Nuclear Reactions Theory on Minor Actinides for Transmutation Applications
M.B. Chadwick, P. Talou, T. Kawano, and P. Moller
Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Abstract
A better understanding of neutron reaction cross sections on minor actinides is needed for the
design of new reactors, for energy production and waste transmutation. We focus on
americium isotopes, and describe both experimental data and nuclear theory predictions that
we have used to predict these nuclear data.
1. Introduction
Many countries, including the US, are now focused on developing new reactor designs for a
new generation of nuclear reactors. These reactors vary in their purpose: some are focused
particularly on power generation; some on hydrogen production using very high temperature
reactors; and some focused on nuclear waste transmutation together with power production. In
all cases there is an emphasis on developing technologies and fuel cycles that lead to a higher
burn up of the nuclear fuels and actinide waste products. Furthermore, technologies that are
proliferation resistant – making it difficult for a terrorist, for example, to obtain plutonium or
highly enriched uranium - are also a priority.
Reactor designs for waste transmutation are typically based on fast-reactor technology, where
the fission to capture ratio is high, allowing minor actinides – especially isotopes of americium
and curium, and higher plutonium isotopes – to be burned up by fission. The focus on burning
up these minor actinides has placed a new emphasis on a better understanding of minor
actinide neutron reaction cross sections. Historically, these materials have been studied to a
lesser extent compared to the major actinides. This is because understanding their properties
was less important for the energy applications of interest in the past, and because many of the
isotopes are short lived, making sample preparation and measurement difficult and costly.
From a scientific perspective, research on minor actinide cross sections is an exciting
challenge. Many of the isotopes of interest remain unmeasured, owing to their short half-life,
and therefore an ability to accurately predict these cross sections with nuclear theory is
important. Typically such approaches do not rely on theory alone, but rather use theory that is
informed by the measured phenomenology of data on nearby isotopes. These theoretical
approaches require information on fission barriers, level densities, optical potentials, gammaray strength functions, etc., and their variation from isotope to isotope.
In this paper we shall focus on americium isotopes 241,242g,242m,243Am, as illustrative examples
of the ongoing research efforts in the US to support advanced reactor development.
2. Theory
2.1 Fission theory
Fission properties such as (n,f), (n,2n), (n,gamma) cross sections, fission-fragment kinetic
energy and mass distributions, and neutron-emission in fission are difficult to model from
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first-principle theory. However, in the last several years we have developed methods to
calculate the fission-potential energy in a macroscopic-microscopic approach as a function of
nuclear shape to much higher accuracy and detail than previously. An illustrative example of
our recent results is shown in Fig. 1. Fission barriers obtained from these studies can then be
used to predict cross sections using our GNASH code, described later in this paper.
Figure 1: A calculation of the evolving shapes, and associated potential energies, of an americium-243 nucleus
as it undergoes fission. The potential energy surface represents a multidimensional landscape – here we show two
dominant pathways for potential energy minima, involving symmetric and asymmetric fragment modes.
It is our aim to decrease the phenomenology in modeling the above quantities by using
appropriately features that we learn from our enhanced fundamental fission models. We have
shown that to describe the outer region beyond the second minimum in the fission barrier it is
necessary to calculate the fission potential energy versus at least 5 independent shape
parameters, namely (1) nuclear elongation, (2) neck radius, (3) emerging left fragment
Spheroidal deformation, (4) emerging right fragment deformation, and (5) reflection ("mass")
asymmetry (Moller et al. 2000). It has been shown that methods and models such as the Brosa
model, self-consistent Hartree-Fock models, and macroscopic-microscopic calculations in
which energy contour diagrams are plotted versus two shape multipoles and minimized with
respect to higher multipoles do not correctly identify the saddle points of the higherdimensional potential-energy space, nor can one learn correctly about the height of ridges
between various fission modes or valleys.
We have felt that to understand how to use calculated knowledge of fission potential-energy
surface structure in modeling cross sections we need to know about the variability of the
potential-energy surface structure for a substantial number of fission systems. We have
therefore calculated fission potential-energy surfaces as functions of the above 5 shape
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parameters for more than 5 million different shapes for all nuclei from A=190 to A=329, more
than 3000 nuclei. After the surfaces have been calculated we determine for each surface all
minima deeper than a prescribed value (we use 0.2 MeV, but it can be chosen differently) and
we also determine the saddle points between all pairs of minima and between all minima and
the lowest energy configuration for the most elongated shape. To identify valleys or fission
modes in the fission surface we consider a succession of 4-dimensional slices in the 5D
surface. Each slice corresponds to a fixed elongation of the nucleus.
Figure 2: Predictions of fission barrier heights, for americium isotopes, compared with data. Note that the data
are not measured directly, but inferred from neutron and charged-particle induced fission reactions.
For each slice we determine all minima deeper than 0.2 MeV and the saddles between all pairs
of minima. Usually only a few minima (one to five) exist at each elongation (in each
successive slice). If, as the elongation increases, a succession of slices have minima
corresponding to shapes with similar emerging fragment shapes and relative volumes, that is
only the elongation and neck radius change, then such sequences correspond to a continuous
valley (or a fission "mode") in the full 5D space. Furthermore, the saddles in the 4D spaces
correspond to ridges in the full 5D space. All these structures are found by use of a powerful
"water immersion" technique often used in analysis of geographical landscapes. An example
showing result of the above calculation and analysis for 243Am is given in Fig. 1.
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In Fig. 2 we compare calculated barrier parameters for a sequence of Am isotopes to
parameters extracted from experimental cross section measurements. For heavier isotopes the
calculated heights of the second peak appear too high compared to experiment. However, a
global calculation of axial-asymmetry effects on nuclear ground state energies show that in
their ground states, nuclei corresponding to the lighter fragment in asymmetric fission of these
heavy Am isotopes gain about 0.7 MeV by becoming triaxially deformed relative to spheroidal
shapes (Moller et al. 2006). We can therefore expect that a similar additional (triaxial) shapedegree of freedom imposed at saddle-point shapes will bring calculated and experimental
barrier parameters into better agreement.
We have calculated such fission barrier information by studying the multidimensional
potential energy surface for over 3000 nuclides, including neutron rich nuclei that are needed
for astrophysics r-process nucleosynthesis studies. In the present work, predictions from this
kind of theoretical estimate are particularly important for understanding the fission process for
americium isotopes that have never been measured, e.g. for 240Am and 242gAm, owing to their
short half lives.
2.2 Nuclear reaction calculations
We are working to improve cross section evaluations for a whole chain of neutron reactions
that are important when americium isotopes are irradiated by neutrons. The reaction chains are
shown in Fig. 3, with (n,2n) reactions moving the isotope to the left hand side, and capture
(n,g) reactions moving the isotopes to the right. The half lives of the isotopes are also shown
in the figure. Note that for 242Am, the ground state is shorter lived than the isomeric state.
Figure 3: The neutron reaction pathways we consider for reactions on americium istopes.
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A nuclear data evaluation usually results from a combination of nuclear model calculations
and experimental data analyses. In the case of americium isotopes, available experimental data
are scant. For some isotopes, data are even nonexistent, as it is the case for the very short-lived
242g
Am. In such cases, evaluations are based almost entirely on nuclear model calculations,
although systematics can be sometimes used to infer model parameters from neighboring
nuclei or similar reactions.
The GNASH nuclear reaction code was used extensively in the present work. The backbone of
GNASH calculations is the Hauser-Feshbach theory that describes the evaporation process
following the formation of a compound nucleus in statistical equilibrium, after the initial
interaction between the incident particle and the target nucleus. Non-statistical processes like
direct reactions and pre-equilibrium emission of high-energy particles were also included in
our calculations.
The neutron-induced fission (n,f) channel plays a significant role in the case of neutroninduced reactions on minor actinides; this is, by the way, the main mechanism leading to the
destruction (or ``transmutation'') of the nuclear waste stream. However, because of its large
size, an even relatively small error in the determination of this cross section can lead to
significant uncertainties in competing channels, such as the (n,2n) and (n,n') decay paths. The
GNASH code infers the fission cross section by calculating penetrabilities over a doublehumped inverted parabola barrier, on top of which are built discrete and continuum-levels.
For the americium isotopes studied in the present work, characteristics of the fission transition
states, and, in particular, the rotational band-heads were taken from the literature. The
assumption of complete damping in the second well was used, since no intermediate structure
exist for those nuclei. The Gilbert-Cameron model was used to describe the continuum of
states on top of the fission barriers, and matched at lower excitation energy to the discrete
collective levels. The collective enhancements due to symmetry breaking at the saddle points
were included in the present calculation, but the final enhancement factors were used as
adjustable parameters. Other fission barrier parameters such as the heights and curvatures of
the two inverted parabolas were used as free parameters, and adjusted to accurately reproduce
the experimental data, whenever available. This was done here in the case of 241Am, 242mAm,
and 243Am for which some experimental information exists. Different experimental data sets
were combined through a Bayesian statistical technique to infer a ``best'' cross section,
through a generalized chi-square procedure taking into account non-diagonal elements
(correlations) in the experimental covariance matrices. An internal Los Alamos version of the
GLUCS code, and the SOK code, were used for the present analyses. This "best" cross section
was then used to infer the GNASH fission barrier parameters (heights and curvatures of the
inverted parabolas). Once these parameters are fixed, GNASH can be used to predict the cross
sections for the competing reaction channels.
The CEA ECIS96 coupled-channels code was used to calculate the total, reaction and shape
elastic cross sections for all americium isotopes. An isospin-dependent deformed optical
model potential was adopted for all isotopes, based on previous studies by Young, whose
optical potential parameters were derived to provide a good agreement with the experimental
241
Am total cross section. The coupled-channels calculations also provided the inelastic
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scattering cross sections and angular distributions for many excited levels in the target nuclei.
The coupled-channels transmission coefficients used in the GNASH Hauser-Feshbach decay
sequence were also obtained with the ECIS96 code. Note that americium-242 is an odd-odd
nucleus, whose description through the rotational model used here is only an approximation.
However, the deformation parameters and coupling scheme were properly taken into account
for 242gAm and 242mAm, including the shift in energy and spin in the case of reactions on the
nucleus in its long-lived isomeric state. Finally, the transmission coefficients for the emission
of particles used in the Hauser-Feshbach equations were obtained by interpolating the values
obtained for both 241Am and 243Am isotopes.
The Hauser-Feshbach calculations of the statistical decay of a compound nucleus depend very
strongly on nuclear level densities. In the present work, the Ignatyuk-Gilbert-Cameron
prescription was used to describe level densities, including a washing-out of shell effects with
increasing excitation energy. The capture cross sections were calculated using the generalizedLorentzian strength function formalism of Kopecky-Uhl at low-energies, and direct-semidirect
calculations were carried out at higher energies.
3. Cross Section Evaluations for Americium Isotopes
The 241Am capture cross section was reevaluated based on experimental capture and
capture/fission ratio data, together with predictions from theory. The new result, which comes
from our GNASH calculation with some calibration to the measured data, is about 15% larger
than the ENDF/B-VI data in the hundreds-keV energy region. This capture cross section is
also the focus of a new measurement program using the DANCE detector at Los Alamos’
LANSCE facility. Within the coming year we hope to have new measurements that will help
resolve the ~ 20% discrepancies seen between the two previous measurements
Figure 4: The 241Am capture cross section as a function of neutron energy.
The isomer-to-ground-state capture ratio was increased significantly over earlier evaluations
(JENDL-3.3 and ENDF/B-VI), based on new differential data and integral measurements.
Having a correct branching ratio for the isomer to ground state is, of course, very important to
understand the transmutation chains that are populated in a neutron irradiation, and in
particular how much of the long-lived isomer versus the shorter lived ground state in 242Am is
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produced.
The 241Am(n,2n) cross section is important in transmutation studies, and has been the focus of
many theoretical and experimental studies in the US and Europe in recent months. At the
outset of this work, the early ENDF/B-VI evaluation was the only evaluation available, and it
was evaluated at a time when the measured data were not available. Our new evaluation
shown in Fig. 5 is based on a GNASH nuclear model calculation, but calibrated to the data
from Los Alamos (Gancarz) and Livermore (Lougheed), as opposed to the lower Russian
(Filatenkov) data. Below 14 MeV new data are available from Greece, but the measurement at
10.5 MeV appears to be too high to us. A new measurement is now being performed by Los
Alamos, Livermore, and TUNL researchers at TUNL in North Carolina, and we expect this to
provide definitive measurements for this cross section from threshold up to 14 MeV region.
Figure 5: The 241Am(n,2n) cross section, as a function of neutron energy. Our new evaluation is given by the
solid line, whilst the earlier ENDF/B-VI evaluation is given by the dashed line (evaluated at a time when the
measured data shown in this picture were not available). Nuclear model calculations using GNASH play an
important role in determining the (n,2n) cross section shape; the calculation is calibrated to data at ~14 MeV.
An example of the importance of nuclear model predictions is shown in Fig. 6, Here, no direct
measurements of the 242gAm fission cross section have been made, owing to the short half life
and the difficulty in fabricating a target. Therefore, predictions are crucial, being guided by
calculations on nearby isotopes, and on the 242mAm isomer, where data do exist. The result is
shown as a solid line in Fig. 6, and is compared with indirect surrogate results inferred from
Los Alamos surrogate charged particle transfer reactions by Younes and Britt.
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Figure 6: The 242gAm fission cross section. Our prediction is shown as a solid curve, and is compared with a
recent prediction from a calculation by Rochman and Herman from Brookhaven, and with the JJENDL-3.3
evaluation. The data shown in this picture are indirect, and come from a surrogate analysis by Younes and Britt.
Space prohibits a more complete description of all the reaction processes we have studied in
this work, though full details can be found in the paper by Talou et al. (2006).
References
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(2006).
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in a five-dimensional deformation space. Nature 409, no 6822, p. 785 (2001).
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