Excitation functions for (p,x) reactions of niobium in the energy range of E p = 40-90 MeV
Andrew S. Voyles, Lee A. Bernstein, Eva R. Birnbaum, Jonathan W. Engle, Stephen A. Graves, Toshihiko Kawano, Amanda M. Lewis, Francois M. Nortier
NNuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34
NuclInstrumMeth B
Excitation functions for (p,x) reactions of niobium in the energyrange of E p = 40–90 MeV Andrew S. Voyles a, , Lee A. Bernstein b,a , Eva R. Birnbaum d , Jonathan W. Engle c ,Stephen A. Graves e , Toshihiko Kawano f , Amanda M. Lewis a , Francois M. Nortier d a Department of Nuclear Engineering, University of California, Berkeley, Berkeley, CA 94720, USA b Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA c Department of Medical Physics, University of Wisconsin – Madison, Madison, WI 53705, USA d Isotope Production Facility, Chemistry Division, Los Alamos National Laboratory, Los Alamos, NM 87544, USA e Department of Radiation Oncology, University of Iowa, Iowa City, IA 52242, USA f Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87544, USA
Abstract
A stack of thin Nb foils was irradiated with the 100 MeV proton beam at Los Alamos National Laboratory’sIsotope Production Facility, to investigate the Nb(p,4n) Mo nuclear reaction as a monitor for intermediate energyproton experiments and to benchmark state-of-the-art reaction model codes. A set of 38 measured cross sectionsfor nat
Nb(p,x) and nat
Cu(p,x) reactions between 40–90 MeV, as well as 5 independent measurements of isomerbranching ratios, are reported. These are useful in medical and basic science radionuclide productions at intermediateenergies. The nat
Cu(p,x) Co, nat
Cu(p,x) Zn, and nat
Cu(p,x) Zn reactions were used to determine proton fluence,and all activities were quantified using HPGe spectrometry. Variance minimization techniques were employed toreduce systematic uncertainties in proton energy and fluence, improving the reliability of these measurements. Themeasured cross sections are shown to be in excellent agreement with literature values, and have been measuredwith improved precision compared with previous measurements. This work also reports the first measurement ofthe nat
Nb(p,x)
Rb reaction, and of the independent cross sections for nat
Cu(p,x)
Mn and nat
Nb(p,x)
Y inthe 40–90 MeV region. The effects of nat
Si(p,x)
Na contamination, arising from silicone adhesive in the Kaptontape used to encapsulate the aluminum monitor foils, is also discussed as a cautionary note to future stacked-targetcross section measurements.
A priori predictions of the reaction modeling codes CoH, EMPIRE, and TALYS arecompared with experimentally measured values and used to explore the differences between codes for the nat
Nb(p,x)and nat
Cu(p,x) reactions.
Keywords:
Nb + p, Cu + p, Niobium, Mo, Nuclear cross sections, Stacked target activation, Monitor reactions,Medical isotope production, Isomer branching ratios, MCNP, LANL
1. Introduction
Every year, approximately 17 million nuclear medicine procedures (both diagnostic and therapeutic) areperformed in the U.S. alone [1, 2]. Most of the radionuclides currently used for these procedures are producedby low- (E <
30 MeV / A) and intermediate-energy (30 < E <
200 MeV / A) accelerators, e.g., C, F, Email addresses: [email protected] (Andrew S. Voyles ), [email protected] (Jonathan W. Engle) a r X i v : . [ nu c l - e x ] J un .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 Ga, Rb, and
I. These accelerators also produce non-medical radionuclides with commercial value,such as Na, As,
Tc, and
Cd [3, 4]. Novel applications are being explored for several radionuclideswhose production methodologies are not established, but their production requires accurate, high-fidelitycross section data. Candidate isotopes to meet these needs have been identified based on their chemicaland radioactive decay properties [2, 5, 6], and a series of campaigns are underway to perform targeted,high-priority measurements of thin-target cross sections and thick-target integral yields. These studies willserve to facilitate the production of clinically relevant quantities of radioactivity.Accurate cross section measurements using activation methods benefit from well- characterized monitorreactions. Currently there is a paucity of such data at intermediate energies, and much of what exists havehigh uncertainties ( > V ( t / = 15.97 d, (cid:15) = 100% to Ti) and Sc ( t / = 43.67 h, β − = 100%to Ti) can both be formed via nat
Ti(p,x) reactions, yielding the same 983.52 keV transition in Ti [7]. It isalso of vital importance that the proposed monitor nucleus have well-characterized decay data. This includesa precise and well-established half-life, and well-characterized decay gamma-ray intensities. From a targetryperspective, it is preferable to use a naturally mono-isotopic target that is readily available and chemicallyinert. Targets which can be formed into a wide thickness range are convenient, as selection is subject to thecontext of an experiment, seeking to maximize thickness without overly perturbing the energy uncertainty ofmeasurements. Lastly, and perhaps most importantly for high-energy monitor reaction applications, it is ofutmost importance to choose a reaction channel which cannot be populated via secondary particles incidentupon the monitor target. Typically, this is mostly a concern for secondary neutrons produced through (z,xn)reactions, but any monitor reaction channel which can be populated by anything other than the primarybeam should be avoided, as it is often difficult to accurately and unambiguously separate out the fractionof secondary particles contributing to the total activation.One reaction which satisfies these requirements is that of a new, intermediate-energy proton monitorreaction standard based on Nb(p,4n) Mo. Niobium is naturally mono-isotopic, readily available com-mercially in high purity, is fairly chemically inert, and can easily be rolled down to foils as thin as 1 µm. Mo also has a sufficiently long lifetime ( (cid:15) = 100% , t / = 5 . ± .
09 h [8]) and seven strong, distinctgamma lines (notably its 122.370 keV [ I γ = 64 ± I γ = 78 ± Mo production. In addition, Mo is completely immune from (n,x)production on Nb, being produced only via the primary proton beam, and the Mo decay lines can onlybe observed in its decay, as its daughter, Nb, is also unstable and decays via (cid:15) to stable Zr.The purpose of the present work is to measure the production of the long-lived radionuclide Mo viathe nat
Nb(p,x) reaction. In addition to the nat
Nb(p,x) Mo measurement, this experiment has also yieldedmeasurements of 37 other (p,x) production cross sections between 40–90 MeV for a number of additionalreaction products, including several emerging radionuclides with medical applications. These include thenon-standard positron emitters Ni, Cu, Y, Zr, Nb, and the diagnostic agent
Rb.In addition to providing a potentially highly-valuable beam monitor, the Nb(p,x) reactions offer anopportunity to study the angular momentum deposition via pre-equilibrium reactions and the spin dis-tribution in g / subshell nuclei via the observation of isomer-to-ground state ratios. Measurements ofisomer-to-ground state ratios have been used for over 20 years to probe the spin distribution of excited nu-clear states in the A ≈
190 region [9, 10]. These include the
Mn ( t / = 21 . ± . π = 2 + ) to Mn2 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 ( t / = 5 . ± .
003 d; J π = 6 + ), Co ( t / = 9 . ± .
09 h; J π = 5 + ) to Co ( t / = 70 . ± .
06 d;J π = 2 + ), Y ( t / = 4 . ± .
13 h; J π = / ) to Y ( t / = 2 . ± .
05 h; J π = / − ), Y( t / = 13 . ± .
03 h; J π = / ) to Y ( t / = 79 . ± . π = / − ), and Nb ( t / = 66 ± π = / − ) to Nb ( t / = 2 . ± .
07 h; J π = / ) ratios [11–15].The measurements described in this paper involve the use of multiple monitor reactions in conjunctionwith statistical calculations and proton transport simulations to reduce systematic uncertainties in beamenergy assignments, leading to some of the first and most precise measurements for many of the excitationfunctions reported here. By expanding the available set of monitor reaction standards and well-characterizedisotope production excitation functions, this work should help optimize medical isotope production modali-ties, making more options available for modern medical imaging and cancer therapy.
2. Experimental methods and materials
The work described herein follows the methods established by Graves et al. for monitor reaction charac-terization of beam energy and fluence in stacked target irradiations [16].
A stacked-target design was utilized for this work in order that the (p,x) cross sections for each reactionchannel could be measured at multiple energy positions in a single irradiation [17]. A series of nominal25 µm nat
Nb foils (99.8%, lot nat
Al foils (99.999%, lot nat
Cufoils (99.9999%, lot × ) for each foil was calculated. The foils were tightly sealed into “packets” using two pieces of3M 5413-Series Kapton polyimide film tape — each piece of tape consists of 43.2 µm of a silicone adhesive(nominal 4.79 mg/cm ) on 25.4 µm of a polyimide backing (nominal 3.61 mg/cm ). The sealed foils weremounted over the hollow center of a 1.575 mm-thick plastic frame. One nat Al, one nat
Cu, and one nat
Nbmounted foil were bundled together using baling wire for each energy position. These foil packet bundleswere lowered into the beamline by inserting them into a water-cooled production target box. The box, seenin Figure 1, is machined from 6061 aluminum alloy, has a thin (0.64 mm) Inconel beam entrance window, andcontains 6 “energy positions” for targets, formed by 5 slabs of 6061 aluminum alloy (previously characterized)which serve as proton energy degraders between energy positions. After loading all targets in the stack,the lid of the target box is sealed in place, using an inset o-ring to create a water-tight seal, and the boxis lowered through a hot cell into the beamline, where it sits electrically isolated. The specifications of thetarget stack design for this work is presented in Table 1.This target stack was assembled and irradiated at the Isotope Production Facility (IPF) at the LosAlamos National Laboratory (LANL), using the LANSCE linear accelerator. The stack was irradiatedfor approximately 2 h with a nominal current of 1 mA, using a 50 µs pulse at a frequency of 2 Hz, for ananticipated integral current of 205.9 nAh. The beam current, measured using an inductive pickup, remainedstable under these conditions for the duration of the irradiation, with the exception of approximately 70 s ofdowntime, which occurred approximately 3 min into irradiation. The proton beam incident upon the stack’sInconel beam entrance window had an average energy of 100 MeV determined via time-of-flight, with anapproximately Gaussian energy distribution width of 0.1 MeV — this energy profile was used for all lateranalysis. At the end of the irradiation, the target stack was withdrawn from the beamline into the IPF hotcell, where it was disassembled and the activated foils removed using robotic manipulators. The activatedfoils were cleaned of all surface contamination, and transported to a counting lab for gamma spectrometry,which started approximately 6 h following end-of-bombardment.3 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 . Their areal densities were determined using the variance minimizationtechniques described in this work and the earlier paper by Graves et al. [16]. At both the front and rear of the target stack’sfoils, a 316 stainless steel foil is inserted to serve as a beam profile monitor — after end-of-bombardment (EoB), decay radiationemitted from these activated stainless steel foils were used to develop radiochromic film (Gafchromic EBT), revealing the spatialprofile of the beam entering and exiting the stack. Target layer Measuredthickness Measured arealdensity (mg/cm ) Areal densityuncertainty (%)SS profile monitor 249.8 µm 194.56 0.29Al-1 25.0 µm 6.52 0.72Cu-1 61.3 µm 53.74 0.15Nb-1 30.0 µm 23.21 0.17Al Degrader 01 4.96 mm - -Al-2 25.5 µm 6.48 0.36Cu-2 61.8 µm 53.85 0.17Nb-2 30.8 µm 22.91 0.17Al Degrader 02 4.55 mm - -Al-3 25.8 µm 6.47 0.31Cu-3 61.5 µm 53.98 0.11Nb-3 31.0 µm 22.91 0.24Al Degrader 03 3.52 mm - -Al-4 26.3 µm 6.51 0.41Cu-4 61.3 µm 53.46 0.22Nb-4 30.8 µm 22.55 0.25Al Degrader 04 3.47 mm - -Al-5 26.5 µm 6.48 0.29Cu-5 61.5 µm 53.57 0.11Nb-5 30.8 µm 22.11 0.25Al Degrader 05 3.46 mm - -Al-6 26.3 µm 6.48 0.62Cu-6 62.0 µm 53.84 0.32Nb-6 31.3 µm 22.12 0.13SS profile monitor 124.4 µm 101.34 0.23 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 Figure 2: A gamma spectrum collected from an activated Nb foil at approximately 80 MeV. While the majority of observedreaction products are visible in this spectrum, the Mo decay lines, which form the basis of the Nb(p,x) Mo monitorreaction, are high in intensity and clearly isolated from surrounding peaks.
A single detector was used in this measurement, an ORTEC GEM Series (model σ c ), which is the sum of direct production of that nucleus, as well as decay of itsprecursors and any other independent cross sections leading to that nucleus. Cumulative cross sections will5 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 be reported whenever it is impossible to use decay spectrometry to distinguish independent production ofa nucleus from decay feeding. For all remaining observed reaction products in the mass chain, and caseswhere no decay precursors exist, independent cross sections ( σ i ) will be reported, allowing for determinationof the independent production via subtraction and facilitating comparison to reaction model calculations.Corrections must be made for the decay of the various reaction products during the time between EoB andthe spectrum acquisition, in order to calculate A , the initial activity at EoB, from the measured activities.The use of multiple gamma-rays at multiple points after EoB to calculate initial activities for each observedproduct nucleus allows for a more accurate determination of A than simply basing its calculation off ofa single gamma-ray observation. For the case of cumulative cross sections, EoB activities were quantifiedby fitting the activities observed at multiple time points t (since EoB) to the well-known radioactive decaylaw. Nonlinear regression was used for this fitting process, minimizing on χ / degree of freedom, so thatnot only would the uncertainty-weighted EoB activities be fitted, but that a 1- σ confidence interval in A could be reported as well. As with the gamma-ray intensities, all lifetimes used in this work are tabulated inTables A.6 and A.7 of AppendixA. In the case of independent cross sections, a similar process was followed,quantifying A i ( t = 0) = A i, , the EoB activity of nuclide i , by instead regressing to the solutions to theBateman equation [21, 22]: A n ( t ) = λ n n X i =1 N i, × n − Y j = i λ j × n X j = i e − λ j t Q ni = j ( λ i − λ j ) (1)where j refers to a precursor nucleus populating a specific end-product. While higher-order terms were addedif needed, typically for an isomeric state in a particular mass chain, the second-order expansion ( n = 2) wasoften sufficient to quantify EoB activities in a mass chain, simplifying to: A ( t ) = A , λ λ − λ (cid:0) e − λ t − e − λ t (cid:1) + A , e − λ t (2)In these cases, the previously-quantified EoB activities from decay precursors ( A , , etc) would be substitutedin, so that the feeding contributions from decay could be separated and an independent cross section reported.After quantifying the cumulative EoB activities at the top of a mass chain and all subsequent independentEoB activities, these will be later used to report the various cross sections for all observed reaction productsand isomeric states. In addition to the LANSCE-IPF beamline’s direct beam current measurements, thin nat
Al and nat
Cu foilswere included along with the nat
Nb targets at each energy position, to provide more sensitive beam currentmonitors. The IAEA-recommended nat
Al(p,x) Na, nat
Al(p,x) Na, nat
Cu(p,x) Co, nat
Cu(p,x) Zn, and nat
Cu(p,x) Zn monitor reactions were used for proton fluence measurement [23]. Due to the large energydegradation between the front and back of the target stack, a non-trivial broadening of the proton energydistribution was expected for all monitor and target foils. As a result, the integral form of the well-knownactivation equation was used to accurately determine proton fluence ( I ∆ t ) in each monitor foil: I ∆ t = A ∆ tρ ∆ r (1 − e − λ ∆ t ) R σ ( E ) dφdE dE (3)where A is the EoB activity for the monitor reaction product, I is the proton current, ρ ∆ r is the foil’sareal density, λ is the monitor reaction product’s decay constant, ∆ t is the length of irradiation, σ ( E ) isthe IAEA recommended cross section at energy E , and dφdE is the differential proton fluence. Using thisformalism, the quantified EoB activities for each monitor reaction may be converted into a measured protonfluence at each energy position.The propagated uncertainty in proton fluence is calculated as the quadrature sum of the uncertaintyin quantified EoB activity, uncertainty in the duration of irradiation (conservatively estimated at 60 s, to6 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 account for any transient changes in beam current), uncertainty in foil areal density, uncertainty in monitorproduct half-life (included, but normally negligible), uncertainty in IAEA recommended cross section, anduncertainty in differential proton fluence. Of these, the first four contributions are all easily quantified inthe preparation and execution of a stacked target irradiation; the last two contributions prove to be morenuanced, however. The uncertainty in proton fluence for irradiated monitor foils is derived from statisticaluncertainty in the modeling of proton transport in the stack irradiation, discussed in subsection 2.4. Theuncertainty in IAEA recommended cross section values must be estimated indirectly, as no uncertainty inthe recommended cross sections is provided in the current IAEA evaluation. Fortunately, the recommendedcross section values for each monitor reaction tend to closely match one of the selected experimental sourcedata sets used in their evaluation. Since these data sets have listed uncertainties in the original manuscripts,uncertainties in IAEA recommended cross section values have been estimated by the uncertainty in the dataset most closely matching the IAEA recommended values. For the monitor reactions employed in this work,these data sets are G. Steyn (1990) for nat Al(p,x) Na [24], M. Uddin (2004) for nat
Al(p,x) Na [25], and S.Mills (1992) for nat
Cu(p,x) Co, nat
Cu(p,x) Zn, and nat
Cu(p,x) Zn [26].
Initial estimates of the proton beam energy in all foils were calculated using the Anderson & Ziegler(A&Z) stopping power formalism [27–29]. These estimates of average beam energy in each foil are useful forthe preliminary stack design. However, for final energy and fluence determinations, a more rigorous methodof proton transport modeling is needed. The Monte Carlo N-Particle transport code MCNP6.1 was usedfor simulation of the full 3-D target stack, including determination of the full proton energy distribution foreach stack position [30]. MCNP6 provides a far more robust method of proton transport, as it is able toaccount for beam losses due to scattering and reactions, as well as production of secondary particles. As it isa Monte Carlo-based code, the uncertainty in energy distribution scales inversely with the number of sourceprotons simulated. 10 source protons were used for all simulations, which places the statistical uncertaintyin proton energy distributions at less than 0.01%.The ability to model the full energy distribution in each target position is vital for stacked targetirradiations, due to the progressively larger energy straggling towards the rear of the stack. The initialproton beam has a finite energy spread (an approximately 0.1 MeV Gaussian width at 100 MeV), and sincestopping power for charged particles is inversely proportional to their energy, the low-energy tail of the energydistribution is degraded more in each stack element than the high-energy tail. This effect compounds towardsthe rear of the stack, creating a significantly broadened low-energy tail, and a progressively larger net shiftof the centroid to a lower energy. To account for this increasing energy uncertainty, a suitably representativeenergy must be established for each foil in the target stack. In this work, the flux-weighted average protonenergy in each foil, h E i , represents the energy centroid for protons in a target stack component, calculatedusing the energy distributions dφdE from MCNP6 modeling of proton transport: h E i = Z E dφdE dE Z dφdE dE (4)Likewise, to represent the energy uncertainty for each stack position, the full width at half maximum(FWHM) of the MCNP6-modeled energy distribution is chosen for each energy position reported. Whilemost experimental uncertainties are reported at the 1 σ level, the 2 . σ FWHM is used here to ensure atthe 98% confidence interval that this width includes the “true” energy centroid value.The “variance minimization” techniques described by Graves et al. have been employed here to furtherreduce the uncertainty in proton energy assignments [16]. This method is based on the assumption that theindependent measurements of proton fluence from the five monitor reactions used in this work should allbe consistent at each energy position. If the monitor reaction cross sections and MCNP6-modeled energydistributions are both accurate, disagreement in the observed proton fluences is due to poorly characterizedstopping power in simulations, or a systematic error in the areal densities of the stack components [16, 31].7 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34
25 30 35 40 45 50 55 6010 Figure 3: Result of the variance minimization performed by adjusting the degrader density in MCNP6 simulations of thetarget stack. A flux-weighted average proton energy of 41.34 MeV entering the last energy position creates a clear minimumin observed reaction fluence variance, corresponding to an areal density 2.52% greater than nominal. The variance minimumoccurring at a lower incident energy than nominal MCNP6 and A&Z calculations indicates that there exists an additionalsystematic beam degradation not accounted for in modeling of proton transport in the stack design.
This disagreement is minor at the front of the stack, and gets progressively worse as the beam is degraded,due to the compounded effect of systematic uncertainties in stack areal densities.Due to the significantly greater areal density of the thick 6061 aluminum degraders as compared to theother stack elements (nominal 3–5 mg/cm , relative to nominal 1000–1400 mg/cm ), the areal density ofeach of the 6061 aluminum degraders were varied uniformly in MCNP6 simulations by a factor of up to ±
25% of nominal values, to find the effective density which minimized variance in the measured protonfluence at the lowest energy position (Al-6, Cu-6). This lowest energy position was chosen as a minimizationcandidate, as it is most sensitive to systematic uncertainties in stack design. The results of this minimizationtechnique, shown in Figure 3, indicate a clear minimum in proton fluence variance for flux-weighted average41.34 MeV protons entering the last energy position. This is approximately 2 MeV lower than the nominalMCNP6 simulations, and approximately 3 MeV lower than nominal A&Z calculations, both of which usedthe nominal 2.80 g/cm measured density of the 6061 aluminum degraders. This energy corresponds to a6061 aluminum areal density of 2.52% greater than nominal measurements, and serves as a lump correctionfor other minor systematic uncertainties in stack design, including stack areal densities and incident beamenergy.The impact of this variance minimization is clearly seen in Figure 4. As expected, the 2.52% increase in6061 aluminum areal density has an almost negligible impact on the higher-energy positions, but causes aprogressively larger downshift in proton energies at the later energy positions. In addition, as one moves tothe rear positions, the disagreement in the independent proton fluence measurements is reduced. It is worthnoting that the proton fluence measured by the nat Al(p,x) Na monitor reaction (threshold 21.0 MeV) is con-sistently higher in magnitude than all other monitor channels, with an increasing disparity at higher energies.This disparity is due to silicon in the Kapton tape (comprised of a silicone adhesive layer on a polyimidebacking) used for sealing the foil packets, making up approximately 10% of the silicone on a stoichiometricbasis. The Na and Na monitor channels can also be populated off of natural silicon (92.2% Si), predom-inantly via Si(p, α Na (threshold 35.3 MeV) and Si(p,4pn) Na (threshold 44.6 MeV). Si and Siare also potential targets for (p,x)
Na, albeit with higher energetic thresholds and smaller cross sections.The attribution of excess Al(p,x)
Na activity to the silicone adhesive is supported by the observation of Na and Na activities in all Cu and Nb foil positions. nat
Si(p, α nat Al(p,x) production route, seen when comparing the total mea-sured activities of
Na in each Al foil packet, relative to the expected EoB activities for each reactionchannel (Figure 5). Since no evaluated cross section data exists in this energy region for Si(p,x) Na8 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34
40 50 60 70 80 90 100050100150200250300350 a)
40 50 60 70 80 90 100050100150200250300350 b) Figure 4: Results of variance minimization through enhancement of the effective areal density of the 6061 aluminum degradersby 2.52%. A noticeable reduction of variance in measured proton fluence is seen, particularly at the rear stack positions.Following minimization, additional apparent fluence is observed in the nat
Al(p,x) Na and nat
Al(p,x) Na monitor channels,due to contamination from nat
Si(p,x)
Na on the silicone adhesive used for sealing foil packets.
40 50 60 70 80 90 10000.511.522.53 a)
40 50 60 70 80 90 1000200400600800100012001400 b) Figure 5: Estimates of EoB nat
Al(p,x)
Na and nat
Si(p,x)
Na activities using TENDL-2015 cross sections, in comparisonwith the IAEA recommended nat
Al(p,x)
Na cross sections. At low energies, experimentally observed apparent
Naactivities in each Al foil packet are consistent with IAEA recommendations, but diverge at higher energies as the nat
Si(p,x) Naexit channels begin to open up.
Na activities consistent with TENDL-2015 estimates are observed in each Nb and Cu foilpacket as well, confirming that contamination may be attributed to activation of silicone adhesives. .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34
40 50 60 70 80 90 100160180200220240260280300320 a)
40 50 60 70 80 90 100160180200220240260280300320 b) Figure 6: The “extra fluence” observed in the nat
Al(p,x) Na and nat
Al(p,x) Na monitor channels is caused by contaminationfrom nat
Si(p,x)
Na on the silicone adhesive used for sealing foil packets. Following subtraction of
Na activities observedin the silicone adhesive of Nb and Cu foils in the same energy “compartment”, the consistency of the nat
Al(p,x) Na monitorreaction improves dramatically. By excluding these contaminated channels, the remaining 3 independent monitor reactionsserve to minimize uncertainty in stack energy assignments and incident fluence. (and only minimal nat
Si data exists), the TENDL-2015 library is used to estimate the expected relative EoBactivities for nat
Al(p,x)
Na and nat
Si(p,x)
Na, relative to IAEA recommended nat
Al(p,x)
Na crosssections. Several observations are immediately obvious. At lower energies, the magnitude of nat
Al(p,x) Nais large compared to nat
Si(p,x) Na, which is why the nat
Al(p,x) Na monitor agrees in fluence at the 40(and almost at the 50) MeV position. At higher energies, the apparent nat
Al(p,x) Na activity begins todiverge from the IAEA expected activities as nat
Si(p,x) Na production begins to open up, which accountsfor the nearly 50% apparent excess fluence in Na between 60–90 MeV. For Na production, we see similarbehavior, with only a minor increase in apparent Na activity, since the observed nat
Si(p,x) Na yield re-mains consistently low in magnitude. The observed Na activities also follow the shape of the TENDL-2015 nat
Si(p,x) Na yields, albeit smaller in magnitude at the higher energy positions.There are several important conclusions to be drawn from this simple estimate using the TENDL nat
Si(p,x)
Na yields. The observation of the
Na activities in Cu and Nb foils represents an indi-rect measurement of the nat
Si(p,x)
Na cross sections, but will not be reported due to uncertainties in theareal density of the Si in the adhesive. However, if we assume a 10% Si stoichiometric basis and an arealdensity of 4.79 mg/cm (based on bulk density), we can subtract out the measured Na activity at eachNb and Cu foil position (correcting for the minor difference in proton energy between adjacent foils) from theapparent
Na activities observed in each Al foil packet, in order to obtain the “true” or uncontaminatedfluence via the Al monitor reactions, shown in Figure 6. Following subtraction, the
Na fluences becomemore consistent with other monitor reaction channels, though Na fluence remains 3–6% higher than theweighted mean of the remaining monitor reaction channels. While the dramatic improvement in monitorreaction consistency builds confidence, in the interest of surety and because they are consistent, only the nat
Cu(p,x) Co, nat
Cu(p,x) Zn, and nat
Cu(p,x) Zn monitor reaction channels will be used for fluence de-termination for the reported cross sections. This serves as a pointed example of the importance of selectingmonitor reaction products inaccessible through channels aside from the primary reaction ( nat
Al(p,x)
Na,in this case ), as noted previously.Using this variance minimized degrader density, the final incident proton energy distributions dφdE fromMCNP6 simulation are shown for the six irradiated Nb foils in Figure 7. As expected, the energy distri-bution becomes increasingly more broadened at the lower energy positions, as a result of the beam energy10 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 -8 -7 -6 -5 -4 -3 -2 Figure 7: Final variance minimized incident proton energy distributions for the Nb foils, as simulated in MCNP6. Thedistribution tallies in each foil are all normalized to be per source proton, which was 10 in all simulations. As the beam isdegraded, proton energy distributions become visibly broadened due to straggling, and drop in magnitude due to scatteringlosses. degradation. In addition, as the beam becomes more degraded, the magnitude of the peak of each energydistribution (as well as the integral of each distribution) is reduced, as beam fluence is lost due to scattering,and the peak-to-low-energy-tail ratio increases as more secondary protons are produced upstream. As withthe monitor foils, these distributions were used to calculate the energy centroid (as the flux-weighted averageproton energy) and uncertainty (as the FWHM of the distribution) for the final proton energy assignmentof each Nb foil.An enhanced version of the final nat Cu(p,x) Co, nat
Cu(p,x) Zn, and nat
Cu(p,x) Zn monitor reactionfluences is shown in Figure 8. Without the reliable use of the nat
Al(p,x) Na and nat
Al(p,x) Na monitorchannels, local interpolation cannot be used for fluence assignment to the Nb foils, and global interpolationis reliant upon a validated model for fluence loss. The uncertainty-weighted mean for the three nat
Cu(p,x)monitor channels was calculated at each energy position, to determine the final fluence assignments forthe Nb and Cu foils. Uncertainty in proton fluence is likewise calculated by error propagation of thefluence values at each energy position. These weighted-mean fluences are plotted in Figure 8, along withthe estimated fluence according to both MCNP6 transport and an uncertainty-weighted linear χ fit tothe individual monitor channel fluence measurements. Both models reproduce the observed fluence dataconsistently within uncertainty, with the MCNP6 model predicting a slightly greater fluence loss throughoutthe stack. These models are used purely to provide an extrapolation from the 90 MeV energy position backto the “front” of the stack at 100 MeV, to compare with the nominal fluence measured by IPF upstreamcurrent monitors. Using the quantified EoB activities along with the variance-minimized proton fluence, it is possible tocalculate the final cross sections for the various observed Nb(p,x) reactions. While thin ( ≈
22 mg/cm ) Nbfoils were irradiated to minimize the energy width of these cross section measurements, it is important tonote that all cross sections reported here are flux-averaged over the energy distribution subtended by eachfoil, as seen in Figure 7. For both the cumulative and independent activities quantified, cross sections werecalculated as: σ = A ρ ∆ rI (1 − e − λ ∆ t ) (5)where A is the EoB activity for the monitor reaction product, I is the proton current, ρ ∆ r is the foil’sareal density, λ is the monitor reaction product’s decay constant, and ∆ t is the length of irradiation. The11 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34
40 50 60 70 80 90 100160170180190200210220230240
Figure 8: Final uncertainty-weighted mean proton fluences throughout the target stack, based on the variance-minimizedobserved fluence from the the nat
Cu(p,x) Co, nat
Cu(p,x) Zn, and nat
Cu(p,x) Zn monitor reactions. The fluence drops byapproximately 7.2–8.9% from the incident fluence of 196.9–198.8 nAh over the length of the target stack, based on fluence lossmodels from MCNP6 simulations and an empirical fit to fluence measurements. beam current, measured using an inductive pickup, remained stable for the duration of the irradiation,with the exception of approximately 70 s of downtime, occurring approximately 3 min into irradiation. Thepropagated uncertainty in cross section is calculated as the quadrature sum of the uncertainty in quantifiedEoB activity (which includes uncertainty in detector efficiencies), uncertainty in the duration of irradiation(conservatively estimated at 60 s, to account for any transient changes in beam current), uncertainty in foilareal density, uncertainty in monitor product half-life (included, but normally negligible), and uncertaintyin proton current (quantified by error propagation of the monitor reaction fluence values at each energyposition, as seen in Figure 8).
3. Results
After irradiation, all foils were confirmed to still be sealed inside their Kapton packets, verifying that noactivation products were lost due to packet failure and dispersal. In addition, each activated foil had a small“blister” under the Kapton tape layer, caused by a combination of thermal swelling and the formation ofshort-lived beta activities. This blister shows the location where the primary proton beam was incident uponthe foil. The nat
Cu(p,x) Co, nat
Cu(p,x) Zn, and nat
Cu(p,x) Zn monitor reactions were used to determinethe uncertainty-weighted mean fluence at each energy position (seen in Figure 8). A fluence of 198.8 ± ± σ tot ρ ∆ r , it is expected that an extrapolation back to the stack entrance will underestimate the nominalfluence incident upon the box. This incident fluence dropped by approximately 8.9% to 180.9 ± ± Cr,
Mn,
Mn, Mn, Co, Ni, Ni, Co,
Co,
Co, Fe, Co, Cu, and Cu were extracted for (p,x) reactions on nat
Cu foils in the 40–90 MeV region, as recorded in Table 2. For (p,x) reactions on nat
Nb foils, the (p,x)cross sections for
Rb, Sr, Y, Y, Zr, Y, Zr, Y, Y, Zr, Y, Nb,
Nb, Zr, Mo, Nb,
Nb,
Nb, and
Mo were extracted, as recorded in Table 3. In addition, as there exist12 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 nat
Cu(p,x) reaction products observed in this work. Cumulative cross sectionsare designated as σ c , independent cross sections are designated as σ i . Production cross section (mb)E p (MeV) 89 . +0 . − . . +0 . − . . +0 . − . . +1 . − . . +1 . − . . +1 . − . Cr ( σ c ) 0 . ± .
079 0 . ± .
023 0 . ± .
028 0 . ± .
016 – – Mn ( σ c ) 1 . ± .
11 0 . ± .
031 0 . ± . . ± . Mn ( σ i ) 0 . ± .
043 0 . ± .
018 0 . ± . . ± . Mn ( σ c ) 1 . ± .
091 0 . ± .
030 0 . ± . . ± . Mn ( σ i ) 5 . ± .
37 3 . ± .
21 4 . ± .
22 4 . ± .
26 1 . ± .
091 – Co ( σ c ) 1 . ± .
11 1 . ± .
058 0 . ± .
012 0 . ± . . ± . Ni ( σ c ) 0 . ± . . ± . . ± . . ± . Ni ( σ c ) 1 . ± .
093 1 . ± .
065 1 . ± .
071 2 . ± .
11 1 . ± .
083 0 . ± . Co ( σ i ) 40 . ± . . ± . . ± . . ± . . ± . . ± . Co ( σ c ) 57 . ± . . ± . . ± . . ± . . ± . . ± . Co ( σ i ) 14 . ± . . ± . . ± . . ± . . ± . . ± . Co ( σ i ) 43 . ± . . ± . . ± . . ± . . ± . . ± . Fe ( σ c ) 0 . ± .
057 0 . ± .
046 0 . ± .
039 0 . ± .
034 0 . ± .
014 – Co ( σ c ) 13 . ± .
87 13 . ± .
78 11 . ± .
94 11 . ± .
80 9 . ± .
87 6 . ± . Cu ( σ c ) 50 . ± . . ± . . ± . . ± . . ± . . ± . Cu ( σ i ) 38 . ± . . ± . . ± . . ± . . ± . . ± . a number of isomers with radioactive ground states in these mass regions, independent measurements ofisomer-to-ground-state branching ratios for Mn,
Co, Y, Y, and
Nb were extractedand are recorded in Table 4. Comparisons of the measured cross sections and isomer branching ratios withliterature data (retrieved from EXFOR [32]) are seen in the figures of AppendixB and AppendixC. Thepropagated uncertainty in these cross sections varies widely based on the reaction product in question, withthe major components arising from uncertainty in EoB activity ( ± ± ± nat Cu(p,x) cross sections measured here arein excellent agreement with the body of measurements in the literature, but have been measured nearlyexclusively with the highest precision to date. Similarly, the various nat
Nb(p,x) cross sections measuredhere are in excellent agreement with literature data, which is far more sparse in the 40–90 MeV regionthan for nat
Cu(p,x) — fewer than three existing measurements have been performed for the majority ofthe reactions presented here. Indeed, the nat
Nb(p,x) Sr, nat
Nb(p,x) Y, nat Nb(p,x) Nb, nat
Nb(p,x) Mo, nat
Nb(p,x)
Nb, and nat
Nb(p,x)
Mo reactions each possess no more than a total of three data pointsin this energy region. Not only do the nat
Nb(p,x) measurements in this work fill in the sparse data in thisenergy region, but they have been measured with the highest precision relative to existing literature data.This work presents the first measurements of several observables in this mass region, including the nat
Nb(p,x)
Rb reaction in the 40–90 MeV region, the independent cross section for nat
Cu(p,x)
Mn, andthe
Mn (2 + ) / Mn (6 + ) isomer branching ratio via nat Cu(p,x). The cumulative cross sections fromthese data are also consistent with existing measurements of the cumulative nat
Cu(p,x) Mn cross section.Similarly, this work offers the first measurement of the independent cross sections for nat
Nb(p,x)
Y, aswell as the first measurement of the
Y ( / ) / Y ( / − ) isomer branching ratio via nat Nb(p,x).Notably, this work is the most well-characterized measurement of the nat
Nb(p,x) Mo reaction below100 MeV to date, with cross sections measured at the 4–6% uncertainty level. This is important, as itpresents the first step towards characterizing this reaction for use as a proton monitor reaction standardbelow 100 MeV. nat
Nb(p,x) Mo can only be populated through the (p,4n) reaction channel, so no correctionsfor (n,x) contamination channels or decay down the A=90 isobar are needed. Mo possesses seven strong,distinct gamma lines which can easily be used for its identification and quantification. Finally, the productionof Mo in the 40–90 MeV region is quite strong, with a peak cross section of approximately 120 mb.Combining the reaction yield and gamma abundance, the use of approximately 23 mg/cm Nb targets easilyprovided sufficient counting statistics for activity quantification in the 40–90 MeV region. This result presents13 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 nat
Nb(p,x) reaction products observed in this work. Cumulative cross sectionsare designated as σ c , independent cross sections are designated as σ i . Production cross section (mb)E p (MeV) 89 . +0 . − . . +0 . − . . +0 . − . . +1 . − . . +1 . − . . +1 . − . Rb ( σ c ) 2 . ± .
22 – – – – – Sr ( σ c ) 4 . ± .
61 4 . ± .
42 3 . ± .
36 – – – Y ( σ c ) 13 . ± .
55 7 . ± .
51 2 . ± .
14 – – –
Y ( σ i ) 2 . ± .
11 2 . ± .
17 0 . ± .
037 – – –
Y ( σ i ) 11 . ± .
54 5 . ± .
48 1 . ± .
13 – – – Zr ( σ c ) 12 . ± .
68 18 . ± .
93 19 . ± .
97 6 . ± .
32 – – Y ( σ i ) 33 . ± . . ± . . ± . . ± .
72 – – Zr ( σ c ) 47 . ± . . ± . . ± . . ± . . ± . . ± . Y ( σ i ) 110 . ± . . ± . . ± . . ± . . ± . . ± . Y ( σ i ) 28 . ± . . ± . . ± .
64 5 . ± . . ± .
47 0 . ± . Y ( σ i ) 82 . ± . . ± . . ± . . ± . . ± . . ± . Zr ( σ c ) 159 . ± . . ± . . ± . . ± . . ± . . ± . Y ( σ i ) 17 . ± . . ± .
86 7 . ± .
72 2 . ± .
25 9 . ± . . ± . Nb ( σ c ) – – 179 ±
14 214 . ± . Nb ( σ i ) – – 145 ±
14 186 . ± . Nb ( σ i ) – – 34 . ± . . ± . Zr ( σ i ) 211 ±
11 243 ±
13 294 ±
15 257 ±
13 55 . ± . . ± . Mo ( σ i ) 21 . ± . . ± . . ± . . ± . . ± . . ± . Nb ( σ i ) 158 . ± . . ± . . ± . ±
14 369 ±
19 163 . ± . Nb ( σ c ) – – – – – 66 . ± . Nb ( σ i ) 43 . ± . . ± . . ± . . ± . . ± . . ± . Mo ( σ i ) 0 . ± .
20 1 . ± .
15 1 . ± .
24 1 . ± .
15 1 . ± .
14 2 . ± . Table 4: Measured isomer-to-ground-state branching ratios for the various nat
Nb(p,x) and nat
Cu(p,x) reaction products ob-served in this work.
Isomer branching ratioE p (MeV) 89 . +0 . − . . +0 . − . . +0 . − . . +1 . − . . +1 . − . . +1 . − . Cu(p,x) Mn 0 . ± .
066 0 . ± .
062 0 . ± .
095 0 . ± .
13 – – nat
Cu(p,x) Co 0 . ± .
088 0 . ± .
10 0 . ± .
099 0 . ± .
097 0 . ± .
12 0 . ± . p (MeV) 89 . +0 . − . . +0 . − . . +0 . − . . +1 . − . . +1 . − . . +1 . − . Nb(p,x) Y 0 . ± .
051 0 . ± .
080 0 . ± .
080 – – – nat
Nb(p,x) Y 0 . ± .
063 0 . ± .
063 0 . ± .
063 0 . ± .
070 0 . ± .
075 0 . ± . nat Nb(p,x) Nb – – 0 . ± .
021 0 . ± .
011 – – .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 Code Version Proton/Neutron Optical Model Alpha Optical Model E1 γ SF ModelEMPIRE-3.2.3[66] Koning-Delaroche[67] Avrigeanu(2009)[68] Modified Lorentzian[69]TALYS-1.8[70] Koning-Delaroche Specific folded potential[70] Brink-Axel Lorentzian[70]CoH-3.5.1[71, 72] Koning-Delaroche Avrigeanu(1994)[73] Generalized Lorentzian[71, 72] the first step towards the use of Mo as a clean and precise charged particle monitor reaction standard inirradiations up to approximately 24 h in duration.In addition to the nat
Nb(p,x) Mo measurement, this experiment has also yielded measurements of anumber of additional emerging radionuclides with medical applications. These include the non-standardpositron emitters Ni [16, 33–35], Cu [36–43], Y [14, 15, 44–52], Zr [53–57], Nb [58, 59], andthe Auger-therapy agent
Rb [60, 61]. Production of these radionuclides offers no major advantagesover established pathways, with the generally lower yields and radioisotopic purities failing to justify theconvenience of natural targets via nat
Cu(p,x) and nat
Nb(p,x). The one possible exception to this trend is thenon-standard positron emitter Ni ( t / = 35 . ± .
06 h, (cid:15) =100% to Co [62]) — the Ni/ Ni ratio ofproduction rates is approximately 290 at 61.58 MeV, and varies from 45–75 at the 70–90 MeV positions. This nat
Cu(p,x) route offers both higher yield and higher radioisotopic purity over the established nat
Co(p,3n)pathway, which suffers from approximately fivefold greater Ni contamination [63, 64].We wish to urge caution in future stacked-target activation experiments by avoiding the use of siliconeadhesive-based tapes for foil containment, especially when paired with the use of Al monitor foils. Acrylic-based tape options are commercially available, and are immune from (p,x) production of
Na activities,due to being of too low-Z for these reaction channels to be possible. Even with subtraction of
Naactivities though irradiating a Kapton tape “blank” or similar, we observe the Al monitor channels to mea-sure consistently higher proton fluence than via Cu monitor channels, by 5–8%. If Al monitors are usedin conjunction with silicone-based tapes, even with subtraction of excess Na activities, a systematicallyenhanced fluence may be determined, leading to cross sections reported with inaccurately diminished magni-tude. Furthermore, since data for monitor reactions are often self-referencing, the propagated impact of thissystematic enhancement in fluence may have far-reaching consequences for both medical isotope production,as well as for the evaluated nuclear data libraries, which use these proton activation experiments as input.As mentioned before, cumulative cross sections are reported here for the first observable product nucleiin a mass chain, or whenever it is impossible to use decay spectrometry to distinguish direct production ofa nucleus from decay feeding. For all remaining observed reaction products in the mass chain, and caseswhere no decay precursors exist, independent cross sections are reported, allowing for determination of thedirect production via subtraction. This, in turn, offers the opportunity to gauge the predictive capabilitiesof modern nuclear models used in the reaction evaluation process. The reaction channels with independentcross sections were compared to calculations with the reaction modeling codes EMPIRE, TALYS, and CoH,run with the default settings. The default optical models and E1 gamma strength function models for eachcode are presented in Table 5. The large energy range covered by many of the exit channels, which extendssignificantly beyond the range of pure compound nuclear/evaporation, allows the data to be used to studythe differences between these modeling codes in the pre-equilibrium regime.The default level density in both CoH and TALYS is the Gilbert-Cameron model, which uses a ConstantTemperature model below a critical energy and Fermi Gas model above it. The default level density inEMPIRE is the Enhanced Generalized Superfluid Model (EGSM) which uses the Generalized Superfluidmodel below a critical energy, and Fermi Gas model above it [65]. The EGSM densities are normalizedto D and the discrete levels, but in such a way that only the level density below the neutron separationenergy is effected by the discrete levels chosen for the normalization. All three codes use a two-excitonphenomenological model to calculate the pre-equilibrium cross section, but the specific implementationdiffers between the codes.Given the large number of exit channels in this data set, we will limit our discussion to cross sections forthe production of a specific residual nucleus with experimental data through the full rise and fall of the peak,and at least 1% of the total reaction cross section. Exit channel cross sections that do not exhibit the full15 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34
30 40 50 60 70 80 90 10001020304050607080
Figure 9: Measured Nb(p,x) Y cross section, with the Nb(p, α p3n) Y reaction channel visibly peaking at approximately70 MeV. rise and fall of the peak, which is identified as being dominated by the formation of a compound nucleus, donot provide enough information to analyze the calculations. Residual nuclei like Zr that can be producedby multiple reaction channels, such as (p, α Y, Mo, and Nb.The Nb(p, α p3n) Y reaction channel, which peaks at approximately 70 MeV, is well within the com-pound regime for the entire energy region of this experiment (Figure 9). The data collected on this residualis consistent with the one other data set available, taken in 1997 by Michel et al. [63]. The Nb(p,4n) Moand Nb(p,p3n) Nb channels both peak early in the energy region, around 50 MeV, and the data clearlyshow the full rise, peak, and fall of the compound cross section (Figure 10 & 11). In both of these channels,this data is consistent with the data by Titarenko et al. in 2011 [61].The Nb production cross section exhibits a persistent pre-equilibrium “tail” that keeps the channelopen well after the compound cross section has fallen away. TALYS, TENDL, and CoH seem to have thecorrect shape for this pre-equilibrium cross section, with magnitudes that are just slightly too low. EMPIRE,however, does not level off as much as the data and the other codes are seen to, and misses the high-energydata points.In all three channels, the TALYS, TENDL, and CoH calculations rise, peak, and fall at lower energiesthan the data, while EMPIRE calculates the peak to occur at higher energies. For Mo, the EMPIRE peakis representative of the data. For Y and Nb, the peak is missed by all three of the codes.The magnitudes of the TALYS and TENDL calculations are consistently too low in the three channelsstudied here. For Y, CoH and EMPIRE also predict smaller cross sections than the data would suggest,which may be influenced by incorrect modeling of other, stronger, channels. The magnitude of the peakin the CoH calculation for Mo is consistent with the data, while EMPIRE predicts a cross section thatis approximately the same magnitude as that of TALYS. Nb is one of the strongest measured channels,approximately 10% of the total reaction cross section, and the values from the three codes are all consistent,but too small, in magnitude. 16 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34
30 40 50 60 70 80 90 100020406080100120140
Figure 10: Measured Nb(p,x) Mo cross section, with the Nb(p,4n) Mo reaction channel visibly peaking at approximately50 MeV.
30 40 50 60 70 80 90 100050100150200250300350400450500
Figure 11: Measured Nb(p,x) Nb cross section, with the Nb(p,p3n) Nb reaction channel visibly peaking at approximately50 MeV. .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34
4. Conclusions
We present here a set of measurements of 38 cross sections for the nat
Nb(p,x) and nat
Cu(p,x) reac-tions between 40–90 MeV, as well as independent measurements of five isomer branching ratios. Nearly allcross sections have been reported with higher precision than previous measurements. We report the firstmeasurements of the nat
Nb(p,x)
Rb reaction, as well as the first measurement of the independent crosssections for nat
Cu(p,x)
Mn, nat
Cu(p,x)
Mn, and nat
Nb(p,x)
Y in the 40–90 MeV region. We advisethat future activation experiments avoid the use of silicone-based adhesives, particularly in conjunctionwith aluminum monitor foils, to avoid reporting an enhanced fluence due to
Na contamination. Wealso use these measurements to illustrate the deficiencies in the current state of reaction modeling for 40–90 MeV nat
Nb(p,x) and nat
Cu(p,x) reactions. Finally, this work provides another example of the usefulness ofthe recently-described variance minimization techniques for reducing energy uncertainties in stacked targetcharged particle irradiation experiments.
5. Acknowledgements
The authors would like to particularly acknowledge the assistance and support of Michael Gallegos andDon Dry in the LANL C-NR Countroom, David Reass and Mike Connors at LANSCE-IPF, and the LANSCEAccelerator Operations staff.We gratefully acknowledge support for this work from the United States Department of Energy, Office ofScience via the Isotope Development and Production for Research and Applications subprogram in the Officeof Nuclear Physics. This work has been carried out under the auspices of the U.S. Department of Energyby Lawrence Berkeley National Laboratory and the U.S. Nuclear Data Program under contract
AppendixA. Decay data
The lifetimes and gamma-ray branching ratios listed in these tables were used for all calculations ofmeasured cross sections reported in this work, and have been taken from the most recent edition of NuclearData Sheets for each mass chain [8, 11–15, 62, 74–92].18 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 nat
Al(p,x) and nat
Cu(p,x).
Nuclide Half-life E γ (keV) I γ (%) Na 2.6018(22) y 1274.537 99.940(14) Na 14.997(12) h 1368.626 99.9936(15) Cr 27.704(3) d 320.0824 9.910(10)
Mn 21.1(2) m 1434.0600 98.2(5) Mn 5.591(3) d 744.233 90.0(12)5.591(3) d 935.544 94.5(13)5.591(3) d 1246.278 4.21(7)5.591(3) d 1434.092 100.0(14) Mn 312.20(20) 834.848 99.9760(10) Co 17.53(3) h 477.2 20.2(17)17.53(3) h 931.1 75.0(35)17.53(3) h 1316.6 7.1(3)17.53(3) h 1408.5 16.9(8) Ni 6.075(10) d 158.38 98.8(10)6.075(10) d 269.50 36.5(8)6.075(10) d 480.44 36.5(8)6.075(10) d 749.95 49.5(12)6.075(10) d 811.85 86.0(9)6.075(10) d 1561.80 14.0(6) Co 77.236(26) d 846.770 99.9399(2)77.236(26) d 1037.843 14.05(4)77.236(26) d 1238.288 66.46(12)77.236(26) d 1360.212 4.283(12)77.236(26) d 1771.357 15.41(6) Ni 35.60(6) h 127.164 16.7(5)35.60(6) h 1377.63 81.7(24)35.60(6) h 1757.55 5.75(20)35.60(6) h 1919.52 12.3(4) Co 271.74(6) d 122.06065 85.60(17)271.74(6) d 136.47356 10.68(8) Co 70.86(6) d 810.7593 99.450(10)70.86(6) d 863.951 0.686(10) Fe 44.495(9) d 1099.245 56.5(18)44.495(9) d 1291.590 43.2(14) Co 5.2714(5) y 1173.228 99.85(3)5.2714(5) y 1332.492 99.9826(6) Cu 3.339(8) h 282.956 12.2(2.2)3.339(8) h 373.050 2.1(4)3.339(8) h 656.008 10.8(20)3.339(8) h 1185.234 3.7(7) Zn 9.193(15) h 243.36 2.52(23)9.193(15) h 246.95 1.90(18)9.193(15) h 260.43 1.35(13)9.193(15) h 394.03 2.24(17)9.193(15) h 548.35 15.3(14)9.193(15) h 596.56 26.0(20) Cu 12.701(2) h 1345.77 0.475(11) Zn 243.93(9) d 1115.539 50.04(10) .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 nat Nb(p,x).
Nuclide Half-life E γ (keV) I γ (%) Rb 6.472(6) h 554.35 62.4(9)6.472(6) h 619.11 37.98(9)6.472(6) h 776.52 84.39(21)6.472(6) h 1044.08 32.07(8) Sr 32.41(3) h 418.37 4.2(3)32.41(3) h 762.65 26.7(22)
Y 4.86(13) h 231.7 22.8(22) Y 2.68(5) h 231.65 84(9)2.68(5) h 913.89 9.0(9) Zr 16.5(1) h 242.8 95.84(2)16.5(1) h 612.0 5.8(3) Y 14.74(2) h 443.13 16.9(5)14.74(2) h 627.72 32.6(1)14.74(2) h 1076.63 82.5(4)14.74(2) h 1153.05 30.5(9)14.74(2) h 1854.38 17.2(5)14.74(2) h 1920.72 20.8(7) Zr 1.68(1) h 380.79 62.79(10)1.68(1) h 1227.0 2.80(4)
Y 13.37(1) h 380.79 78.05(8) Y 79.8(3) h 388.5276 82.2(7)79.8(3) h 484.805 89.8(9) Zr 83.4(3) d 392.87 97.29(14) Y 106.627(21) d 898.042 93.7(3)106.627(21) d 1836.063 99.2(3)
Nb 66(2) m 588.0 95.57(13) Nb 2.03(7) h 1511.4 1.9(4)2.03(7) h 1627.2 3.5(7)2.03(7) h 1833.4 3.3(7) Zr 78.41(12) h 909.15 99.04(3)78.41(12) h 1713.0 0.745(13) Mo 5.56(9) h 122.370 64(3)5.56(9) h 162.93 6.0(6)5.56(9) h 203.13 6.4(6)5.56(9) h 257.34 78(4)5.56(9) h 323.20 6.3(6)5.56(9) h 472.2 1.42(16)5.56(9) h 941.5 5.5(7) Nb 14.6(5) h 132.716 4.13(4)14.6(5) h 141.178 66.8(7)14.6(5) h 1611.76 2.38(7)
Nb 60.86(22) d 104.62 0.574(1)60.86(22) d 1204.67 2.0(3)
Nb 10.15(2) d 912.6 1.78(10)10.15(2) d 934.44 99.15(4)
Mo 6.85(7) d 263.049 57.4(11)6.85(7) d 684.693 99.9(8)6.85(7) d 1477.138 99.1(11) .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 AppendixB. Measured excitation functions
Figures of the cross sections measured in this work are presented here, in comparison with literature data[16, 26, 50, 61, 63, 93–108], the TENDL-2015 data library [70], and the reaction modeling codes CoH-3.5.1,EMPIRE-3.2.3, and TALYS-1.8 [66, 70, 72]. 21 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34
30 40 50 60 70 80 90 10000.511.522.53
60 65 70 75 80 85 90 95 10000.511.522.560 65 70 75 80 85 90 95 10000.511.522.5 60 65 70 75 80 85 90 95 10000.511.522.5
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30 40 50 60 70 80 90 10000.511.522.533.544.5
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30 40 50 60 70 80 90 10002468101214 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 AppendixC. Measured isomer-to-ground state branching ratios
Plots of the isomer-to-ground state ratios measured in this work are presented here, in comparison withliterature data and reaction modeling codes [16, 61, 63, 104].28 .S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34
60 65 70 75 80 85 90 95 10000.10.20.30.40.50.60.70.80.91 30 40 50 60 70 80 90 10000.20.40.60.811.250 55 60 65 70 75 80 85 90 95 10000.10.20.30.40.50.60.70.80.91 30 40 50 60 70 80 90 10000.20.40.60.811.2
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