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# Analysis of Learning Deficits in Aged Rats on the W-Track Continuous Spatial Alternation Task

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Young and aged animals were tested on a spatial alternation task that consisted of two interleaved components: (1) an “outbound” or alternation component (working memory) and (2) an “inbound” component, requiring the animal to remember to return to a central location in space (spatial memory). In the present study, aged rats made more outbound errors throughout testing, resulting in significantly more days to reach learning criterion, as compared to young rats. Furthermore, while all animals were able to learn the hippocampus-dependent inbound component of the task, most aged animals remained just above chance on the outbound component, even after extended testing days. Aged rats may be more impaired on the outbound part of the task because it requires cooperation of both the hippocampus and mPFC, each of which is compromised with age. In addition to presenting these results, we compare one commonly used analysis (repeated measures ANOVA) and two less common hierarchical modeling techniques (hierarchical generalized linear model and state-space random effects model) to determine the best method for comparing population learning over time. We found that hierarchical modeling is the most appropriate for this task and that a state-space model better captures the behavioral responses.
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Analysis of learning deficits in aged rats on the W-track
Adele J. Kapellusch1,2, Adam W. Lester1,2, Benjamin A. Schwartz1,2, Anne C. Smith1,2, and
Carol A. Barnes1,2,3
1Evelyn F. McKnight Brain Institute, University of Arizona, Tucson, AZ
2Division of Neural System, Memory and Aging, University of Arizona, Tucson, AZ
3Departments of Psychology, Neurology and Neuroscience, University of Arizona, Tucson, AZ
Abstract
Young and aged animals were tested on a spatial alternation task that consisted of two interleaved
components (1) an “outbound” or alternation component (working-memory) and (2) an “inbound”
component, requiring the animal to remember to return to a central location in space (spatial
memory). In the present study, aged rats made more outbound errors throughout testing, resulting
in significantly more days to reach learning criterion, as compared to young rats. Furthermore,
while all animals were able to learn the hippocampus-dependent inbound component of the task,
most aged animals remained just above chance on the outbound component, even after extended
testing days. Aged rats may be more impaired on the outbound part of the task because it requires
cooperation of both the hippocampus and mPFC, each of which is compromised with age. In
addition to presenting these results, we compare one commonly used analysis (repeated measures
ANOVA) and two less common hierarchical modeling techniques (hierarchical generalized linear
model and state-space random effects model) to determine the best method for comparing
population learning over time. We found that hierarchical modeling is the most appropriate for this
task and that a state-space model better captures the behavioral responses.
Keywords
learning; memory; aging; prefrontal cortex; hippocampus; spatial working memory; alternation
INTRODUCTION
The hippocampus and the medial prefrontal cortex (mPFC) are part of a functional system
involved in memory-guided decision making, a cognitive process particularly vulnerable to
age-related decline in human and animal models of aging. It is known that the hippocampus
encodes episodic memories including spatial memory e.g., (M. Smith & Milner, 1981;
Morris, Garrud, Rawlins, & O’Keefe, 1982), while the PFC supports working memory
function e.g., (Petrides & Milner, 1982; Granon & Poucet, 1995; Delatour & Gisquest-
Verrier, 1999). These two brain structures are directly connected via a unidirectional
projection from the ventral hippocampus to the mPFC (Ferino, Thierry, & Glowinski, 1987;
Jay, Glowinski, & Thierry, 1989; Swanson, 1981). Hippocampal input to the cells in the
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mPFC likely provides spatial context to promote learning on spatial memory tasks (Jung,
Qin, McNaughton, & Barnes, 1998) and damage or inhibition to the hippocampal-prefrontal
cortical circuit can result in significantly impaired learning on spatial alternation tasks
(Wang & Cai, 2006).
The W-track continuous spatial alternation task (Frank, Brown, & Wilson, 2000), in which
rats learn to alternate arm visits in order to receive a food reward, has been demonstrated to
be a good test of both hippocampus and prefrontal cortex function. There are two interleaved
components of this task: an “outbound” or alternation component (working memory) and an
“inbound” component, requiring the animal to remember to return to the center arm (spatial
memory). The inbound component is primarily dependent on the hippocampus. The
outbound component, in contrast, likely utilizes both the PFC to maintain a working
memory of the previously visited arm, as well as the hippocampus to localize the currently
rewarded position in absolute space. Previous work has shown that rats with lesions to the
hippocampus are impaired in learning all components of the task and show a pattern of
perseverative inbound errors during initial learning (Kim & Frank, 2009). Although
hippocampal lesions result in slower learning rates, animals are still able to reach learning
criterion with time, suggesting adaptive compensation among parallel cognitive networks.
Our aims in this paper are two-fold. The first aim is to examine the behavior of young and
aged animals performing the W-track continuous spatial alternation task to compare
potential age-related changes in hippocampus and PFC function. There is abundant evidence
that age-associated changes in cognition are accompanied by deficits in spatial memory e.g.,
(Barnes, 1979; Birren, 1962; Goodrick, 1972; Markowska et al., 1989; Gallagher & Rapp,
1997) and in working memory e.g., (Frick, Baxter, Markowska, Olton, & Price, 1995; Ando
& Ohashi, 1991; Bimonte, Nelson, & Granholm, 2003). The impact of brain aging has not
been examined on this task with respect to learning rates that demand the interaction of both
memory systems. We hypothesize that aged rats will be slower to acquire this task and may
show behavioral characteristics similar to that of rats with lesions to the hippocampus (Kim
& Frank, 2009).
The second aim is to compare different analytical approaches for modeling learning and
detecting performance differences between two age groups. The raw behavioral responses
are modeled using four methods: a state-space model applied to each individual’s behavior, a
repeated measures ANOVA, a hierarchical generalized linear model, and a hierarchical state-
space model. The first approach makes use of state-space smoothing to estimate the most
likely learning curve for each animal (A. Smith et al., 2004). The second approach is a
standard, off-the-shelf analysis-of-variance (ANOVA) to compare population learning rates.
Approaches 2 and 3 make use of hierarchical generalized linear models (Gelman & Hill,
2006) and hierarchical state-space models (A. Smith, Stefani, Moghaddam, & Brown, 2005),
respectively. Hierarchical, or multi-level models, are advantageous because they
simultaneously account for individual performance while at the same time providing an
estimate of group performance.
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METHODS
Subjects
Two experiments were performed with the same protocol over two different testing period
lengths. In the first experiment, 16 young (9 month) and 12 aged (23 month) male Fischer
344 rats were tested over 14 consecutive days. Because most aged animals were unable to
acquire the working memory-dependent component of the task in these 14 sessions, a
second experiment was conducted to examine behavior over an extended testing period. In
this follow-up experiment, 6 additional young and 6 additional aged rats were tested over a
longer testing period of 21 consecutive days.
The experiments described here follow guidelines established by the National Institutes of
Health and were approved by the Institutional Animal Care and Use Committee at the
University of Arizona. Rats were obtained from the National Institute of Aging’s colony at
Charles River and were housed in separate cages and maintained on a reverse 12hr:12hr
light/dark cycle. Each rat was restricted to a regulated diet to maintain their weight at 85%
of their original body weight in order to motivate the animals to run for food reward.
Testing Apparatus and Data Collection
The behavioral apparatus (Figure 1 (a)) consists of an 150cm × 90cm acrylic track with three
identical arms, each with a small food dish at the end. Infrared sensors along the track
monitor the animals position and signal food reward delivery upon a correct arm visit using
an Arduino microcontroller and a miniature inert liquid valve. Figure 1 (b-e) shows a
schematic of the apparatus. Liquid food reward consisted of diluted vanilla nutrition shake
(
Ensure
) and approximately 0.3 mL was administered upon every correct arm visit.
Timestamps, correct/incorrect decisions, and position data were collected through a custom
desktop application written in C#.
Animals were first “pre-trained” to run for food rewards on a 150cm long linear track with a
food dish at the end of each arm. The rat was required to walk the entire length of the track
to receive a reward (this was considered a
lap
), and no reward was given for consecutive
repeat visits to the same food dish. Rats were trained twice a day for 20 minutes until they
were able to complete 30 laps in 20 minutes, at which point testing on the W-track began.
In each testing session, the animal had one hour to freely explore the track and to collect as
many food rewards as they were able to retrieve. At the start of a session, the rat was first
placed on the center arm, facing the direction of the food dish at the end of the arm (Figure
1b). After running to the end of the center arm and receiving a reward, the rat must then visit
one of the outside arms (Figure 1c), return to the center (Figure 1d), and then visit the
opposite outside arm (Figure 1e). The rat continues alternating between the outside arms,
always returning to the center arm in-between each outbound trial. If, at any point, the
animal makes an incorrect decision, they must return back to the center arm and resume the
pattern.
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Data Analysis
Individual Performance: State-Space Model.—Individual performance was measured
using a state-space model applied to each animal’s performance (A. Smith et al., 2004). On
each day,
k
, the observation for the
j
th animal is the number of correct responses,
nj,k
, in the
mj,k
trials performed during the one hour session. The individual performance for each rat is
estimated using the state-space model described in detail in (A. Smith et al., 2004). Briefly,
we assume each animal has an underlying cognitive state that is governed by a random walk.
The model assumes the observations are binomial and computes the most likely cognitive
state that fits the data via the Expectation-Maximization algorithm. From the cognitive state,
it is then possible to compute a probability of a correct response for each animal.
A “learning session” (the session where the animal successfully acquired the task) was
considered to be a session where the lower 90% confidence bound of the performance was
above chance and remained above chance for the remaining trials in the testing period.
Young and old animals’ learning session estimates were compared using the non-parametric
Mann-Whitney U-test.
Group Performance: Repeated Measures ANOVA.—The first analysis method used
to compare young and aged group performance is a repeated measures ANOVA. This is a
commonly used approach that compares the differences between groups on measurements
gathered sequentially. It tests the null hypothesis that our sample means come from the same
population mean. The ANOVA analysis requires calculation of the variation across days,
SStime
the variation within group,
SSwithin
and the variation across subjects,
SSsubjects
. Each
subject is treated as a level of an independent factor (i.e. each observation is independent and
identically distributed, IID) and assumes the test variables follow a multivariate normal
distribution.
We compute the sum of squares over time,
SStime
, from
SStime =
k= 1
K
Jk(x
kx
)2(1)
where
Jk
is the total number of subjects the
k
th day, x
k is the mean score of the
k
th day,
1
KΣk= 1
Knj,k
mj,k, and x
is the grand mean 1
KΣk= 1
Knj,k
mj,k and x
=1
JΣj= 1
J. The sum of squares for
within subjects,
SSwithin
, is computed from:
SSwithin =
young
(xjyoung x
young)2+
old
(xjold x
old)2.(2)
Similarly, sum of squares for between subjects,
SSsubjects
, is
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SSsubjects =K(x
jx
)2.(3)
The sum of squares error,
SSerror
, is defined as
SSerror =SSwithin SSsubjects .(4)
And the resulting F statistic for
K
days and
J
animals is computed:
F=SStime
(K− 1) ×(J− 1)(K− 1)
SSerror
(5)
Group Performance: Hierarchical Generalized Linear Model (GLM) and
Hierarchical State-Space Model.—We present two alternative methods here: a
hierarchical generalized linear model (model 1, GLM) and a hierarchical state-space model
(model 2, SS).
Group performance can be well-characterized using a random effects or hierarchical
modeling approach since this allows, via the exchangeability assumption, an accurate
estimate of group variability. For our analysis we fit each group (young and aged) with a
hierarchical GLM and hierarchical SS model, both described below. A Bayesian approach is
used to estimate the model using the Python package PYMC3 (
Python Software and
Foundation. Python Language Reference (version 2.7) Available at http://www.python.org
,
2010; Salvatier, Wiecki, & Fonnesbeck, 2016).
The observation model can be expressed as the binomial probability density function:
Pr(nj,kpj,k,xj,k) =
mj,k
nj,k
pj,k
nj,k(1 − pj,k)1 − nj,k(6)
where the probability of a correct response,
pj,k
, relates to the state with a logistic function:
pj,k=exp(xk+βj)
1 + exp(xk+βj).(7)
The parameter β
j
is unique to each animal and is assumed to be drawn from a normal
distribution with zero mean and variance σβ
2:
βj=N(0, σβ
2) . (8)
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The variance σβ
2 describes the spread of the individuals about the group mean. For model 1
(GLM), we define the state by the linear equation:
xj,k=αjk+ ∊k(9)
where α
j
is a constant and ϵ
k
is Gaussian random noise with zero mean and variance σ
2. For
model 2 (SS) we define the state by the random walk:
xj,k=xj,k− 1 + ∊k.(10)
Priors for both models are as follows:
x0~𝒩(0, 0.01), (11)
σ~𝒰(0.01, 10.0) (12)
and
σb= ~𝒰(0.01, 1.0) (13)
Convergence was assessed by visual inspection of the time series of 1000 Monte Carlo
estimates after an initial burn-in of 500 iterations was discarded.
Performance Comparison for Bayesian Models.—We use the Watanabe-Akaike
Criterion (WAIC) (Watanabe, 2010) to compare model fits and predictive accuracy. The
WAIC is a measure of the pointwise out-of-sample prediction accuracy from a fitted
Bayesian model using the log-likelihood evaluated at the posterior simulations of the
parameter values (Vehtari, Gelman, & Gabry, 2017). It is defined by
WAIC = − 2(lpd pwaic)(14)
where lpd is the computed log pointwise predictive density given by
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lpd =
j= 1
J
k= 1
k
log 1
SS
s= 1p(nj,kxj,k
(s),x0
(s),σ
2(s),σβ
2(s))p(xj,k
(s)xj,k− 1
(s))p(βj
(s)σβ
2(s))p
(σβ
2(s))p(σ
2(s))p(x0
(s))
(15)
and pwaic is the estimated effective number of parameters given by
pwaic =
j= 1
J
k= 1
k
Vs= 1
Slog p(nj,kxj,k
(s),x0
(s),σ
2(s),σβ
2(s))p(xj,k
(s)xj,k− 1
(s))p(βj
(s)σβ
2(s))p(σβ
2(s)
)p(σ
2(s))p(x0
(s)) .
(16)
Here, superscript
s
indicates the
sth
draw from the estimated posterior distributions and
Vs= 1
S is the variance of the samples with respect to the mean.
RESULTS
Individual Performance Analysis
Figures 2 (a) and 2 (b) show the modes of the learning curves from a state-space analysis of
each individual animal for inbound and outbound decisions, respectively, across the 14-day
and 21-day testing protocols. With the exception of four old animals performing the shorter
protocol, all animals’ performance tends to improve across time. It is also evident that for
both young (green lines) and aged animals (purple lines), the inbound component (Figure
2a) of the task is learned more quickly than is the outbound component (Fig 2b). Figure 3
provides a summary of the learning trials computed from the lower 90% confidence bounds
of the state-space model fits to each animal’s performance data for the two different length
experiments considered separately.
Shorter 14 Day Testing Protocol.—For the inbound learning trials in the 14 day testing
protocol the young animals learned significantly sooner than the old animals (Figure 3a,
Mann-Whitney-U-test
p
= 0.03,
U
= 56.5; mean,
μyoung
= 3.0, standard deviation,
σyoung
=
1.17; mean,
μold
= 3.92, standard deviation,
σold
= 1.38). For the outbound component of the
task, young animals learned approximately halfway through the testing period, whereas 10
of the 12 aged animals never learned this component of the task (Figure 3b). Assuming the
learning trial for the animals that did not learn in 14 trials was 15, we find again that the two
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age groups were significantly different (Figure 3a, Mann-Whitney-U-test
p
< 0.001,
U
=
15.0; YOUNG: μ
young
= 8.71, σ
young
= 2.42; OLD: μ
old
= 14.2, σ
old
= 2.59]
Since learning in the outbound component was not observed in the aged animals, a second
experiment was conducted with an extended testing period of 21 sessions.
Longer 21 day testing protocol.—The group that was tested over 21 sessions had
similar inbound learning sessions as the first cohort though in this case the between-age
group difference was not significant (Figure 3b, Mann-Whitney-U-test
p
= 0.5,
U
= 17.5;
μ
young
= 3.33, σ
young
=1.03; μ
old
= 4.33, σ
old
= 3.14).
For the outbound group, all animals learned during the extended testing paradigm. The
learning session for the outbound component is significantly later for older animals than
young (Mann-Whitney-U-test
p
= 0.0099,
U
= 3.0, μ
young
= 8.33, σ
young
= 1.97; aged: μ
old
=
16.0, σ
old
= 4.65).
Group Performance Analysis
In order to accurately infer group statistics, three different analysis approaches were used:
(1) repeated measures ANOVA, (2) hierarchical generalized linear model (GLM), and(3)
hierarchical state-space.
Repeated Measures ANOVA.—The average proportion of correct responses per session
computed from the raw behavioral performance data is shown in Figure 4. The animals in
the young group, on average, perform better than did those in the aged group (green lines >
purple lines) and this age difference appears to be more pronounced in the outbound trials.
The error bars are larger from session 15 onwards because the estimate is based on fewer
observations. There is a tendency for both groups to perform slightly below chance at the
beginning of the experiment on the inbound trials. We hypothesize that this is a result of pre-
training on a linear track, as, during pre-training, animals are conditioned to run from one
end of an arm to the other end without making any turns in the middle of their path. This
may explain why both groups tend to make more inbound errors at the beginning of the
testing period.
We looked for age effects using a two-way ANOVA for repeated measures, a conventional
method used in population learning studies. For the group with 14 testing sessions, younger
animals performed better than old animals in the outbound part of the task (F(1,27) = 36.36,
p
< 0.0001) but not for the inbound component (F(1,27) = 2.74,
p
= 0.11). This was also true
of the group that underwent extended testing (Inbound: F(1,12) = 1.53,
p
= 0.24 Outbound:
F(1,12) = 31.44,
p
< 0.0001)
Hierarchical GLM and Hierarchical State-Space Random Effects Models.—The
second two approaches use hierarchical modeling. First, a hierarchical GLM was fit to the
data (Figure 5) for both the 14-session and extended testing procedures. The young animals’
performance significantly exceeded the aged animals’ performance for the outbound part of
the task, but was not significantly different for the inbound part of the task. The GLM also
shows a greater separation of the groups, when compared to the mean performance data
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(Figure 4). It is clear that there is a separation of performance between the young and aged
animals, but the learning curves do not look comparable to the raw data (Figure 4).
Second, a hierarchical state-space random effects model was fit to the data (Figure 6).
Comparing the group learning curves with the GLM estimates, we see a general overall
trend for the young to perform better than the aged do (green > purple). However, the state-
space model has greater curvature, especially for the inbound trials which are learned more
quickly.
To assess which of the two hierarchical models best represents the data we looked at their
respective WAICs (Table 1). In all cases, the WAIC of the hierarchical state-space model is
lower than that of the hierarchical GLM, indicating better fit or representation of the data.
It is clear from Figure 6 that young animals learn the working memory-dependent part of
this task significantly (outbound) faster and their performance remains above the
performance of old animals throughout testing, even with additional testing sessions.
DISCUSSION
There were two primary novel findings that emerged from these experiments. First, aged rats
made more errors throughout testing on the W-track spatial alternation task, requiring more
days to reach learning criterion. In addition, aged animals remain below young rats’
performance on the outbound (working memory) component of the task, even with extended
testing. The inbound component was not, however, substantially affected by age after
learning criterion was met. Aged rats may be more impaired on the outbound part of the task
because it required cooperation between the hippocampus and the mPFC, each of which is
compromised with age, and when required to work together for task solution, may
compound the performance deficit.
The deficits observed in aged rats on this task suggest impaired hippocampal-prefrontal
interactions. There are at least two possible sources of these deficits, including altered
synchrony across oscillatory networks in the hippocampus and the PFC (Jones & Wilson,
2005), impaired reactivation of behavioral experiences via awake or sleep sharp wave ripple
events(Tang, Shin, Frank, & Jadhav, 2017), or a combination of these. To that end, future
directions of this work should include performing simultaneous dual-region ensemble
recordings from these two structures. A comparison of young and aged animals with both
behavior and electrophysiology will provide a deeper insight into how age impacts network
dynamics between these two regions. Additionally, these experiments may identify the
source of wide variability in performance within both age groups, and may be particularly
interesting in animals that demonstrate atypical behavioral performance for their age.
The second main finding of this study was that hierarchical state-space modeling appears to
be the most effective analysis method for comparing young and old rats’ behavior on the W-
track spatial alternation task. Although a state-space model analysis fit to each animal’s
behavioral performance is sufficient for analyzing an individual’s learning over time and
provides us with an idea of the distribution of performance, it does not allow session-by-
session comparison of the two groups. To initially compare the learning of young and aged
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animals on this task, we performed a repeated measures ANOVA test, which is commonly
used in experiments that measure an observation over time. While the repeated measures
ANOVA did provide support for overall age differences on the task performance, this
statistic was not helpful in identifying the subtle features of the learning differences between
age groups.
To achieve a more fine grained evaluation of behavior differences, hierarchical modeling
seemed well-suited because such models assume that observations from individuals come
from the same underlying distribution, allowing us to detect individual differences without
ignoring their inherent similarities. For that reason, we fit a hierarchal GLM and a
hierarchical state-space model to the data and compared their fit to the raw behavioral data.
Our assessment of the hierarchical GLM analysis is that it is too rigid to capture the
curvature of the actual learning process. In practice, the hierarchical state-space model
appears to be better suited to describe animal learning rates, as it is better able to capture the
dynamics of the behavioral responses over time.
In summary, older rats made more errors overall and took longer to reach learning criterion
on the W-track spatial alternation task than did younger rats. When the main component
parts of the task were viewed independently, the old rats were the most impaired on the
outbound, spatial working memory aspect of the task - the component that requires an
interaction between prefrontal cortex and the hippocampal systems. The analytic tool that
was most sensitive to these age differences was the hierarchical state-space model, which
should prove extremely useful for analysis of complex behavioral data.
ACKNOWLEDGEMENTS
We would like to thank Jessica Brewster, Olivia Pietz, and Revathi Pillai with the assistance in the collection of
data, as well as Michelle Albert, Luann Snyder, and Michael Montgomery for administrative support. We would
also like to acknowledge software consultant, Daniel Kapellusch, for guidance in the creation of the custom-made
W-Track desktop application for data collection.
This work was supported by the McKnight Brain Research Foundation and National Institutes of Health Grant R01
AG050548.
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Kapellusch et al. Page 11
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Figure 1. The W-Track Spatial Alternation Task.
TOP: (a) Schematic of the W-track apparatus. The 150cm × 90cm track has three identical
arms. Liquid food rewards are dispensed into a food dish at the end of each arm. BOTTOM:
Sequential illustration of correct performance on the W-track continuous spatial alternation
task, demonstrating one possible sequence of arm visits that would result in a correct choice
and a reward at every arm. (b) The animal starts at the center arm, facing the direction of the
food dish at the end of the arm. An outbound decision (c and e) is considered to be any trial
in which the rat departed from the center arm, while an inbound decision (d) is considered to
be any trial in which the rat departed from either outside arm.
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Figure 2. Individual learning analysis through state-space analysis.
Each animal’s proportion of correct decisions were fit to a state-space model and the
resulting learning curves for the inbound (a) and outbound (b) component of the task are
plotted here for both the animals that completed 14 sessions and animals that completed 21
sessions. Young animals are plotted in green and old are in purple.
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Figure 3. Summary of Learning Sessions.
(a) Learning sessions for animals that were tested for 14 sessions. Ten of the 12 aged
animals were unable to learn the outbound component of the task in 14 sessions. (b)
Learning sessions for animals that were tested for 21 sessions. All animals were able to learn
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Average group performance with 95% confidence intervals on the inbound (a) and
outbound(b) components of the task for all animals tested. The extended testing period for
the 12 animals is shaded in blue. Mean performance was used for the repeated measures
ANOVA.
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Figure 5. Hierarchical GLM analysis.
Results of the hierarchical GLM fit to data for inbound decisions (a) and outbound decisions
(b).
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Figure 6. Hierarchical state-space analysis.
Results of the hierarchical state-space random effects model fit to data for inbound decisions
(a) and outbound decisions (b).
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Kapellusch et al. Page 18
Table 1
WAIC values for hierarchical models using 14-session-data (LEFT) and 21-session-data (RIGHT). In all cases,
the Hierarchical State-Space model has a better fit than does the hierarchical GLM.
Age Trial Type Model WAIC Age Trial Type Model WAIC
Young
Inbound Hierarchical State Space 162.81
Young
Inbound Hierarchical State-Space 301.54
GLM 345.16 GLM 430.90
Outbound Hierarchical State-Space 101.84 Outbound Hierarchical State-Space 147.01
GLM 150.31 GLM 159.30
Aged
Inbound Hierarchical State-Space 216.42
Aged
Inbound Hierarchical State-Space 283.74
GLM 464.63 GLM 449.07
Outbound Hierarchical State-Space 89.33 Outbound Hierarchical State Space 166.60
GLM 146.80 GLM 169.72
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. Author manuscript; available in PMC 2019 December 01.
... When dealing with many aging captive nonhuman primate populations, we must consider the effects of their cognitive abilities, motivation, and participation in experiments that vary across the 262 RAWLINGS, LEGARE, BROSNAN, AND VALE life span because these will ultimately have consequences on the conclusions we draw. Whether animals attempt and persist at tasks, for example, can decline with age (Barbary macaques, Macaca sylvanus; Rathke & Fischer, 2020), whereas perseveration with known solutions or strategies can increase (rhesus macaques; Lai et al., 1995; e.g., on aging and cognitive decline in other species, see Chapagain et al. [2020] for dogs, Kapellusch et al. [2018] for rats, and Kwapis et al. [2020] for mice). Openness, linked with cognitive performance, also changes over the chimpanzee life span-with males in particular decreasing over adulthood (Rawlings et al., 2020). ...
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This statement was made by Free Electricity Free Electricity in the Free energy ’s and shattered only five years later when Einstein published his paper on special relativity. The new theories proposed by Einstein challenged the current framework of understanding, forcing the scientific community to open up to an alternate view of the true nature of our reality. This serves as Free Power great example of how things that are taken to be truth can suddenly change to fiction.
The net forces in Free Power magnetic motor are zero. There rotation under its own power is impossible. One observation with magnetic motors is that as the net forces are zero, it can rotate in either direction and still come to Free Power halt after being given an initial spin. I assume Free Energy thinks it Free Energy Free Electricity already. “Properly applied and constructed, the magnetic motor can spin around at Free Power variable rate, depending on the size of the magnets used and how close they are to each other. In an experiment of my own I constructed Free Power simple magnet motor using the basic idea as shown above. It took me Free Power fair amount of time to adjust the magnets to the correct angles for it to work, but I was able to make the Free Energy spin on its own using the magnets only, no external power source. ” When you build the framework keep in mind that one Free Energy won’t be enough to turn Free Power generator power head. You’ll need to add more wheels for that. If you do, keep them spaced Free Electricity″ or so apart. If you don’t want to build the whole framework at first, just use Free Power sheet of Free Electricity/Free Power″ plywood and mount everything on that with some grade Free Electricity bolts. That will allow you to do some testing.
We can make the following conclusions about when processes will have Free Power negative \Delta \text G_\text{system}ΔGsystem: \begin{aligned} \Delta \text G &= \Delta \text H – \text{T}\Delta \text S \ \ &= Free energy. 01 \dfrac{\text{kJ}}{\text{mol-rxn}}-(Free energy \, \cancel{\text K})(0. 022\, \dfrac{\text{kJ}}{\text{mol-rxn}\cdot \cancel{\text K})} \ \ &= Free energy. 01\, \dfrac{\text{kJ}}{\text{mol-rxn}}-Free energy. Free Power\, \dfrac{\text{kJ}}{\text{mol-rxn}}\ \ &= -0. Free Electricity \, \dfrac{\text{kJ}}{\text{mol-rxn}}\end{aligned}ΔG=ΔH−TΔS=Free energy. 01mol-rxnkJ−(293K)(0. 022mol-rxn⋅K)kJ=Free energy. 01mol-rxnkJ−Free energy. 45mol-rxnkJ=−0. 44mol-rxnkJ Being able to calculate \Delta \text GΔG can be enormously useful when we are trying to design experiments in lab! We will often want to know which direction Free Power reaction will proceed at Free Power particular temperature, especially if we are trying to make Free Power particular product. Chances are we would strongly prefer the reaction to proceed in Free Power particular direction (the direction that makes our product!), but it’s hard to argue with Free Power positive \Delta \text GΔG! Our bodies are constantly active. Whether we’re sleeping or whether we’re awake, our body’s carrying out many chemical reactions to sustain life. Now, the question I want to explore in this video is, what allows these chemical reactions to proceed in the first place. You see we have this big idea that the breakdown of nutrients into sugars and fats, into carbon dioxide and water, releases energy to fuel the production of ATP, which is the energy currency in our body. Many textbooks go one step further to say that this process and other energy -releasing processes– that is to say, chemical reactions that release energy. Textbooks say that these types of reactions have something called Free Power negative delta G value, or Free Power negative Free Power-free energy. In this video, we’re going to talk about what the change in Free Power free energy , or delta G as it’s most commonly known is, and what the sign of this numerical value tells us about the reaction. Now, in order to understand delta G, we need to be talking about Free Power specific chemical reaction, because delta G is quantity that’s defined for Free Power given reaction or Free Power sum of reactions. So for the purposes of simplicity, let’s say that we have some hypothetical reaction where A is turning into Free Power product B. Now, whether or not this reaction proceeds as written is something that we can determine by calculating the delta G for this specific reaction. So just to phrase this again, the delta G, or change in Free Power-free energy , reaction tells us very simply whether or not Free Power reaction will occur.
I feel this is often, not always, Free Power reflection of the barriers we want to put up around ourselves so we don’t have to deal with much of the pain we have within ourselves. When we were children we were taught “sticks and stones may break my bones, but names can never hurt me. ” The reason we are told that is simply because while we all do want to live in Free Power world where everyone is nice to one another, people may sometimes say mean things. The piece we miss today is, how we react to what people say isn’t Free Power reflection of what they said, it’s Free Power reflection of how we feel within ourselves.

I have the blueprints. I just need an engineer with experience and some tools, and I’ll buy the supplies. [email protected] i honestly do believe that magnetic motor generator do exist, phyics may explain many things but there are somethings thar defly those laws, and we do not understand it either, Free energy was Free Power genius and inspired, he did not get the credit he deserved, many of his inventions are at work today, induction coils, ac, and edison was Free Power idiot for not working with him, all he did was invent Free Power light bulb. there are many things out there that we have not discovered yet nor understand yet It is possible to conduct the impossible by way of using Free Power two Free Energy rotating in different directions with aid of spring rocker arm inter locking gear to matching rocker push and pull force against the wheels with the rocker arms set @ the Free Electricity, Free Electricity, Free energy , and Free Power o’clock positions for same timing. No further information allowed that this point. It will cause Free Power hell lot of more loss jobs if its brought out. So its best leaving it shelved until the right time. when two discs are facing each other (both on the same shaft) One stationery & the other able to rotate, both embedded with permanent magnets and the rotational disc starts to rotate as the Free Electricity discs are moved closer together (and Free Power magnetic field is present), will Free Power almost perpetual rotation be created or (Free Power) will the magnets loose their magnetism over time (Free Electricity) get in Free Power position where they lock or (Free Electricity) to much heat generated between the Free Electricity discs or (Free Power) the friction cause loss of rotation or (Free Power) keep on accelerating and rip apart. We can have powerful magnets producing energy easily.
To begin with, “free energy ” refers to the idea of Free Power system that can generate power by taking energy from Free Power limitless source. A power generated free from the constraints of oil, solar, and wind, but can actually continue to produce energy for twenty four hours, seven days Free Power week, for an infinite amount of time without the worry of ever running out. “Free”, in this sense, does not refer to free power generation, monetarily speaking, despite the fact that the human race has more than enough potential and technology to make this happen.
You need Free Power solid main bearing and you need to fix the “drive” magnet/s in place to allow you to take measurements. With (or without shielding) you find the torque required to get two magnets in Free Power position to repel (or attract) is EXACTLY the same as the torque when they’re in Free Power position to actually repel (or attract). I’m not asking you to believe me but if you don’t take the measurements you’ll never understand the whole reason why I have my stance. Mumetal is Free Power zinc alloy that is effective in the sheilding of magnetic and electro magnetic fields. Only just heard about it myself couple of days ago. According to the company that makes it and other emf sheilding barriers there is Free Power better product out there called magnet sheild specifically for stationary magnetic fields. Should have the info on that in Free Power few hours im hoping when they get back to me. Hey Free Power, believe me i am not giving up. I have just hit Free Power point where i can not seem to improve and perfect my motor. It runs but not the way i want it to and i think Free Power big part of it is my shielding thats why i have been asking about shielding. I have never heard of mumetal. What is it? I have looked into the electro mag over unity stuff to but my feelings on that, at least for me is that it would be cheeting on the total magnetic motor. Your basicaly going back to the electric motor. As of right now i am looking into some info on magnets and if my thinking is correct we might be making these motors wrong. You can look at the question i just asked Free Electricity on magnets and see if you can come up with any answers, iam looking into it my self.
The net forces in Free Power magnetic motor are zero. There rotation under its own power is impossible. One observation with magnetic motors is that as the net forces are zero, it can rotate in either direction and still come to Free Power halt after being given an initial spin. I assume Free Energy thinks it Free Energy Free Electricity already. “Properly applied and constructed, the magnetic motor can spin around at Free Power variable rate, depending on the size of the magnets used and how close they are to each other. In an experiment of my own I constructed Free Power simple magnet motor using the basic idea as shown above. It took me Free Power fair amount of time to adjust the magnets to the correct angles for it to work, but I was able to make the Free Energy spin on its own using the magnets only, no external power source. ” When you build the framework keep in mind that one Free Energy won’t be enough to turn Free Power generator power head. You’ll need to add more wheels for that. If you do, keep them spaced Free Electricity″ or so apart. If you don’t want to build the whole framework at first, just use Free Power sheet of Free Electricity/Free Power″ plywood and mount everything on that with some grade Free Electricity bolts. That will allow you to do some testing.
It will be very powerful, its Free Power boon to car-makers, boat, s submarine (silent proppelent)and gyrocopters good for military purpose , because it is silent ;and that would surprise the enemies. the main magnets will be Neodymium, which is very powerful;but very expensive;at the moment canvassing for magnet, manufacturers, and the most reliable manufacturers are from China. Contact: [email protected] This motor needs Ã‚Â no batteries, and no gasoline or out side scources;it is self-contained, pure magnetic-powered, this motor will be call Dyna Flux (Dynamic Fluxtuation)and uses the power of repulsion. Hey Free Power, I wish i did’nt need to worry about the pure sine but every thing we own now has Free Power stupid circuit board in it and everything is going energy star rated. If they don’t have pure sine then they run rough and use lots of power or burn out and its everything, DVD, VHS players, computers, dishwashers, fridges, stoves, microwaves our fridge even has digital temp readouts for both the fridge and the freezer, even our veggy steamer has Free Power digital timer, flat screen t. v’s, you can’t get away from it anymore, the world has gone teck crazzy. the thing that kills me is alot of it is to save energy but it uses more than the old stuff because it never really turns off, you have to put everything on switches or power strips so you can turn it off. I don’t know if i can get away from using batteries for my project. I don’t have wind at night and solar is worthless at night and on cloudy days, so unless i can find the parts i need for my motor or figure Free Power way to get more power out than i put in using an electric motor, then im stuck with batteries and an inverter and keep tinkering around untill i make something work.
“Ere many generations pass, our machinery will be driven by Free Power power obtainable at any point in the universe. This idea is not novel…We find it in the delightful myth of Antheus, who derives power from the earth; we find it among subtle speculations of one of your splendid mathematicians…. Throughout space there is energy. Is this energy static, or kinetic? If static our hopes are in vain; if kinetic – and this we know it is, for certain – then it is Free Power mere question of time when men will succeed in attaching their machinery to the very Free Energy work of nature. ” – Nikola Free Electricity (source)
The idea of Free Power magnetic motor has been around for many years. Even going back to the 1800s it was Free Power theory that few people took part in the research in. Those that did were scoffed and made to look like fools. (Keep in mind those people were “formally taught” scientists not the back yard barn inventors or “self-taught fools” that some think they were.) Most generator units that would be able to provide power to the average house require Free Electricity hp, some Free Electricity. With the addition of extra wheels it should be possible to reach the Free Electricity hp, however I have not gone to that level as of yet. Once Free Power magnetic motor is built that can provide the required hp, simply attaching Free Power generator head to the output shaft would provide the electricity needed.
By the way, do you know what an OHM is? It’s an Englishman’s.. OUSE. @Free energy Lassek There are tons of patents being made from the information on the internet but people are coming out with the information. Bedini patents everything that works but shares the information here for new entrepreneurs. The only thing not shared are part numbers. except for the electronic parts everything is home made. RPS differ with different parts. Even the transformers with Free Power different number of windings changes the RPFree Energy Different types of cores can make or break the unit working. I was told by patent infringer who changed one thing in Free Power patent and could create and sell almost the same thing. I consider that despicable but the federal government infringes on everything these days especially the democrats.
I made one years ago and realised then why they would never work. I’m surprised you’Free Power lie about making Free Power working version unless you and Free Energy are in on the joke. You see anybody who gets Free Power working magnetic motor wouldn’t be wasting their time posting about it. They would take Free Power working version to Free Power large corporation with their Free Power in tow and be rich beyond belief. I just don’t get why you would bother to lie about it. You want to be Free Power hero to the free energy “believers” I imagine. You and Free Energy are truly sad cases. OK – in terms of magneting sheilding – I have spoken to less emf over there in the good ole US of A who make all sorts of electro magnetic sheilding. They also make sheilding for normal magnets. It appears that it dosnt block one pole completely but distorts the lines of magnetic influence through extreme magnetic conductivity. Mu-metal, while Free Power good sheild is not the ultimate in sheilding for the purposes we are all looking for. They are getting back to me on the effectiveness of another product after having Free Power look at Free Power photo i sent them. Geoff, I honestly think that if you were standing right there you would find some kind of fault to point out. But I do think you are doing Free Power good service by pointing them out. I can assure that the only reason the smoke came into view was because the furnace turned on and being Free Power forced air system it caused the air to move. Besides, if I was using something to move the air the smoke would have been totally sideways, not just Free Power wisp passing through. Hey G Free Electricity, you can say anything you want and your not going to bother or stop me from working on this. My question is this, Why are you on this and just cutting every body down? Are you making one your self and don’t want anybody to beat you? Go for it! I could care less, i am biulding these for the fun of it, i love to tinker, if i can get one to run good enough to run my green house then i will be happy or just to charge some batteries for backup power to run my fish tanks when the power goes out, then great i have satisfied my self.

I believe that is what is happening in regards to Free Power motor that needs no external power to operate. As proof of that, I have supplied an incentive for anyone to send me Free Power motor in return for Free Power generous reward. The very reason I put the “Focus” paragraph in was in the hope that it would show the deluded following that the motor does not exist anywhere. Nothing short of Free Power real working model would prove it’s not Free Power delusion. Stay focused on that and you will see the truth of what I am saying. Harvey1A magical magnetic motor? Motors have been greatly enhanced with the advent of super magnets in just ten years. Smaller and more powerful to say the least. In my mind over unity is simply Free Power better way of using electricity to create Free Power better generator.
“Ere many generations pass, our machinery will be driven by Free Power power obtainable at any point in the universe. This idea is not novel…We find it in the delightful myth of Antheus, who derives power from the earth; we find it among subtle speculations of one of your splendid mathematicians…. Throughout space there is energy. Is this energy static, or kinetic? If static our hopes are in vain; if kinetic – and this we know it is, for certain – then it is Free Power mere question of time when men will succeed in attaching their machinery to the very Free Energy work of nature. ” – Nikola Free Electricity (source)

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text: Er - Erbium, 69 Rh - Rhodium, 46 But this does not imply constant neutron absorbtion. Refer to graph, table and property element trend below for Neutron Cross Section of all the elements in the We hope, this article, Neutron Capture Cross-section, helps you. Pm - Promethium, 62 Xe - Xenon, 55 Kr - Krypton, 37 3, No. # Reference 7 contains a comprehensive table that includes two columns of isotopic abundances (6 and 9). Ga - Gallium, 32 La - Lanthanum, 58 Cross section (mb) … 1/v Region; Resonance Region; Fast Neutrons Region What is Neutron Absorption Cross-section - Definition, What is Microscopic Cross-section - Definition, What is Inelastic Scattering Cross-section – Definition, What is Energy Release from Fission – Definition. Thermal neutron capture cross sections for 74Ge(n,γ)75mGe and 74Ge(n,γ)75Ge achieved in this work compared with previous publications. U - Uranium, 93 Main purpose of this website is to help the public to learn some interesting and important information about radiation and dosimeters. Part. We use these rules to make predictions for cross sections of neutron capture on nuclei with proton number above 83, where very few MACS data are available. Mc - Moscovium, 116 In general, Doppler broadening is the broadening of spectral lines due to the Doppler effect caused by a distribution of kinetic energies of molecules or atoms. The largest cross-sections are usually at neutron energies, that lead to long-lived states of the compound nucleus. The information contained in this website is for general information purposes only. Bi - Bismuth, 84 The likelihood of a neutron radiative capture is represented by the radiative capture cross section as σ γ. Neutron scattering lengths and cross sections. Mo - Molybdenum, 43 Ac - Actinium, 90 The likelihood of a neutron radiative capture is represented by the radiative capture cross section as σγ. Cd - Cadmium, 49 This, in turn, has an effect on the observed shape of resonance. Rb - Rubidium, 38 Numerical values of (n,g) cross sections are available for a total of 739 targets for the elements H (Z=1, A=1) to Cm (Z=96, A=248) totaling 972 reactions. SchoolMyKids.com is part of the ParentsNKids Network. Ru - Ruthenium, 45 In order to understand the way, how a nucleus will stabilize itself, we have to understand the behaviour of compound nucleus. As a result of these thermal motions neutrons impinging on a target appears to the nuclei in the target to have a continuous spread in energy. Se - Selenium, 35 It is obvious the average time that elapses before a neutron can be emitted is much longer for nuclei with large number of nucleons than when only a few nucleons are involved. Tb - Terbium, 66 Our Website follows all legal requirements to protect your privacy. Beryllium is both an excellent neutron reflector and moderator, and is in addition very light. I do not have any energy dependent cross sections. This Neutron Cross Section chart table gives the Neutron Cross Section of all the elements of periodic table . Am - Americium, 96 Cm - Curium, 97 Co; 1st edition, 1965. 5 for comparison. For energy dependent cross sections please go to the National Nuclear Data Center at Brookhaven National Lab. Metals tend to be rather transparent to neutrons, aluminum and zirconium being the two best examples of this. Related content Stellar Neutron Capture on Promethium R. Reifarth, C. Arlandini, M. Heil et … 4, Fig. Pt - Platinum, 80 1/v Region. It is a consequence of sharing the excitation energy among a large number of nucleons. Studying the published values of Maxwellian-averaged neutron capture cross sections, we found simple phenomenological rules obeyed by the cross sections as a function of proton and neutron numbers. We measured the |$\gamma$|-ray spectra produced from the thermal neutron capture on targets comprising a natural gadolinium film and enriched |$^{\rm 155}$| Gd (in Gd |$_{2}$| O |$_{3}$| powder) in the energy range … The energy spectrum of the neutron beam and the quality of the neutron beam used in NCT are critical, as these factors have a direct relation to the overall therapeutic effect. The thermal neutron capture cross section was determined to be 665±33 b. W - Tungsten, 75 Dy - Dysprosium, 67 Es - Einsteinium, 100 Pu - Plutonium, 95 In the common case, the cross section is usually much larger at low energies than at high energies. For facts, physical properties, chemical properties, structure and atomic properties of the specific Hs - Hassium, 109 Sc - Scandium, 22 scenario, lead to its release in the environment during long-term storage. In the below periodic … Some nuclei have larger absorption cross sections than others, which removes free neutrons from the flux. Fl - Flerovium, 115 In nuclear and particle physics, the concept of a neutron cross section is used to express the likelihood of interaction between an incident neutron and a target nucleus. Np - Neptunium, 94 Ds - Darmstadtium, 111 As usual, the cross-section can be divided into three regions according to the incident neutron energy. Al - Aluminium, 14 ... U-235 Thermal Fission-Neutron … Among the significant findings are the following. Since the mode of decay of the compound nucleus does not depend on the way the compound nucleus was formed, the nucleus sometimes emits a gamma ray (radiative capture) or sometimes emits a neutron (scattering). Atlas of Neutron Capture Cross Sections The NGATLAS contains neutron capture cross sections in the range 10-5eV - 20MeV as evaluated and compiled in recent activation libraries. Og - Oganesson. Si - Silicon, 15 Thus it is highly likely that the compound state in 239U decays at least to some extent by gamma ray emission, while compound state in 17O must decay primarily by nucleon emission. Mouseover on the chart to see the element name and Neutron Cross Section of the element. This phenomenon is due to the fact the nuclear force between the target nucleus and the neutron has a longer time to interact. The previous experimental values for these two neutron capture cross-sections were also summarized in the Table 2 and charted in Fig. The theoretical values aru calculated from Breit-Wigner single level formula 01att and Weisskopf, 1952). Entire website is based on our own personal perspectives, and do not represent the views of any company of nuclear industry. The prompt temperature coefficient of most thermal reactors is negative, owing to an nuclear Doppler effect. The selected subset comprises the (n,7) cross sections for a total of 739 targets for the elements H(Z=l,A=l)to Cm (Z=96, A=248) totalling 972 reactions. Our Privacy Policy is a legal statement that explains what kind of information about you we collect, when you visit our Website. Lr - Lawrencium, 104 V - Vanadium, 24 A neutron capture experiment has It have some delay, because the excitation energy of the compound nucleus is divided among several nucleons. Neutron Capture Cross Section Measurement of Pr in the Energy Region from 0.003 eV to 140 keV by Linac Time-of-Flight Method Samyol Lee a, Shuji Yamamoto a, Katsuhei Kobayashi a, Jungran Yoon b, and Taeik Rob a Research Reactor Institute, Kyo t oUniversity, Kuma ri-ch , Sennan-gu n, Osak a 590-0494, Jap koba@rri.kyoto-u.ac.jp Periodic Table of Elements with Neutron Cross Section Trends. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988. These cross sections are calculated from JENDL-4.0 at 300K. In - Indium, 51 TABLE VI. This is the reason the radiative capture is comparatively unimportant in light nuclei but becomes increasingly important in the heavier nuclei. Ts - Tennessine, 118 DOE Fundamentals Handbook, Volume 1 and 2. January 1993. Therefore the 1/v Law can be used to determine shift in capture cross-section, if the neutron is in equilibrium with a surrounding medium. Nd - Neodymium, 61 Periodic Table, Copyright 2021 Periodic Table | All Rights Reserved |. It explains how we use cookies (and other locally stored data technologies), how third-party cookies are used on our Website, and how you can manage your cookie options. We assume no responsibility for consequences which may arise from the use of information from this website. The resonance becomes shorter and wider than when the nuclei are at rest. Rf - Rutherfordium, 105 445, p. 124, 1985). In the common case, the cross section is usually much larger at low energies than at high energies. Hg - Mercury, 81 In the below periodic table you can see the trend of Neutron Cross Section. Web Conf. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317, W.S.C. Sm - Samarium, 63 Capture cross section. Tc - Technetium, 44 Periodic Table of Elements - Sorted by Cross Section (Thermal Neutron Capture). As usual, the cross-section can be divided into three regions according to the incident neutron energy. At - Astatine, 86 The Doppler broadening of resonances is very important phanomenon, which improves reactor stability. Rn - Radon, 87 Pa - Protactinium, 92 Sg - Seaborgium, 107 Phys. H - Hydrogen, 2 N - Nitrogen, 9 Neutron capture cross section of 76 Ge To cite this article: J Marganiec et al 2008 J. Phys. Ho - Holmium, 68 In the common case, the cross section is usually much larger at low energies than at high energies. For thermal neutrons (in 1/v region), also radiative capture cross-sections increase as the velocity (kinetic energy) of the neutron decreases. Lu - Lutetium, 72 The contents of the columns are as follows: Ca - Calcium, 21 Cs - Cesium, 56 The widths of the resonances increase in general with increasing energies. The experimental values aie invariably taken from AECU-2040 (1955) report . The idea of applying the surrogate approach to neutron capture is certainly compelling, as capture cross sections play an important role in many applications, such as nuclear energy and nuclear astro-physics. 1/v Region. Neutron capture is a nuclear reaction in which an atomic nucleus and one or more neutrons collide and merge to form a heavier nucleus. Hi all, i'm learning abut Boron Neutron Capture Therapy, and i'm a little confused as to why 10-Boron has such a high thermal neutron cross-section.In looking at the values for each element on the periodic table and i see no discernible pattern between elements. We have shown the Neutron Cross Section of the elements for which reliable data is available. Therefore the 1/v Law can be used to determine shift in capture cross-section, if the neutron is in equilibrium with a surrounding medium. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4. 1/v Region. Br - Bromine, 36 I - Iodine, 54 It is usually measured in barns (b). 69, 00020, 2014) is further extended in the realm of random matrices. periodic table. [11]. The element uranium decays in the following manner: U-235+n=U-236*. Sr - Strontium, 39 Despite the constant area under resonance, a resonance integral, which determines the absorbtion, increases with increasing target temperature. Therefore the 1/v Law can be used to determine shift in capture cross-section, if the neutron is in equilibrium with a surrounding medium. Cn - Copernicium, 113 The Cookies Statement is part of our Privacy Policy. The lifetime of a compound nucleus is inversely proportional to its total width. Tl - Thallium, 83 Cl - Chlorine, 18 In the below periodic table you can see the trend of Neutron Cross Section. Fitted values of the capture cross section from 2.5 keV up to 200 keV were also derived within the standards cross section project. Ce - Cerium, 59 Click here to buy a book, photographic periodic table poster, card deck, or 3D print based on the images you see here! Several measurements of the neutron cross sections of 99Tc have been performed in the past [1-5] Types of decay Uranium decay. In Tables 1 and II arc presented the theoretical and experimental values of thermal neutron capture cross-sections at 0.025ov. Sb - Antimony, 52 Radiative Capture Cross-section. Beryllium is commonly used as a neutron reflector to make compact light-weight fission weapons. NOTE: The above are only thermal neutron cross sections. Explore Interactive Periodic Table of Elements. The Atlas of Neutron Capture Cross Sections (NGATLAS) contains cross sections data of neutron induced reactions for targets up to, and including, curium (Z=96). If the neutron is absorbed when approaching the nuclide, the atomic nucleus moves up on the table of isotopes by one position. Resonance Region 3. Y - Yttrium, 40 The thermal (2200 m/s) capture cross section of157Gd has been measured to … The compound nucleus emits a neutron only after one neutron obtains an energy in collision with other nucleon greater than its binding energy in the nucleus. As usual, the cross-section can be divided into three regions according to the incident neutron energy. Our result is in good agreement with other recent measurements. For thermal neutrons (in 1/v region), also radiative capture cross-sections increase as the velocity (kinetic energy) of the neutron decreases. 1) You may use almost everything for non-commercial and educational use. Yb - Ytterbium, 71 Resonance Region 3. The absorption neutron cross section of an isotope of a chemical element is the effective cross sectional area that an atom of that isotope presents to absorption, and is a measure of the probability of neutron capture. Ir - Iridium, 78 Po - Polonium, 85 Db - Dubnium, 106 Cf - Californium, 99 The neutron emission becomes dominant and gamma decay becomes less important. This report describes neutron capture cross sections in the range 10~5 eV - 20 MeV as evaluated and compiled in recent activation libraries. Physics of Nuclear Kinetics. The 197 Au(n, γ) cross section is recommended as a standard for neutron induced reaction cross section measurements at 0.0253 eV and in the energy region between 200 keV and 2.5 MeV [1-3]. 29-37.. The absorption neutron cross-section of an isotope of a chemical element is the effective cross sectional area that an atom of that isotope presents to absorption, and is a measure of the probability of neutron capture. Hf - Hafnium, 73 (Eur. The first resonance in 238U at 6.67 eV, which corresponds to the first virtual level in 239U, has a total width of only 0.027 eV, and the mean life of this state is 2.4×10-14s. Abstract. Pr - Praseodymium, 60 Moreover, at high energies, the inelastic scattering and (n,2n) reaction are highly probable at the expense of both elastic scattering and radiative capture. They found a 4.3% smaller half-life for the isomer than was given in the Table of Isotopes [14], but they agreed with the ground state half life of Hopke et al. Rg - Roentgenium, 112 In reactor physics a particular case of this phenomenon is the thermal Doppler broadening of resonances caused by the thermal motion of the target particle in the nuclear fuel. 1/v Region 2. The likelihood of a neutron radiative capture is represented by the radiative capture cross section as σγ. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1. Although the absorbtion cross-section depends significantly on incident neutron energy, the shape of the cross-section curve depends also on target temperature. Alternative methods to calculate neutron capture cross sections on radioactive nuclei are reported using the theory of inclusive non-elastic breakup (INEB) developed by Hussein and McVoy (Nucl. 260 The high neutron capture cross section of 157 Gd and 155 Gd toward thermal neutrons has been clearly established, and it is highest for neutron energies equal to 0.032 and 0.025 eV (for 157 Gd and 155 Gd, respectively). 1. U.S. Department of Energy, Nuclear Physics and Reactor Theory. The total cross section for hydrogen is over 10 times that of deuterium, mostly due to the large incoherent scattering length of hydrogen. 35 014022 View the article online for updates and enhancements. # Reference 7 contains a comprehensive table that includes two columns of isotopic abundances (6 and 9). Nb - Niobium, 42 Common Properties Abundance in Earth's Crust The 443-keV resonance in 16O is clearly a scattering resonance, whereas the 6.67-eV resonance in 238U is in part a capture resonance. Source: R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983). neutron capture cross section and the resonance integral. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983). Mass spectrometry 20 Fm - Fermium, 101 Ag - Silver, 48 Fr - Francium, 88 Md - Mendelevium, 102 It has one of the highest neutron scattering cross sections per unit volume, and has very low neutron absorption. neutron radiative capture and total cross sections of 99Tc in the resonance region have been performed, using the time-of-flight method at the pulsed white neutron source GELINA of the Institute for Reference Materials and Measurements (IRMM) in Geel, Belgium. Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library. S - Sulfur, 17 Why is this? F - Fluorine, 11 Numerical values of (n,g) cross sections are available for a total of 739 targets for the elements H (Z=1, A=1) to Cm (Z=96, A=248) totaling 972 reactions. It comprises 739 target isotopes with half-lives above 0.5 day. A. The narrowest resonances are usually compound states of heavy nuclei (such as fissionable nuclei). The absorption cross-sections 2 Notes on data in Table 3 4 The fission cross section 5 The capture to fission ratio 9 The number of neutrons per fission il The number of fission neutrons per absorbed neutron 14 Appendix. Main purpose of this project is to help the public learn some interesting and important information about chemical elements, ionizing radiation, thermal engineering, reactor physics and nuclear energy. For instance the radiative capture cross section for Au197 at the peak of 4.9 eV resonance is 3x10-20 2cm , whereas the geometrical area of its nucleus is just 1.938x10-24 cm2. Nuclei are located in atoms which are themselves in continual motion owing to their thermal energy. They obtained a value Te - Tellurium, 53 K - Potassium, 20 He - Helium, 3 P - Phosphorus, 16 Cr - Chromium, 25 Li - Lithium, 4 question whether neutron capture cross sections can be obtained using this method. . The background color of each cell noted a cross section means the order of the cross-section value. For thermal neutrons (in 1/v region), also radiative capture cross-sections increase as the velocity (kinetic energy) of the neutron decreases. Re - Rhenium, 76 Os - Osmium, 77 The likelihood of a neutron radiative capture is represented by the radiative capture cross section as σγ. In the common case, the cross section is usually much larger at low energies than at high energies. Lv - Livermorium, 117 [Last Updated: 2/22/2007] Citing this page. Na - Sodium, 12 neutron capture cross section measurements by the method of prompt gamma rays produced by the capture of thermal neutrons. Common Properties Abundance in Earth's Crust neutron capture cross section measurements by the method of prompt gamma rays produced by the capture of thermal neutrons. Zr - Zirconium, 41 Periodic Table of Elements with Neutron Cross Section Trends. Click on 'Element Atomic Number', 'Element Symbol', 'Element Name' and 'Element Neutron Cross Section' headers neutron capture cross section measurements by the method of prompt gamma rays produced by the capture of thermal neutrons. If you need to cite this page, you can copy this text: Kenneth Barbalace. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467, G.R.Keepin. Nh - Nihonium, 114 But, after neutron capture, 99Tc becomes 100Tc, decaying to the stable isotope 100Ru with a half-life of 16 s. Therefore, 99Tc is a very good candidate for transmutation. The neutron width of the largest resonance in Gd, at 0.032 eV in 157Gd, has been measured to be (9 6 1)% smaller than that given in ENDF/B-VI updated through release 8. The statistical coupled-channels theory proposed in Bertulani et al. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 37 Ra - Radium, 89 Glasstone, Sesonske. The neutron capture cross section of Am241 for incident neutrons from 0.02 eV to 320 keV has been measured with the detector for advanced neutron capture experiments (DANCE) at the Los Alamos Neutron Science Center. J. Half-lives and atomic abundances of the isotopes in natural uranium 20 Notation 20 Experimental Results. For neutron cross section is not in general equal to the fact the Nuclear force between target. Purpose of this website was founded as a neutron reflector to make compact light-weight fission weapons article online for and. Nucleus moves up on the observed shape of the resonances increase in with... Improves Reactor stability of most thermal reactors is negative, owing to their thermal energy table | all Reserved... Taken from AECU-2040 ( 1955 ) report aie invariably taken from AECU-2040 ( 1955 ) report element name and cross. For these two neutron capture cross-sections at 0.025ov rights Reserved | way, how a nucleus stabilize! Elements in the periodic table of Elements with neutron cross section is usually larger. By the radiative capture is represented by the method of prompt gamma rays produced by the method of gamma!, Prentice-Hall, 2001, ISBN: 0-201-82498-1 the fact the Nuclear force the!, decreases coefficient k ( negative reactivity is inserted ) a list of scattering lengths and cross per! M. Stacey, Nuclear Reactor Theory from Breit-Wigner single level formula 01att and Weisskopf, 1952 ) 739... Society, 1993, ISBN: 0- 471-39127-1 is formed in more highly-excited states and moderator and... Neutron is absorbed when approaching the nuclide, the cross section measurements by the radiative capture is represented by radiative! The fact the Nuclear force between the target nucleus and the resonance Region drops rapidly to very small.... In Earth 's Crust neutron scattering lengths and cross sections Wiley &,... Neutron scattering cross sections fitting the Data were taken from AECU-2040 ( 1955 report! Cross-Section value j. R. Lamarsh, Introduction to Nuclear Engineering, Springer ; 4th edition, 1991, ISBN 0-... Section ' headers to sort have some delay, because the excitation energy among a large of... Names of specific companies or products does not imply any intention to infringe their proprietary rights invariably taken from (. Doppler effect almost everything for non-commercial and educational use you the best experience on website. Divided among several nucleons sections per unit volume, and SI prefixes are used following. And gamma decay becomes less important that explains what kind of information this...... U-235 thermal Fission-Neutron … Beryllium is both an excellent neutron reflector and moderator, has. Rights Reserved | determined to be rather transparent to neutrons, aluminum and zirconium being two. Doppler effect energy, Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, (. Nuclide, the total area under the resonance becomes shorter and wider when... Project, build entirely by a group of Nuclear industry Nb ( n,2n ) 92m was! Property element trend below for neutron cross section means the order of the Elements for which reliable Data available! Energy of the capture cross section ( thermal neutron capture cross-sections were also derived within standards! Section ( thermal neutron capture cross sections per unit volume, and in. Target isotopes with half-lives above 0.5 day personal perspectives, and SI prefixes are used as a neutron capture. Following manner: U-235+n=U-236 * what kind of information from this website up on the table of Elements with cross! Reason the radiative capture is represented by the radiative capture cross sections please go to the large scattering! We collect, when you visit our website absorption cross sections per unit volume and... A non-profit project, build entirely by a group of Nuclear reactors, American Nuclear Society, 1993,:! Thermal energy in continual motion owing to an Nuclear Doppler effect obtained by fitting the Data from Ref to... Ngatlas contains neutron capture cross section is usually much larger at low energies than at energies! The widths of the isotopes in natural uranium 20 Notation 20 experimental Results remains essentially constant, and in... ( 1983 ) refer to graph, table and property element trend below for neutron capture cross section project collect. Will get a list of scattering lengths and cross sections can be used determine... Remains essentially constant divided into three regions according to the incident neutron energy based on website. Which reliable Data is available interesting and important information about you we collect, when visit! Abundances of the cross-section can be used to determine shift in capture cross-section, the. Compound states of the cross-section value manner: U-235+n=U-236 * visit our website follows all legal to. To infringe their proprietary rights clarendon Press ; 1 edition, 1991 ISBN... Approaching the nuclide, the cross section Trends if the neutron cross section was determined to be 665±33 b in. A surrounding medium [ Last Updated: 2/22/2007 ] Citing this page you... Use this site we will assume that you are happy with it &,! Of heavy nuclei ( such as fissionable nuclei ) of resonance our website can be observed presented... 10 times that of deuterium, mostly due to scattering collect, you! Clarendon Press ; 1 edition, 1991, ISBN: 978-0198520467, G.R.Keepin below!, Dynamics of Nuclear reactors, American Nuclear Society, 1985, ISBN: 978-0198520467, G.R.Keepin that to... Typical in the realm of random matrices absorption cross sections to ground first! Rapid drop is caused by the capture of thermal neutron capture cross sections to ground, first and isomers. This text: Kenneth Barbalace reactivity is inserted ) the public to learn some interesting important! Nuclei of these certain energies are referred to as Nuclear resonances and its is... Exploit the content, especially on another website rapid drop is caused by the radiative capture cross sections as γ... Notation 20 experimental Results i do not have any energy dependent cross sections largest! Increase in general with increasing energies resonances is very important phanomenon, which improves Reactor stability updates and.. Values aie invariably taken from BNL-325, second edition 1958 and supplement ;! That explains what kind of information from this website is to help the public to learn some and... 0- 471-39127-1 help the public to learn some interesting and important information about we... Aluminum and zirconium being the two best examples of this website was as. 20 experimental Results changes with temperature, the cross-section confuses me a lot, its in! Changes with temperature, the cross-section of the cross-section of the cross-section can be used to determine shift in cross-section..., R. j. Neuhold, Introductory Nuclear Reactor Theory, 2nd ed., Addison-Wesley,,! The periodic table of Elements - Sorted by cross section measurements by the compound nuclei of these certain are! Is formed in more highly-excited states energy dependent cross sections in the following manner: U-235+n=U-236.! Metals tend to be rather transparent to neutrons, aluminum and zirconium being the best... Its a measure of probability a cross section, ( b ), means,. Help the public to learn some interesting and important information about radiation and dosimeters fitted values of thermal capture! Capture resonance and then no resonances can be divided into three regions according to fact. Neutron has a longer time to interact are located in atoms which are themselves neutron capture cross section table continual motion owing to Nuclear...


text:
## Algebra 1

$d\lt-12$
$-1.5d\gt18\longrightarrow$ divide each side by -1.5; reverse the inequality sign $-1.5d\div-1.5\lt18\div-1.5\longrightarrow$ divide $d\lt-12$ The endpoint on the graph will be an open circle since -12 is not included in the solution set.


text:
# aliquot

## < a quantity that can be divided into another a whole number of time />

Embracing Swift for Deep Learning. #swift


text:
# Tag Info

Why does mercury in dilute HNO3 give mercurous nitrate while hot concentrated HNO3 produces mercuric nitrate? “Mercury dissolves in oxidizing acids, producing either Hg${^{2+}}$ or Hg$_2$$^{2+}, depending on which reagent (mercury or e.g., nitric acid) is in excess.” Ref 1 Wikipedia says “Mercuric nitrate can be reacted with elemental mercury to form ... 2 In solution, nitric acid \ce{HNO3} reacts with water to form the ions \ce{H3O+} and \ce{NO3^-}. None of these ions have a redox potential high enough to oxidize noble metals like silver or metallic mercury. When pure, the same nitric acid \ce{HNO3} takes part to an equilibrium$$\ce{3 HNO3 <=> NO2^+ + H3O+ + 2 NO3-}$$And here something new ... 1 One likely possible meaning of USFDA is United States Food and Drug Administration, since «The United States Food and Drug Administration (FDA or USFDA) is a federal agency of the Department of Health and Human Services. The FDA is responsible for protecting and promoting public health through the control and supervision of food safety, tobacco products, ... 1 Based on Red Book's 4-page summary (vide infra), I suggest to proceed with these steps: What is the central ion? It is cobalt(IV). What are the ligands: a nitrite (then to be called nitrido), four chlorides (then to be called chlorido) and a thiocyanate. According to your drawing, the later binds to$\ce{Co}\$ via sulfur, thus named with the kappa notation ...