11institutetext: F Hoffmann-La Roche AG, Basel, Switzerland

# Characterizing the Interpretability of Attention Maps in Digital Pathology

Tomé Albuquerque  0000-0003-3246-7206 Anil Yüce  0000-0003-2688-1873 Markus D.
Herrmann  0000-0002-7257-9205 Alvaro Gomariz  0000-0002-6172-5190

###### Abstract

Interpreting machine learning model decisions is crucial for high-risk
applications like healthcare. In digital pathology, large whole slide images
(WSIs) are decomposed into smaller tiles and tile-derived features are
processed by attention-based multiple instance learning (ABMIL) models to
predict WSI-level labels. These networks generate tile-specific attention
weights, which can be visualized as attention maps for interpretability.
However, a standardized evaluation framework for these maps is lacking,
questioning their reliability and ability to detect spurious correlations that
can mislead models. We herein propose a framework to assess the ability of
attention networks to attend to relevant features in digital pathology by
creating artificial model confounders and using dedicated interpretability
metrics. Models are trained and evaluated on data with tile modifications
correlated with WSI labels, enabling the analysis of model sensitivity to
artificial confounders and the accuracy of attention maps in highlighting
them. Confounders are introduced either through synthetic tile modifications
or through tile ablations based on their specific image-based features, with
the latter being used to assess more clinically relevant scenarios. We also
analyze the impact of varying confounder quantities at both the tile and WSI
levels. Our results show that ABMIL models perform as desired within our
framework. While attention maps generally highlight relevant regions, their
robustness is affected by the type and number of confounders. Our versatile
framework has the potential to be used in the evaluation of various methods
and the exploration of image-based features driving model predictions, which
could aid in biomarker discovery.

##  1 Introduction

The integration of digital pathology (DP), particularly with images of
Hematoxylin and Eosin (H&E) stained tissue sections, in clinical practice
opens the possibility to advance diagnostics through artificial intelligence
(AI). Machine learning (ML) models could assist diagnostic tasks by
discovering input-output correlations in training data. However, these models
usually rely on correlations rather than causal connections [3]. Consequently,
ML predictions may be based on spurious correlations, including confounding
artifacts such as pen marks on an image [14]. Such confounders can
inaccurately inflate prediction performance, posing risks when human
practitioners depend on these predictions. Indeed, the lack of explainability
of black-box models is a significant barrier to implementing AI in high-stakes
fields, namely in healthcare [6]. Therefore, tools to understand and trace ML
decision processes are essential to ensure reliable AI support in medical
decisions. The rapid advancement of explainable AI has led to numerous
techniques enhancing the transparency of black-box ML systems [9]. However,
the intricacies of DP datasets call for the use of dedicated methodologies.

_Whole slide images (WSI)_ in DP are very large and usually cannot be
processed by typical deep learning classification models due to computational
constraints. The multiple instance learning (MIL) framework has been adopted
in the community, where WSIs are decomposed into smaller _tiles_ that inherit
the WSI’s label during training [12]. The popular attention-based MIL (ABMIL)
[10] network employs a global attention mechanism to learn weights accounting
for the contribution of each tile representation to the final WSI prediction.
Tiles in the WSI are often visualized by their weights values as attention
maps, enabling the interpretation of which regions are prioritized by the
ABMIL model prediction process [4].

The described interpretability methods make ML predictions more transparent
and may reveal new pathological insights. However, the proficiency of
attention maps in identifying misleading correlations, also known as spurious
correlations, has been criticized [2, 7]. In the context of X-ray chest
images, a framework has been proposed [15] to assess the identification of
spurious correlations in classification models by systematically introducing
confounders in the training and evaluation data.

In the DP ABMIL setting, only some of the tiles may contain the information
necessary for model predictions, hence requiring a different experimental
design and evaluation metrics for the assessment of attention maps employed
for interpretability. We herein build on the work of Sun et al. [15] by
providing a framework suitable for ABMIL with DP WSIs, including new
experimental designs and metrics that emphasize the role of tiles in model
predictions. Our framework, illustrated in Fig. 1, includes the study of tile-
and WSI-based confounders, which are first validated with synthetic
confounders involving image modifications. We then explore the more clinically
relevant scenario of enriching for confounders via sampling tiles based on
image-based features.

Figure 1: Overview of our framework for the evaluation of attention maps in
DP.

##  2 Methods

###  2.1 Attention Maps in Digital Pathology

We adopt the ABMIL [10] framework described above for binary classification. A
WSI $s_{i},\,i\in\\{1,\ldots,S\\}$ is decomposed into non-overlapping tiles
$t_{i}^{j}\in\mathbb{R}^{n\times n}$, with $n$ the tile size and $S$ the
number of WSIs. Tiles are processed by a feature extraction model
${G:\mathbb{R}^{n\times n}\rightarrow\mathbb{R}^{k}}$, yielding embedding
vectors of length $k$. We define the ABMIL model as ${F:\mathbb{R}^{T\times
k}\rightarrow\\{0,1\\}}$, which employs an attention mechanism on the $T$
embeddings to predict the binary WSI label, with ground truth $y_{s_{i}}$.
Attention maps are generated by visualizing the resulting attention weights
${a_{i}^{j}\in\mathbb{R}}$ corresponding to each of the tiles $t_{i}^{j}$.
These maps help identify which regions contribute most to the WSI-level
prediction, enhancing interpretability and aiding in the detection of spurious
correlations or areas of interest.

###  2.2 Framework for the Interpretability of Attention Maps

As illustrated in Fig. 1, our framework applies controlled modifications to
the tiles in WSIs of a specific class. These modifications act as spurious
correlations that aid the classification model. A confounded model may change
its prediction when such modification is also used in a test image. When this
occurs, we can assess whether the attention map highlights the modified tiles,
hence enabling our evaluation.

Let $M_{p}\sim\textit{Bernoulli}(p)$ be a Bernoulli random function. We define
$M_{p}$ separately for tiles ($M_{p}^{t}$) and WSIs ($M_{p}^{s}$). This means
that a modified WSI $\hat{s}^{i}$ is produced when $M_{p}^{s}(s_{i})=1$, which
occurs with probability $p$. As the goal of $M_{p}$ is to introduce
confounders, it is only applied to WSIs with positive label. Consequently,
$M_{p}^{s}(s_{i})$ is always 0 for WSIs with negative label ($y_{s_{i}}=0$).
Only modified WSIs $\hat{s}^{i}$ can have modified tiles $\hat{t}_{i}^{j}$, as
defined by $M_{p}(t_{i}^{j})$. Thus, within a modified WSI, only some tiles
are actually modified. Two different modification designs are employed in our
experimental setting:

$\bullet$ Tile-based: Different percentages of tiles are modified for all
WSIs. Specifically, $M_{p}^{s}$ is set to 1, and a range of $M_{p}^{t}$ values
is assessed. This strategy enables the examination of how the amount of
systematic confounders (i.e., present in all WSIs) influences the model.

$\bullet$ WSI-based: We study the effect of sporadic confounders that only
affect a varying number of WSIs, whose tiles are affected with the same
probability, i.e. a range of $M_{p}^{s}$ is assessed while $M_{p}^{t}$ is set
to 0.5. This value of $M_{p}^{t}$ is heuristically defined based on the tile-
based observations.

###  2.3 Evaluation of Artificially Confounded Datasets

ABMIL models $F$ are trained for different training sets created with
different modifications $M_{p}$. Two types of evaluations are performed for
assessing the predictions and interpretability separately:

Model predictions:  The performance of $F$ is measured with the Area Under the
receiver operator characteristics Curve (AUC) in the binary classification
task. A test set is employed with the same $M_{p}$ process as the training set
of that model. The goal is to assess whether the performance increases with
$p$, which would confirm that the modification is indeed acting as a
confounder and aiding the model in an artificial way, hence enabling the
interpretability evaluation.

Interpretability:  Each model $F$ is evaluated on each WSI of the test set,
once with and once without modification ($F(\hat{s}_{i})$ and $F(s_{i})$
respectively). The goal is to assess attention differences in the subset of
WSIs where the modification alters the prediction, defined as
$\bar{S}=\\{s_{i}\mid F(\hat{s}_{i})\neq F(s_{i})\\}$. These differences are
measured as a confusion matrix, where modified tiles $\hat{t_{i}^{j}}$ are
considered positives, and unmodified tiles $t_{i}^{j}$ are considered
negatives. The predicted attention $a_{i}^{j}$ is considered a positive
prediction when it is in the top 20% of attention tiles, and negative
otherwise. We use the function $F_{\text{att}}^{\text{top}}$ to denote when a
tile is among the top 20% tiles ($F_{\text{att}}^{\text{top}}(t_{i}^{j})=1$)
or not ($F_{\text{att}}^{\text{top}}(t_{i}^{j})=0$). Two metrics are used in
our evaluation:

$\bullet$ _Confounder Robustness (CR):_ We propose this metric to quantify the
ability of an ABMIL model to attribute its decision to a confounder,
specifically as the ratio of WSIs for which the attention to modified tiles is
better than random guess. With the confounder matrix as defined above, it
follows that $\textit{Prevalence}=\left(1/T\right)\sum_{t_{i}^{j}\in
s_{i}}M(t_{i}^{j})$ and

$\textit{Precision}=\frac{\sum_{t_{i}\in\bar{S}}F_{\text{att}}^{\text{top}}(t_{i}^{j})M(t_{i}^{j})}{\sum_{t_{i}\in\bar{S}}F_{\text{att}}^{\text{top}}(t_{i}^{j})}$

Considering that by definition a random assignment would, in average, match
the precision to the prevalence, we define the CR metric as:

$\textit{CR}=\frac{1}{\bar{S}}\sum_{s\in\bar{S}}\mathbbm{1}\left(\textit{Precision}>\textit{Prevalence}\right)$

$\bullet$ _Normalized Cross Correlation (NCC):_ This metric measures the
sensitivity to changes in attention when applying a modification.

$\textit{NCC}=\frac{1}{\bar{S}}\sum_{s_{i}\in\bar{S}}\frac{\sum_{t_{i}^{j}\in
s_{i}}\left(a_{i}^{j}-\overline{a_{i}}\right)\left(\hat{a}_{i}^{j}-\overline{\hat{a}_{i}}\right)}{\sum_{t_{i}^{j}\in
s_{i}}\sqrt{\left(a_{i}^{j}-\overline{a_{i}}\right)^{2}\left(\hat{a}_{i}^{j}-\overline{\hat{a}_{i}}\right)^{2}}}$

where the mean of the attention across tiles in $s_{i}$ is denoted as
$\overline{a_{i}}$ and $\overline{\hat{a}_{i}}$ for its original and modified
version respectively.

In this framework, NCC$=$$1$ and CR$=$$0$ when $p$$=$$0$, as there are no
modifications and the model produces the same predictions. For low $p$, the
model may not be confounded yet, hence not paying attention to the
modifications and yielding high NCC and low CR values. When $p$$=$$1$, the
model should be completely confounded and base its predictions only on the
existence of confounders in the test data, which, in an ideal scenario, would
lead to NCC$=$$0$ and CR$=$$1$.

##  3 Experiments and Results

Dataset: We employ CAMELYON16 [11], a publicly available dataset formed by 399
WSIs of sentinel lymph node tissue sections used for binary classification of
WSIs into lymph node tissue with (60%) or without (40%) cancer metastasis. We
use all tissue tiles and follow the train-test split proposed for the original
challenge, with $20\%$ of the training data employed as validation set, which
is employed to select the best training epoch based on the loss value.

Implementation: WSIs are decomposed into patches of size $n$$=$$256$ pixels,
which are processed by a ResNet50 pre-trained on DP samples as described in
[1, 8, 5]. The resulting embeddings are aggregated using ABMIL with bags of of
1024 tiles, 32 bags per batch, a maximum of $300$ epochs, feature layers with
$[1024,1024,512,128,64,32]$ nodes, dropout rate of $0.1$, binary crossentropy
loss with label smoothing, and learning rate $0.0001$.

###  3.1 Synthetic Modifications

We employ transformations that change the appearance of individual tiles as
indicated in Fig. 2, which allow for controlled experiments to assess the
impact of these modifications both on the classification and interpretability
performance. Note that the modifications are only added to the metastatic
tissue class to act as model confounders. The _Clever Hans_ modification is
created by inserting text ("Clever Hans") into the tile at a random position,
applying random rotation, and overlaying it onto the original image using
alpha compositing. The _blur_ artifact is achieved using a Gaussian filter
with a standard deviation of $4$ pixels. The _pen mark_ modification is
generated with two random points, between which a red line is drawn and
overlaid with alpha compositing.

Original | Clever Hans | Blur | Pen mark
---|---|---|---
|  |  |
Figure 2: Examples of synthetic tile modifications employed.

Classification Performance: The AUC in Fig. 3 shows that, with a few minor
exceptions, the ABMIL model gradually obtains better classification results as
the amount of confounders increases, both for the tile- and WSI-based
experiments, and for all three types of modifications. This performance
improvement confirms that the synthetic modifications act as a confounder for
the model. These results highlight the model’s susceptibility to spurious
correlation, hence enabling an accurate evaluation of the interpretability of
the attention maps. Interestingly, the increase in performance is generally
lower for the WSI-based approach. This suggests that a lower amount of
systematic (tile-based) confounders can mislead the model more easily than a
higher amount of sporadic (WSI-based) confounders. The varying influence of
each type of modification underscores the different effects that various
confounders can have.

$0.9$$0.92$$0.94$$0.96$$0.98$$1$AUCClever HansTile-BasedWSI-
Based$0$$0.5$$1$CR0205080100$0$$0.5$$1$% of modificationNCC

$0.9$$0.95$$1$AUCBlur$0$$0.5$$1$CS0205080100$0$$0.5$$1$% of modificationNCC

$0.9$$0.92$$0.94$$0.96$$0.98$$1$AUCPen Mark$0$$0.5$$1$CS0205080100$0$$0.5$$1$%
of modificationNCC

Figure 3: Classification (top) and explainability performance results (middle
and bottom) for synthetic experiments.

Interpretability Performance: The explainability metrics in Fig. 3 confirm
that, as the amount of confounders increases, the attention maps tend to focus
more on the modified tiles. This effect is reflected by the fact that, as the
% of modification $p$ increases, the NCC decreases and the CS increases, which
would otherwise be close to 1 and 0 respectively for any degree of
modifications. When the WSI-based % of modifications is low, the CR increases
substantially more for Clever Hans than for the other transformations. This
observation highlights the dependence of model’s sensitivity to different
confounders, which in our setup is lower for Clever Hans. The low value of NCC
for the blur experiments is also relevant. We hypothesize this is due to the
difficulty in extracting pertinent information from blurred tiles, which
creates higher variations in attention weights.

###  3.2 Feature-based Sampling Strategy

While the synthetic confounders presented above allow for controlled
experiments in our framework, the results may not be representative of real-
world cases with more subtle confounders. We herein present a proof of concept
using tile ablations to dilute an existing signal, namely by leveraging the
known influence of real WSI-derived features on the model prediction. The size
of nuclei of breast cancer cells is known to be more variable than the size of
nuclei of normal lymphocytes in the lymph nodes [13]. Hence a higher variance
in nuclear size can be leveraged as a proxy for the presence of breast cancer
metastases. We employ the _Standard Deviation of the Average Nuclear Area_
(SDANA), which is calculated by first taking the average area of the cell
nuclei for each tile and then taking the standard deviation of these values
across the entire WSI. SDANA is herein studied as a feature that the ABMIL
model $F$ leverages for its predictions.

In this setting, the prevalence of specific tiles is systematically reduced
with the goal of obtaining a similar SDANA in WSIs from either class, so that
the model cannot leverage this feature. The original training set has the
distribution of SDANA per WSI shown in Fig. 4(a), with a clear separation
between metastatic and healthy tissue WSIs. We analyze how to reduce this
separation by selectively removing tiles, only for metastatic tissue WSIs,
with an average cell area above a specific threshold. Fig. 4(b) shows the
resulting p-value, as measured by a t-test, of the separation between both
distributions (SDANA for healthy and ablated WSIs) for different thresholds.
The p-value is maximized at threshold 470, which is used hereon. By
eliminating the tiles in the metastatic tissue WSIs with a mean area of cells
above $470$, we bring the class distributions for SDANA as close as possible,
as shown in Fig. 4(c), and hence prevent the ABMIL model from using SDANA as a
discriminative feature.

a) (a)

$350$$400$$450$$500$$550$$600$$0$$0.2$$0.4$$0.6$$0.8$$1$Threshold average
nuclear areap-valueb)

(b)

c) (c)

0205080100$0.88$$0.9$$0.92$$0.94$$0.96$$0.98$$1$% of modificationAUCTile-
BasedTile-Based BaselineWSI-BasedWSI-Based Baselined)

(d)

Figure 4: Feature-based sampling strategy. (a) Original distribution. (b)
SDANA class separation. (c) Distribution after ablation. (d) Classification
results.

In this setting, the modification function $M_{p}$ is not random. Instead, $p$
denotes the ratio of tiles with cell area above the selected threshold of 470
to be removed. The removed tiles are chosen based on their cell area from
highest to lowest. This setting only accounts for classification performance,
since our interpretability metrics require a consistent number of modified
tiles; however, in this setting tiles are removed. Baseline results with a
random ablation are included for comparison. This baseline is based on an
equivalent ablation, where the same number of tiles are removed as in the
feature-based experiment, with the difference that they are selected randomly
across the WSI. The ablation for this random baseline is repeated with 5
replicates using different random tiles, for which the average AUC is
employed.

The results in Fig. 4(d) show that, as hypothesized, the AUC decreases as the
amount of removed tiles increases, which brings the SDANA distributions closer
across both classes. This is a realistic scenario with less control on the
data, which explains why the trend is not as clear as with the synthetic
experiment results. Still, the decrease in performance is clear when compared
to the random baseline experiment. Hence, this feature-based framework enables
the study of the relevance of specific concept features for DP classification
tasks, further improving our understanding of the model’s decision-making
process.

##  4 Conclusions

We herein establish a framework for evaluating the ability of attention maps
to highlight regions in a WSI containing patterns that correlate with the WSI-
level label. Our results based on synthetic tile ablations underscore the
value of this framework, as both the classification and interpretability
metrics follow the expected trends. The results further confirm that the
robustness and interpretability of ABMIL models depend on the type and
systematic nature of confounders. Additionally, we propose a feature-based
sampling strategy, where real DP features are employed for diluting the
signal, i.e. by reducing the prevalence of tiles containing patterns known to
be relevant for the task. This setting demonstrates the value of our framework
in real-world scenarios, where the impact of specific DP features can be
quantitatively measured. Our framework can also be extended to evaluate real-
world confounders that may negatively affect ML models, which could be
assessed on a dataset where natural confounders have been labeled. Moreover,
different feature extraction models and attention mechanisms could be
evaluated in our framework to characterize their behavior in the presence of
confounders. This versatility enhances the potential application of our
framework, paving the way for more robust and interpretable AI solutions in
digital pathology.

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# Measurement of fragment-correlated $\gamma$-ray emission from 252Cf(sf)

Stefano Marin<EMAIL_ADDRESS>Department of Nuclear Engineering and
Radiological Sciences, University of Michigan, Ann Arbor, MI 48109, USA  Ivan
A. Tolstukhin<EMAIL_ADDRESS>Physics Division, Argonne National
Laboratory, Lemont, IL 60439, USA  Nathan P. Giha  Department of Nuclear
Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI
48109, USA  Physics Division, Argonne National Laboratory, Lemont, IL 60439,
USA  Fredrik Tovesson  Physics Division, Argonne National Laboratory, Lemont,
IL 60439, USA  Vladimir Protopopescu  Oak Ridge National Laboratory, Oak
Ridge, TN 37830, USA  Sara A. Pozzi  Department of Nuclear Engineering and
Radiological Sciences, University of Michigan, Ann Arbor, MI 48109, USA
Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA

###### Abstract

This paper presents recent experimental results on the yield of prompt fission
$\gamma$ rays from the spontaneous fission of 252Cf. We use an ionization
chamber to tag fission events and measure the masses and kinetic energies of
the fission fragments and trans-stilbene organic scintillators to measure the
neutrons and $\gamma$ rays emitted by the fission fragments. The combination
of the ionization chamber and trans-stilbene scintillators allows us to
determine the properties of neutrons and $\gamma$ rays in coincidence with the
fragments. The yield of $\gamma$ rays is known to be influenced by the angular
momenta (AM) of the fission fragments. We present new experimental evidence
that indicates that the total $\gamma$-ray multiplicity, i.e., the sum of both
fragments’ emission, saturates at sufficiently high internal fragment
excitation energies. We also observe distinct behaviors for the yield of
$\gamma$ rays from the light and heavy fragment, which for certain mass and
total kinetic energy (TKE) regions are weakly or anti-correlated, indicating
the presence of complex AM generation modes. We also observed a mass- and TKE-
dependent anisotropy of the $\gamma$ rays, which challenges and expands on the
conventional notion that the fragments’ AM are always aligned perpendicularly
to the fission axis. Moreover, the dependence of the anisotropy on mass and
TKE indicates a dependence of these properties on the specific fission
channels, thus providing an insight into the deformations and dynamics in
fission and their connection with experimentally observable quantities.

angular momentum; fission fragments; gamma rays

##  I Introduction

Nuclear fission has received renewed interest in the past decade, thanks in
part to new experimental data [1, 2, 3] and large computational models of
nuclei [4, 5]. However, there are several aspects of nuclear fission that
still remain unresolved, in particular, the generation of the fragment angular
momenta (AM) in fission. AM is an important aspect to understand in fission
because of its role in the description of deformation processes, of which
fission is a chief and extreme example [6]. At the same time, AM strongly
influences the feeding of rotational bands in fission fragments and is thus
important in the measurement and spectroscopy of $\gamma$ rays.

The main unresolved question revolves around identifying the mechanism
responsible for generating AM in the fission fragments, particularly
considering that the fissioning nucleus possesses minimal or no initial AM. A
current obstacle in answering this question is that several conceptually
distinct theoretical models have been proposed for the generation of AM, all
of which have reasonable but quite distinct assumptions and predictions.
Indeed, at least three mechanisms for the generation of fragment AM have been
proposed: deformation of fission fragments [7, 4], statistical excitation of
rotational modes [8, 9, 10], and Coulomb torque [11, 12]. The predictions made
by these models tend to agree on established results, such as the average
magnitude of the fragment AM, but disagree on other more complex observables,
such as the relative orientations of the fragments’ AM. The purpose of the
current experimental work is to add to the rich literature of fission
observables data, enabling the discrimination of the theoretical models and
potentially elucidating the mechanism responsible for AM generation in
fission.

In an experimental setting, it is challenging to gain direct access to the
fragment AM. This quantity is related to a rotational symmetry of the nuclear
wave function of the nucleus that decays quickly by neutron and $\gamma$-ray
radiation. Some of the most common and successful techniques that have been
used in determining the AM are $\gamma$-ray spectra [3], isomeric yield ratios
[13, 14], $\gamma$-ray angular distributions [15, 11], and $\gamma$-ray
multiplicity distributions [16, 17]. The work presented in this paper draws
conclusions on the fragment AM based on the multiplicity and angular
distribution of the $\gamma$ rays they emit.

In Section II we briefly discuss the specifics of the experimental system. The
study of $\gamma$-ray multiplicity for different fragment mass regions and
kinetic energies is presented in Section III. In Section IV we study the
angular distribution of $\gamma$ rays with respect to the fission axis,
attempting to determine the polarization of the fragment AM in fission. We
discuss the results of this experiment and their interpretation in Section V.

##  II Experimental Methods

###  II.1 Instruments

The experiments we present in this paper use the connection between the
$\gamma$-ray yield and the fission fragments’ AM. In particular, just as
neutron multiplicity is often used as a proxy observable for the fragment
excitation energy [16, 18], $\gamma$-ray multiplicity and angular distribution
carry important information regarding the fragments’ AM. By correlating these
$\gamma$-ray observables with coincident data on fragment properties, such as
masses and TKE, we can study trends in AM as the underlying fragment
properties change.

The experiment was performed using the FS-3 array of trans-stilbene organic
scintillators coupled to the Argonne National Laboratory twin Frisch-gridded
ionization chamber (TFGIC). A recent paper [19] details the technical aspects
and performance of this experimental setup.

The target in this experiment was prepared at Oregon State University and
consists of a molecular plating of 252Cf on a $\approx 100$ $\mu\text{g}\
\text{cm}^{-2}$ carbon foil. The thin target allows both fragments to escape
into the separate sides of the chamber and be detected. The $2E$ method [20]
is used to determine the fragment masses from the measured kinetic energies.
The molecular plating technique leaves a non-uniform “crud” of cracked solvent
molecules, which makes the resolution of the system slightly inferior to those
using more uniform types of depositions. We have accounted for this effect in
our analysis; however, remnants of the correction are still noticeable at
larger angles, where the fragments have to travel through a greater amount of
material. For this reason, we have constrained the analysis of the angular
distribution only to $|\cos\theta|>0.3$, where $\theta$ is the angle between
the fragment direction and the axis of the fission chamber, which is itself
normal to the source plane.

Two configurations were used to provide the results of the work presented
here: one including all detectors of the FS-3 system and a 252Cf target with
total activity of approximately $9$ kBq, and one where only the two FS-3
detectors collinear with the TFGIC are used. For the second configuration, a
stronger 252Cf source of total activity $\sim 130$ kBq is used to compensate
for the reduced efficiency of the detectors.

###  II.2 Multiplicity and spectrum analysis

The full FS-3 detector array consists of 39 active detectors placed in
spherical configuration around the source, and a geometric coverage of
approximately $12$%. Simple unfolding techniques, based on the simulated
energy-dependent response matrix of the system to $\gamma$-rays, has been
applied to recover the multiplicity and spectra of the measured $\gamma$ rays.
Given the broad energy resolution of trans-stilbene detectors, peaks cannot be
resolved but gross features of the spectrum can be seen.

Fig. 1 shows the measured and unfolded spectra of $\gamma$ rays detected
during this experiment. We have compared our unfolded results to a recent
measurement by Oberstedt et al. [21], which used dedicated inorganic
scintillators. While the finer features are not exactly reproduced, we can see
from the figure that the unfolding procedure of the $\gamma$-ray spectrum
significantly improves our measurements and allows us to validate the
simulated experimental response.

Figure 1: The measured $\gamma$-ray spectrum (scaled here simply by the
inverse of the simulated efficiency) is unfolded using simulated $\gamma$-ray
response matrices. The resulting unfolded spectrum reproduces the shape of the
emitted $\gamma$-ray spectrum as observed by recent experiments [21]. Since
the size of the statistical error bars is smaller than the line width, the
error bars are not included. Systematic errors, associated with both the
measurement apparatus and the unfolding process, are not included either.

In addition to the total $\gamma$-ray multiplicity, it is also possible to
extract from the experiment the individual $\gamma$-ray multiplicities emitted
from each fragment. This is performed by applying the Meier-Leibniz Doppler-
shift method [2]. In this method, only detectors collinear with the TFGIC are
used, i.e., the second configuration of our experiment, and the aberration of
$\gamma$-rays yield is used to infer the average multiplicity emitted by each
fragment.

###  II.3 Angular distribution and correlation analysis

The study of angular distributions and correlations of radiation is a well-
established technique in all branches of nuclear and atomic physics,
especially when dealing with AM [15]. In this experiment, we measure the
angular distribution of $\gamma$ radiation using the technique developed by
Göök et al. [1], who measured the angular distribution of neutrons from
fission. In particular, in Fig. 2 we adapt Fig. 1 from their paper to show the
relevant dimensions.

In spontaneous fission it is customary to indicate the axis of fragment motion
as the fission axis; the direction of the light fragment is here taken by
convention to be the direction of the fission-axis vector. All angular
variables are expressed with respect to this direction. In Fig. 2, the angle
indicated as $\theta_{L}$ is the angle that the light fragment makes with the
axis of cylindrical symmetry of the TFGIC. The angular distribution of
$\gamma$ rays is determined by measuring the count rate in the detector
aligned with the TFGIC axis. This technique allows us to use the same detector
for all measurements, thereby simplifying the analysis and corrections applied
to the data. Furthermore, this type of angular measurement can be employed
even when an azimuthal measurement of the fragment direction is not available,
as is the case in this experiment.

Figure 2: Schematic representation of the present experiment, adapting a
figure first used in Ref. [1]. The geometric and electric specifications of
our system are indicated on the figure. The angle between the chamber axis and
the fission axis, taken to be the direction of the light fragment, is
indicated as $\theta_{L}$.

##  III Multiplicity

In this section, the focus turns to the development of results concerning the
multiplicity of $\gamma$ rays from fission. We start by presenting results
related to neutron multiplicity, which serves to validate the detection
system, considering the extensive study of neutrons in the literature.
Following that, an analysis is conducted on the total multiplicity of $\gamma$
rays with respect to both fragment masses and TKE. Finally, the Meier-Leibniz
Doppler-Shift method is applied to the data collected in the second
configuration, utilizing only two detectors. In this third step, the
$\gamma$-ray multiplicity emitted by each individual fragment is presented.

###  III.1 Neutron multiplicity

The multiplicity of fission neutrons is one of the most intensely studied
topics in the field, due in large part to its importance in technological
applications of fission. The dependence of the emitted neutron multiplicity on
the fragment TKE for selected masses is shown in Fig. 3 and compared to the
results by Göök et al. [1]. In contrast to the $\gamma$-ray multiplicity,
which is obtained by unfolding the measured multiplicity using a simulated
matrix response, the emitted neutron multiplicity is determined by a simple
efficiency scaling, where the efficiency has been simulated and the resulting
mean neutron multiplicity agrees well with the known value of $\langle
N_{n}\rangle\approx 3.75$. We observe the clear anti-correlation between
neutron multiplicity and TKE. This correlation aligns with expectations, as
neutron multiplicity is known to be an excellent information carrier for the
total fragment excitation energy, $E^{*}$, which is the sum of the two
fragments’ excitation energies. This quantity is related to the total energy
released in fission, $Q$, and TKE through the equation

$E^{*}=Q(A)-TKE\ .$ (1)

The total energy released has a mass dependence, based on the different
binding energies of the fission fragments. The x-intercept of the neutron
multiplicity on TKE is thus strongly related to the total $Q$ value of that
fission reaction, although it is an underestimate, as a minimum amount of
energy is required to emit the first neutron. The diminishing slope of neutron
multiplicity with decreasing TKE can be attributed to several factors. First,
nucleons in the fragment become more tightly bound as neutrons are emitted,
thus increasing the energy needed to remove them. Second, we cannot exclude
that the $E^{*}$ generated during fission is not all available for neutron
emission, and might be found in nuclear degrees of freedom, such as rotational
motion and intrinsic deformations, that do not contribute to the neutron
evaporation process.

Our data compares well with the data from Göök et al., indicating that our
detection system is capable of properly identifying trends in the multiplicity
of the emitted radiation and the underlying fragment. We note that especially
for rarer fragmentations of extreme asymmetry and symmetry, the data are
significantly broadened. This symptom is attributed to a degradation of the
TKE resolution of the detector system in some part due to the energy losses of
the fragments in the target.

Figure 3: Measured mass-binned TKE-dependent neutron multiplicity compared to
studies performed by Göök et al. [1]. The yield of TKE, at the specified mass,
is shown as the black curve, with arbitrary scaling.

###  III.2 Total $\gamma$-ray multiplicity

The total $\gamma$-ray multiplicity accompanying a fission event encodes
information regarding the total fragments’ AM. In fact, after the emission of
neutron and statistical $\gamma$ rays, the fragments’ rotational energy is
generally dissipated by emission of collective $\gamma$ rays along rotational
bands. The most common type of emission is electric quadrupole (E2) which
lowers the fragment AM by $2$ $\hbar$ [22]. In an ideal scenario, it would be
possible to establish a direct correlation between $\gamma$-ray multiplicity
and AM through a proportional relationship. However, this overly simplified
picture of the de-excitation process is somewhat misleading; while
correlations exist between $\gamma$-ray multiplicity and AM, their
relationship is not as simple. A significant portion of the $\gamma$ rays,
estimated with model calculations [23] to be as many as half of all $\gamma$
rays on average, are emitted from states in the quasi-continuum, and
predominantly favor electric dipole (E1) transitions. The AM dissipated in
each of these statistical transitions is not known, and is a topic of current
research [24, 25]. Furthermore, within the collective $\gamma$-ray
transitions, we can find different $\gamma$-ray multipolarities, such as
magnetic dipole (M1), as well as E2 emissions that are not stretched, i.e.,
that connect states which have a difference of AM smaller than $2\hbar$.

With the above disclaimers, there is still find compelling value in studying
the total $\gamma$-ray multiplicity in the absence of more refined
measurements. We can study the trends of $\gamma$-ray multiplicity with
respect to fragment variables, thus assuming that the aforementioned effects
do not themselves vary significantly with fragment properties. This assumption
is more valid if we focus on regions of large $E^{*}$, where statistical
$\gamma$-ray emission approximately saturates, and changes in $\gamma$-ray
yield can be attributed primarily to rotational-band feeding.

Fig. 4 shows the trends of total $\gamma$-ray multiplicity with respect to
$E^{*}$, as calculated using Eq. 1. To highlight the role of AM, we compare
the experimental data to calculations performed using FIFRELIN, which treats
the excitation and de-excitation of fission fragments [22, 14]. Specifically,
we compare our data to two different calculations, where in both cases the AM
is sampled uniformly from all available states at the simulated fragment
energy. In the first, the level density above the known states is assumed to
be AM independent; in the second a Bethe spin-cutoff formula is used to model
the preponderance of higher AM states at higher $E^{*}$. It should be noted
that this second calculation is technically more accurate, as it is known that
the AM distribution changes with $E^{*}$ [6].

Figure 4: Comparison of measured total $\gamma$-ray multiplicity, summed
contributions from each fragment, with model calculations performed in
FIFRELIN. Each panel corresponds to bins centered at the specified light
fragment mass $A$, and with a bin width of $5$ AMU. The dashed vertical line
corresponds to the average total $E^{*}$ for the specified fragmentation.

It is apparent from our comparison in Fig. 4 that the constant model of AM is
in strong agreement with the experimental data, more so than the energy-
dependent model. The difference is most noticeable in the region of high
excitation energy, where the model with the $E^{*}$-dependent AM distribution
gives rise to a monotonically increasing dependence. This agreement is
undoubtedly surprising, since one would expect the $E^{*}$-dependent
calculation to be more accurate than the constant model. The constant model of
AM generation treats the AM level density as $E^{*}$ independent, at variance
with experimental findings. The agreement between our experimental data and a
constant AM distribution indicates the existence of physical mechanisms of AM
generation beyond the simple statistical sampling. This mechanism would
compensate for the existence $E^{*}$-dependent AM level density. In
particular, we note that an overall observation holds across several mass
regions: the $\gamma$-ray multiplicity saturates at sufficiently high
excitation energies, in disagreement with the prediction of a statistical
model of AM generation. The energy required to saturate the $\gamma$-ray yield
varies with the light fragment mass, reaching a minimum in the most common
splits around $A_{L}\approx 110$. The maximum average $\gamma$-ray yield
appears to not vary strongly with mass, at approximately $8$ $\gamma$ rays
emitted from both fragments.

We observe a drop in the $\gamma$-ray multiplicity at the highest $E^{*}$, or
equivalently the lowest TKE for a given mass split. However, the statistics
are quite poor in this region. Other systematic errors, not shown in the
figure, are also expected to have a strong effect. These systematic errors
include unaccounted-for attenuation in the source sample, contamination within
mass, and TKE bins. An overall systematic correction of up to $20$% on all
points is expected due to efficiency estimation. Variation of this efficiency
with energy introduces much smaller ($\approx 1$ %) variation of this
systematic correction across mass and TKE bins. While our results in that
region are not statistically significant, a similar observation of
multiplicity drop was reported by Gonnenwein et al [10] who interpreted it as
an indication of the validity of the statistical model of AM generation. Their
argument is that at the lowest TKE, i.e., the highest $E^{*}$ in the figure,
the Coulomb potential is very weak, indicating a large separation of the
fragments and thus a highly deformed configuration at scission. Because a lot
of the energy is stored in nuclear deformations, it is not available to
statistically excite the fragment rotational modes, thus leading to a drop in
AM.

The results shown here are, to our knowledge, the first of their kind for
252Cf(sf), with the exception of Nifenecker et al. [16], who reported a linear
correlation between $\gamma$-ray multiplicity and total neutron multiplicity,
a proxy for $E^{*}$. Our results put into question the validity of the
Nifenecker results. While a linearly increasing trend can be observed for some
of the more symmetric and asymmetric fragmentations, this is not true overall
for this fission reaction. On average, the relationship between total
$\gamma$-ray multiplicity and $E^{*}$, or total neutron multiplicity, is not
linear, but reaches a saturation plateau.

###  III.3 Individual $\gamma$-ray multiplicity

As explained in Section II, we can exploit the aberration of $\gamma$-rays in
the forward and backward fragment propagation directions to separate the
$\gamma$-ray multiplicities emitted by the light and heavy fragments. This
technique, known as the Maier-Leibniz Doppler Shift analysis, has been
optimized by Travar et al. [2], correcting the traditional techniques and
reducing the effect of systematic biases.

The drawback of this technique is that only two of the many detectors in FS-3
are used, significantly lowering the statistical significance of the
experimental results. Each of the two detectors in this second configuration
of the experiment can be analyzed independently of the other to determine the
$\gamma$-ray multiplicity, thus reducing the effects of systematic error after
averaging the two results.

We show the individual mean $\gamma$-ray multiplicities as a function of
fragment mass in Fig. 5. We find the results from both detectors to agree
quite well with one another with respect to the mass-dependence. Our
observations of a sawtooth pattern in the $\gamma$-ray multiplicity
distribution align with recent findings by Travar et al. [2]. These recent
results, together with the direct measurement of the AM of several isotopes by
Wilson et al. [3], have confirmed the existence of an AM sawtooth in fission.

Figure 5: The dependence of the individual mean $\gamma$-ray multiplicity from
each fragment as a function of their masses. The sawtooth shape is in good
agreement with the investigation by Travar et al. [2]. The results of our
experiment are integral-normalized to be compared to the literature result.

In analogy to the neutron sawtooth [18], we interpret the $\gamma$-ray
sawtooth, and its associated AM sawtooth, as indicative of a deformation-
dependent AM. As already pointed out by Wilhelmy et al. [15], there is a
strong correlation between the average AM of a fragment and the ground state
electric quadrupole moment of the same isotope, a measure of its
deformability.

A new, insightful way of looking at the same data is to differentiate the
$\gamma$-ray sawtooth with respect to TKE, as is done in Fig. 6. Each panel in
Fig. 6 shows a different mass split, with data points indicating the yield of
$\gamma$ rays from the light and heavy fragment, as well as the total
multiplicity. This plot shows the complicated relationship between the two
fragments’ $\gamma$-ray yield and, if interpreted as such, between the
fragments’ AM. We see that in general the $\gamma$-ray yield from the light
and heavy fragment changes at different rates with $E^{*}$. For example, near
the symmetric fragmentation, we see that the light fragment emits most of the
$\gamma$ rays and only when this reaches a plateau does the heavy fragment
begin to increase its $\gamma$-ray yield. For the most common fragmentation
masses, $A_{L}\approx 110$, we find that the light fragment $\gamma$-ray yield
increases with energy, while the heavy fragment yield remains constant if not
slightly decreasing. This decrease in the $\gamma$-ray yield is not
statistically significant given the current data, but is worth future
exploration. In fact, a competition between the fragment AM magnitudes could
signal the existence of excited bending modes in the statistical population of
rotational modes.

Figure 6: Individual $\gamma$-ray multiplicity emitted from each fragment,
binned by masses across $E^{*}$. Each panel is a separate fragmentation, with
the bin center indicated on the figure and bin width of $8$ AMU. The sum of
the two multiplicities is also shown.

This result shows not only that $\gamma$-ray multiplicity increases at
different rates for the light and heavy fragment, as one might expect from the
presence of the $\gamma$-ray sawtooth, but also a competition between the
$\gamma$ rays from opposite fragments. This effect can be seen for the more
symmetric and asymmetric fragmentations, where we see the $\gamma$ ray
multiplicity from one fragment increases while the multiplicity of the other
fragment decreases with TKE. A similar result had been already observed by
Pleasonton et al. [26] in thermal neutron-induced fission events. More
recently, Piau et al. [27] observed a similar trend by comparing the number of
$\gamma$-rays emitted by the light and heavy fragment groups in general. These
observations are at variance with the investigation of Wang et al. [28], which
determined a more complicated relationship. In their investigation, Wang et
al. determined that the yield of $\gamma$ rays from the light fragment remains
relatively constant with increasing excitation energy (as measured by the
fragment’s neutron multiplicity). For the heavy fragment, the $\gamma$-ray
yield increases up to a maximum multiplicity, and then drops again. The
observations of Wang et al. do reproduce some of our own, for example the
saturated and decreasing multiplicities, but cannot be compared directly since
their mass bins are too large. One point of agreement is their observation
that for symmetric fragmentation splits the $\gamma$-ray yield increases
almost linearly with the excitation energy, as we have also observed.

The roughly linear trend between $\gamma$-ray multiplicity and $E^{*}$ for the
symmetric masses, previously discussed in connection to the results presented
by Nifenecker et al., can now be understood better. In fact, we see that the
linear trend arises as the sum of two approximately linear piecewise
functions: at low $E^{*}$ the light fragment’s $\gamma$-ray emission increases
linearly with $E^{*}$ while the heavy fragment remains approximately constant;
at higher $E^{*}$, the roles are reversed. When these two emissions are added
together, the total emission appears to be linear over a wide range of
$E^{*}$, but this trend also eventually saturates at the highest $E^{*}$. We
also note that the symmetric region, especially in the vicinity of the 120-132
split that confers to the heavy fragment a high level of sphericity due to its
closeness to the doubly magic nucleus 132Sn, the energy split between the two
fragments is highly skewed towards the light fragment. In fact, based on the
neutron sawtooth measurement, we can expect the light fragment to carry, on
average, approximately 6-7 times more energy than its heavy partner. Thus, the
low $\gamma$-ray yield from the heavy fragment in this mass split is expected:
the low excitation energy, coupled with the large level spacing in this mass
region, reduces the population of high-spin states.

##  IV Angular distribution

Given the close connection between AM and rotational symmetry, the angular
distribution of $\gamma$ rays often represents the most direct probe of AM in
nuclear systems. To do this, we fit the experimental data using a sum of
Legendre polynomials,

$\sum_{i=0}^{l_{m}ax}C_{i}P_{i}(\cos\theta)$ (2)

where $P_{i}$ is the ith-order Legendre polynomial, and $C_{i}$ is the
corresponding amplitude. The sum is taken up to order $l_{i}$, the choice of
which does not influence the fit of the other components. In addition, to
improve the fit further, each component in the fitting function is integrated
within the experimental bins. Here, we examine how the anisotropy, defined as
the ratio $C_{2}/C_{0}$ of Legendre polynomial coefficients, changes with the
masses and TKE of the fission fragments.

###  IV.1 $\gamma$-ray angular distribution

The angular distribution of $\gamma$-rays is measured as the count rate in the
detector in front of the TFGIC cylindrical axis. We then select those fission
events that make an angle $\theta$ with this TFGIC axis. The procedure yields
curves of $\gamma$-ray multiplicity over the angle $\theta$. As mentioned, we
characterize the strength of the $\gamma$-ray anisotropy by taking the ratio
of Legendre-polynomial-expansion coefficients. However, due to the limitations
of the TFGIC and the fission target, angles below $|\text{cos}\theta|<0.3$
cannot be properly measured. We correct for this inaccessible region
recursively, but we expect the Legendre coefficients so determined to have
correlated systematic uncertainties.

From physical arguments, we expect only even-order coefficient to have
physical significance [29]. The odd-order coefficients can be induced by the
aberration of $\gamma$ rays, a phenomenon exploited in the previous section
for the separation of fragment emissions. In Fig. 7 we present the ratio
$C_{2}/C_{0}$ as a function of the mass of the light fragment.

Figure 7: Mass-dependent anisotropy of the $\gamma$-ray angular distribution,
as determined by the ratio of Legendre coefficiencts.

It is a well-known fact in fission physics that the fragments’ AM appear to be
approximately aligned in a plane perpendicular to the fission axis [15, 11].
Our results indicate a significant modulation of the $\gamma$-ray anisotropy
with fragment mass. While not in quantitative agreement with the work by
Pollitt et al. [30], especially in the region of symmetric split, both results
agree on the levels of variation in the anisotropy across the mass spectrum.
The changing anisotropy could be an indication of a different degree of the
polarization of the fragments’ AM; however, this interpretation is not yet
warranted by these data on their own. Several confounding variables could be
participating in this phenomenon, including a depolarization of the AM by
neutron evaporation and statistical $\gamma$-ray emission.

We note that the highest level of anisotropy, suggestive of a high degree of
AM polarization, is found at light-fragment masses near 110. On the other
hand, the lowest anisotropies, indicating a more isotropic AM distribution
with respect to the fission axis, are found at the very symmetric and
asymmetric extremes. The increase in anisotropy at approximately $A_{L}\approx
84$ is in agreement with the previously observed feature in Pollitt et al.
[30].

###  IV.2 Channel differentiation

The data presented in Fig. 7 can be further differentiated with respect to
TKE. This differentiation allows us to gain an insight into the dynamics of
the fission process itself. Yields of mass and TKE have often been employed in
the literature to draw conclusions about scission shapes and configurations.
The discussion of standard, symmetric, and asymmetric splits should be
familiar from the classic description of fission as a multi-channel process
[18]. According to this formalism, fission can proceed through several
reaction channels, each characterized by a shape of the fissioning nucleus at
the moment of fission. These channels differentiate, for example, between
spherical and elongated shapes, associated with high and low TKE due to the
different strength of the Coulomb repulsion; and between symmetric and
asymmetric mass splits, as already pointed out earlier.

The result of this further differentiation of the $\gamma$-ray angular
anisotropy data are presented in Fig. 8. It is immediately clear that the
anisotropy of $\gamma$ rays follows a distribution that is similar to, but not
overlapping with, the yield of fragments, which has been highlighted by
contour lines on the plots.

Figure 8: Yield-differentiated $\gamma$-ray anisotropy coefficients. The top
panel shows the fragment yields themselves. The bottom panel shows the
anisotropy of $\gamma$ rays for the different mass regions. Contour lines are
determined from the yield. Data with $>30$ % statistical uncertainty has been
removed.

In the first place we note that, in general, the anisotropy increases when TKE
decreases. This result is reminiscent of the multiplicity saturation
discussion presented in the previous section. Our anisotropy results also show
a similar mass dependence, showing that at sufficiently high excitation
energies, or conversely low TKE, an anisotropy in the $\gamma$-ray yield can
be observed. Unfortunately the amount of data collected is not sufficient to
draw quantitative conclusions across the entire yield.

We recognize the four fission channels [31] in our figure, a symmetric channel
around $A_{L}=110$ and TKE$\sim 180$ MeV; super-long and super-short channels
at symmetric masses $A_{L}\sim 125$ and TKE$\sim 140$ and TKE$\sim 210$,
respectively; a super-asymmetric channel at $A_{L}\sim 85$ and TKE$\sim 140$.
Most noticeable is the presence of strong polarization in the regions we
associate with the standard, super-long, and super-asymmetric channels. These
channels are associated with the larger degree of deformation in the
scissioning configuration, thus suggesting an interpretation that the
magnitude and direction of the fragments’ AM are closely connected to the
shape of the nucleus at scission. On the other hand, we do not observe a
significant degree of polarization in the super-short channel, which is
characterized by the least deformed configuration. These observations give
credit to a scission deformation-dependent AM generation mechanism.

##  V Conclusion

We have presented new experimental results on 252Cf(sf) from a recent
experiment performed using a combination of a TFGIC and organic scintillators.
The results add important information to the already rich literature on
nuclear fission and specifically on the generation of AM in fission. Our three
main conclusions stem from our results regarding the multiplicity and the
angular distribution of $\gamma$-rays: saturation, competition, and
polarization.

We have determined that the multiplicity of $\gamma$ rays does not increase
steadily with fission fragment excitation energy. On the contrary, we have
determined that the mean $\gamma$-ray multiplicity increases up to a value of
approximately $8$ $\gamma$ rays and appears to level off after that. This
could be an indication of a saturation of the AM, which would significantly
restrict the ways in which AM is generated, but could also be explained by a
larger portion of AM being carried by neutrons and statistical $\gamma$ rays.
Future experiments should focus on the issue of AM removal by this type of
radiation. If this saturating pattern persists, it would indicate the
existence of non-statistical mechanisms in the generation of AM. In
combination with the existence of the AM sawtooth, this result indicates the
importance of deformation-dependent mechanisms of AM generation.

By exploiting the aberration of $\gamma$ rays emitted by moving sources, we
have separated the average emission of $\gamma$ rays for the light and heavy
fragment. The results of this analysis indicate that the emission from the two
fragments do not necessarily grow together with $E^{*}$. Instead, we observe
that the emission can be uncorrelated, with the increase of $\gamma$ rays
being produced primarily by one or the other fragment, or even anti-
correlated, where the emission of $\gamma$ rays increases in one fragment
while decreasing in the other. If these findings are indeed indicative of AM
patterns and trends, they would indicate the presence of complex modes of AM
generation.

Lastly, we have challenged an important and established experimental
observation in fission, namely the predominance of transversely polarized
fragment AM. Specifically, we observed that the $\gamma$-ray anisotropy
possesses a mass and TKE dependence. The strongest anisotropy, corresponding
to the most strongly transversely polarized fragments’ AM, were found in
correlation with the supershort channel, the channel with the most deformation
at scission. The polarization of AM could be a determining factor in the
development of future models of AM generation in fission.

Overall, the experimental results of this paper challenge some of the
assumptions made in the discussion of $\gamma$-rays in fission, especially
regarding the mass and TKE dependence of their multiplicity and angular
distribution. Future research should be focused on understanding the impact of
the emission of neutrons and statistical $\gamma$ rays on the fragment AM, as
the study of the rotational band $\gamma$ rays has remained the most prominent
technique for AM assignment.

###### Acknowledgements.

This work was in part supported by the Office of Defense Nuclear
Nonproliferation Research and Development (DNN R & D), National Nuclear
Security Administration, US Department of Energy. This work was funded in-part
by the Consortium for Monitoring, Technology, and Verification under
Department of Energy National Nuclear Security Administration award number DE-
NA0003920. This material is based upon work supported by the U.S. Department
of Energy, Office of Science, Office of Nuclear Physics, under Contract Number
DE-AC02-06CH11357. Authors also gratefully acknowledge the use of the Bebop
cluster in the Laboratory Computing Resource Center (LCRC) at Argonne National
Laboratory. The work of V.A.P. was performed under the auspices of UT-
Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of
Energy. SM is grateful to Prof. Kiedrowski at the University of Michigan for
helpful discussion regarding Legendre polynomial extraction. Authors would
like to acknowledge the efforts in the design and support during operation
provided by the LETS group at the Physics Division of ANL, especially M.
Oberling and R. Knaack.

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