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# Excitation functions for (p,x) reactions of niobium in the energy range of Ep = 40–90 MeV

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## Abstract and Figures

A stack of thin Nb foils was irradiated with the 100 MeV proton beam at Los Alamos National Laboratory's Isotope Production Facility, to investigate the $^{93}$Nb(p,4n)$^{90}$Mo nuclear reaction as a monitor for intermediate energy proton experiments and to benchmark state-of-the-art reaction model codes. A set of 38 measured cross sections for $^{\text{nat}}$Nb(p,x) and $^{\text{nat}}$Cu(p,x) reactions between 40-90 MeV, as well as 5 independent measurements of isomer branching ratios, are reported. These are useful in medical and basic science radionuclide productions at intermediate energies. The $^{\text{nat}}$Cu(p,x)$^{56}$Co, $^{\text{nat}}$Cu(p,x)$^{62}$Zn, and $^{\text{nat}}$Cu(p,x)$^{65}$Zn reactions were used to determine proton fluence, and all activities were quantified using HPGe spectrometry. Variance minimization techniques were employed to reduce systematic uncertainties in proton energy and fluence, improving the reliability of these measurements. The measured cross sections are shown to be in excellent agreement with literature values, and have been measured with improved precision compared with previous measurements. This work also reports the first measurement of the $^{\text{nat}}$Nb(p,x)$^{82\text{m}}$Rb reaction, and of the independent cross sections for $^{\text{nat}}$Cu(p,x)$^{52\text{g}}$Mn and $^{\text{nat}}$Nb(p,x)$^{85\text{g}}$Y in the 40-90 MeV region. The effects of $^{\text{nat}}$Si(p,x)$^{22,24}$Na contamination, arising from silicone adhesive in the Kapton tape used to encapsulate the aluminum monitor foils, is also discussed as a cautionary note to future stacked-target cross section measurements. \emph{A priori} predictions of the reaction modeling codes CoH, EMPIRE, and TALYS are compared with experimentally measured values and used to explore the differences between codes for the $^{\text{nat}}$Nb(p,x) and $^{\text{nat}}$Cu(p,x) reactions.
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Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34
Nucl
Instrum
Meth B
Excitation functions for (p,x) reactions of niobium in the energy
range of Ep= 40–90 MeV
Andrew S. Voylesa,, Lee A. Bernsteinb,a, Eva R. Birnbaumd, Jonathan W. Englec,
Stephen A. Gravese, Toshihiko Kawanof, Amanda M. Lewisa, Francois M. Nortierd
aDepartment of Nuclear Engineering, University of California, Berkeley, Berkeley, CA 94720, USA
bNuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
cDepartment of Medical Physics, University of Wisconsin – Madison, Madison, WI 53705, USA
dIsotope Production Facility, Chemistry Division, Los Alamos National Laboratory, Los Alamos, NM 87544, USA
eDepartment of Radiation Oncology, University of Iowa, Iowa City, IA 52242, USA
fTheoretical 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’s
Isotope Production Facility, to investigate the
93Nb
(p,4n)
90Mo
nuclear reaction as a monitor for intermediate energy
proton experiments and to benchmark state-of-the-art reaction model codes. A set of 38 measured cross sections for
natNb
(p,x) and
natCu
(p,x) reactions between 40–90 MeV, as well as 5 independent measurements of isomer branching
ratios, are reported. These are useful in medical and basic science radionuclide productions at intermediate energies.
The
natCu
(p,x)
56Co
,
natCu
(p,x)
62Zn
, and
natCu
(p,x)
65Zn
reactions were used to determine proton ﬂuence, and all
activities were quantiﬁed using HPGe spectrometry. Variance minimization techniques were employed to reduce
systematic uncertainties in proton energy and ﬂuence, improving the reliability of these measurements. The measured
cross sections are shown to be in excellent agreement with literature values, and have been measured with improved
precision compared with previous measurements. This work also reports the ﬁrst measurement of the
natNb
(p,x)
82mRb
reaction, and of the independent cross sections for
natCu
(p,x)
52gMn
and
natNb
(p,x)
85gY
in the 40–90 MeV region.
The eﬀects of
natSi
(p,x)
22,24Na
contamination, arising from silicone adhesive in the Kapton tape used to encapsulate
the aluminum monitor foils, is also discussed as a cautionary note to future stacked-target cross section measurements.
A priori predictions of the reaction modeling codes CoH, EMPIRE, and TALYS are compared with experimentally
measured values and used to explore the diﬀerences between codes for the natNb(p,x) and natCu(p,x) reactions.
Keywords: Nb + p, Cu + p, Niobium, 90Mo, 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) are
performed in the U.S. alone [
1
,
2
]. Most of the radionuclides currently used for these procedures are produced
by low- (E
<
30 MeV / A) and intermediate-energy (30
<
E
<
200 MeV / A) accelerators, e.g.,
11C
,
18F
,
68Ga
,
82Rb
, and
123I
. These accelerators also produce non-medical radionuclides with commercial value,
Email addresses: andrew.voyles@berkeley.edu (Andrew S. Voyles ), jwengle@wisc.edu (Jonathan W. Engle)
1
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 2
such as
22Na
,
73As
,
95mTc
, and
109Cd
[
3
,
4
]. Novel applications are being explored for several radionuclides
whose production methodologies are not established, but their production requires accurate, high-ﬁdelity
cross section data. Candidate isotopes to meet these needs have been identiﬁed based on their chemical
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 will
serve to facilitate the production of clinically relevant quantities of radioactivity.
Accurate cross section measurements using activation methods beneﬁt from well- characterized monitor
reactions. Currently there is a paucity of such data at intermediate energies, and much of what exists have
high uncertainties (
>
15%). Indeed, the development of new monitor reaction standards and the improved
evaluation of existing standards is one of the areas of greatest cross-cutting need for nuclear data [
6
]. New
reactions can expand the available range of options for the monitoring of charged particle beams. This work
is an attempt to characterize a new monitor reaction for proton beams in excess of 40 MeV, for possible use at
isotope production facilities such as the Brookhaven Linac Isotope Producer (BLIP) at Brookhaven National
Laboratory, the Isotope Production Facility (IPF) at Los Alamos National Laboratory, or the Separated
Sector Cyclotron at the iThemba Laboratory for Accelerator Based Sciences.
Desirable monitor reactions possess several hallmark characteristics, including intense, distinct gamma-
rays, which can be used for unique identiﬁcation during post-activation assay, and lifetimes long enough to
enable removal after a reasonable length irradiation. Care should also be taken to avoid cases where two
radionuclides which are produced by two diﬀerent reactions on the same monitor foil lead to states in the same
daughter nuclide. For example,
48V
(
t1/2
= 15.97 d,
= 100% to
48Ti
) and
48Sc
(
t1/2
= 43.67 h,
β
= 100%
to
48Ti
) can both be formed via
nat
Ti(p,x) reactions, yielding the same 983.52 keV transition in
48Ti
[
7
]. It is
also of vital importance that the proposed monitor nucleus have well-characterized decay data. This includes
a precise and well-established half-life, and well-characterized decay gamma-ray intensities. From a targetry
perspective, it is preferable to use a naturally mono-isotopic target that is readily available and chemically
inert. Targets which can be formed into a wide thickness range are convenient, as selection is subject to the
context of an experiment, seeking to maximize thickness without overly perturbing the energy uncertainty of
measurements. Lastly, and perhaps most importantly for high-energy monitor reaction applications, it is of
utmost importance to choose a reaction channel which cannot be populated via secondary particles incident
upon 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 primary
beam should be avoided, as it is often diﬃcult to accurately and unambiguously separate out the fraction of
secondary particles contributing to the total activation.
One reaction which satisﬁes these requirements is that of a new, intermediate-energy proton monitor reac-
tion standard based on
93Nb
(p,4n)
90Mo
. Niobium is naturally mono-isotopic, readily available commercially
in high purity, is fairly chemically inert, and can easily be rolled down to foils as thin as 1
µ
m.
90Mo
also
has a suﬃciently long lifetime (
= 100%
, t1/2
= 5
.
56
±
0
.
09 h [
8
]) and seven strong, distinct gamma lines
(notably its 122.370 keV [
Iγ
= 64
±
3%] and 257.34 keV [
Iγ
= 78
±
4%] lines) which can be used to uniquely
and easily quantify
90Mo
90Mo
is completely immune from (n,x) production on
93Nb
, being produced only via the primary proton beam, and the
90Mo
decay lines can only be observed in
its decay, as its daughter, 90Nb, is also unstable and decays via to stable 90Zr.
The purpose of the present work is to measure the production of the long-lived radionuclide
90Mo
via
the
nat
Nb(p,x) reaction. In addition to the
nat
Nb(p,x)
90Mo
measurement, this experiment has also yielded
measurements of 37 other (p,x) production cross sections between 40–90 MeV for a number of additional
reaction products, including several emerging radionuclides with medical applications. These include the
non-standard positron emitters 57Ni, 64Cu, 86Y, 89Zr, 90Nb, and the diagnostic agent 82mRb.
In addition to providing a potentially highly-valuable beam monitor, the Nb(p,x) reactions oﬀer an
opportunity to study the angular momentum deposition via pre-equilibrium reactions and the spin distribution
in g
9/2
subshell nuclei via the observation of isomer-to-ground state ratios. Measurements of isomer-to-
ground state ratios have been used for over 20 years to probe the spin distribution of excited nuclear
states in the A
190 region [
9
,
10
]. These include the
52mMn
(
t1/2
= 21
.
1
±
0
.
2 m; J
π
= 2
+
) to
52gMn
(
t1/2
= 5
.
591
±
0
.
003 d; J
π
= 6
+
),
58mCo
(
t1/2
= 9
.
10
±
0
.
09 h; J
π
= 5
+
) to
58gCo
(
t1/2
= 70
.
86
±
0
.
06 d;
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A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 3
J
π
= 2
+
),
85mY
(
t1/2
= 4
.
86
±
0
.
13 h; J
π
=
9/2+
) to
85gY
(
t1/2
= 2
.
68
±
0
.
05 h; J
π
=
1/2
),
87mY
(
t1/2
= 13
.
37
±
0
.
03 h; J
π
=
9/2+
) to
87gY
(
t1/2
= 79
.
8
±
0
.
3 h; J
π
=
1/2
), and
89mNb
(
t1/2
= 66
±
2 m;
Jπ=1/2) to 89gNb (t1/2= 2.03 ±0.07 h; Jπ=9/2+) ratios [11–15].
The measurements described in this paper involve the use of multiple monitor reactions in conjunction
with statistical calculations and proton transport simulations to reduce systematic uncertainties in beam
energy assignments, leading to some of the ﬁrst and most precise measurements for many of the excitation
functions reported here. By expanding the available set of monitor reaction standards and well-characterized
isotope production excitation functions, this work should help optimize medical isotope production modalities,
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].
2.1. Stacked-target design
A stacked-target design was utilized for this work in order that the (p,x) cross sections for each reaction
channel could be measured at multiple energy positions in a single irradiation [
17
]. A series of nominal 25
µ
m
natNb
foils (99.8%, lot #T23A035), 25
µ
m
natAl
foils (99.999%, lot #M06C032), and 50
µ
m
natCu
foils
(99.9999%, lot #N26B062) were used (all from Alfa Aesar, Ward Hill, MA, 01835, USA) targets were used.
Six foils of each metal were cut down to 2.5
×
2.5 cm squares and characterized — for each foil, length
and width measurements were taken at four diﬀerent locations using a digital caliper (Mitutoyo America
Corp.), thickness measurements were taken at four diﬀerent locations using a digital micrometer (Mitutoyo
America Corp.), and four mass measurements were taken using an analytical balance after cleaning the foils
with isopropyl alcohol. Using these length, width, and mass readings, the areal density and its uncertainty
(in mg/cm
2
) for each foil was calculated. The foils were tightly sealed into “packets” using two pieces of
3M 5413-Series Kapton polyimide ﬁlm tape — each piece of tape consists of 43.2
µ
(nominal 4.79 mg/cm
2
) on 25.4
µ
m of a polyimide backing (nominal 3.61 mg/cm
2
). The sealed foils were
mounted over the hollow center of a 1.575 mm-thick plastic frame. One
natAl
, one
natCu
, and one
natNb
mounted foil were bundled together using baling wire for each energy position. These foil packet bundles
were lowered into the beamline by inserting them into a water-cooled production target box. The box, seen
in Figure 1, is machined from 6061 aluminum alloy, has a thin (0.64 mm) Inconel beam entrance window, and
contains 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 box is
lowered through a hot cell into the beamline, where it sits electrically isolated. The speciﬁcations of the
target 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 Los
Alamos National Laboratory (LANL), using the LANSCE linear accelerator. The stack was irradiated for
approximately 2 hours with a nominal current of 1 mA, using a 50
µ
s pulse at a frequency of 2 Hz, for an
anticipated integral current of 205.9 nAh. The beam current, measured using an inductive pickup, remained
stable under these conditions for the duration of the irradiation, with the exception of approximately 70 s of
downtime, which occurred approximately 3 minutes into irradiation. The proton beam incident upon the
stack’s Inconel beam entrance window had an average energy of 100 MeV determined via time-of-ﬂight, with
an approximately Gaussian energy distribution width of 0.1 MeV — this energy proﬁle was used for all later
analysis. At the end of the irradiation, the target stack was withdrawn from the beamline into the IPF hot
cell, where it was disassembled and the activated foils removed using robotic manipulators. The activated
foils were cleaned of all surface contamination, and transported to a counting lab for gamma spectrometry,
which started approximately 6 hours following end-of-bombardment.
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A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 4
Figure 1: Photograph of the assembled IPF target stack, before the stack’s o-ring lid was sealed in place. The baling wire
handles aﬃxed to each bunch of Al+Cu+Nb foils are visible in each energy position, to facilitate removal of activated foils via
manipulators in the IPF hot cell. The circular Inconel beam entrance aperture is visible in the bottom center of the photograph.
Table 1: Speciﬁcations of the target stack design in the present work. The proton beam enters the stack upstream of the
249.8
µ
m SS proﬁle monitor, and is transported through the stack in the order presented here. The 6061 aluminum degraders
have a measured density of approximately 2.80 g/cm
3
. Their areal densities were determined using the variance minimization
techniques described in this work and the earlier paper by Graves et al. [
16
]. At both the front and rear of the target stack’s
foils, a 316 stainless steel foil is inserted to serve as a beam proﬁle monitor — after end-of-bombardment (EoB), decay radiation
emitted from these activated stainless steel foils were used to develop radiochromic ﬁlm (Gafchromic EBT), revealing the spatial
proﬁle of the beam entering and exiting the stack.
Target layer Measured
thickness
Measured areal
density (mg/cm2)
Areal density
uncertainty (%)
SS proﬁle monitor 249.8 µm 194.56 0.29
Al-1 25.0 µm 6.52 0.72
Cu-1 61.3 µm 53.74 0.15
Nb-1 30.0 µm 23.21 0.17
Al Degrader 01 4.96 mm - -
Al-2 25.5 µm 6.48 0.36
Cu-2 61.8 µm 53.85 0.17
Nb-2 30.8 µm 22.91 0.17
Al Degrader 02 4.55 mm - -
Al-3 25.8 µm 6.47 0.31
Cu-3 61.5 µm 53.98 0.11
Nb-3 31.0 µm 22.91 0.24
Al Degrader 03 3.52 mm - -
Al-4 26.3 µm 6.51 0.41
Cu-4 61.3 µm 53.46 0.22
Nb-4 30.8 µm 22.55 0.25
Al Degrader 04 3.47 mm - -
Al-5 26.5 µm 6.48 0.29
Cu-5 61.5 µm 53.57 0.11
Nb-5 30.8 µm 22.11 0.25
Al Degrader 05 3.46 mm - -
Al-6 26.3 µm 6.48 0.62
Cu-6 62.0 µm 53.84 0.32
Nb-6 31.3 µm 22.12 0.13
SS proﬁle monitor 124.4 µm 101.34 0.23
4
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 5
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10 1
10 2
10 3
10 4
10 5
10 6
Figure 2: A gamma spectrum collected from an activated Nb foil at approximately 80 MeV. While the majority of observed
reaction products are visible in this spectrum, the
90Mo
decay lines, which form the basis of the
93Nb
(p,x)
90Mo
monitor
reaction, are high in intensity and clearly isolated from surrounding peaks.
2.2. Measurement of induced activities
A single detector was used in this measurement, an ORTEC GEM Series (model #GEM10P4-70) High-
Purity Germanium (HPGe) detector. The detector is a mechanically-cooled coaxial p-type HPGe with a
1 mm aluminum window, and a 49.2 mm diameter, 27.9 mm long crystal. Samples were counted at ﬁxed
positions ranging 4.5–83.5 cm (5% maximum permissible dead-time) from the front face of the detector, with
a series of standard calibration sources used to determine energy, eﬃciency, and pileup calibrations for each
position. The foils were counted for a period of 2 weeks following end-of-bombardment (EoB), to accurately
quantify all induced activities, with dead time never exceeding 5%. An example of one of the gamma-ray
spectra collected in such a fashion is shown in Figure 2. For all spectra collected, net peak areas were ﬁtted
using the gamma spectrometry analysis code UNISAMPO [
18
], which has been shown to perform best in
comparisons with other common analysis codes [19].
Following acquisition, the decaying product nuclei corresponding to each observed peak in the collected
spectra were identiﬁed. The calibrated detector eﬃciencies, along with gamma-ray intensities for each
transition and corrections for gamma-ray attenuation within each foil packet, were used to convert the net
counts in each ﬁtted gamma-ray photopeak into an activity for the decay of the activation products. The
nuclear decay data used in this work is tabulated in Table A.6 and Table A.7 of Appendix A. Data for
photon attenuation coeﬃcients were taken from the XCOM photon cross sections database [
20
]. Decay
gamma-rays from the product nuclei were measured at multiple points in time (up to 2 weeks after EoB),
and as nearly all of the product nuclei have multiple high-intensity gamma-rays, this provided independent
activity measurements at each time point. The total propagated uncertainty of the measured activity is the
quadrature sum of the uncertainty in ﬁtted peak areas, uncertainty in detector eﬃciency calibration, and
uncertainty in the gamma-ray branching ratio data.
Since many of the reaction products populated by energetic protons are more than one decay oﬀ of
stability, many of these are produced not only directly by reactions, but also indirectly by decay down a
mass chain. To this end, it is useful to diﬀerentiate between the types of cross sections reported in this
work. For the ﬁrst observable product nuclei in a mass chain, its (p,x) cross section will be reported as a
cumulative cross section (
σc
), which is the sum of direct production of that nucleus, as well as decay of its
precursors and any other independent cross sections leading to that nucleus. Cumulative cross sections will
5
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 6
be reported whenever it is impossible to use decay spectrometry to distinguish independent production of a
nucleus from decay feeding. For all remaining observed reaction products in the mass chain, and cases where
no decay precursors exist, independent cross sections (
σi
) will be reported, allowing for determination of 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 and
the spectrum acquisition, in order to calculate
A0
, 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 observed
product nucleus allows for a more accurate determination of
A0
than simply basing its calculation oﬀ of
a single gamma-ray observation. For the case of cumulative cross sections, EoB activities were quantiﬁed
by ﬁtting the activities observed at multiple time points
t
(since EoB) to the well-known radioactive decay
law. Nonlinear regression was used for this ﬁtting process, minimizing on
χ2
/ degree of freedom, so that not
only would the uncertainty-weighted EoB activities be ﬁtted, but that a 1-
σ
conﬁdence interval in
A0
could
be reported as as well. As with the gamma-ray intensities, all lifetimes used in this work are tabulated in
Table A.6 and Table A.7 of Appendix A. In the case of independent cross sections, a similar process was
followed, quantifying
Ai(t= 0)
=
Ai,0
, the EoB activity of nuclide
i
, by instead regressing to the solutions
to the Bateman equation [21, 22]:
An(t) = λn
n
X
i=1
Ni,0×
n1
Y
j=i
λj
×
n
X
j=i
eλjt
Qn
i6=j(λiλj)
(1)
where
j
refers to a precursor nucleus populating a speciﬁc end-product. While higher-order terms were added
if needed, typically for an isomeric state in a particular mass chain, the second-order expansion (
n
= 2) was
often suﬃcient to quantify EoB activities in a mass chain, simplifying to:
A2(t) = A1,0λ2
λ1λ2eλ2teλ1t+A2,0eλ2t(2)
In these cases, the previously-quantiﬁed EoB activities from decay precursors (
A1,0
, etc) would be substituted
in, 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 independent
EoB activities, these will be later used to report the various cross sections for all observed reaction products
and isomeric states.
2.3. Proton ﬂuence determination
In addition to the LANSCE-IPF beamline’s direct beam current measurements, thin
natAl
and
natCu
foils
were included along with the
natNb
targets at each energy position, to provide more sensitive beam current
monitors. The IAEA-recommended
natAl
(p,x)
22Na
,
natAl
(p,x)
24Na
,
natCu
(p,x)
56Co
,
natCu
(p,x)
62Zn
, and
natCu
(p,x)
65Zn
monitor reactions were used for proton ﬂuence measurement [
23
]. Due to the large energy
degradation between the front and back of the target stack, a non-trivial broadening of the proton energy
distribution was expected for all monitor and target foils. As a result, the integral form of the well-known
activation equation was used to accurately determine proton ﬂuence (It) in each monitor foil:
It=A0t
ρr(1 eλt)Rσ(E)
dE dE
(3)
where
A0
is the EoB activity for the monitor reaction product,
I
is the proton current,
ρ
r
is the foil’s areal
density,
λ
is the monitor reaction product’s decay constant, ∆
t
σ(E)
is the IAEA
recommended cross section at energy
E
, and
dE
is the diﬀerential proton ﬂuence. Using this formalism, the
quantiﬁed EoB activities for each monitor reaction may be converted into a measured proton ﬂuence at each
energy position.
The propagated uncertainty in proton ﬂuence is calculated as the quadrature sum of the uncertainty
in quantiﬁed EoB activity, uncertainty in the duration of irradiation (conservatively estimated at 60 s, to
6
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 7
account for any transient changes in beam current), uncertainty in foil areal density, uncertainty in monitor
product half-life (included, but normally negligible), uncertainty in IAEA recommended cross section, and
uncertainty in diﬀerential proton ﬂuence. Of these, the ﬁrst four contributions are all easily quantiﬁed in
the preparation and execution of a stacked target irradiation; the last two contributions prove to be more
nuanced, however. The uncertainty in proton ﬂuence for irradiated monitor foils is derived from statistical
uncertainty in the modeling of proton transport in the stack irradiation, discussed in subsection 2.4. The
uncertainty in IAEA recommended cross section values must be estimated indirectly, as no uncertainty in
the recommended cross sections is provided in the current IAEA evaluation. Fortunately, the recommended
cross section values for each monitor reaction tend to closely match one of the selected experimental source
data 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 data
set most closely matching the IAEA recommended values. For the monitor reactions employed in this work,
these data sets are G. Steyn (1990) for
natAl
(p,x)
22Na
[
24
], M. Uddin (2004) for
natAl
(p,x)
24Na
[
25
], and S.
Mills (1992) for natCu(p,x)56Co, natCu(p,x)62Zn, and natCu(p,x)65Zn [26].
2.4. Proton transport calculations
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 for
the preliminary stack design. However, for ﬁnal energy and ﬂuence determinations, a more rigorous method
of proton transport modeling is needed. The Monte Carlo N-Particle transport code MCNP6.1 was used for
simulation of the full 3-D target stack, including determination of the full proton energy distribution for
each stack position [
30
]. MCNP6 provides a far more robust method of proton transport, as it is able to
account for beam losses due to scattering and reactions, as well as production of secondary particles. As it is
a Monte Carlo-based code, the uncertainty in energy distribution scales inversely with the number of source
protons simulated. 10
8
source protons were used for all simulations, which places the statistical uncertainty
in proton energy distributions at less than 0.01%.
The ability to model the full energy distribution in each target position is vital for stacked target
irradiations, due to the progressively larger energy straggling towards the rear of the stack. The initial
proton beam has a ﬁnite energy spread (an approximately 0.1 MeV Gaussian width at 100 MeV), and since
stopping power for charged particles is inversely proportional to their energy, the low-energy tail of the energy
distribution is degraded more in each stack element than the high-energy tail. This eﬀect compounds towards
the rear of the stack, creating a signiﬁcantly broadened low-energy tail, and a progressively larger net shift of
the centroid to a lower energy. To account for this increasing energy uncertainty, a suitably representative
energy must be established for each foil in the target stack. In this work, the ﬂux-weighted average proton
energy in each foil,
hEi
, represents the energy centroid for protons in a target stack component, calculated
using the energy distributions
dE from MCNP6 modeling of proton transport:
hEi=ZE
dE dE
Z
dE 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. While
most experimental uncertainties are reported at the 1
σ
level, the 2
.
355
σ
FWHM is used here to ensure at
the 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 further
reduce the uncertainty in proton energy assignments [
16
]. This method is based on the assumption that the
independent measurements of proton ﬂuence from the ﬁve monitor reactions used in this work should all
be consistent at each energy position. If the monitor reaction cross sections and MCNP6-modeled energy
distributions are both accurate, disagreement in the observed proton ﬂuences is due to poorly characterized
stopping power in simulations, or a systematic error in the areal densities of the stack components [
16
,
31
].
7
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 8
25 30 35 40 45 50 55 60
100
101
102
103
Figure 3: Result of the variance minimization performed by adjusting the degrader density in MCNP6 simulations of the target
stack. A ﬂux-weighted average proton energy of 41.34 MeV entering the last energy position creates a clear minimum in observed
reaction ﬂuence variance, corresponding to an areal density 2.52% greater than nominal. The variance minimum occurring at a
lower incident energy than nominal MCNP6 and A&Z calculations indicates that there exists an additional systematic 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 the
other stack elements (nominal 3–5 mg/cm
2
, relative to nominal 1000–1400 mg/cm
2
), the areal density of each
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 proton ﬂuence at the
lowest energy position (Al-6, Cu-6). This lowest energy position was chosen as a minimization candidate, as
it is most sensitive to systematic uncertainties in stack design. The results of this minimization technique,
shown in Figure 3, indicate a clear minimum in proton ﬂuence variance for ﬂux-weighted average 41.34 MeV
protons entering the last energy position. This is approximately 2 MeV lower than the nominal MCNP6
simulations, and approximately 3 MeV lower than nominal A&Z calculations, both of which used the nominal
2.80 g/cm
3
measured density of the 6061 aluminum degraders. This energy corresponds to a 6061 aluminum
areal density of 2.52% greater than nominal measurements, and serves as a lump correction for other minor
systematic uncertainties in stack design, including stack areal densities and incident beam energy.
The impact of this variance minimization is clearly seen in Figure 4. As expected, the 2.52% increase in
6061 aluminum areal density has an almost negligible impact on the higher-energy positions, but causes a
progressively larger downshift in proton energies at the later energy positions. In addition, as one moves
to the rear positions, the disagreement in the independent proton ﬂuence measurements is reduced. It is
worth noting that the proton ﬂuence measured by the
natAl
(p,x)
22Na
monitor reaction (threshold 21.0 MeV)
is consistently 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 polyimide backing) used for sealing the foil packets, making up approximately 10% of the silicone on
a stoichiometric basis. The
22Na
and
24Na
monitor channels can also be populated oﬀ of natural silicon
(92.2%
28Si
), predominantly via
28Si
(p,
α
2pn)
22Na
(threshold 35.3 MeV) and
28Si
(p,4pn)
24Na
(threshold
44.6 MeV).
29Si
and
30Si
are also potential targets for (p,x)
22,24Na
, albeit with higher energetic thresholds and
smaller cross sections. The attribution of excess Al(p,x)
22,24Na
activity to the silicone adhesive is supported
by the observation of 22Na and 24Na activities in all Cu and Nb foil positions.
natSi
(p,
α
2pn) is competitive with the
natAl
(p,x) production route, seen when comparing the total measured
activities of 22,24Na in each Al foil packet, relative to the expected EoB activities for each reaction channel
(Figure 5). Since no evaluated cross section data exists in this energy region for
28Si
(p,x)
22Na
(and only
minimal
natSi
data exists), the TENDL-2015 library is used to estimate the expected relative EoB activities
8
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 9
a)
b)
Figure 4: Results of variance minimization through enhancement of the eﬀective areal density of the 6061 aluminum degraders
by 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
natAl
(p,x)
22Na
and
natAl
(p,x)
24Na
monitor channels,
due to contamination from natSi(p,x)22,24Na on the silicone adhesive used for sealing foil packets.
40 50 60 70 80 90 100
0
0.5
1
1.5
2
2.5
3
a)
40 50 60 70 80 90 100
0
200
400
600
800
1000
1200
1400
b)
Figure 5: Estimates of EoB
natAl
(p,x)
22,24Na
and
natSi
(p,x)
22,24Na
activities using TENDL-2015 cross sections, in comparison
with the IAEA recommended
natAl
(p,x)
22,24Na
cross sections. At low energies, experimentally observed apparent
22,24Na
activities in each Al foil packet are consistent with IAEA recommendations, but diverge at higher energies as the
natSi
(p,x)
22Na
exit channels begin to open up.
22,24Na
activities consistent with TENDL-2015 estimates are observed in each Nb and Cu foil
packet as well, conﬁrming that contamination may be attributed to activation of silicone adhesives.
9
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 10
a)
b)
Figure 6: The “extra ﬂuence” observed in the
natAl
(p,x)
22Na
and
natAl
(p,x)
24Na
monitor channels is caused by contamination
from
natSi
(p,x)
22,24Na
on the silicone adhesive used for sealing foil packets. Following subtraction of
22,24Na
activities observed
in the silicone adhesive of Nb and Cu foils in the same energy “compartment”, the consistency of the
natAl
(p,x)
22Na
monitor
reaction improves dramatically. By excluding these contaminated channels, the remaining 3 independent monitor reactions
serve to minimize uncertainty in stack energy assignments and incident ﬂuence.
for
natAl
(p,x)
22,24Na
and
natSi
(p,x)
22,24Na
, relative to IAEA recommended
natAl
(p,x)
22,24Na
cross sections.
Several observations are immediately obvious. At lower energies, the magnitude of
natAl
(p,x)
22Na
is large
compared to
natSi
(p,x)
22Na
, which is why the
natAl
(p,x)
22Na
monitor agrees in ﬂuence at the 40 (and almost
at the 50) MeV position. At higher energies, the apparent
natAl
(p,x)
22Na
activity begins to diverge from the
IAEA expected activities as
natSi
(p,x)
22Na
production begins to open up, which accounts for the nearly 50%
apparent excess ﬂuence in
22Na
between 60–90 MeV. For
24Na
production, we see similar behavior, with
only a minor increase in apparent
24Na
activity, since the observed
natSi
(p,x)
24Na
yield remains consistently
low in magnitude. The observed
24Na
activities also follow the shape of the TENDL-2015
natSi
(p,x)
24Na
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
natSi
(p,x)
22,24Na
yields. The observation of the
22,24Na
activities in Cu and Nb foils represents an indirect
measurement of the
natSi
(p,x)
22,24Na
cross sections, but will not be reported due to uncertainties in the
areal density of the Si in the adhesive. However, if we assume a 10% Si stoichiometric basis and an areal
density of 4.79 mg/cm2(based on bulk density), we can subtract out the measured 22,24Na activity at each
Nb and Cu foil position (correcting for the minor diﬀerence in proton energy between adjacent foils) from the
apparent
22,24Na
activities observed in each Al foil packet, in order to obtain the “true” or uncontaminated
ﬂuence via the Al monitor reactions, shown in Figure 6. Following subtraction, the
22,24Na
ﬂuences become
more consistent with other monitor reaction channels, though
22Na
ﬂuence remains 3–6% higher than the
weighted mean of the remaining monitor reaction channels. While the dramatic improvement in monitor
reaction consistency builds conﬁdence, in the interest of surety and because they are consistent, only the
natCu
(p,x)
56Co
,
natCu
(p,x)
62Zn
, and
natCu
(p,x)
65Zn
monitor reaction channels will be used for ﬂuence
determination for the reported cross sections. This serves as a pointed example of the importance of selecting
monitor reaction products inaccessible through channels aside from the primary reaction (
natAl
(p,x)
22,24Na
,
in this case ), as noted previously.
Using this variance minimized degrader density, the ﬁnal incident proton energy distributions
dE
from
MCNP6 simulation are shown for the six irradiated Nb foils in Figure 7. As expected, the energy distribution
becomes increasingly more broadened at the lower energy positions, as a result of the beam energy degradation.
In addition, as the beam becomes more degraded, the magnitude of the peak of each energy distribution
10
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 11
0 20 40 60 80 100
10 -8
10 -7
10 -6
10 -5
10 -4
10 -3
10 -2
Figure 7: Final variance minimized incident proton energy distributions for the Nb foils, as simulated in MCNP6. The
distribution tallies in each foil are all normalized to be per source proton, which was 10
8
in all simulations. As the beam is
degraded, proton energy distributions become visibly broadened due to straggling, and drop in magnitude due to scattering
losses.
(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 with the
monitor foils, these distributions were used to calculate the energy centroid (as the ﬂux-weighted average
proton energy) and uncertainty (as the FWHM of the distribution) for the ﬁnal proton energy assignment of
each Nb foil.
An enhanced version of the ﬁnal
natCu
(p,x)
56Co
,
natCu
(p,x)
62Zn
, and
natCu
(p,x)
65Zn
monitor reaction
ﬂuences is shown in Figure 8. Without the reliable use of the
natAl
(p,x)
22Na
and
natAl
(p,x)
24Na
monitor
channels, local interpolation cannot be used for ﬂuence assignment to the Nb foils, and global interpolation
is reliant upon a validated model for ﬂuence loss. The uncertainty-weighted mean for the three
natCu
(p,x)
monitor channels was calculated at each energy position, to determine the ﬁnal ﬂuence assignments for the Nb
and Cu foils. Uncertainty in proton ﬂuence is likewise calculated by error propagation of the ﬂuence values
at each energy position. These weighted-mean ﬂuences are plotted in in Figure 8, along with the estimated
ﬂuence according to both MCNP6 transport and an uncertainty-weighted linear
χ2
ﬁt to the individual
monitor channel ﬂuence measurements. Both models reproduce the observed ﬂuence data consistently within
uncertainty, with the MCNP6 model predicting a slightly greater ﬂuence loss throughout the stack. These
models are used purely to provide an extrapolation from the 90 MeV energy position back to the “front” of
the stack at 100 MeV, to compare with the nominal ﬂuence measured by IPF upstream current monitors.
2.5. Calculation of measured cross sections
Using the quantiﬁed EoB activities along with the variance-minimized proton ﬂuence, it is possible to
calculate the ﬁnal cross sections for the various observed Nb(p,x) reactions. While thin (
22 mg/cm
2
) Nb
foils were irradiated to minimize the energy width of these cross section measurements, it is important to
note that all cross sections reported here are ﬂux-averaged over the energy distribution subtended by each
foil, as seen in Figure 7. For both the cumulative and independent activities quantiﬁed, cross sections were
calculated as:
σ=A0
ρrI (1 eλt)(5)
where
A0
is the EoB activity for the monitor reaction product,
I
is the proton current,
ρ
r
is the foil’s
areal density,
λ
is the monitor reaction product’s decay constant, and ∆
t
is the length of irradiation. The
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 minutes into irradiation. The
11
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 12
Figure 8: Final uncertainty-weighted mean proton ﬂuences throughout the target stack, based on the variance-minimized
observed ﬂuence from the the
natCu
(p,x)
56Co
,
natCu
(p,x)
62Zn
, and
natCu
(p,x)
65Zn
monitor reactions. The ﬂuence drops by
approximately 7.2–8.9% from the incident ﬂuence of 196.9–198.8 nAh over the length of the target stack, based on ﬂuence loss
models from MCNP6 simulations and an empirical ﬁt to ﬂuence measurements.
propagated uncertainty in cross section is calculated as the quadrature sum of the uncertainty in quantiﬁed
EoB 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 foil
areal density, uncertainty in monitor product half-life (included, but normally negligible), and uncertainty
in proton current (quantiﬁed by error propagation of the monitor reaction ﬂuence values at each energy
position, as seen in Figure 8).
3. Results
After irradiation, all foils were conﬁrmed to still be sealed inside their Kapton packets, verifying that
no activation 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
of short-lived beta activities. This blister shows the location where the primary proton beam was incident
upon the foil. The
natCu
(p,x)
56Co
,
natCu
(p,x)
62Zn
, and
natCu
(p,x)
65Zn
monitor reactions were used to
determine the uncertainty-weighted mean ﬂuence at each energy position (seen in Figure 8). A ﬂuence of
198.8
±
6.7 nAh was calculated to be incident upon the target stack using the MCNP6 ﬂuence model, and a
ﬂuence of 196.9
±
11.3 nAh using the linear ﬁt model, both of which are consistent with the nominal ﬂuence of
205.9 nAh based on IPF upstream current monitors. As ﬂuence loss in the target box’s entrance window scales
with
σtotρ
r
, it is expected that an extrapolation back to the stack entrance will underestimate the nominal
ﬂuence incident upon the box. This incident ﬂuence dropped by approximately 8.9% to 180.9
±
5.4 nAh (and
by 7.2% to 182.7
±
13.5 nAh using the linear ﬁt model) over the length of the target stack, which is consistent
with similar measurements at IPF in the past [
16
]. This loss of ﬂuence is due to a combination of (p,x)
reactions throughout the target stack, as well as large-angle deﬂections (primarily in the aluminum degraders)
from scattering of the beam.
Using the ﬁnal proton ﬂuence at each energy position, cross sections for
51Cr
,
52gMn
,
52mMn
,
54Mn
,
55Co
,
56Ni
,
57Ni
,
57Co
,
58gCo
,
58mCo
,
59Fe
,
60Co
,
61Cu
, and
64Cu
were extracted for (p,x) reactions on
natCu
foils in the 40–90 MeV region, as recorded in Table 2. For (p,x) reactions on
natNb
foils, the (p,x)
cross sections for
82mRb
,
83Sr
,
85gY
,
85mY
,
86Zr
,
86Y
,
87Zr
,
87gY
,
87mY
,
88Zr
,
88Y
,
89gNb
,
89mNb
,
89Zr
,
90Mo
,
90Nb
,
91mNb
,
92mNb
, and
93mMo
were extracted, as recorded in Table 3. In addition, as there exist
a number of isomers with radioactive ground states in these mass regions, independent measurements of
isomer-to-ground-state branching ratios for
52m/gMn
,
58m/gCo
,
85m/gY
,
87m/gY
, and
89m/gNb
were extracted
12
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 13
Table 2: Measured cross sections for the various
natCu
(p,x) reaction products observed in this work. Cumulative cross sections
are designated as σc, independent cross sections are designated as σi.
Production cross section (mb)
Ep(MeV) 89.74+0.48
0.43 79.95+0.67
0.64 70.17+0.91
0.85 61.58+1.03
0.98 52.10+1.25
1.20 41.05+1.62
1.54
51Cr (σc) 0.919 ±0.079 0.373 ±0.023 0.450 ±0.028 0.303 ±0.016 –
52Mn (σc) 1.70 ±0.11 0.570 ±0.031 0.0407 ±0.0022 0.00526 ±0.00057 –
52gMn (σi) 0.673 ±0.043 0.239 ±0.018 0.0164 ±0.0023 0.000986 ±0.000053 –
52mMn (σc) 1.023 ±0.091 0.331 ±0.030 0.0244 ±0.0036 0.00427 ±0.00052 –
54Mn (σi) 5.87 ±0.37 3.77 ±0.21 4.14 ±0.22 4.84 ±0.26 1.680 ±0.091 –
55Co (σc) 1.71 ±0.11 1.015 ±0.058 0.193 ±0.012 0.0299 ±0.0028 0.00235 ±0.00022 –
56Ni (σc) 0.0806 ±0.0051 0.1005 ±0.0055 0.0906 ±0.0046 0.0304 ±0.0016 –
57Ni (σc) 1.465 ±0.093 1.202 ±0.065 1.400 ±0.071 2.13 ±0.11 1.565 ±0.083 0.0262 ±0.0015
57Co (σi) 40.1±2.5 35.6±1.9 35.8±1.8 48.5±2.5 47.7±2.5 3.21 ±0.18
58Co (σc) 57.7±4.5 55.0±4.7 42.7±3.4 33.7±2.8 39.0±3.8 62.3±4.6
58gCo (σi) 14.0±2.5 10.8±2.1 6.1±1.6 7.8±1.4 7.1±1.7 1.12 ±0.32
58mCo (σi) 43.6±3.7 44.2±4.3 36.6±3.0 25.8±2.5 31.9±3.3 61.1±4.6
59Fe(σc) 0.865 ±0.057 0.837 ±0.046 0.749 ±0.039 0.616 ±0.034 0.209 ±0.014 –
60Co (σc) 13.23 ±0.87 13.47 ±0.78 11.14 ±0.94 11.44 ±0.80 9.30 ±0.87 6.6±1.1
61Cu (σc) 50.5±3.3 56.1±3.2 65.1±3.6 72.2±4.0 80.6±4.7 157.1±8.6
64Cu (σi) 38.7±2.7 42.8±2.4 45.5±2.7 50.2±2.8 55.7±3.0 63.3±3.6
and are recorded in Table 4. Comparisons of the measured cross sections and isomer branching ratios with
32
]) are seen in the ﬁgures of Appendix B and Appendix C. The
propagated uncertainty in these cross sections varies widely based on the reaction product in question, with
the major components arising from uncertainty in EoB activity (
±
3–7%), proton ﬂuence (
±
4–6%), and foil
areal density (±0.1–0.6%).
These results have several notable features. The various
natCu
(p,x) cross sections measured here are
in excellent agreement with the body of measurements in the literature, but have been measured nearly
exclusively with the highest precision to date. Similarly, the various
natNb
(p,x) cross sections measured
here are in excellent agreement with literature data, which is far more sparse in the 40–90 MeV region
than for
natCu
(p,x) — fewer than three existing measurements have been performed for the majority of
the reactions presented here. Indeed, the
natNb
(p,x)
83Sr
,
natNb
(p,x)
85Y
,
natNb
(p,x)
89Nb
,
natNb
(p,x)
90Mo
,
natNb
(p,x)
91mNb
, and
natNb
(p,x)
98mMo
reactions each possess no more than a total of three data points
in this energy region. Not only do the
natNb
(p,x) measurements in this work ﬁll in the sparse data in this
energy 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
natNb
(p,x)
82mRb
reaction in the 40–90 MeV region, the independent cross section for
natCu
(p,x)
52gMn
, and
the
52mMn
(2
+
) /
52gMn
(6
+
) isomer branching ratio via
natCu
(p,x). The cumulative cross sections from
these data are also consistent with existing measurements of the cumulative
natCu
(p,x)
52Mn
cross section.
Similarly, this work oﬀers the ﬁrst measurement of the independent cross sections for
natNb
(p,x)
85gY
, as well
as the ﬁrst measurement of the 85mY (9/2+) / 85gY (1/2) isomer branching ratio via natNb(p,x).
Notably, this work is the most well-characterized measurement of the
natNb
(p,x)
90Mo
reaction below 100
MeV to date, with cross sections measured at the 4–6% uncertainty level. This is important, as it presents
the ﬁrst step towards characterizing this reaction for use as a proton monitor reaction standard below 100
MeV.
natNb
(p,x)
90Mo
can only be populated through the (p,4n) reaction channel, so no corrections for (n,x)
contamination channels or decay down the A=90 isobar are needed.
90Mo
possesses seven strong, distinct
gamma lines which can easily be used for its identiﬁcation and quantiﬁcation. Finally, the production of
90Mo
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
2
Nb targets easily provided
suﬃcient counting statistics for activity quantiﬁcation in the 40–90 MeV region. This result presents the ﬁrst
step towards the use of
90Mo
as a clean and precise charged particle monitor reaction standard in irradiations
up to approximately 24 hours in duration.
13
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 14
Table 3: Measured cross sections for the various
natNb
(p,x) reaction products observed in this work. Cumulative cross sections
are designated as σc, independent cross sections are designated as σi.
Production cross section (mb)
Ep(MeV) 89.37+0.47
0.45 79.55+0.68
0.64 69.70+0.90
0.85 61.07+1.05
0.98 51.51+1.25
1.21 40.34+1.58
1.55
82mRb (σc) 2.48 ±0.22 –
83Sr (σc) 4.02 ±0.61 4.78 ±0.42 3.49 ±0.36 –
85Y (σc) 13.78 ±0.55 7.52 ±0.51 2.11 ±0.14 –
85gY (σi) 2.37 ±0.11 2.08 ±0.17 0.557 ±0.037 –
85mY (σi) 11.41 ±0.54 5.44 ±0.48 1.55 ±0.13 –
86Zr (σc) 12.68 ±0.68 18.21 ±0.93 19.28 ±0.97 6.16 ±0.32 –
86Y (σi) 33.4±1.8 41.6±2.2 39.9±2.1 13.56 ±0.72 –
87Zr (σc) 47.4±7.3 28.0±2.8 32.2±2.9 49.8±5.0 38.2±3.7 1.12 ±0.17
87Y (σi) 110.0±7.2 54.7±2.8 61.0±2.9 90.0±4.9 67.2±3.6 2.91 ±0.17
87gY (σi) 28.0±5.8 7.4±1.3 6.55 ±0.64 5.8±2.2 2.63 ±0.47 0.942 ±0.073
87mY (σi) 82.0±4.3 47.3±2.5 54.4±2.8 84.2±4.4 64.6±3.6 1.97 ±0.15
88Zr (σc) 159.1±7.8 144.6±6.8 62.4±3.1 21.2±1.0 33.6±1.8 65.3±4.0
88Y (σi) 17.2±1.1 13.27 ±0.86 7.98 ±0.72 2.91 ±0.25 9.2±1.4 9.88 ±0.69
89Nb (σc) – – 179 ±14 214.4±9.8 –
89gNb (σi) 145 ±14 186.4±9.6 –
89mNb (σi) – – 34.7±2.6 28.0±2.0 –
89Zr (σi) 211 ±11 243 ±13 294 ±15 257 ±13 55.4±3.0 15.5±1.0
90Mo (σi) 21.3±1.1 26.4±1.3 34.5±1.6 61.9±3.1 122.0±6.1 24.2±1.5
90Nb (σi) 158.3±8.1 174.9±8.5 209.3±9.9 272 ±14 369 ±19 163.9±9.8
91mNb (σc) – – – – – 66.5±5.8
92mNb (σi) 43.7±2.4 47.3±2.4 49.8±2.6 52.9±2.8 55.3±3.1 59.9±3.9
93mMo (σi) 0.97 ±0.20 1.29 ±0.15 1.62 ±0.24 1.85 ±0.15 1.86 ±0.14 2.00 ±0.15
Table 4: Measured isomer-to-ground-state branching ratios for the various
natNb
(p,x) and
natCu
(p,x) reaction products observed
in this work.
Isomer branching ratio
Ep(MeV) 89.74+0.48
0.43 79.95+0.67
0.64 70.17+0.91
0.85 61.58+1.03
0.98 52.10+1.25
1.20 41.05+1.62
1.54
natCu(p,x)52Mn 0.603 ±0.066 0.581 ±0.062 0.598 ±0.095 0.81 ±0.13 –
natCu(p,x)58Co 0.757 ±0.088 0.80 ±0.10 0.858 ±0.099 0.767 ±0.097 0.82 ±0.12 0.98 ±0.10
Ep(MeV) 89.37+0.47
0.45 79.55+0.68
0.64 69.70+0.90
0.85 61.07+1.05
0.98 51.51+1.25
1.21 40.34+1.58
1.55
natNb(p,x)85Y 0.828 ±0.051 0.724 ±0.080 0.736 ±0.080 – – –
natNb(p,x)87Y 0.746 ±0.063 0.865 ±0.063 0.893 ±0.063 0.936 ±0.070 0.961 ±0.075 0.676 ±0.065
natNb(p,x)89Nb – – 0.193 ±0.021 0.130 ±0.011 –
14
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 15
Table 5: Default settings for the reactions codes
Code Version Proton/Neutron Optical Model Alpha Optical Model E1 γSF Model
EMPIRE-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]
nat
Nb(p,x)
90Mo
measurement, this experiment has also yielded measurements of a
number of additional emerging radionuclides with medical applications. These include the non-standard
positron emitters
57Ni
[
16
,
33
35
],
64Cu
[
36
43
],
86Y
[
14
,
15
,
44
52
],
89Zr
[
53
57
],
90Nb
[
58
,
59
], and
the Auger-therapy agent
82mRb
[
60
,
61
over established pathways, with the generally lower yields and radioisotopic purities failing to justify the
convenience of natural targets via
natCu
(p,x) and
natNb
(p,x). The one possible exception to this trend is the
non-standard positron emitter
57Ni
(
t1/2
= 35
.
60
±
0
.
06 h,
=100% to
57Co
[
62
]) — the
57Ni
/
56Ni
ratio of
production rates is approximately 290 at 61.58 MeV, and varies from 45–75 at the 70–90 MeV positions. This
natCu
(p,x) route oﬀers both higher yield and higher radioisotopic purity over the established
natCo
(p,3n)
pathway, which suﬀers from approximately ﬁve-fold greater 56Ni contamination [63, 64].
We wish to urge caution in future stacked-target activation experiments by avoiding the use of silicone
adhesive-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
22,24Na
activities,
due to being of too low-Z for these reaction channels to be possible. Even with subtraction of
22,24Na
activities though irradiating a Kapton tape “blank” or similar, we observe the Al monitor channels to
measure consistently higher proton ﬂuence than via Cu monitor channels, by 5–8%. If Al monitors are used
in conjunction with silicone-based tapes, even with subtraction of excess
22Na
activities, a systematically
enhanced ﬂuence may be determined, leading to cross sections reported with inaccurately diminished
magnitude. Furthermore, since data for monitor reactions are often self-referencing, the propagated impact
of this systematic 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 nuclei
in a mass chain, or whenever it is impossible to use decay spectrometry to distinguish direct production of
a nucleus from decay feeding. For all remaining observed reaction products in the mass chain, and cases
where no decay precursors exist, independent cross sections are reported, allowing for determination of the
direct production via subtraction. This, in turn, oﬀers the opportunity to gauge the predictive capabilities of
modern nuclear models used in the reaction evaluation process. The reaction channels with independent
cross 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 each
code are presented in Table 5. The large energy range covered by many of the exit channels, which extends
signiﬁcantly beyond the range of pure compound nuclear/evaporation, allows the data to be used to study
the 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 Constant
Temperature model below a critical energy and Fermi Gas model above it. The default level density in
EMPIRE is the Enhanced Generalized Superﬂuid Model (EGSM) which uses the Generalized Superﬂuid
model below a critical energy, and Fermi Gas model above it [
65
]. The EGSM densities are normalized
to
D0
and the discrete levels, but in such a way that only the level density below the neutron separation
energy is eﬀected by the discrete levels chosen for the normalization. All three codes use a two-exciton
phenomenological model to calculate the pre-equilibrium cross section, but the speciﬁc implementation diﬀers
between the codes.
Given the large number of exit channels in this data set, we will limit our discussion to cross sections for
the 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 full
rise and fall of the peak, which is identiﬁed as being dominated by the formation of a compound nucleus, do
15
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 16
30 40 50 60 70 80 90 100
0
10
20
30
40
50
60
70
80
Figure 9: Measured
93Nb
(p,x)
86Y
cross section, with the
93Nb
(p,
α
p3n)
86Y
reaction channel visibly peaking at approximately
70 MeV.
not provide enough information to analyze the calculations. Residual nuclei like
88Zr
that can be produced
by multiple reaction channels, such as (p,
α
2n) and by (p,2p4n) are also not discussed in depth. We exclude
reactions with cross sections with peak values less than 1% of the total reaction cross section because their
behavior is extremely sensitive to more dominant channels. The three residual nuclei that meet all of the
above criteria for which there is an independent measurement of the residual production cross section are
86Y, 90Mo, and 90Nb.
The
93Nb
(p,
α
p3n)
86Y
reaction channel, which peaks at approximately
70 MeV
, is well within the
compound regime for the entire energy region of this experiment (Figure 9). The data collected on this
residual is consistent with the one other data set available, taken in 1997 by Michel et al. [
63
]. The
93Nb
(p,4n)
90Mo
and
93Nb
(p,p3n)
90Nb
channels both peak early in the energy region, around 50 MeV, and
the data clearly show 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
90Nb
production cross section exhibits a persistent pre-equilibrium “tail” that keeps the channel
open well after the compound cross section has fallen away. TALYS, TENDL, and CoH seem to have the
correct 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-energy
data points.
In all three channels, the TALYS, TENDL, and CoH calculations rise, peak, and fall at lower energies
than the data, while EMPIRE calculates the peak to occur at higher energies. For
90Mo
, the EMPIRE peak
is representative of the data. For 86Y and 90Nb, 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 channels
studied here. For
86Y
, 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 peak
in the CoH calculation for
90Mo
is consistent with the data, while EMPIRE predicts a cross section that
is approximately the same magnitude as that of TALYS.
90Nb
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
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 17
30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
140
Figure 10: Measured
93Nb
(p,x)
90Mo
cross section, with the
93Nb
(p,4n)
90Mo
reaction channel visibly peaking at approximately
50 MeV.
30 40 50 60 70 80 90 100
0
50
100
150
200
250
300
350
400
450
500
Figure 11: Measured
93Nb
(p,x)
90Nb
cross section, with the
93Nb
(p,p3n)
90Nb
reaction channel visibly peaking at approximately
50 MeV.
17
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 18
4. Conclusions
We present here a set of measurements of 38 cross sections for the
natNb
(p,x) and
natCu
(p,x) reactions
between 40–90 MeV, as well as independent measurements of ﬁve isomer branching ratios. Nearly all
cross sections have been reported with higher precision than previous measurements. We report the ﬁrst
measurements of the
natNb
(p,x)
82mRb
reaction, as well as the ﬁrst measurement of the independent cross
sections for
natCu
(p,x)
52mMn
,
natCu
(p,x)
52gMn
, and
natNb
(p,x)
85gY
in the 40–90 MeV region. We advise
that future activation experiments avoid the use of silicone-based adhesives, particularly in conjunction with
aluminum monitor foils, to avoid reporting an enhanced ﬂuence due to
22,24Na
contamination. We also use
these measurements to illustrate the deﬁciencies in the current state of reaction modeling for 40–90 MeV
natNb
(p,x) and
natCu
(p,x) reactions. Finally, this work provides another example of the usefulness of the
recently-described variance minimization techniques for reducing energy uncertainties in stacked target
5. Acknowledgements
The authors would like to particularly acknowledge the assistance and support of Michael Gallegos and
Don Dry in the LANL C-NR Countroom, David Reass and Mike Connors at LANSCE-IPF, and the LANSCE
Accelerator Operations staﬀ.
We gratefully acknowledge support for this work from the United States Department of Energy, Oﬃce
of Science via the Isotope Development and Production for Research and Applications subprogram in the
Oﬃce of Nuclear Physics. This work has been carried out under the auspices of the U.S. Department of
Energy by Lawrence Berkeley National Laboratory and the U.S. Nuclear Data Program under contract
# DE-AC02-05CH11231. This research was performed under appointment to the Rickover Fellowship
Program in Nuclear Engineering, sponsored by the Naval Reactors Division of the U.S. Department of Energy.
Additional support has been provided by the U.S. Nuclear Regulatory Commission.
This research used the Savio computational cluster resource provided by the Berkeley Research Computing
program at the University of California, Berkeley (supported by the UC Berkeley Chancellor, Vice Chancellor
for Research, and Chief Information Oﬃcer).
Appendix A. Decay data
The lifetimes and gamma-ray branching ratios listed in these tables were used for all calculations of
measured cross sections reported in this work, and have been taken from the most recent edition of Nuclear
Data Sheets for each mass chain [8, 11–15, 62, 74–92].
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A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 19
Table A.6: Decay data for gamma-rays observed in natAl(p,x) and natCu(p,x).
Nuclide Half-life Eγ(keV) Iγ(%)
22Na 2.6018(22) y 1274.537 99.940(14)
24Na 14.997(12) h 1368.626 99.9936(15)
51Cr 27.704(3) d 320.0824 9.910(10)
52mMn 21.1(2) m 1434.0600 98.2(5)
52Mn 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)
54Mn 312.20(20) 834.848 99.9760(10)
55Co 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)
56Ni 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)
56Co 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)
57Ni 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)
57Co 271.74(6) d 122.06065 85.60(17)
271.74(6) d 136.47356 10.68(8)
58Co 70.86(6) d 810.7593 99.450(10)
70.86(6) d 863.951 0.686(10)
59Fe 44.495(9) d 1099.245 56.5(18)
44.495(9) d 1291.590 43.2(14)
60Co 5.2714(5) y 1173.228 99.85(3)
5.2714(5) y 1332.492 99.9826(6)
61Cu 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)
62Zn 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)
64Cu 12.701(2) h 1345.77 0.475(11)
65Zn 243.93(9) d 1115.539 50.04(10)
19
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 20
Table A.7: Decay data for gamma-rays observed in natNb(p,x).
Nuclide Half-life Eγ(keV) Iγ(%)
82mRb 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)
83Sr 32.41(3) h 418.37 4.2(3)
32.41(3) h 762.65 26.7(22)
85mY 4.86(13) h 231.7 22.8(22)
85Y 2.68(5) h 231.65 84(9)
2.68(5) h 913.89 9.0(9)
86Zr 16.5(1) h 242.8 95.84(2)
16.5(1) h 612.0 5.8(3)
86Y 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)
87Zr 1.68(1) h 380.79 62.79(10)
1.68(1) h 1227.0 2.80(4)
87mY 13.37(1) h 380.79 78.05(8)
87Y 79.8(3) h 388.5276 82.2(7)
79.8(3) h 484.805 89.8(9)
88Zr 83.4(3) d 392.87 97.29(14)
88Y 106.627(21) d 898.042 93.7(3)
106.627(21) d 1836.063 99.2(3)
89mNb 66(2) m 588.0 95.57(13)
89Nb 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)
89Zr 78.41(12) h 909.15 99.04(3)
78.41(12) h 1713.0 0.745(13)
90Mo 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)
90Nb 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)
91mNb 60.86(22) d 104.62 0.574(1)
60.86(22) d 1204.67 2.0(3)
92mNb 10.15(2) d 912.6 1.78(10)
10.15(2) d 934.44 99.15(4)
93mMo 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)
20
A.S. Voyles et al. / Nuclear Instrum. and Methods in Phys. Res. B 00 (2018) 1–34 21
Appendix B. 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].
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30 40 50 60 70 80 90 100
0
0.5
1
1.5
2
2.5
3
60 65 70 75 80 85 90 95 100
0
0.5
1
1.5
2
2.5
60 65 70 75 80 85 90 95 100
0
0.5
1
1.5
2
2.5
60 65 70 75 80 85 90 95 100
0
0.5
1
1.5
2
2.5
30 40 50 60 70 80 90 100
0
1
2
3
4
5
6
7
8
9
10
30 40 50 60 70 80 90 100
0
0.5
1
1.5
2
2.5
3
3.5
4
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30 40 50 60 70 80 90 100
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
30 40 50 60 70 80 90 100
0
0.5
1
1.5
2
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3
3.5
4
4.5
30 40 50 60 70 80 90 100
0
20
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120
30 40 50 60 70 80 90 100
0
5
10
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45
50
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30 40 50 60 70 80 90 100
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70
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0.5
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1.5
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3
30 40 50 60 70 80 90 100
0
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30
30 40 50 60 70 80 90 100
0
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200
30 40 50 60 70 80 90 100
0
20
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30 40 50 60 70 80 90 100
0
0.5
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4
30 40 50 60 70 80 90 100
0
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8
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12
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50 55 60 65 70 75 80 85 90 95 100
0
1
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8
50 55 60 65 70 75 80 85 90 95 100
0
5
10
15
20
25
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35
40
30 40 50 60 70 80 90 100
0
5
10
15
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25
30
30 40 50 60 70 80 90 100
0
20
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140
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0
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10
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0
20
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70
30 40 50 60 70 80 90 100
0
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160
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220
30 40 50 60 70 80 90 100
0
50
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250
30 40 50 60 70 80 90 100
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30 40 50 60 70 80 90 100
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2
4
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8
10
12
14
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Appendix C. Measured isomer-to-ground state branching ratios
Plots of the isomer-to-ground state ratios measured in this work are presented here, in comparison with
literature data and reaction modeling codes [16, 61, 63, 104].
28
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0
0.1
0.2
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0.6
0.7
0.8
0.9
1
30 40 50 60 70 80 90 100
0
0.2
0.4
0.6
0.8
1
1.2
50 55 60 65 70 75 80 85 90 95 100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
30 40 50 60 70 80 90 100
0
0.2
0.4
0.6
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... The degraders selectively reduce the primary beam energy throughout the stack while the monitor foils can be used to characterize the evolving beam properties as it propagates through the targets. Detailed explanations of the technique can be read in [21,[23][24][25][26][27]. ...
... Decay curves for observed residual products were constructed from the count data with appropriate timing, efficiency, and attenuation corrections. EoB activities A 0 were then determined by fitting decay curves to the applicable Bateman equations [21,23,24]. A sample γ -ray spectrum from an electroplated arsenic target is given in Fig. 3. ...
... The proton beam energy and current at each target in a given stack was determined by monitor foil activation data, CURIE's Andersen-Ziegler based Monte Carlo particle transport code, and a "variance minimization" approach, following the established methodology presented in Voyles et al. [23], Morrell et al. [24], Graves et al. [25]. The nat Ti(p, x) 48 V, 46 Sc and nat Cu(p, x) 63, 62 Zn, 58 Co monitor reactions, taken from the IAEA-recommended data reference for charged-particle reactions [32], were used for the LBNL beam characterization. ...
Article
As72 is a promising positron emitter for diagnostic imaging that can be employed locally using a Se72 generator. However, current reaction pathways to Se72 have insufficient nuclear data for efficient production using regional 100–200 MeV high-intensity proton accelerators. In order to address this deficiency, stacked-target irradiations were performed at LBNL, LANL, and BNL to measure the production of the Se72/As72 positron emission tomography (PET) generator system via As75(p,x) between 35 and 200 MeV. This work provides the most well-characterized excitation function for As75(p,4n)Se72 starting from threshold. Additional focus was given to report the first measurements of As75(p,x)Ge68 and bolster an already robust production capability for the highly valuable Ge68/Ga68 PET generator. Thick target yield comparisons with prior established formation routes to both generators are made. In total, high-energy proton-induced cross sections are reported for 55 measured residual products from As75, Cunat, and Tinat targets, where the latter two materials were present as monitor foils. These results were compared with literature data as well as the default theoretical calculations of the nuclear model codes talys, coh, empire, and alice. Reaction modeling at these energies is typically unsatisfactory due to few prior published data and many interacting physics models. Therefore, a detailed assessment of the talys code was performed with simultaneous parameter adjustments applied according to a standardized procedure. Particular attention was paid to the formulation of the two-component exciton model in the transition between the compound and preequilibrium regions, with a linked investigation of level density models for nuclei off of stability and their impact on modeling predictive power. This paper merges experimental work and evaluation techniques for high-energy charged-particle isotope production in an extension to an earlier study of this kind.
... The degraders selectively reduce the primary beam energy throughout the stack while the monitor foils can be used to characterize the evolving beam properties as it propagates through the targets. Detailed explanations of the technique can be read in [21,[23][24][25][26][27]. ...
... Decay curves for observed residual products were constructed from the count data with appropriate timing, efficiency, and attenuation corrections. EoB activities A 0 were then determined by fitting decay curves to the applicable Bateman equations [21,23,24]. A sample gamma-ray spectrum from an electroplated arsenic target is given in Figure 3. ...
... The proton beam energy and current at each target in a given stack was determined by monitor foil activation data, Curie's Andersen & Ziegler-based Monte Carlo particle transport code, and a "variance minimization" approach, following the established methodology presented in Voyles et al. [23], Morrell et al. [24], and Graves et al. [25]. ...
Preprint
{72}$As is a promising positron emitter for diagnostic imaging that can be employed locally using a$^{72}$Se generator. However, current reaction pathways to$^{72}$Se have insufficient nuclear data for efficient production using regional 100-200 MeV high-intensity proton accelerators. In order to address this deficiency, stacked-target irradiations were performed at LBNL, LANL, and BNL to measure the production of the$^{72}$Se/$^{72}$As PET generator system via$^{75}$As(p,x) between 35 and 200 MeV. This work provides the most well-characterized excitation function for$^{75}$As(p,4n)$^{72}$Se starting from threshold. Additional focus was given to report the first measurements of$^{75}$As(p,x)$^{68}$Ge and bolster an already robust production capability for the highly valuable$^{68}$Ge/$^{68}$Ga PET generator. Thick target yield comparisons with prior established formation routes to both generators are made. In total, high-energy proton-induced cross sections are reported for 55 measured residual products from$^{75}$As, Cu, and Ti targets, where the latter two materials were present as monitor foils. These results were compared with literature data as well as the default theoretical calculations of the nuclear model codes TALYS, CoH, EMPIRE, and ALICE. Reaction modeling at these energies is typically unsatisfactory due to few prior published data and many interacting physics models. Therefore, a detailed assessment of the TALYS code was performed with simultaneous parameter adjustments applied according to a standardized procedure. Particular attention was paid to the formulation of the two-component exciton model in the transition between the compound and pre-equilibrium regions, with a linked investigation of level density models for nuclei off of stability and their impact on modeling predictive power. ... The main aim of those studies was to measure or standardize reaction cross sections for medical applications. The results show that, in general, the experimental cross section for the total reaction channel is described fairly well by the model calculation up to the projectile energy of about 50 MeV, especially when a product is formed mainly by emission of nucleons (see as examples [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). Some difficulty is observed in deuteron-induced reactions. ... ... For experimental studies on isomer pairs, the activation technique is ideally suited. Through detailed investigations on 52m,g Mn, 58m,g Co, 73m,g Se, 94m,g Tc, 120m,g I and some other isomer pairs, involving different combinations of target nucleus, incident charged projectile and various ejectiles, the dependence of the isomeric cross-section ratio on the excitation energy of the product nucleus, the nuclear spins of the two states concerned and the reaction channel involved has been amply demonstrated [1][2][3][4]13,16,20]. Furthermore, in theoretical calculation of the isomer ratio in a charged-particle induced reaction, the effects of input level structure of the product nucleus, of the assumed angular momentum distribution in the preequilibrium decay and the spin distribution of the level density, have been elaborated [1][2][3][4][21][22][23][24][25]. ... Article Cross sections of proton-induced nuclear reactions on enriched 86Sr target were measured by the activation technique up to proton energies of 44 MeV. The isomeric cross-section ratios for 86m,gY and 85m,gY as a function of projectile energy were deduced from their measured data. The present experimental data for the nuclear reaction products, namely 86mY, 86g+xmY, 85mY, 85gY, 84Rb and 83Rb were compared with the results of nuclear model calculations using the code TALYS, which combines the statistical, precompound, and direct interactions. In general, the experimental cross-section data as well as the isomeric cross-section ratios are reproduced well by the model calculations, provided the input model parameters are properly chosen and the level structure of the product nucleus is thoughtfully considered. The quality of the agreement between experimental data and model calculations was numerically quantified. For products formed via emission of a light complex particle as well as multi-nucleons (e.g., α and 2p2n), the contribution of the latter process starts increasing when its energy threshold is crossed. ... Using methods similar to those established by Graves, Voyles, and Morrell, this measured 39 the 160 Gd(p,n) 160 Tb excitation function utilizing a stacked-target activation technique and 40 natural gadolinium foils [1,10,11]. Iterative simulations of proton transport are used to 41 reduce systematic uncertainties in key quantities such as proton energy and fluence. The showed that the beam was centered and collimated within the first copper foil, Cu-01. ... ... Based on this comparison, it is difficult to declare any of these models as clearly superior 283 in terms of predictive power. However, as has been seen in recent work [1,2,45], the default 284 predictive power of these codes, even for strongly-fed channels, often holds only locally and 285 does not extend to adjacent channels. This problem exhibits a complex residual topology 286 for any global optimization, as these channels are both highly correlated and constrained, 287 leading to high sensitivity in seeking a global minimum in parameter space. ... Article Full-text available The ¹⁶⁰Gd(p,n)¹⁶⁰Tb excitation function was measured between 4–18 MeV using stacked-target activation at Lawrence Berkeley National Laboratory’s 88-Inch Cyclotron. Nine copper and eight titanium foils served as proton fluence monitor foils, using the natCu(p,x)⁶⁵Zn, natTi(p,x)⁴⁸V, and natTi(p,x)⁴⁶Sc monitor standards, respectively. Variance minimization using an MCNP v.6.2 model reduced the systematic uncertainties in proton energy and fluence. A priori predictions of the ¹⁶⁰Gd(p,n) reaction using ALICE, CoH, EMPIRE, and TALYS, as well as the TENDL database, are compared to the experimentally measured values. ... Radiation is something that cannot be seen, felt or known to exist [4]. In this case, ionizing radiation is a type of radiation that is widely used in the field of radiodiagnostics using x-ray device radiation sources, which are further used for various medical purposes such as X-rays [3][5] [6] [7]. In occupational safety, a radiation worker or radiographer is encouraged to receive the radiation dose as minimum as possible, namely by monitoring the radiation using a radiation gauge [8] [9]. ... Article Full-text available Radiation cannot be felt directly by the five human senses. For the occupational safety and security, a radiation worker or radiographer is endeavored to receive radiation dose as minimum as possible, which is by monitoring the radiation using a radiation measuring device. The purpose of this study was to analyze the effect of collimation area and irradiation distance on x-ray dose measurement using Geiger Muller. In this case, the author tried to make a dosimeter by using the Muller Geiger module and displayed it on a personal computer. This research employed Muller Geiger sensor to detect X-ray dose and velocity, Arduino for data programming, Bluetooth HC-05 for digital communication tool between hardware and personal computer, and personal computer to display the reading. Current research was conducted using Pre-Experimental research design. Based on the results of data collection and comparison with the standard tool, it can be concluded that the greater the tube current setting (mA), the greater the dose and rate of radiation exposure at a distance of 100cm with 50KV and 70KV settings, and a distance of 150cm with 50KV settings. However, it is inversely proportional to the measurement results at a distance of 150cm with a 70KV setting. The results of this study are further expected to determine the ability of Geiger Muller to measure the dose to the irradiation distance or collimation area and can be used as a reference for further research in this field. ... The deposits in this work were prepared on 25 µm thick Kapton film backings, which is a typical material used for sealing targets in stacked-target activations [19][20][21][22]. Free-standing targets were initially explored but suffered from cracking issues during separations from the substrate. ... Preprint Thin uniform arsenic targets suitable for high-fidelity cross section measurements in stacked-target experiments were prepared by electrodeposition of arsenic on titanium backings from aqueous solutions. Electrolytic cells were constructed and capable of arsenic deposits ranging in mass from approximately 1 to 29 mg (0.32-7.22 mg/cm$^2$, 0.57-12.62$\mu\$m). Examination of electrodeposit surface morphology by scanning electron microscopy and microanalysis was performed to investigate the uniformity of produced targets. Brief studies of plating growth dynamics and structural properties through cyclic voltammetry were also undertaken. An alternative target fabrication approach by vapor deposition was additionally conducted. We further introduce a non-destructive characterization method for thin targets by neutron activation, which is independent of neutron flux shape, environmental factors, and source geometry, while correcting for any potential scatter or absorption effects.
... The radionuclide is formed directly, and also accumulated as a result of 88 Zr decay. [25] Half-life periods of the most generated products are between minutes and tens of hours, resulting in their almost complete decay within a few weeks. 88 Zr (t 1/2 = 83.4 ...
Article
The radiation resistance of sorbents AG 50 W-X8, Ac resin, and UTEVA resin in contact with hydrochloric solutions under irradiation with 10 MeV electrons in a wide absorbed-dose range up to 2 MGy was studied. Mass distribution ratios and total sorption capacity were used as quantitative measures to determine the changes in ion exchange or extractive abilities of the resins. Based on the data obtained and on a review of the performance of the ²²⁵Ac/²¹³Bi generators reported in the literature, the applicability of investigated resins for high activity loaded onto different generator systems was concluded.
Article
Production cross sections for the 93Nb(p, x)90Mo, 92m,90,89mNb, 89,88,86Zr, and 88,87m,87gY reactions were measured using a stacked-foil technique in the proton energy range of 58–100 MeV. The target was arranged in the stack including Nb, Al, Au foils, and Pb plates and was irradiated with 100-MeV protons. After the irradiation, the production yields of the interested radionuclei were measured by a γ -ray spectroscopy system using HPGe detectors. Proton beam intensities were measured using the 27Al(p, 3pn)24Na, 197Au(p, p3n)194Au, and 197Au(p, pn)196Au monitor reactions. Some 54 cross section data points were measured, including independent and cumulative cross sections and were compared with other experimental data. The excitation functions of the reactions were also calculated by nuclear models using the TALYS code with a default mode as well as different nuclear level-density models. The calculated cross sections were compared to the measured data and to the TENDL library. It was figured out that the theoretical calculations could reproduce the shape of the measured cross sections well, whereas the magnitude of the cross sections was not reproduced. It was also shown that the preequilibrium mechanism played an important role in the cross section calculations in this paper.
Article
Full-text available
Theoretical models often differ significantly from measured data in their predictions of the magnitude of nuclear reactions that produce radionuclides for medical, research, and national security applications. In this paper, we compare a priori predictions from several state-of-the-art reaction modeling packages (CoH, EMPIRE, TALYS, and ALICE) to cross sections measured using the stacked-target activation method. The experiment was performed using the Lawrence Berkeley National Laboratory 88-Inch Cyclotron with beams of 25 and 55 MeV protons on a stack of iron, copper, and titanium foils. Thirty-four excitation functions were measured from 4–55 MeV, including the first measurement of the independent cross sections for $$^{\mathrm{nat}}\hbox {Fe}$$ nat Fe (p,x) $$^{49,51}\hbox {Cr}$$ 49 , 51 Cr , $$^{51,{\mathrm{52m}},{\mathrm{52g}},56}\hbox {Mn}$$ 51 , 52 m , 52 g , 56 Mn , and $$^{{\mathrm{58m,58g}}}\hbox {Co}$$ 58 m , 58 g Co . All of the models, using default input parameters to assess their predictive capabilities, failed to reproduce the isomer-to-ground state ratio for reaction channels at compound and pre-compound energies, suggesting issues in modeling the deposition or distribution of angular momentum in these residual nuclei.
Article
A discrepancy, well outside reported uncertainties, has been observed between the accepted and measured values of the intensity ratio of the two strongest γ rays following ⁶¹Cu β+ decay. This discrepancy has significant impact since the natNi(d,x)⁶¹Cu reaction has historically been one of only a few IAEA recommendations for use as a deuteron flux monitor and a considerable number of published cross sections measured in ratio to that beam monitor cross section may depend on the choice of either the first or second strongest γ ray in those calculations. To determine the magnitude of this error most precisely, over a hundred separate measurements of the 283 keV to 656 keV γ-ray emission ratio were collected from seven experiments and a variety of detectors and detection geometries. A weighted average of all these measurements indicates an error in the value listed in the Nuclear Data Sheets of 11% in either the primary or second-highest intensity γ ray of ⁶¹Cu, potentially introducing an 11% error in ⁶¹Cu production cross section measurements, cross sections using nickel activation as a deuteron beam current monitor, or in dose rates when ⁶¹Cu is used in nuclear medicine. General agreement with the Data Sheets with ten other intensity ratios suggests the most probable error is in the secondary (656 keV) emission, which accordingly should be updated from 10.8% to 9.69%.