Here are described the main characteristics of the experiment, in so far they are needed for understanding without going back to our previous papers, and the adaptations made for this work.

Targets and transport system
The targets were water enriched in 18 O. The water used in this work was supplied by Campro Scientific [10]. The water had been irradiated by protons to produce 18 F and had been recycled. It consequently contained a residual of acetonitrile (CH 3 CN) solvant. The respective fractions of oxygen isotopes and solvant were obtained with a gas chromatograph and weighting. The fraction of 18 O atoms in the targets was 68(3)%.
The target holder attached to the transport chain was of similar design as the one used in ref. [9], but was bigger and made of aluminum. It had a cavity of 2.5 by 2.5 cm facing the beam and of 3 mm thickness closed with a 1 mm mylar foil. Several water targets of about 2.3 g weight have been used in the course of the experiment. The exact amount of water was obtained by weighting before and after the data had been taken. The cavity could also accomodate metal foils used for measuring the neutron spectrum, squares of 2.5 cm side and 1 mm thickness. The foils were of aluminum, nickel, indium and bismuth. They have been grouped as a stack of Ni, In and Bi foils in the same aluminum holder as it was used for water targets, and as another stack of 3 Al foils in a plastic holder of same geometry. At a given deuteron energy the neutron energy distributions obtained from the analysis of the residual radioactivity of the foils were therefore the same as those which irradiated the water targets. The neutron spectra differed only for the normalisation due to different beam currents and the duration of irradiations. The distance from the 0.5 mm entrance Al window of the neutronconverter target to the center of the 3-foil stack or of the water target was 3.3(1) cm.
The beam current was measured each second using the reading of the charge collected in the neutron-converter target. It allowed numerical integration of the growth and decay equations to be carried out.
The transport system was a loop of a bicycle chain. A single target, either a foil stack or a water target, had been placed in its holder on the chain. The chain was moved by a step motor controlled by a specially-built module. The module sets TTL levels to start and stop the motor, to deflect the ion beam before injection to the cyclotron, and to gate the acquisition. In that way, the beam was off during transport and counting, while counting was enabled only when the target was at its counting position.
Pulsing and gating strongly limits the background due to thermal neutrons having passed the concrete and paraffin shielding. These neutrons (e.g. 1.8 · 10 −10 n/cm 2 per deuteron of 40 MeV [9]) activate material near the detector. In ref. [9] radiation induced by thermal neutrons caused a high rejection of true events because they triggerred the active BGO shields surrounding the Ge-clovers. The acceptance, moreover, varied with the time in the cycle. The acquisition needed several seconds to recover its full acceptance. Here, the BGO shields were replaced with a passive lead shield of most often, i.e. below and on the sides of the detector cap, 10 cm thickness, and else of 5 cm. The stability of the counting rate of a 137 Cs source versus time in the counting period showed that the acceptance rate of events did not vary. It was not any longer necessary to make the acquisition in list mode of (time, energy) events, but only to record energy signals as singles.
The activity does not fully fall back to zero after completion of a cycle. It is the so-called build-up. The numerical calculation detailed in ref. [9] has been used here too. The absence of radioactive filiation renders it very simple.
It is interesting to note that a simple analytic formula can be derived in case of constant beam current. The expression for the number of decays N 1 for a single irradiation, e.g. for the counting of the foils to measure the neutron spectrum, is well known with p the production rate (per deuteron in our convention). Indices refer to irradiation (i), transport or waiting (t) and counting (c) times. We derive the overlap for the k-th reaction σ k n via division by the number of atoms per unit surface n at .
For identical cycles, times and beam current, build-up is governed by a unique parameter a = e −λ tcyc , the cycle time t cyc being t i + 2 t t + t c , while λ is the radioactive constant. The number of decays N nc cumulated during n c cycles can be expressed as which gives the expected value of 1 for a = 0 and (n c +1)/2 in the limit of a → 1 to the correction factor within the braces.

Acquisition and data correction
The γ-rays have been counted by a Ge-detector monocrystal belonging to the phase 1 of the JUROGAM array at JYFL. The counting distance from the detector cap to the center of the 3 mm thick stack or target was 10.2 cm. Corrections for position of the foils in the stack, volume and absorption of the γ-rays have been carried out in the same way as described in our former measurements (ref. [8] and references therein). The energy spectra have been recorded as gated singles with a Canberra Multi-Channel-Analyser running the Canberra Genie 2000 software. A CAEN two-parameter system [11] has also been used. This system directly analyses the pulses from the preamplifier into histograms. It accepts higher input rates and provides better energy resolution than the conventional analogue acquisition chain. Unfortunately, failure to analyse all high-amplitude pulses such as those of the radioactivity of 15 C prevented its use for the quantitative analysis. The system has been yet very useful. Matrices of γ-ray energy versus time in cycle helped greatly to sort background γ-rays on the basis of the evolution of their counting rate during the cycle.
It had been noticed during previous experiments that the dead time given by the MCA is underestimated. A calibration was made by looking at the rate of the 40 K background peak in the presence of a 1 MBq 60 Co source moved from 2.3 m to 10 cm. It covered a range of input rates up to 13 kHz, for which the MCA showed 20% while 27% had been measured. A quadratic correction is suitable in this range. At higher rate the acquisition eventually shows a decreasing dead time, whereas it is actually blocked.
Coincidence-summing corrections have been either calculated in simple cases or have been obtained empirically by recording efficiency curves at various source-to-detector distances. At large distance, e.g. 40 cm, the small dispersion of experimental points with respect to the fit verifies that the analysis of peaks is correct. At 10 cm the dispersion increases as the result of the different individual different probabilities for coincidence summing. The effect was significative only for 206 Bi decay. The decay scheme is very complex, but two lines are little affected by coincidence summing and can be used as reference. They indicate the actual efficiency for a point source after the usual corrections for the finite size of the foil have been applied back. The 895.1 and 1018.6 keV lines are only in prompt coincidence with the 184.0 keV γ-ray which, moreover, is strongly converted (the total internal conversion coefficient is α = 1.67) and attenuated by self-absorption in the Bi-foil and when it passes the In and Ni layers. Indeed, the analytic approximation for γ-rays normal to the foil planes, valid in the large-distance limit, is a transmission of 0.375 of the 184 keV photons. In contrast, the strongest 206 Bi lines used for the analysis of neutron spectra, namely the 343.5, 537.5, 803.1, 881.0 and 1718.7 keV, belong to high-multiplicity cascades. Their apparent efficiency was depressed by about 4%, which, according to this discussion, indicates the correction.

Efficiency of the Ge detector at 5 MeV
Derivation of the production rate p of a γ-ray from the peak area implies the knowledge of its decay branching b γ and of the detector efficiency ε(E γ ). For all lines used in this work, the former are reported with enough accuracy to have negligible impact into the final error. Yet, establishing the Ge-efficiency at 5298 keV, far above the energies of commonly available standards, deserves attention. The efficiency curve up to 1408 keV was made with 152 Eu and 137 Cs standards (3% error). Some of the activated foils allowed for extra points if their lines are distributed partly inside the calibrated range and partly above. Especially useful is 27 Al(n, α) 24 Mg offering γ-rays of 1368.6 and 2754.0 keV. A linear function of log(ε) versus log(E γ ) was used to describe the range from 336 keV -the lowest energy of interest, associated with 115 In(n, n ) 115 In mup to 2754 keV. The relative r.m.s. deviation of the points for 152 Eu and for foils once the correction for their finite size had been applied was 4% with respect to the fitted curve. All in all, this results in a 5% systematical relative error for the efficiency of the lines used to determine the neutron spectra.
A method to get beyond 2.7 MeV is to use the prompt γ-rays in the thermal-neutron capture by materials close to the detector. Relative intensities per target nucleus are listed in the CapGam library of NNDC. Not only fullenergy peaks, but also escape peaks could be exploited. It turned out that the intensity ratios of escape to fullenergy peaks do not obviously depend on the direction of the incoming γ-ray. These ratios have been calibrated as a function of γ-ray energy using the 2754 keV line, together with the prompt lines in thermal-neutron captures in the paraffin shielding ( 1 H) and in other materials near the detector. Ten nA of continuous deuteron beam during typically 4 hours turned out to be sufficient to see many strong lines up to 8 MeV. Among the activities with γ-rays of energies below and above 2.7 MeV, the most intense were due to captures by 56 Fe (supports, chain), 28 Si (concrete) and 35 Cl. The first two were by far the strongest. This is due to a large number of atoms rather than a high capture cross-section (σ = 2.59 b for 56 Fe, 0.17 b for 28 Si). The spatial distribution of these nuclei is not enough well defined to apply corrections back to a point source. In contrast, 35 Cl which presumably is due to spots of cleaning liquid dried on the detector cap has a larger capture cross-section (43.6 b). A measurement with 130 g of NaCl placed at the target position allowed for a source with controlled geometry. After subtracting the background, applying the absorption corrections and a normalisation, the low-energy data points for ε ( 35 Cl) merged with the efficiency curve. The extra points above 2.7 MeV, the most important one at 6111.0 keV, provided references close to the energies of interest. The clearly too low efficiency obtained at 7790.5 keV ( 56 Fe) indicated that the MCA system missed the highest-amplitude pulses too, though only at higher energy and in a smaller fraction than the CAEN system. A quadratic term in log(ε) − log(E γ ) starting to act at 2.7 MeV has been added to the linear term to reproduce the efficiency in the high-energy range. Consequently, the extra error increases like log 2 (E γ /2754). The accuracy of the ratio ε(5298)/ε(2754) is estimated to 12%. The large error is due to statistics because the added salt did increase the level of 35 Cl activity only by 22% of its level in the background.

Measurement procedures
The deuteron beam energies used were 22, 31.5, 40 and 45 MeV. These values result from the request for a short break to change the beam energy. The neutron-converter targets had been planned to be graphite powder all, but D 2 O has been used at 22 and 40 MeV. The change of converter target was meant to lower the energy distribution of the neutrons as a substitute for lower beam energy. It had been seen in ref. [5] that the average neutron energy is lower with D 2 O or even H 2 O than with carbon. The beam current has been adjusted between 10 nA to 100 nA, according to the beam energy, to keep the dead time of the acquisition below 10%.
For neutron measurements a single irradiation of typically half-an-hour, has been carried out for each of the Ni-In-Bi and Al stacks. To account for the very different half-lives of the residual activities, the counting was divided into 3 periods. The first one followed the irradiation for about 2 hours, and was split into short countings for safety. The second one, of 2 to 4 hours, took place when a new beam energy was being prepared, i.e. about 20 hours after irradiation. Finally, the third one was done during a few days after the run to obtain better data about the surviving 6.24 days 206 Bi and 70.9 days 58 Co activities. The number of cycles for measurements of 15 C was about n = 1000. The acquisition was divided in at least 3 parts to allow for a check of consistency. A cycle consisted of an irradiation of 6 s, a counting of 12 s, and transport times back and forth of 2 s each. These values have been chosen to avoid large build-up. Typical values for the terms between braces in the build-up formula, were 1.002 ( 15 C) and 1.133 ( 16 N). The 7.13 s 16 N activity is produced by (n, p) on 16 O remaining in the target.

Neutron spectra
Overlaps of cross-section and neutron spectra for reactions with activation foils are shown in table 1. It is remarkable that overlaps at E d = 40 MeV with heavy-water converter are larger than those at 45 MeV with graphite converter. The gain in neutron flux when using D 2 O instead of carbon is higher than the increase due to higher beam energy, which empirically [8] is (45/40) 2.5 = 1.34. This confirms the observation that at E d = 42 MeV [5] the neutron flux with heavy-water was 1.5 times higher than with graphite. The table does not include the errors due to the Ge-efficiency, nor another 3% error for the calibration of the beam-current reading device. These errors add 6% to the error on the listed overlaps. Since the reference cross-sections are often given with 10% overall accuracy, addition of all errors suggests that the neutron flux is correct within 15%.
The unfolded experimental neutron spectra are shown in fig. 2. The energy distributions for graphite (solid lines) and heavy water (dashed lines) are clearly different, in agreement with measurements at 40 MeV [9]. The neutron spectra to be expected have been obtained from the interpolation and integration of the double-differential distributions measured previously by us with the same method (ref. [8] and references therein) and of spectra integrated on quite the same angles as this experiment at E d = 55 MeV [12]. At short distance the neutron source cannot be regarded as a point, but is a line corresponding to the range of the deuterons. An estimated center of gravity of neutron emission [12] has been used to define the maximum angle of integration.
It is noteworthy that the integrated flux is on the average 3.4 times less than it has been expected. The result of a misalignment of beam axis and foil has been investigated by integration of the experimental double-differential distributions available from our former experiments, and also by a Monte-Carlo simulation. The calculation was carried out with the Particle and Heavy Ion Transport code Systems (PHITS-3.02) developed at the Japan Atomic Energy Agency [13]. The misalignment is expressed by the angle θ which locates the center of the foil with respect to the nominal beam axis, when it is viewed from the center of the converter. For the 40 MeV deuteron beam on the carbon converter target a decrease by a factor of 3 was obtained for a misalignment of about 25 • (experiment) and 30 • (simulation) degrees. These values are very surprisingly large. Yet, whatever had happened, the measurements of activation foils and of oxygen targets have been carried out under the same conditions. The experimental neutron spectra must be the ones to use to unfold the overlaps for 15 C.   fig. 4. Table 2 shows the experimental overlaps and their ratio to those calculated by folding the experimental neutron spectra shown in fig. 2 with the cross-sections discussed above, fig. 4. The errors quoted are due to counting only. They are mainly due to the dispersion of the results for the various subsets rather than to statistical fluctuations. The unweighted average of the tabulated ratios is 1.10. If one recalls the 13% uncertainty on the Ge-efficiency at 6128 keV and a 10% error on the abundance of 16 O in the target, the agreement should appear as an accident. Yet, it tends to show that no large systematical error was bound with the analysis. We note that, if the expected neutron flux had been used instead of the observed one,   The ratios, however, are not constant. They are slightly lower than 1.0 at E d = 22, 31 and 40 MeV, but the ratio is clearly higher at 45 MeV. The factor 1.4 cannot be accounted for by a realistic increase of the high-energy tail of σ. It is, consequently, probable that there exists some uncontrolled experimental factor. While it had been tempting to readjust the scale to the 16 O(n, p) 16 N data, this procedure is difficult to justify, considering that the experimental uncertainties are larger than the correction factor.  ENDF/B-VII are in agreement, but they strongly overestimate the σ n overlaps. The other sets EAF-2010, the lowest one, and RUSFOND-2010 underestimate them.

Cross-section of 18 O(n, α) 15 C
Here also, the high-energy tail of cross-sections have been tentatively extrapolated, except for EAF-2010 for which values are listed. The variation of experimental/calculated overlap ratios is an overall decrease with beam energy. The existence of a set of different neutron spectra could have allowed for an unfolding of the σ n k overlaps in order to extract the cross-section. The method had been similar to the one carried out when the neutron spectra have been obtained, except that the role of spectrum n k (E) and σ(E) had been exchanged. However, the present number of 4 beam energies is too limited for a conventional fit. The cross-section in fig. 5 has therefore been drawn by trialand-error, moving the dots by steps. During the iterations, the χ 2 of the comparison of experimental and calculated overlaps was kept low, while the curve was constrained by the reaction threshold and the attempt to draw the rising Table 4. In-target production rates of 15 C expected per second for 1 mA of 40 MeV deuterons and other conditions like in this work, but with an expected three times higher flux per deuteron, see text. They are the experimental points (Exper) and points calculated from the fold of neutron spectra, fig. 2, with the tentative cross-section, fig. 5  edge to remind the one of the evaluated cross-sections. The curve presented in fig. 5 is therefore a rough and subjective guess of σ.

Production rate of 15 C
The data allow for an estimate of the production rate of 15 C in the target of RIB facility, under the same conditions as this experiment. In table 4 the beam intensity has been raised to 1 mA according to the expected performance of the SPIRAL2 linac. The values have been normalised to a weight of 2 g, somewhat less than the various experimental ones, to allow for easier interpolation versus beam energy. The abundancy of 18 O in the target has been kept to 68%. In addition, the production rates have been scaled up a factor of 3 for the assumed missing neutron flux. The 3% error on the ion-beam current, the 13% due to efficiency of the detector at 5.3 MeV and the 4% on the abundance of 18 O in the target, in total a 14% systematical error, should be added to the listed errors. Comparison of the production rates in the columns "exper" and "curve" (calculated by folding) indicates the quality of the adjustment of the proposed σ(E) for 18 O(n, α) 15 C. The thickness used in table 4 is still 3 mm. A longer target, of a few cm, should not be technically problematic, but the increase might be then less than linear with thickness. The geometry varies because of the longer average distance. It is a minor drawback. Another factor is neutron moderation in hydrogen. It may move some neutrons below the peak of sigma and even below the reaction threshold. Yet, in a target of few cm length, a gain factor of 10 may not be unrealistic, so that the production rate of 15 C nuclei in the target could reach 2 · 10 10 per second.

Summary of the method
Fast neutrons have been produced by stopping deuteron beams in a thick target, the so-called converter. The pro-duction of 15 C via 18 O(n, α) 15 C, using an enriched water target placed behind the converter, has been studied. In addition, a set of targets chosen for their known neutronactivation cross-sections, σ k (E), have been irradiated in the same geometric conditions. The neutron spectrum n(E) was obtained by unfolding the set of experimental overlaps σ k n . Measurements have been repeated at various beam energies in order to obtain different neutron spectra. A tentative unfolding, now with a known neutron spectrum at each beam energy, allowed for a rough estimate of the 18 O(n, α) 15 C cross-section. In the measurement of the production rate all factors need to be known because it is an absolute value. In contrast, the cross-section measurement involves factors, e.g. ion-beam current calibration and the scale of the neutron spectra, which cancel. Those which do not, such as target enrichment and weight, acquisition dead time, nuclear decay data, contributed only weakly to the error. All together, 10% accuracy on the cross-section could have been easily reached if the ratio of Ge-efficiencies at 5 MeV and at, say, 1 MeV had been better known. Statistical errors have not been playing a big part in the present measurement neither, being smaller than systematical errors. Based on the counting statistics obtained in this measurement, the lower limit of sensitivity of such a measurement could be for a cross-section peaking at about 1 mb.
The presence of 16 N lines in the γ-spectra suggests a comparative measurement as an alternative, if a reference σ is well known. Yet, the energy distribution of the neutrons has to be established at each beam energy. In order to ensure fully identical conditions, the target stack should have included foils for neutron spectra and targets for the σ of interest to be irradiated together.

Scheme for production of 15 C
The production rate of 15 C to be expected in the target at SPIRAL2 is estimated from this experiment by scaling the data. With 1 mA of 40 MeV deuterons on a carbon converter, a water target of 6 cm 2 area and 4 cm length with 70% enrichment in 18 O, the 15 C rate is a few 10 10 per second.
The proposed target construction is a cell filled with water enriched in 18 O, with perhaps a supply of oxygen to saturate the liquid, and a tube to extract CO 2 . The cell can be placed behind the neutron converter, quite near and is at room temperature. It is a very safe construction. Release of 15 C combined with oxygen as bubbles should be fast and efficient, in contrast to the options with a heated solid target. The loss factors are therefore those during ionisation, maybe optional charge breeding, and acceleration. They cannot be avoided in the ISOL method and deserve a further independent study. the CAEN acquisition module, and the RADEF group for the beam current monitoring module. They are also indebted in Mr. J. Hyvönen who kindly accepted to change the beam energy outside of his regular schedule. One author (GL) wishes to thank both the GANIL and JYFL laboratories for granting e-mail and computer access.

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