Production of high purity ^{52g}Mn from ^{nat}V targets with α-beams at cyclotrons
PProduction of high purity g Mn from nat
V targets with α beams at cyclotrons Colombi A. ,a,b Carante M.P. ,a Barbaro F. ,c Canton L. ,c and Fontana A. ∗ , a a INFN - Sezione di Pavia b Dipartimento di Fisica, Universit`a di Pavia c INFN - Sezione di Padova ∗ Email: [email protected] of pages: 31Number of tables: 3Number of figures: 15 a r X i v : . [ nu c l - e x ] F e b bstract Radioisotope g Mn is of special interest for multimodal imaging. Using state-of-art nuclear re-action codes, we study the alternative nuclear reaction route nat V( α ,x) g Mn in comparison withthe standard production routes based upon the use of chromium targets. The integral yields of g Mn and contaminants have been evaluated. The main outcome of this investigation is thatthe production of the main contaminant isotope Mn is expected to be lower than with nat
Cr.The study also reveals a large spread in the cross-section data set and points out the need ofmore precise measurements of the reaction nat V( α ,x) g Mn as well as the need of a more accuratetheoretical description.
Keywords — Cyclotron radionuclide production, g Mn, Mn, Mn, multi-modal imaging, α -induced reactions, nuclear reactions modeling 2 . BACKGROUND The search and production of innovative radioisotopes for medical applications is a topic ofgreat interest nowadays, particularly for advancements in theranostics and multimodal imaging.In this work, we are interested in the latter case, which boosts up the diagnostic image informa-tion by simultaneously using two different physical processes. For example, to obtain a combinedPET/MRI scan using a single, manganese-labelled, molecular agent it is necessary to first pro-duce a g Mn-labelled compound for PET and, separately, the same compound containing onlyparamagnetic manganese for MRI. These two molecular agents should have the same chemicalcomposition in order to probe the same biological vector, but they act separately because of thedifferences in sensitivity requested by PET and MRI scans. Manganese radionuclides suitable forPET scan are g Mn, m Mn, and Mn [1]. We are interested here in the production of g Mn:its decay properties, and those of contaminants typically involved in the production methods, arereported in Tab. I.The radionuclide g Mn appears of particular interest because of its relatively long half-life(5.6 d) suitable for the radiolabeling of antibodies and other slow biological compounds for thestudy of pharmacokinetics. Its β + emission is characterized by a very low (i.e. endpoint) energy,about 0.6 MeV, thus leading to a very good resolution of PET scans. On the other hand, g Mndecay to Cr occurs with the emission of three prompt γ rays (with energies 744 . , . . γ -based image reconstruction.The effective dose burden due to the use of g Mn as brain tracer under the simple MnCl chemical compound has been carefully investigated with computational dosimetry codes in Ref. [2].It was found that the radiation dose released by g Mn has been estimated to be about 130 timesthe dose released by Mn. Since the manganese-chloride compounds are retained in the body fora long time ( i.e. g Mn radionuclide affects negatively the effective dose imparted tothe patient.The standard cyclotron-based production of g Mn relies on the following nuclear reactionroutes: Cr(p,n) g/m Mn, Cr(p,2n) g/m Mn, and Cr(p,3n) g/m Mn, which can be exploitedat proton energies within 20 MeV or, even, with 16 MeV cyclotrons [1]. The use of natural3hromium targets has been extensively investigated in the past: Cr constitutes 84% of nat
Cr,while Cr is 10% and Cr is 2%; the remaining 4%, made of Cr, contributes only to contam-inants production but not to the production of the radionuclide concerned. The cross section forthe proton driven reaction route on nat
Cr is large enough to provide sufficient yield for pre-clinicalapplications. Production with natural Chromium targets is favourable also because the radionu-clidic purity is very high [4] for long periods (up to a few months), thanks also to the long half-lifeof g Mn.The main drawback due to the use of a natural target is the expected yield of impuritiesduring the irradiation, in particular the long-lived Mn and Mn radionuclides, mainly via thereaction routes: Cr(p,n) Mn, Cr(p,2n) Mn, and Cr(p,n) Mn. The production of bothlong-lived contaminants can be avoided by irradiation of highly enriched Cr targets and shouldtherefore not impose stringent limitations for potential clinical uses of g Mn. However the use ofenriched material significantly increases the production costs and implies the development of anefficient and cost-effective target material recovery protocol.TABLE IDecay characteristics of the manganese radioisotopes (IT: Isomeric Transition, EC: ElectronicCapture). Radioactive decay products are indicated with an asterisk.Radionuclide Half-life Decay mode Branching ratio Daughter Mn 46.2 m β + Cr ∗ g Mn 5.6 d β + Cr m Mn 21.1 m β + Cr m Mn 21.1 m IT 1.75% g Mn ∗ Mn 3 . × y EC 100% Cr Mn 312 d EC 100% CrThe main purpose of this study is therefore the search for an alternative and competitiveroute to produce g Mn with high radionuclidic purity and high production yield. This work hasbeen carried out in support to the activities of the METRICS (Multimodal pET/mRi Imagingwith Cyclotron produced / Mn and stable paramagnetic Mn iSotopes) project in the frameworkof the SPES/LARAMED research program at INFN-LNL.As a promising radionuclide production pathway, the nuclear reaction route nat V( α ,x) g/m Mn,which is dominated by V( α ,3 n ) g/m Mn, has been investigated. Generally, this possible produc-4ion route is neither mentioned in the medical radioisotope literature (see for a recent review [5]),nor in the IAEA Livechart website [6], an internationally recognized reference for the production ofmedical radioisotopes. The IAEA Livechart website mentions helium beams only for He particlesin the generator-like sequence: Cr( He,3n) Fe to Fe(EC β + ) Mn.The nat V( α ,x) Mn reaction route has been studied by various authors in the last 50 years,both for the ground and for the metastable state. The experimental data for this reaction arecollected in the EXFOR database [7]. Different routes to yield the Mn isotope have been mea-sured and reported in [8] based upon the use of natural targets with Cr, V and Fe bombardedwith proton, deuteron or alpha beams. Both cross-sections and integral yields are given with anestimated error of 13%. A first attempt to compare theory models and experimental results with α -particle beams on a variety of targets, including V, is given in Ref.[9]. Several measurementshave thus been performed with important advances in the experimental techniques and comparedwith reaction models (statistical and pre-equilibrium mechanisms) that have been gradually refinedand improved over the years: [10], [11], [12], [13], [14], [15], [16], [17], [18]. Finally, new results onalpha particles on Vanadium targets have been published recently, in [19].Overall, the measured excitation functions show a similar structure with an initial peakfollowed by a decrease: the peak corresponds to alpha emission mainly due to the evaporationprocess of the compound nucleus, while the tail is dominated by the pre-equilibrium decay. Thespread of collected data is significant and can be attributed to the long period over which the datawere taken and to the different experimental techniques used over the years. The large number ofpublished measurements and the large spread in the data demands for an accurate nuclear dataevaluation of the cross sections, given its importance for medical applications. In addition, itis important to assess also the theoretical uncertainty arising from the different nuclear modelsemployed and this will be taken into account in the present work.To identify the energy intervals and irradiation conditions most suited for the radionuclideproduction, different nuclear model tools have been used. After performing the excitation functionsanalysis, the thick target yield for a hypothetical irradiation with α particles, on a nat V target of agiven thickness, has been calculated and from there the time-evolution of the related isotopic andradionuclidic purities, assuming a sufficiently long cooling time.At last the results obtained by using nat
V targets and α beams have been compared with5hose derived from natural Chromium with proton beams. In addition, a comparison with enrichedChromium targets, considering both proton and deuteron beams, is provided. II. METHODSII.A. Nuclear model calculations
The study of the aforementioned highlighted nuclear reaction routes implies the adoptionof different models to describe both the compound nucleus formation/decay and pre-equilibriumdynamics. To this purpose three of the most up-to-date nuclear reaction codes: Talys [20], Empire[21] and Fluka [22] have been used. The nuclear reaction mechanisms relevant for radionuclide’sproduction at cyclotrons are dominated by the compound nucleus formation and by pre-equilibriumemission and all the three codes are based upon the nuclear reaction models developed to describethese processes. A quick review about all nuclear models used can be found in [23] and in thecodes’s references.Talys (version 1.9) is a software for the simulation of nuclear reactions that includes manystate-of-the-art nuclear models to cover most of the reaction mechanisms encountered in lightparticle-induced nuclear reactions [20]. The nuclear reaction rates evaluated by the code arebased upon the Hauser-Fesbach model [24] for the equilibrium mechanisms and on four differenttheoretical frameworks for the pre-equilibrium process. The level density is another importantaspect to consider for describing the reaction and Talys has six possible options for its description,ranging from the simplest Fermi gas model to more complex microscopic approaches.Empire (version 3.2.3) is a nuclear reaction code based on various nuclear models and designedfor calculations over a broad range of energies (from a few keV up to hundreds MeV) and variousincident particles (nucleons, photons, deuterons and light ions). The code accounts for the majorcurrent nuclear reaction models, such as Optical Models, Coupled Channels and DWBA (DistortedWave Born Approximation) models for elastic and inelastic scattering; Exciton model and HybridMonte Carlo Simulations for pre-equilibrium emission; and finally the Hauser-Feshbach model forcompound nucleus [21].Fluka (development version 2018.2) is a general purpose code for modelling particle transportand interaction with matter; it covers an extended range of applications, spanning from proton andelectron accelerator shielding to calorimetry, dosimetry, detector design, radiotherapy and more [22,65, 26]. The code, based on the PEANUT (PreEquilibrium Approach to Nuclear Thermalisation)module, can be used to calculate the production of residual nuclei and, in many cases, resultshave already been validated with experimental data. Residual nuclei (and, thus, radionuclides)emerge directly from the inelastic hadronic interaction models and can be calculated for arbitraryprojectile-target configurations (including nucleus-nucleus interactions) and energies. Regardingthe production of isomers, the Fluka version used in this work does not have a built-in routine topredict the correct branching for the production of different states of the same radionuclide, butit distributes the cross section equally over the different states: for this reason, we only considerthe results of Fluka in the cases where the separation between ground and metastable nuclides isnot explicitly involved.
II.B. Uncertainty evaluation with Talys
A total of 24 different model combinations may be available with Talys by taking advantageof the different possible level density and pre-equilibrium options. Many calculations found inliterature report the use of a default option, however this is not always the best choice and thereforealternative option configurations have been introduced and evaluated. As an exemplum giving, theso-called “Talys adjusted” configuration reported in Ref. [27] has been often used. However, bothcases rely on the selection of a single model for level density and pre-equilibrium, disregardingall the others, and not exploiting the full potentiality and versatility of the code. In the next,we introduce a novel way to deal with the theoretical variability provided by the different models.Instead of plotting all the 24 curves, we compare the different models introducing a statistical band,along with similar ideas explored in Ref. [28]. Starting from the 24 different model calculations, aband is constructed from the interquartile range, given by the difference between the third ( Q ) andthe first ( Q ) quartile. In addition we introduce for each energy a “Best Theoretical Evaluation”(BTE) of the cross section by taking the average of the first and third quartile, and associate to itthe uncertainty given by the half-width of the interquartile band: σ BT E = Q + Q , ∆ σ BT E = Q − Q . (1)Some models of the ensemble may show a too large variability, over- or under-estimating by largethe data. If we consider the interquartile band, spanning quartiles Q and Q , only the central70% calculations are retained, and this leads to a more reasonable description.In this way a reference value for cross-section depending upon all models provided by thecode, and a statistical uncertainty depending upon the variability of the models themselves, mayat last be obtained. The same procedure has been applied to get an assessment not only for crosssections, but also yields, activities, isotopic, and radionuclidic purities, both for the radionuclideconcerned and as well as its main contaminants. The BTE approach derives from descriptivestatistics and connects to the concept of trimmed average: it provides a robust estimator of thetheoretical cross section and allows to discard, in a consistent way, the outlier values provided bya subset of the models. These outliers are shown, for instance, in Fig. 1 with the two dashedlines, corresponding to the maximum and minimum values provided by the 24 model calculations.This approach is alternative to other, more sophisticated techniques, developed to introduce atheoretical uncertainty band, like for example the multistep method [29], in which a rescaling ofthe models to experimental data is performed, or total Monte Carlo techniques [30], in whichthe parameters of the models are sampled randomly to assess the variability of the calculationoutcomes. Our description appears more practical, since it trims the calculations at the edge ofthe set and provides quickly the final result in a single deterministic step. III. RESULTSIII.A. Cross sections analysis
The cross section of the nuclear reaction route nat V( α ,x) g Mn is plotted in Fig. 1. Theexperimental data taken from the available databases (EXFOR) are compared with the calculatedresults obtained with the reaction codes Talys, Empire, and, when relevant, Fluka (see SubSect.II.A). A dispersion of data, accumulated over a period of few decades, may be clearly seen, thuscomplicating the precise evaluation of the production yield. Talys results are shown following thescheme discussed in section II to take into account the variability of the models: a “best theoreticalevaluation” (solid line), an interquartile range (gray band), and the min and max values resultingfrom all the models considered (dashed lines). Unfortunately, even taking into account the varietyof Talys models, in the energy region below 45 MeV, calculations overestimate significantly thetrend of data, however the spread of data prevents a precise determination of the overestimationfactor. Likewise, Empire calculations are slightly lower than the measured cross section, but the8xtension of the underestimation is difficult to be evaluated. As it will be shown in the following,the problems with the theoretical description seem to be restricted to this particular channel;indeed the description of the other production routes or the contaminants cross-sections turn outto be in better agreement. In this work we do not provide a solution to this problem, e.g. byan attempt to improve the theoretical models. Nevertheless, the analysis of yields and puritiesperformed from various sources in the second part of this work (see Tab. II) are deemed sufficientto consider this route of interest. C r o ss s e c t i on ( m b ) Energy (MeV)
Nat V( α ,x) Mn Talys BTETalys Q -Q Talys min-maxEmpireDmitriev 1969Bowman 1969Michel 1983Rama Rao 1987Levkovskij 1991Sonzogni 1993Singh 1993Ismail 1993Chowdhury 1995Kumar 1998
Fig. 1. Cross section for nat V( α ,x) g Mn route as predicted by three different codes and comparedwith the experimental data currently available in the EXFOR database [7]. To take into accountthe theoretical uncertainty of the all the models available in Talys, a grey band for the quartiles Q - Q and two dashed line for the minimum and maximum are plotted.The cross-sections ratio between g Mn and the sum of all Mn contaminants expected crosssections is shown in Fig. 2, in order to determine the optimal energy region where such a quantityis as high as possible. Based upon the codes expected cross-section trends, the resulting max-imum for such a ratio turns out to be close to the maximum of the cross section at 40 MeV.Performing an irradiation in an energy range around such a value would thus lead to an high aspossible radionuclide quality for the g Mn, having the minimum expected level of contamination.This residual contamination, however, would not be negligible, since the cross section ratio has a9aximum value of about 0.6. C r o ss s e c t i o n r a t i o ( a d i m ) Energy (MeV)
Mn/( Mn+ Mn+ Mn+ Mn+ Mn+ Mn+ Mn+ Mn)
Talys BTETalys Q -Q Talys min-maxFlukaEmpire
Fig. 2. Ratio of the calculated cross sections for nat V( α ,x) g Mn and total of other Mn isotopes.Nevertheless, it is important to observe that the majority of the produced isotopes are char-acterized either by a very short, or by a very long, half-life. In particular, Mn, Mn, g/m Mn, Mn and m Mn have half-lives smaller than one hour and their contamination, both in termsof isotopic and radionuclidic purity, are thus negligible just after a few hours. Mn is stable anddoes not affect the radionuclidic purity. Moreover, it is produced in the electromagnetic channelwith very low excitation function. Also, Mn, whose half-life is of about 3.6 × years, does notaffect the radionuclidic purity in a significant way and does not release a significant dose to thepatient. Finally Mn, with an intermediate half-life of about 312 days, could represent an issuein terms of the expected dose increase to the patient.For this reason, in Fig. 3 the cross section of the reaction nat V( α ,x) Mn is shown. Theagreement between experimental data ([13], [15], [16], [17], [18], [19], [31], [32], [33]) and the threenuclear codes is satisfactory, especially if compared to Fig. 1. Still, there are about 25% differencesamong the various calculations around the peak (at 13 MeV) which is not far from a 30% variabilityof the experimental data in the same energy region. On the contrary, at the maximum production10 C r o ss s e c t i on ( m b ) Energy (MeV)
Nat V( α ,x) Mn Talys BTETalys Q -Q Talys min-maxFlukaEmpireLevkovskij 1991Sonzogni 1993Singh 1993Hansper/A 1993Hansper/B 1993Singh 1995Chowdhury 1995Kumar 1998Peng 1999Alì 2018
Fig. 3. Cross section for nat V( α ,x) Mn. The meaning of the theoretical lines and bands is thesame as in Fig. 1.of g Mn, around 40 MeV, the cross section for Mn is very low. This fact is plain if we take intoaccount only Mn as contaminant and we plot the quantity r = σ g Mn σ g Mn + σ Mn , (2)as shown in Fig. 4. Above the energy of about 30 MeV, the production of g Mn is almostpure, with respect to its most dangerous contaminant. In the next Section we will focus on theregion around 40 MeV, to evaluate the g Mn production yields and purities.
III.B. Yields and purities
Once the most convenient energy window for the production of g Mn is identified, it ispossible to plan the optimal irradiation conditions. The production rate of a nuclide for a beamimpinging on a target of a given material and thickness can be calculated with the formula [34, 35] R = I z proj | e | N a A (cid:90) E in E out σ ( E ) (cid:18) dEρ t dx (cid:19) − dE , (3)11 C r o ss s e c t i on pa r t i a l r a t i o ( ad i m ) Energy (MeV)
Mn/(
Mn+ Mn)
Talys BTETalys Q -Q Talys min-maxFlukaEmpire
Fig. 4. Partial ratio of the calculated cross sections for nat V( α ,x) g Mn and the Mn isotope.The energy window with the possibility of high purity production of g Mn due to the favorableinterplay of the different reactions thresholds is clearly visible.where I is the charge per unit time hitting the target, z proj the charge state of the incidentparticle (2 in the case of a completely ionized He beam), e the electron charge, N a the Avogadronumber, A the target atomic mass, E in and E out the energy of the projectile impinging on the targetand after exiting from the target, respectively, σ ( E ) the production cross section for the nuclide, ρ t the target density and dE/dx the stopping power of the projectile in the target, calculated withthe Bethe-Bloch formula [36]. In this case the irradiation parameters are: beam current of 1 µA ,incident energy of 48 MeV, target thickness of 200 µm (corresponding to E out = 33 . Mn to Mn are produced in this energy window.The yield rate for all the Mn isotopes of interest are calculated, and for g Mn it was foundto be between 5.6 × and 1.45 × nuclei · s − , depending upon the different codes and models.From the rate, the time evolution of the number of nuclei of a specific isotope can be obtained,during and after the irradiation, by means of standard Bateman equations. Every manganeseradionuclide of interest decays in different chemical elements, with the only exception of m Mn,which decays in g Mn with a branching ratio of 1.75% and with a half-life of about 21.1 minutes.12inally, the isotopic purity ( IP ) of g Mn may be calculated, as IP = n g Mn n Mn + n Mn + n g + m ) Mn + n Mn + n g + m ) Mn + n Mn + n Mn + n Mn , (4)where n is the number of nuclei. The corresponding radionuclidic purity ( RN P ) is given by
RN P = A g Mn A Mn + A Mn + A g + m ) Mn + A Mn + A g + m ) Mn + A Mn + A Mn , (5)where A represents the activity of the specific isotope. In Figs. 5-6 the time evolution of IP andRNP are shown, both for a short and a long time scale. I P ( ad i m ) Time (d) nat V( α ,x) Mn Isotopic Purity
Talys BTETalys Q -Q Talys min-maxEmpire 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.2 0.4 0.6 0.8 1
Fig. 5. Post-irradiation time evolution of the g Mn Isotopic Purity (IP) expected by nuclearmodels for a long time window with an hypothetical one hour irradiation of a nat
V target with abeam energy of 48 MeV, thickness 200 µm (corresponding to an exit energy of 33.9 MeV), currentof 1 µA . The inset shows the evolution for the first 24h, including the irradiation (i.e. build-up)time. At the End of Bombardment (EoB), the IP achieves values of about 0.45-0.75 (Fig. 5), andthe disagreement between the two codes reflects the different results for the cross sections alreadyshown in Fig.1. The value is not so high due to the production of Mn which can be consideredstable at the timescale shown, and therefore does not affect significantly the RNP. Indeed, the13 RN P ( ad i m ) Time (d) nat V( α ,x) Mn Radio Nuclidic Purity
Talys BTETalys Q -Q Talys min-maxEmpire 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
Fig. 6. Time evolution of the RadioNuclidic Purity (RNP) expected by the considered nuclearmodels for a long and a short (inset) time window.RNP achieves a value close to 1 after few hours, due to the very short half-lives of Mn, Mnand m Mn, as well as to the small production of Mn and the negligible activity for Mn.The Talys BTE value (with the corresponding uncertainty) estimated for the activity of g Mn at EoB is about 6 . ± .
80 MBq, while the values foreseen by the Empire code gives 3.20MBq. It is important to observe from Fig. 1 that the experimental cross-section data stand inbetween the upper limit identified by the Talys BTE calculation and the lower limit characterizedby the Empire prediction. Despite this discrepancy, the RNP remains however close to one forabout 20 days for both calculation tools, as shown in Fig. 6. For this reason the nuclear reac-tion nat V( α ,x) g Mn may be considered of particular interest as an alternative route for g Mnproduction. 14
V. DISCUSSIONIV.A. Comparison with other production routes
The standard route usually considered for the cyclotron production of g Mn is nat
Cr(p,x) g Mn and has been recently reviewed in Refs. [4, 5]. The first reference reports newdata for the cross section and confirms the peak between 12 and 16 MeV, suited for an hospital-based cyclotron production. The second reference is a comprehensive and historical review onthe production of medical radionuclides and refers to the nat
Cr(p,x) g Mn reaction as the mainproduction pathway. Also the deuteron-induced reaction Cr(d,2n) g Mn, with enriched target,has been previously explored as an alternative route and compared with the proton channel [12].Cross sections, yields, rates and expected radionuclide purities have been evaluated also forreactions involving chromium targets. In particular, in Fig.7, the cross sections from nat
Cr and nat
Vtargets are compared. In the figure are also plotted the experimental data from EXFOR databasefor the nat
Cr(p,x) g Mn reaction (see Refs. [37], [38], [39], [40], [41]). Instead, the experimentaldata for nat V( α ,x) g Mn are here not included because they have been already shown in Fig.1.Cross section values for both reactions routes appear comparable in magnitude, and obviouslyshifted in the energy range. In case of nat
Cr targets, Empire provides good reproduction with aslight overestimation of the peak, while Talys provides an almost excellent description, with aminimum underestimation of the peak. The situation with nat
V targets has been extensivelydescribed while commenting Fig.1, with the main outcome that Talys probably overestimatessignificantly the data, the Empire calculations may produce a possible underestimation. However,the experimental data are excessively scattered to get a definitive conclusion.It is interesting to compare also the radionuclidic purities that can be obtained with bothreactions, as shown in Fig. 8. The two reaction codes show a different trend, which reflects thedifferent behaviour with the estimated cross section trends. Talys highlights a more favorabletime evolution of the RNP for α impinging on natural V target. On the contrary, Empire showsa similar behaviour for the two RNPs with a very small advantage for the Chromium targets.However, to draw a definitive conclusion, better cross section experimental data for the reaction nat V( α ,x) g Mn are nevertheless needed.For all the production routes considered, we assess from the integral yields the irradiation15 C r o ss s e c t i on ( m b ) Energy (MeV)
Cross sections for
Mn production routes nat
V Talys BTE nat
V Talys Q -Q Cr Talys BTE nat
Cr Talys Q -Q V Empire nat
Cr Empire 0 50 100 150 200 250 300 350 400 0 10 20 30 40 50 60 C r o ss s e c t i on ( m b ) Energy (MeV)
Cross sections for
Mn production routes
Barrandon 1975Klein 2000Titarenko 2011Buchholz 2013Wooten 2015
Fig. 7. Comparison of g Mn production cross sections from nat
Cr (proton beams) and nat
V ( α beams) targets. Data are shown only for nat Cr targets (refer to Fig. 1 for data on nat
V targets). RN P ( ad i m ) Time (d)
Nat V( α ,x) Mn vs
Nat
Cr(p,x)
Mn Radio Nuclidic Purity
Nat
V Talys BTE
Nat
V Talys Q -Q V Empire
Nat
Cr Talys BTE
Nat
Cr Talys Q -Q V Empire
Nat
Cr Empire 0.98 0.985 0.99 0.995 1 1.005 1.01 0 5 10 15 20
Fig. 8. Comparison of RNP for nat
V vs nat
Cr.energy range corresponding to the highest purities expected. This kind of optimization is crucialbecause the quantity and quality of the final product are essential for following radiochemistry16tudies, dosimetric evaluations and, eventually, pre-clinical studies, to confirm the feasibility of theproduction route.In Figs. 9 and 10 the integral yields obtained for the reactions nat V( α ,x) g Mn and nat
Cr(p,x) g Mn are respectively shown. For comparison, in the latter figure the integral yieldobtained with the enriched chromium target, Cr(p,n) g Mn has also been added and finally, theanalysis has been completed by considering also the production channel Cr(d,2n) g Mn, shownin Fig. 11.In all cases, the reference irradiation parameters assumed in this work to estimate the integralyields are: 1h irradiation time; 1 µA for the beam current; and a target thickness large enoughto stop completely the beam inside the target. Curves show the variation of the integral yieldagainst the incident beam energy, and represents the production yield for a hypothetical beamstopper target. From these curves it is possible to draw the yield for a target of a given thicknessby taking the difference between the values corresponding to the ingoing and outgoing energies(values delimited by the green shaded area). For all targets a thickness of 200 µm has been assumedand the beam output energy of such target, E o , has been derived from the Bethe-Bloch equation[36]. The yield of a target with 200 µm thickness is then given by the difference of the integralyield evaluated at E i and E o , where E i denotes the incoming-beam energy.In all cases concerned, the beam energy window has been optimized taking into account thesteepness of the integral yield, the minimization in the contaminant production and the 200 µ mconstraint of the target thickness. The resulting energy ranges are reported in the left column ofTab. II, and highlighted as well by a vertical green shaded area in Figs. 9, 10, and 11.The results with nat V are given in Fig. 9 with the integral yields obtained by Talys andEmpire codes. For Talys the results are given in terms of the BTE value and its associateduncertainty, following Eq. 1, which is highlighted as a gray band on figure. In addition, the databy Dmitriev at al. [8] are reported as well, along with a linear interpolation obtained from thesedata. As it is clearly shown, it appears that Talys overestimates the yield by a factor of about 2,in line with our findings with the cross sections (see Fig.1). On the other hand, the experimentaldata (and/or its linear interpolation) and Empire calculations appear fairly consistent.In Fig. 10 the integral yields for a proton beam on nat
Cr as well as on 100% enriched Cr targets are compared. The results are similar with the enriched target case overperforming17 I n t eg r a l y i e l d ( M B q / µ A h ) Energy (MeV) nat V( α ,x) Mn Integral yield
Talys BTETalys Q -Q Talys min-maxEmpireDmitriev 1969Dmitriev 1969 best fit line
Fig. 9. g Mn integral yield for a α -beam with 1 µA current and one hour irradiation time. Thegreen shaded area indicates the optimized energy interval used for the 200- µ m thick target.with respect to the natural one. The expected results from Talys are very close to the IAEArecommended yields [6] for the enriched chromium target, and similarly, for the natural target,they are close to the data interpolation. In both cases, Empire gives similar results, with a slightyield overestimation.In Fig. 11 the case of deuteron beam on enriched Cr target is plotted. In the range ofinterest, [20-15.5] MeV, Talys and the IAEA recommended values are very close, with the IAEArecommended curve slightly steeper, while Empire results are still close although somewhat lower.The analysis performed in Figs. 9, 10, and 11 allows to draw the production yields of atarget of given thickness, for instance the benchmark 200 µ m assumed in our comparative study.Such quantity is readily calculated as the difference of the plotted integral yields at the bombardingenergy E i , and at the target exit energy E o , which takes into account the energy loss in the material.Tab. II compares the derived g Mn production yield determined by the nuclear reaction codes,and when available, from experimental measures [8], as well as from nuclear data evaluations [6].We have added in the comparison also the output obtained by the ARRONAX Radionuclide YieldCalculator (RYC) [42], based on the TENDL library [30].18 I n t eg r a l y i e l d ( M B q / µ A h ) Energy (MeV) Cr vs nat
Cr(p,x)
Mn integral yield Cr(p,n) Talys BTE Cr(p,n) Talys Q -Q Cr(p,n) Empire nat
Cr(p,x) Talys BTE nat
Cr(p,x) Talys Q -Q Cr(p,x) Empire nat
Cr(p,x) Dmitriev 1969 nat
Cr(p,x) Dmitriev 1969 best fit line Cr(p,n) IAEA recommended
Fig. 10. g Mn integral yield from nat
Cr and enriched Cr targets for a proton-beam with 1 µA current and one hour irradiation time. The green shaded area indicates the optimized energyinterval used for the 200- µ m thick target.It is difficult to recommend a value for the first route reported in Tab. II and this reflectsthe large experimental uncertainty obtained for the cross section, as reported in Fig. 1. ClearlyTalys evaluations and the similar RYC value overestimate the yield, while Empire probably under-estimates it. One can tentatively extract a significant guess by observing that the Empire curvereproduces the overall trend of the cross section data, if it is rescaled by a factor 1.5/1.7. Underthis assumption, we can accordingly rescale the Empire yield in Tab. II obtaining approximately4.3/4.9 MBq/ µ Ah. This crude ”guesstimate” compares well with the production yield of 4.4 calcu-lated with Talys for protons on nat
Cr target (see the second line in the Table). As one can see fromFig.7, for this reaction the Talys results are quite reliable and the corresponding yield provides agood estimate. Therefore, we may conjecture that the production yield for the two routes couldbe very similar, although a definitive conclusion can be drawn only with much better data forthe nat V( α ,x) g Mn cross section. Alternatively, a careful nuclear data evaluation of the existingmeasurements for this cross section is strongly needed. The comparison in Tab. II is completedwith two Cr-target reactions, the first with proton and the second with deuteron beams. These19 I n t eg r a l y i e l d ( M B q / µ A h ) Energy (MeV) Cr(d,2n)
Mn Integral yield
Talys BTETalys Q -Q Talys min-maxEmpireIAEA recommended
Fig. 11. g Mn integral yield for a deuteron-beam irradiation on enriched Cr. The irradiatonconditions are the same of Figs. 9 and 10.two routes are well known and listed in the IAEA medical radioisotopes production database [6]with recommended evaluations for the cross sections. The use of enriched material in the Cr(p,n)route provides an additional 15% production yield in comparison to nat
Cr, with the advantage ofa drastic reduction of contaminants, as will be shown in Tab. III. The Cr(d,2n) route produceseven more g Mn (almost a 100% addition), but here the contaminant reduction is not so efficient.The production of the most relevant contaminants derived under the same irradiation condi-tions are given in Tab.III. By far the most critical radionuclide is Mn. In the case of α particlescolliding on nat V the cross section peaks around 12/14 MeV and rapidly decreases toward very lowvalues at higher energies, in particular in the energy interval of our interest. By comparing data,the yield of this contaminant is significantly lower by using nat
V targets than for nat
Cr ones. Thisis a clear advantage when comparing natural targets. Obviously, the use of about 100% enrichedtargets allows to drastically reduce or completely remove the level of contamination, as shown inthe third and fourth line of Tab. III.The effect of the contamination by Mn on the total dose released to the patient has notbeen carefully analyzed yet [1], but it should be of minor importance due to its very long half-life.20he very small activities reported in Tab. III for this radionuclide strengthen this assumption.Nevertheless the nat
V route produces a slightly larger yield than the nat
Cr one, but still small andvery close to each other. For the enriched target cases the route via the reaction Cr(d,n) Mngives yield comparable to those with natural targets, while the Cr(p, γ ) Mn reaction gives evensmaller yield.TABLE IIComparison of the four production routes analyzed. The irradiation parameters correspond to 1 µ A current and 1 h irradiation time. The optimized energy windows for each route, shown inthe left column, correspond to a 200 µ m target thickness. We report Talys calculations with atheoretical error evaluation depending on the variability of the models.Reaction [E i -E o ] (MeV) Yield (MBq/ µ Ah)Talys Empire RYC Data fit orinterpolation nat V( α ,x) g Mn [48-33.9] 6.28 ± nat Cr(p,x) g Mn [17-14] 4.41 ± Cr(p,n) g Mn [17-14] 6.64 ± Cr(d,2n) g Mn [20-15.5] 12.00 ± Mn and Mn, with the same irradiation conditions discussedin Tab. II. Contaminants YieldTalys Empire RYC Unit nat V( α ,x) Mn 1.94 ± µ Ah nat Cr(p,x) Mn 4.80 ± Cr(p,x) Mn - - - Cr(d, γ ) Mn 7.52 ± µ Ah nat V( α ,x) Mn 10.6 ± µ Ah nat Cr(p,x) Mn 7.52 ± Cr(p, γ ) Mn 0.23 ± Cr(d,n) Mn 9.90 ± . CONCLUSION The nat V( α ,x) g Mn nuclear reaction route, as a viable alternative for the production of theradionuclide g Mn, has been investigated in the present work. This radionuclide is of significantmedical interest for the innovative PET-MRI multi-modal imaging technique. This uncommonreaction route has not been considered so far for the production of the radionuclide concerned anddoes not often appear in the relevant literature. We have compared this production method withthe well known approach via low-energy protons on nat
Cr targets. The study has been completedby also considering enriched Cr targets bombarded both with proton and deuteron beams.The experimental data so far available on world databases for nat V( α ,x) g Mn appear with aremarkable spread, thus preventing a precise determination for the cross section values. All Talysmodels that we have included in the calculations provide an overestimation of the peak behaviouraround 40 MeV, while the Empire results somewhat underestimates the cross section. Althoughthe nuclear model tools used in the present work do not describe the specific reaction for g Mn inan optimal way, they provide at least an upper (Talys) and lower (Empire) bound that delimit themeasurements. The cross sections for all other Mn contaminants are in better agreement and havebeen considered to find out a favorable production energy window, in terms of yields, isotopic andradionuclidic purities.Our study shows that, even if we consider the most conservative estimation from Empire,the production yield is significant to make nat V( α ,x) g Mn of interest. In addition, concerningthe production of the main contaminant, Mn, the reaction provides a better product in termsof purity with respect to nat
Cr(p,x) g Mn. One must acknowledge the fact that with nat
Cr theproduction can be achieved with hospital cyclotrons exploiting low-energy proton beams, while the nat
V production requires a 50 MeV cyclotron and α particles, which can be currently found onlyin few research centers. Nevertheless, for infrastructures where this kind of machines are available,it might be convenient to consider this alternative reaction.The g Mn production based upon enriched Cr targets presents significant advantages inproduction yields and quality, due to minor presence of Mn contaminants, but on the other handit requires the use of more expensive materials and specific technologies for target recovery.22
ECLARATIONSEthics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Availability of data and material
All experimental data used for this work have been referenced. Contact the correspondingauthors for material and data presented in this work.
Competing interests
The authors declare that they have no competing interests.
Funding
This research was carried out within the METRICS applied physics program (2018–2020/2021),approved and founded by the INFN–CSN5 (Technological Research Committee).
Author’s contributions
All authors contributed equally to the work presented.
Acknowledgements
The authors are grateful to Arjan Koning, Roberto Capote, Paola Sala, and Alfredo Ferrari,for stimulating discussions and insights about the use of the nuclear reaction codes. Discussionswith Laura De Nardo and Juan Esposito on the research subject are thankfully acknowledged.
APPENDIX
We focus here on how the enrichment of both chromium and vanadium targets affects theproduction of g Mn and contaminants. Specifically, we illustrate in Figs. 12 and 13, respec-23ively, the time evolution of RNP with proton and deuteron beams impinging on Cr target withhypothetical 100% enrichment.If we compare these two figures with the corresponding RNP obtained with natural targets,Fig. 8, it is evident that very high purity levels can be maintained over a much longer time in caseof enriched targets. With natural targets, more than 20 days are needed before RNP reduces by1.5 %. Much higher values are needed for protons and deuterons on enriched targets, 150 and 65days, respectively. However, considering the 5.6 d half-life of g Mn, the result with natural targetsappears adequate to maintain a sufficiently high RNP, at least for more than three half-lives.Vanadium has to be considered a monoisotopic element made of V, but the presence in smallfraction (0.25%) of the radioactive V, with 1.5 × y half-life, does not make it mononuclidic.It might be odd, but since it is possible to find commercially samples of vanadium with Vabundance different from nat
V, we discuss how this could affect the production. In Figs. 14 and 15the cross sections for V( α ,x) g, Mn and V( α ,x) g, Mn provide a clear representation of thereaction dynamics at stake, and exhibit the fine balance between production of the radionuclideof interest and its main contaminant. Following the scheme previously adopted, the calculationshave been performed by evaluation of the Talys interquartile range and corresponding BTE.Radioactive V has the advantage of a minimum production of Mn contaminant, andimplies a g Mn peak around 20 MeV, at significantly lower energies than the peak with V.These features could be attractive in an ideal and very hypothetical situation of about 100% Vtarget, but become an issue in the case of a V compresence. Indeed, the g Mn peak shifts atlower energies with increasing abundance of V, and this interferes with the Mn productionfrom V, which significantly increases at lower energies as well. On the other hand, there is noappreciable advantage when considering enriched V targets, either. A V target with 100%enrichment does not improve the g Mn production nor reduce the contaminant production.24 RN P ( ad i m ) Time (d) Cr(p,n)
Mn Radio Nuclidic Purity
Talys BTETalys Q -Q Talys min-maxEmpire 0.98 0.985 0.99 0.995 1 1.005 1.01 0 20 40 60 80 100 120 140 160 180
Fig. 12. Time evolution of the radionuclidic purity for the reaction Cr(p,n) g Mn assuming an100% target enrichment. The irradiation conditions are those discussed for Tab.II. RN P ( ad i m ) Time (d) Cr(d,x)
Mn Radio Nuclidic Purity
Talys BTETalys Q1-Q3Talys min-maxEmpire 0.98 0.985 0.99 0.995 1 1.005 1.01 0 10 20 30 40 50 60 70 80 90
Fig. 13. The same as Fig. 12 for the reaction Cr(d,2n) g Mn.25 C r o ss s e c t i on ( m b ) Energy (MeV) V( α ,x) Mn vs V( α ,x) Mn Mn Talys BTE
Mn Talys Q1-Q3 0 0.05 0.1 0.15 0.2 0.25 0 5 10 15 20 25 30 35 40 Mn Talys BTE Mn Talys Q1-Q3
Fig. 14. Cross sections for the production of g Mn and Mn with alpha beams on V. C r o ss s e c t i on ( m b ) Energy (MeV) V( α ,x) Mn vs V( α ,x) Mn Mn Talys BTE
Mn Talys Q1-Q3 Mn Talys BTE Mn Talys Q1-Q3
Fig. 15. Cross sections for the production of g Mn and Mn with alpha beams on V.26
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