# EmoBERTa: Speaker-Aware Emotion Recognition in Conversation with RoBERTa

Taewoon Kim  Piek Vossen
Vrije Universiteit Amsterdam
<EMAIL_ADDRESS>

###### Abstract

We present EmoBERTa: Speaker-Aware Emotion Recognition in Conversation with
RoBERTa, a simple yet expressive scheme of solving the ERC (emotion
recognition in conversation) task. By simply prepending speaker names to
utterances and inserting separation tokens between the utterances in a
dialogue, EmoBERTa can learn intra- and inter- speaker states and context to
predict the emotion of a current speaker, in an end-to-end manner. Our
experiments show that we reach a new state of the art on the two popular ERC
datasets using a basic and straight-forward approach. We’ve open sourced our
code and models at https://github.com/tae898/erc.

##  1 Introduction

The scope of emotion recognition is very wide, ranging from stills of face
images, audio data to the actual utterances or text as in tweets. In this
paper, we focus on emotion recognition in conversation (ERC), which is a
subfield of emotion recognition. More specifically, the task is to predict the
emotion of a current speaker who’s engaging in a conversation with one person
or more. Recognizing emotion is important to areas such as affective computing
and human-robot communication, in which it can be an important feedback
mechanism.

As humans use multiple sensory inputs to have a conversation (e.g., vision,
voice, etc.) the ERC task can also include multiple modalities (e.g., visual,
audio, text, etc.). Here, we report on our first experiments on the text
modality, leaving using multiple modalities within our framework to future
work.

Since the introduction of the Transformer (Vaswani et al., 2017), transformer-
based deep neural network models have become the dominating neural network
model in sequence modeling. Especially, pretrained encoder-only models such as
BERT (Devlin et al., 2019) and RoBERTa (Liu et al., 2019) have shown that they
can be successfully fine-tuned for downstream tasks, such as sentence
classification and question answering. ERC can be seen as a special case of
sequence modeling, since emotions are expected to be triggered by a preceding
event in any modality.

Our approach to ERC enriches such transformer models by including the speaker
identity in the sequence information spanning multiple utterances. By adapting
the RoBERTa sequence representation, we improve the SOTA on two popular
benchmark datasets.

##  2 Related Work

Most of the existing works on ERC combine different kinds of neural network
architectures (e.g., CNNs, RNNs, Transformers, GNNs, etc.) (Li et al., 2020b),
(Li et al., 2020c), (Ishiwatari et al., 2020), (Wang et al., 2020), (Hazarika
et al., 2021), (Sheng et al., 2020), (Ghosal et al., 2020), (Ghosal et al.,
2019). The biggest downside of such approaches is that each part of the model
is responsible for extracting their own features. These extracted features
might not be ideal for the other parts of the model. Also, since these models
are combinations of sub-models, it is hard to understand what each sub-model
is contributing and how to improve the overall model. Some of the approaches
try to take advantage of external knowledge bases (Ghosal et al., 2020),
(Zhong et al., 2019a), which adds even more complexity to the model.

A substantial number of approaches are heavily based on RNNs (e.g., GRU) to
model the sequence (Jiao et al., 2019), (Lu et al., 2020). The biggest problem
with this is that it inherently decouples the word embedding extraction and
the sequence modeling, whereas BERT-like models tackle them at once, often
leading to a better performance. Also, they have to rely on external
decontextualized word embedding extractors (e.g., GloVe (Pennington et al.,
2014) or word2vec (Mikolov et al., 2013)). Furthermore, training an RNN is
very inefficient since “backpropagation through time” has to wait until the
last input of a sequence has been processed.

The approaches that are most closely related to us are HiTrans (Li et al.,
2020a) and DialogXL (Shen et al., 2020). HiTrans packs multiple utterances
with [CLS] tokens prepended into one input sequence. This sequence is first
fed into a BERT and then to another transformer. DialogXL is based on XLNet
(Yang et al., 2019). Our approach differs in that we just use RoBERTa and
encode the speaker information with multiple utterances.

##  3 Methodology

###  3.1 Problem Definition

Let’s say a dialogue of $M$ utterances is given and $I$ interlocutors are
engaging in a conversation. Then the dialogue can be expressed as a list of
vectors: $dialogue=[\bm{x_{1}},\bm{x_{2}},...,\bm{x_{M}}]$, where an utterance
$\bm{x_{t}}$ contains several words (tokens). Each utterance $\bm{x_{t}}$ is
spoken by a unique $speaker\in$ $I$. Since this is a supervised setup, every
utterance $\bm{x_{t}}$ has one corresponding label $y_{t}$ that is annotated
by a human.

The simplest way to solve this problem is to come up with a function $f$ that
takes $\bm{x_{t}}$ as an input and outputs the correct label $y_{t}$. However,
this doesn’t take context into account. It’s easily conceivable that the
function $f$ should also consider the past utterances
$[\bm{x_{1}},\bm{x_{2}},...,\bm{x_{t-1}}]$ or even the future utterances
$[\bm{x_{t+1}},\bm{x_{t+2}},...,\bm{x_{M}}]$ to model the context.

###  3.2 EmoBERTa

EmoBERTa starts from the pretrained roberta-large model (Liu et al., 2019).
Since the task is basically a sequence classification task, we simply add a
randomly initialized linear layer with the softmax nonlinearity to the first
hidden state (this state corresponds to the [CLS] token) of the last layer of
the pretrained model.

We chose RoBERTa, among the many BERT-like models, because its structure is
not only relatively simple, but also it can deal with more than two segments.
The original authors of RoBERTa simply used two </s> tokens consecutively as
[SEP] token, which separates the first and the second segments. Although the
pretrained model has not been trained on more than two segments, we show that
EmoBERTa can be generalized to three segments per input sequence.

The first, second, and third segments contain the past utterances, the current
utterance, and the future utterances, respectively, in a dialogue. Each
utterance is prepended with the name of a speaker so that the model is aware
which utterance is spoken by whom. The task is to predict the emotion of the
current utterance.

RoBERTa uses <s> and </s> as [CLS] and [EOS] tokens, respectively. Building an
input sequence for EmoBERTa is outlined in Algorithm 2. Example sequences can
be found in Figure 6.

Given the current utterance
$\bm{x_{t}}\in\\{\bm{x_{1}},\bm{x_{2}},...,\bm{x_{M}}\\}$;
$max\\_tokens=512-2$;

$sequence=[SEP]+tokenize(\bm{x_{t}})+[SEP]$;

$i=1$;

while  _$len(sequence) <=max\\_tokens$_ do

Prepend $speaker(\bm{x_{t-i}})+``:"+\bm{x_{t-i}}$ to $sequence$;

Append $speaker(\bm{x_{t+i}})+``:"+\bm{x_{t+i}}$ to $sequence$;

$i=i+1;$

end while

Remove the last appended / prepended utterances;

$sequence=[CLS]+sequence+[EOS];$

Algorithm 1 Building an input sequence222The pretrained RoBERTa model can have
a maximum of 512 tokens in one input sequence. The while loop terminates if
there are no more available past / future utterances to add in the dialogue.
We empirically found that capitalizing the names of the interlocutors leads to
slightly better results.

###  3.3 Training

The loss is calculated as the sum of cross entropy loss and $L^{2}$ weight
decay (Krogh and Hertz, 1991). We use adaptive gradient descent (Kingma and
Ba, 2015), (Loshchilov and Hutter, 2019) with gradual linear warmup learning
rate scheduling (Goyal et al., 2017). The peak learning rate was determined
using Optuna (Akiba et al., 2019). Mixed floating point precision was used to
reduce the training time and increase the batch size (Micikevicius et al.,
2017). See Appendix A.1 for the details (e.g., hyperparameters, training time,
hardware, etc.). We mostly used the huggingface transformer pytorch library
for training (Wolf et al., 2020).

Then the training loss function is

$\mathcal{L}(\bm{w})=-\frac{1}{N}\sum^{N}_{i=1}\sum^{C-1}_{c=0}y_{c}^{(i)}\log(\hat{y}_{c}^{(i)})+\frac{\lambda}{2}\|\bm{w}\|_{2}^{2}$
(1)

where $\bm{y}^{(i)}$ , is a one-hot label vector, $\hat{\bm{y}}^{(i)}$ is the
softmax output vector given the input ${\bm{x^{(i)}}}$, $N$ is the number of
training data samples, $C$ is the number of classes, $\lambda$ is a $L^{2}$
regularization rate, and $\bm{w}$ are the weights of the model. In practice,
the data samples are batched, and stochastic gradient descent is used.

Although the weights $\bm{w}$ were tuned to minimize the loss value, the final
model is chosen where the weighted $f_{1}$ score on the validation split is
the highest, since that’s the metric that we report.

##  4 Experiments

###  4.1 Datasets and Evaluation Metrics

Dataset | number of dialogues (utterances)
---|---
train | val | test
MELD | 1,038 (9,989) | 114 (1,109) | 280 (2,610)
IEMOCAP | 100 (4,778) | 20 (980) | 31 (1,622)
Dataset | mean number of utterances per dialogue (std.)
train | val | test
MELD | 9.6 (5.8) | 9.7 (5.4) | 9.3 (5.7)
IEMOCAP | 47.78 (16.47) | 49.0 (17.44) | 52.32 (17.36)

Table 1: The upper half of the table shows the number of dialogues and
utterances of the datasets.444The IEMOCAP dataset does not officially have
train, val, and test splits. Therefore, we follow the splits used by (Zhong et
al., 2019b), as these splits are widely used.. The bottom half shows the mean
and the standard deviation of the number of utterances per dialogue. As shown,
IEMOCAP has about 5 times more utterances per dialogue than MELD.

We test EmoBERTa on the two popular ERC datasets. MELD (Poria et al., 2019) is
a multimodal (visual, audio, and text) and multi-party (more than two
interlocutors in a dialogue) conversational dataset. It was collected from the
TV series Friends. The seven emotions are neutral, joy, surprise, anger,
sadness, disgust, and fear. Weighted $f_{1}$ score is used to evaluate the
performance, as the class distribution is highly imbalanced.

IEMOCAP Busso et al. (2008) is a multimodal (visual, audio, and text) and
dyadic (only two interlocutors in a dialogue) conversational dataset. Ten
actors participated in the data collection. Although the original dataset
contains 11 different emotions, only six of them are used for evaluation. They
are neutral, frustration, sadness, anger, excited, and happiness. As MELD, the
class distribution is highly imbalanced and thus a weighted $f_{1}$ score will
be used for evaluation. Unlike MELD, IEMOCAP does not officially have the
names of the speakers. Therefore, we gave each actor a random name. See
Appendix A.2 for the details.

Some statistics on train, val, and test splits of both datasets can be found
at Table 4.

###  4.2 Baselines

We compare our model with the models we mentioned in Section 2.

##  5 Results and Analysis

###  5.1 Quantitative Analysis

Table 2 shows the performance of our models and the baselines. Our models
outperform the other models on both MELD and IEMOCAP.

Model | MELD | IEMOCAP
---|---|---
BERT+MTL (Li et al., 2020b) | 61.90 | -
BiERU-lc (Li et al., 2020c) | 60.84 | 64.65
DialogueGCN (Ghosal et al., 2019) | 58.1 | 64.18
RGAT (Ishiwatari et al., 2020) | 60.91 | 65.22
CESTa (Wang et al., 2020) | 58.36 | 67.1
VHRED (Hazarika et al., 2021) | - | 58.6
SumAggGIN (Sheng et al., 2020) | 58.45 | 66.61
COSMIC (Ghosal et al., 2020) | 65.21 | 65.28
KET (Zhong et al., 2019b) | 58.18 | 59.56
BiF-AGRU (Jiao et al., 2019) | 58.1 | 63.5
Iterative (Lu et al., 2020) | 60.72 | 64.37
HiTrans (Li et al., 2020a) | 61.94 | 64.5
DialogXL (Shen et al., 2020) | 62.41 | 65.94
EmoBERTa | No past and future utterances | 63.46 | 56.09
Only past utterances | 64.55 | 68.57
Only future utterances | 64.23 | 66.56
Both past and future utterances | 65.61 | 67.42
|  $\,\to\,$ without speaker names | 65.07 | 64.02

Table 2: All of the reported values are weighted $f_{1}$ (%) score on the test
splits. The best model and the best performance values are in bold. Since the
values are stochastic in nature, we report the mean values of five random
seeds.

EmoBERTa shows very good results: max weighted $f_{1}$ scores (%) of $65.61$
(MELD) and $68.57$ (IEMOCAP) respectively and above the best reported SOTA,
especially considering that no modifications were made to the original RoBERTa
model architecture. We also trained a model without the speaker names
prepended, which drops the performance: weighted $f_{1}$ scores (%) of $65.07$
(MELD) and $64.02$ (IEMOCAP) respectively, providing evidence that encoding
the speaker information helps.

Especially on IEMOCAP dataset, although we had to come up with random names
for the actors, EmoBERTa was able to learn what’s important. As for IEMOCAP,
the results were better using only past utterances, rather than using both
past and future utterances. We believe that this is due to the fact that
IEMOCAP has many more utterances than MELD, and thus we couldn’t fit all the
past and future utterances in one sequence, meaning that only using past
utterances can fit more past utterances than aiming for both. Past utterances
were apparently more useful than future utterances to predict the emotion of a
current utterance.

There was a bigger performance gain by incorporating past and/or future
utterances in IEMOCAP than MELD ($12.48$ vs. $2.15$). We believe that this is
due to the fact that the nature of IEMOCAP is more contextual than that of
MELD.

###  5.2 Qualitative Analysis

To get more insight in the value of encoding the speaker, we did a qualitative
analysis on 10 correctly and 10 incorrectly classified random samples from
each test split.

Our manual inspection shows that the model tries to learn the dynamics of the
interlocutors in the beginning layer, as the current speaker tokens attend to
the interlocutor tokens (We observed this behavior from all the 20 MELD and 20
IEMOCAP random test samples). As for MELD, in all 100% of the correctly
classified samples, based on the top 10 attended tokens, the <s> token of the
last layer attended to the speaker token of the target (current) utterance,
whereas this ratio was only 60% for the incorrectly classified samples. This
verifies that the current speaker token increasingly contains important
information, as the tokens move on to the higher layers.

Figure 6 shows a visualization of one correctly and one incorrectly classified
random samples.

As the <s> token in the last layer focuses on the current speaker and his/her
utterance, we believe that this information is what the model finds most
useful to make the final prediction.

Note that in the incorrectly classified example, the <s> token in the last
layer does not focus on the current speaker but some random punctuation marks
throughout the conversation, thus leading to an incorrect prediction.

See Appendix A.3 for the random IEMOCAP test samples.

(a) A correctly classified example. Both the prediction and the truth are joy.

(b) An incorrectly classified example. The prediction is joy while the truth
is anger.

Figure 1: Two examples from the 20 randomly selected test samples are shown.
The current speaker utterance, of which the emotion that the model has to
predict, is in bold. The green highlighted tokens are the top 10 most attended
tokens to the current speaker (i.e., JOEY) in the beginning layer of the
model. The yellow highlighted tokens are the top 10 most attended tokens to
the [CLS] token (i.e., <s>) in the last layer.666Since there are 16 attention
heads used per layer in RoBERTa, the visualized weight coefficients are the
mean values of them. Since RoBERTa uses a BPE tokenizer (Sennrich et al.,
2016), the speaker names (e.g., JOEY) are often separated into more than one
token (e.g., JO and EY). Therefore, we highlight the full names, even though
only some parts of them are highlighted.. Best viewed when zoomed in.

##  6 Conclusion

In this paper, we showed that our new model, EmoBERTa, outperforms other
models in the ERC task. Since EmoBERTa can directly attend to the input tokens
and interlocutor names, we can easily observe the attention coefficients to
see which part of the dialogue the model finds most important to make a final
classification.

## Acknowledgements

This research was (partially) funded by the Hybrid Intelligence Center, a
10-year programme funded by the Dutch Ministry of Education, Culture and
Science through the Netherlands Organisation for Scientific Research,
https://hybrid-intelligence-centre.nl.

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##  Appendix A Appendix

###  A.1 Training Details

We used GCP (Google Cloud Platform) Compute Engine to carry out our
experiments. We used an NVIDIA Tesla V100 machine (disclaimer: we are
supported by neither Google nor NVIDIA). This GPU has 16 GB of memory and
depending on the length of the input sequence, we were able to fit 4 to 16
samples in one batch, using mixed precision. The pretrained roberta-large
model has about 355 million parameters. We found that without mixed precision,
it’s very difficult to train this model, since it’s a pretty big model.

We set the value of $L^{2}$ regularization rate as 0.01. Training was done for
five epochs. No weights were frozen during the training. The learning rate
scheduler was set to linearly increase in the first 20% of training and then
linearly decrease in the remaining 80%.

Since the optimal peak learning rate highly depends on the batch size and the
other hyperparameters, we used Optuna (Akiba et al., 2019) to find its best
value. 10% of the training data and the same amount of validation data were
used to search for the best value. Optuna ran five trials and looked for the
best learning rate, between $1e-6$ and $1e-4$, that minimizes the cross
entropy loss on the validation data split.

The hyperparameters not mentioned here are all set to the default values.

One full five-epoch training took about 45 minutes.

###  A.2 IEMOCAP Speaker Names

Since the IEMOCAP dataset was created in the US, we used the top five male and
female American names over the past 100 years
(https://www.ssa.gov/oact/babynames/decades/century.html).

The female names used are Mary, Patricia, Jennifer, Linda, and Elizabeth. The
male names used are James, John, Robert, Michael, and William.

###  A.3 Qualitative Analysis on IEMOCAP

Unlike MELD, only 20% of the correctly classified samples showed the behavior
of the last layer <s> token attending to the current target speaker. This
ratio was 10% for the incorrectly classified samples. We believe this is due
to the fact that the speaker names in the test split of IEMOCAP (i.e., WILLIAM
and ELIZABETH) were never seen during training.)

Figure 2 gives you a visualization of the qualitative analysis on the IEMOCAP
dataset.

(a) A correctly classified example. Both the prediction and the truth are
excited.

(b) An incorrectly classified example. The prediction is neutral while the
truth is frustration.

Figure 2: Two examples from the 20 randomly selected test samples are shown.
The current speaker utterance, of which the emotion that the model has to
predict, is in bold. The green highlighted tokens are the top 10 most attended
tokens to the current speaker (i.e., WILLIAM and ELIZABETH, for Figure 2a and
2b, respectively.) in the beginning layer of the model. The yellow highlighted
tokens are the top 10 most attended tokens to the [CLS] token (i.e. <s>) in
the last layer. Unlike Figure 6, there is only one [SEP] token (i.e.,
</s></s>), since this model only has two segments, past and current. Best
viewed when zoomed in

We see a similar behavior as in MELD. Again, in the incorrectly classified
example, the <s> in the last layer does not attend to the current speaker.


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#  $\beta$-Delayed neutron spectroscopy of 133In

Z. Y. Xu  Department of Physics and Astronomy, University of Tennessee,
Knoxville, Tennessee 37996, USA  M. Madurga  Department of Physics and
Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA  R.
Grzywacz  Department of Physics and Astronomy, University of Tennessee,
Knoxville, Tennessee 37996, USA  Physics Division, Oak Ridge National
Laboratory, Oak Ridge, Tennessee 37831, USA  T. T. King  Department of Physics
and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831,
USA  A. Algora  Instituto de Física Corpuscular, CSIC-Universidad de Valencia,
E-46071, Valencia, Spain  Institute for Nuclear Research (ATOMKI), H-4026
Debrecen, Bem ter 18/c, Hungary  A. N. Andreyev  Department of Physics,
University of York, North Yorkshire YO10 5DD, United Kingdom  Advanced Science
Research Center, Japan Atomic Energy Agency, Tokai-mura, Japan  J. Benito
Grupo de Física Nuclear and IPARCOS, Facultad de CC. Físicas, Universidad
Complutense de Madrid, E-28040 Madrid, Spain  T. Berry  Department of Physics,
University of Surrey, Guildford GU2 7XH, United Kingdom  M. J. G. Borge
Instituto de Estructura de la Materia, IEM-CSIC, Serrano 113 bis, E-28006
Madrid, Spain  C. Costache  Horia Hulubei National Institute for Physics and
Nuclear Engineering, RO-077125 Bucharest, Romania  H. De Witte  KU Leuven,
Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium  A.
Fijalkowska  Department of Physics and Astronomy, Rutgers University, New
Brunswick, New Jersey 08903, USA  Faculty of Physics, University of Warsaw, PL
02-093 Warsaw, Poland  L. M. Fraile  Grupo de Física Nuclear and IPARCOS,
Facultad de CC. Físicas, Universidad Complutense de Madrid, E-28040 Madrid,
Spain  H. O. U. Fynbo  Department of Physics and Astronomy, Aarhus University,
DK-8000 Aarhus C, Denmark  A. Gottardo  IPN, IN2P3-CNRS, Université Paris-Sud,
Université Paris Saclay, 91406 Orsay Cedex, France  C. Halverson  Department
of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996,
USA  L. J. Harkness-Brennan  Department of Physics, Oliver Lodge Laboratory,
University of Liverpool, Liverpool L69 7ZE, United Kingdom  J. Heideman
Department of Physics and Astronomy, University of Tennessee, Knoxville,
Tennessee 37996, USA  M. Huyse  KU Leuven, Instituut voor Kern- en
Stralingsfysica, B-3001 Leuven, Belgium  A. Illana  KU Leuven, Instituut voor
Kern- en Stralingsfysica, B-3001 Leuven, Belgium  University of Jyväskylä,
Department of Physics, P.O. Box 35, FI-40014, Jyväskylä, Finland  Ł. Janiak
Faculty of Physics, University of Warsaw, PL 02-093 Warsaw, Poland  National
Centre for Nuclear Research, 05-400 Otwock, świerk, Poland  D. S. Judson
Department of Physics, Oliver Lodge Laboratory, University of Liverpool,
Liverpool L69 7ZE, United Kingdom  A. Korgul  Faculty of Physics, University
of Warsaw, PL 02-093 Warsaw, Poland  T. Kurtukian-Nieto  CENBG, Université de
Bordeaux—UMR 5797 CNRS/IN2P3, Chemin du Solarium, 33175 Gradignan, France  I.
Lazarus  STFC Daresbury, Daresbury, Warrington WA4 4AD, United Kingdom  R.
Lică  ISOLDE, EP Department, CERN, CH-1211 Geneva, Switzerland  Horia Hulubei
National Institute for Physics and Nuclear Engineering, RO-077125 Bucharest,
Romania  R. Lozeva  Université Paris-Saclay, IJCLab, CNRS/IN2P3, F-91405
Orsay, France  N. Marginean  Horia Hulubei National Institute for Physics and
Nuclear Engineering, RO-077125 Bucharest, Romania  R. Marginean  Horia Hulubei
National Institute for Physics and Nuclear Engineering, RO-077125 Bucharest,
Romania  C. Mazzocchi  Faculty of Physics, University of Warsaw, PL 02-093
Warsaw, Poland  C. Mihai  Horia Hulubei National Institute for Physics and
Nuclear Engineering, RO-077125 Bucharest, Romania  R. E. Mihai  Horia Hulubei
National Institute for Physics and Nuclear Engineering, RO-077125 Bucharest,
Romania  A. I. Morales  Instituto de Física Corpuscular, CSIC-Universidad de
Valencia, E-46071, Valencia, Spain  R. D. Page  Department of Physics, Oliver
Lodge Laboratory, University of Liverpool, Liverpool L69 7ZE, United Kingdom
J. Pakarinen  University of Jyväskylä, Department of Physics, P.O. Box 35,
FI-40014, Jyväskylä, Finland  Helsinki Institute of Physics, University of
Helsinki, P.O. Box 64, FIN-00014, Helsinki, Finland  M. Piersa-Siłkowska
Faculty of Physics, University of Warsaw, PL 02-093 Warsaw, Poland  Zs.
Podolyák  Department of Physics, University of Surrey, Guildford GU2 7XH,
United Kingdom  P. Sarriguren  Instituto de Estructura de la Materia, IEM-
CSIC, Serrano 113 bis, E-28006 Madrid, Spain  M. Singh  Department of Physics
and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA  Ch.
Sotty  Horia Hulubei National Institute for Physics and Nuclear Engineering,
RO-077125 Bucharest, Romania  M. Stepaniuk  Faculty of Physics, University of
Warsaw, PL 02-093 Warsaw, Poland  O. Tengblad  Instituto de Estructura de la
Materia, IEM-CSIC, Serrano 113 bis, E-28006 Madrid, Spain  A. Turturica  Horia
Hulubei National Institute for Physics and Nuclear Engineering, RO-077125
Bucharest, Romania  P. Van Duppen  KU Leuven, Instituut voor Kern- en
Stralingsfysica, B-3001 Leuven, Belgium  V. Vedia  Grupo de Física Nuclear and
IPARCOS, Facultad de CC. Físicas, Universidad Complutense de Madrid, E-28040
Madrid, Spain  S. Viñals  Instituto de Estructura de la Materia, IEM-CSIC,
Serrano 113 bis, E-28006 Madrid, Spain  N. Warr  Institut für Kernphysik,
Universität zu Köln, 50937 Köln, Germany  R. Yokoyama  Department of Physics
and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA  C. X.
Yuan  Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen
University, Zhuhai, 519082, Guangdong, China

(today)

###### Abstract

The decay properties of 133In were studied in detail at the ISOLDE Decay
Station (IDS). The implementation of the Resonance Ionization Laser Ion Source
(RILIS) allowed separate measurements of its $9/2^{+}$ ground state (133gIn)
and $1/2^{-}$ isomer (133mIn). With the use of $\beta$-delayed neutron and
$\gamma$ spectroscopy, the decay strengths above the neutron separation energy
were quantified in this neutron-rich nucleus for the first time. The allowed
Gamow-Teller transition $9/2^{+}\rightarrow 7/2^{+}$ was located at 5.92 MeV
in the 133gIn decay with a $\mathrm{log}ft=4.7(1)$. In addition, several
neutron-unbound states were populated at lower excitation energies by the
First-Forbidden decays of 133g,mIn. We assigned spins and parities to those
neutron-unbound states based on the $\beta$-decay selection rules, the
$\mathrm{log}ft$ values, and systematics.

##  I Introduction

Doubly magic nuclei far from the stability line, such as 24O, 78Ni, 100Sn, and
132Sn, have attracted tremendous interest in the last decades. Their simple
structures and imbalanced neutron-proton ratios provide a testing ground to
study the nuclear shell evolution as a function of isospin both experimentally
and theoretically, see, for example, Refs. Kanungo  _et al._ (2009); Taniuchi
_et al._ (2019); Hinke  _et al._ (2012); Jones  _et al._ (2010); Vernon  _et
al._ (2022) and references therein. It has been suggested that the residual
$NN$ interactions are responsible for the drift of single-particle orbitals
and the modification of nuclear shell structure at extreme neutron-proton
ratios Sorlin and Porquet (2008). Since these phenomena impact the decay
properties of nuclei, nuclear $\beta$ decay is a viable probe to study the
shell evolution. Specifically, nuclear $\beta$ decay is extremely sensitive to
the occupation of proton and neutron orbitals. In the neutron-rich nuclei, the
predominant allowed Gamow-Teller (GT) transitions require $\Delta L=0$ ($L$
refers to the orbital angular momentum of proton and neutron) between neutron
and proton spin-orbital partners in the same shell. The First-Forbidden (FF)
transitions, on the other hand, connect neutron and proton orbitals with
$\Delta L=1$ from neighboring shells. Due to their different selection rules,
the GT and FF operators transform the initial state of the parent nucleus into
diverse groups of final states in the daughter. Thus, measuring the decay
strengths as a function of excitation energy provides nuclear-structure
information in the parent and daughter nuclei. In addition, $\beta$ decays
play an important role in various nucleosynthesis processes. In the
$r$-process, for example, they compete with the rapid neutron-capture reaction
and affect the final elemental distribution Burbidge  _et al._ (1957); Cameron
(1957). Owing to these reasons, it is of particular interest to measure the
$\beta$-decay properties in the vicinity of 132Sn. Its proton and neutron
shell closures at $Z=50$ and $N=82$ define one of the strongest doubly magic
cores on the neutron-rich side of the nuclear chart Kerek  _et al._ (1973);
Björnstad  _et al._ (1986); Jones  _et al._ (2010), providing a reference
point to study nuclear structure with extreme neutron excess. Furthermore, the
proximity of the $r$-process path to 132Sn gives those decay properties key
impacts on the $r$-process abundance pattern near the mass number $A=130$
region Mumpower  _et al._ (2016).

In this work, we studied the $\beta$ decay of 133In, a nucleus southeast of
132Sn. Because of its substantial $Q_{\beta}$ window ($\sim 13$ MeV), a large
number of states with different microscopic configurations can be populated in
the daughter 133Sn. The states below the neutron separation energy were
attributed to a single neutron outside the 132Sn core Hoff  _et al._ (1996);
Jones  _et al._ (2010); Allmond  _et al._ (2014). The decay channels feeding
those states can be understood by transforming a neutron above $N=82$ into a
proton below $Z=50$ (e.g., $\nu f_{7/2}\rightarrow\pi g_{9/2}$). The
subsequent $\gamma$ decays had been surveyed thoroughly by Piersa et al. and
Benito et al. Piersa  _et al._ (2019); Benito  _et al._ (2020). The current
study focused on the measurement of decay strength above the neutron
separation energy, which was less known experimentally. The investigated
states were highly excited because they were dominated by the neutron or
proton particle-hole (p-h) excitations with respect to the 132Sn core.
Promptly after the $\beta$ decays, neutrons were emitted from those states,
leaving the residual 132Sn in either the ground state or excited states. Some
of the experimental findings and their consequences were highlighted in Ref.
Xu  _et al._ . This article explains in full detail the experimental setup
(Section II), the procedure to reconstruct the excitation energies of the
neutron-unbound states and their $\beta$-decay feeding probabilities (Section
III), and the spin-parity assignments of these states (Section IV).

##  II Experiment

The neutron-rich indium isotopes were produced at the Isotope Separator On-
Line (ISOLDE) facility at CERN Catherall  _et al._ (2017). A 1.4-GeV proton
beam was delivered by the Proton Synchrotron Booster (PSB) and impinged on a
tungsten solid neutron converter Gottberg  _et al._ (2014) with an average
current of 2 $\mu$A. Radioactive isotopes, including 133In, were produced in a
uranium carbide (UCx) target next to the neutron converter through neutron-
induced fission. The indium atoms were ionized using the Resonance Ionization
Laser Ion Source (RILIS) at ISOLDE Fedosseev  _et al._ (2017). By using the
narrow-band titanium-sapphire (Ti:Sa) laser at RILIS Rothe  _et al._ (2013),
selective ionization of 133In of either the ground state or isomer can be
achieved Piersa  _et al._ (2019). Following the General Purpose Separator
(GPS) Catherall  _et al._ (2017) separating the isotopes of interest based on
the mass-to-charge ratio, electrostatic quadrupoles transported the ion beam
to IDS. The beam was implanted into a movable tape at the center of a decay
chamber. After each proton pulse, the beam gate at ISOLDE was switched on for
300 ms for continuous implantation. Then, the implantation was stopped for 300
ms before the tape was rolled down to a shielded box to remove long-lived
activities originating from the daughter and granddaughter $\beta$ decays. The
implantation and tape move cycle provided a 600-ms time window to measure
decay products from the implanted 133In.

Figure 1: Schematic drawing of the experimental setup at IDS. The radioactive
beam from ISOLDE was implanted on the tape at the center of the setup. The
$\beta$-delayed $\gamma$ rays from 133In were detected by four HPGe clover
detectors at backward angles relative to the beam direction. The INDiE array
was placed on the other side to measure neutron spectroscopy following the
133In decay.

Figure 1 draws the detector configuration at IDS. Four high-purity germanium
(HPGe) clover detectors were placed closely outside the decay chamber to
measure $\beta$-delayed $\gamma$ radiation. The photopeak efficiency was 10%
and 3% for 100-keV and 1-MeV $\gamma$ rays, respectively, including combining
energy deposition from Compton scattering inside all four crystals in each
clover (addback). The neutron energies $E_{n}$ were deduced from their time-
of-flight (TOF) measured by the IDS Neutron Detector (INDiE), an array similar
to the Versatile Array of Neutron Detectors at Low Energy (VANDLE) Peters  _et
al._ (2016); Madurga  _et al._ (2016). The detection setup consisted of 26
EJ-200 plastic scintillator modules. Each module was $3\times 6\times 120$ cm3
and had one photomultiplier tube (PMT) coupled to each end. The modules were
mounted in a custom-built support frame describing an arch for a radius of 100
cm from the decay chamber. The intrinsic neutron efficiency of each module was
35% at 1 MeV Peters  _et al._ (2016). The total solid angle covered by 26
modules was about 15% of 4$\pi$. However, only 22 out of 26 modules were used
in the analysis due to the shadow from the supporting frame of the decay
chamber. The resulting solid angle was 12.6% of $4\pi$. Two plastic
scintillators surrounding the implantation tape defined the start signal of
TOF. It provided average efficiency of up to $\sim$80% for $\beta$ particles.
The neutron data were taken in the so-called triple coincidence mode,
requiring both PMTs of an INDiE module and one of the $\beta$ triggers to
record an event. This way, the neutron detection threshold was pushed down to
100 keV (or 5-keVee energy loss in the detectors). The traces of $\beta$ and
INDiE signals were sampled by the 12-bit 250-MHz digitizers. The sub-
nanosecond time resolution was achieved using the algorithm introduced in Ref.
Paulauskas  _et al._ (2014). The FWHM of the $\gamma$-flash peak in the
obtained TOF spectrum was 1.5 ns. The actual neutron TOF distance between the
implantation point and INDiE modules was determined as 104.2(3) cm using the
online $\beta$ decay of 17N, which emits three fully resolved and well-studied
neutron lines Ohm  _et al._ (1976).

##  III Analysis of the neutron spectrum

Figures 2 (a–g) present the neutron data taken in coincidence with the $\beta$
decay of 133In. The figures on the left (a, b, c, and d) are taken with the
133gIn decay and those on the right (e, f, and g) with an admixture of 133gIn
(40%) and 133mIn decays (60%). When RILIS was set on the $1/2^{-}$ isomer,
there are still 133gIn implanted into the decay station at the same time,
giving rise to the contamination peaks in the isomer’s neutron spectra.

Figure 2: The neutron data taken in coincidence with the 133In $\beta$ decay,
with figures on the left corresponding to the pure ground-state decay and
those on the right to an admixture of ground-state (40%) and isomeric decays
(60%). Figures (a, e) plot the neutron TOF against their energy loss in INDiE,
with the projections along TOF in Figs. (b, f), respectively. Figure (c) shows
the ground-state neutron spectrum in coincidence with the 4041-keV $\gamma$
decay in 132Sn. Figures (d, g) focus on the TOF of high-energy neutrons with
$E_{n}>3$ MeV. They were made by projecting Figs. (a, e), respectively, along
TOF with energy loss greater than 1 MeVee. All the neutron TOF spectra were
fitted by the neutron response functions (magenta), with the neutron peaks
attributed to the ground-state and isomeric decays drawn in blue and red,
respectively. The dashed line is the $\beta$ and $\gamma$-ray background in
the neutron TOF spectra.

Figures 2 (a, e) show the collected neutron spectra in two-dimensional (2D)
histograms plotting the neutron TOF versus their energy loss in INDiE. The
neutron events are seen following the banana-shaped distribution in the
histograms. The neutron TOF spectra in Figs. 2 (b, f) were made by projecting
the 2D histograms along the x-axis with energy loss greater than 5 keVee. Due
to the simple structure of 133Sn and the $\beta$-decay selection rules, only a
few prominent neutron peaks were visible in the spectra. Furthermore, no major
peaks were observed in coincidence with $\gamma$ decays in 132Sn, including
the strongest $2^{+}_{1}\rightarrow 0^{+}_{g.s.}$ transition, see Fig. 2 (c).
This implied those 133Sn unbound states had a direct feeding to the 132Sn
ground state via neutron emissions. This lack of neutron-$\gamma$ cascades was
due to the first excited state ($2^{+}$) in 132Sn being above 4 MeV, making it
energetically impossible for most of the neutron unbound states observed in
the 133In decay. Nevertheless, there was a small number of neutron emissions
populating the 132Sn excited states. Their numbers were estimated from the TOF
spectra gated by the 4041-, 4352-, and 4416-keV $\gamma$ rays observed by the
clover detectors. These $\gamma$ rays correspond to the $2^{+}_{1}\rightarrow
0^{+}_{g.s.}$, $3^{-}_{1}\rightarrow 0^{+}_{g.s.}$, and $4^{+}_{1}\rightarrow
0^{+}_{g.s.}$ transitions in 132Sn, respectively. According to Ref. Benito
_et al._ (2020), they carry mostly the entire $\gamma$-decay strength, via
$\gamma$-$\gamma$ cascade, from an excited state to the ground state, with a
5131-keV state being the sole exception. However, Ref. Benito  _et al._ (2020)
reported an extremely weak ground-state feeding branching ratio from this
state. Thus, the error introduced by not considering this weak
neutron-$\gamma$ cascade was much smaller than the statistical uncertainties
in the analysis. The result showed about 7.0(5)% of total neutron emissions
going to the 132Sn excited states. Their contribution was subtracted from the
total neutron activity to ensure the neutron intensities feeding the ground
state were extracted properly.

The neutron TOF spectra in Figs. 2 (b, f) were fitted by a template neutron
response function. The procedure to determine the response function of
individual peaks is explained as follows. First, the TOF spectrum was
simulated for monoenergetic neutrons with GEANT4 Agostinelli  _et al._ (2003),
which took into account all the neutron-scattering material at IDS and the
time resolution of INDiE modules. Second, the simulated profile was convolved
with a Breit-Wigner style distribution Nyman  _et al._ (1990) if a state had a
sizeable width in energy (broad resonance) greater than our resolution. The
obtained response function was verified using the $\beta$ decays of 49K and
17N, reproducing their neutron spectra with only known peaks from the
literature Carraz  _et al._ (1982); Ohm  _et al._ (1976). Fitting the spectra
of the 133In decays only involved "zero-width" peaks in the response function.
This indicated the observed resonances in 133Sn were narrower than our energy
resolution, which was about 80 and 250 keV for 1- and 3-MeV neutrons,
respectively, at the minimum energy threshold (5 keVee). Since the
contribution from neutron-$\gamma$ cascades had been subtracted from the fit,
the peak intensity in the response function gave access to the neutron
intensities directly feeding the 132Sn ground state. The experimental
background, which was drawn as the dashed lines in Fig. 2, consisted of a
double-exponential decaying tail from fast $\beta$-decay electrons and a
constant plateau from random $\gamma$ rays.

Table 1:  A list of neutron-unbound states identified in 133Sn. Those were derived from the neutron emissions directly feeding the 132Sn ground state. The excitation energies $E_{ex}$ were calculated from neutron TOF and the $S_{\mathrm{n}}=2.399(3)$ MeV Wang  _et al._ (2021). The $I_{\beta}$ is the $\beta$-decay feeding probability given in % per $\beta$ decay. A value with $\ast$ means the state decayed via competing neutron and $\gamma$ channels, whereas that with $\dagger$ is likely a doublet at 6018 and 6088 keV respectively. See text for details. The $\mathrm{log}ft$ values were calculated using the half-lives from Ref. Piersa  _et al._ (2019), $\beta$-decay $Q_{\beta}$ from the atomic mass difference between 133In Izzo  _et al._ (2021) and 133Sn Wang  _et al._ (2021), and $E_{ex},\ I_{\beta}$ from this work. Spins and parities $I^{\pi}$ were assigned tentatively based on the $\beta$-decay selection rules, $\mathrm{log}ft$, and systematics.  Parent |  $E_{ex}$ (keV) | $I^{\pi}$ |  $I_{\beta}$ (%) | $\mathrm{log}ft$
---|---|---|---|---
133gIn | 3562(18) | $(11/2^{-})$ | 12.0(8)$\ast$ | 5.8(1)
| 3923(27) | $(7/2^{-}\sim 11/2^{-})$ | 1.8(1)$\ast$ | 6.5(1)
| 4123(35) | $(7/2^{-}\sim 11/2^{-})$ | 0.6(1)$\ast$ | 6.9(1)
| 4236(36) | $(7/2^{-}\sim 11/2^{-})$ | 0.8(1) | 6.8(1)
| 4329(38) | $(7/2^{-}\sim 11/2^{-})$ | 1.1(1) | 6.6(1)
| 4906(55) | $(7/2^{-}\sim 11/2^{-})$ | 9.5(3) | 5.6(1)
| 5924(91) | $(7/2^{+})$ | 37.6(13) | 4.7(1)
| 6068(96) | $(7/2\sim 11/2)$ | 14.0(7)$\dagger$ | 5.1(1)
| 6250(100) | $(7/2\sim 11/2)$ | 2.2(2) | 5.9(1)
| 6550(120) | $(7/2\sim 11/2)$ | 0.3(1) | 6.6(1)
| 6750(120) | $(7/2\sim 11/2)$ | 2.2(1) | 5.7(1)
| 6950(130) | $(7/2\sim 11/2)$ | 0.3(1) | 6.6(1)
| 7320(150) | $(7/2\sim 11/2)$ | 1.0(1) | 5.9(2)
| 7700(160) | $(7/2\sim 11/2)$ | 1.1(1) | 5.8(2)
| 7900(170) | $(7/2\sim 11/2)$ | 0.6(1) | 5.9(2)
| 8300(190) | $(7/2\sim 11/2)$ | 0.2(1) | 6.4(2)
| 8500(200) | $(7/2\sim 11/2)$ | 0.4(1) | 5.9(2)
| 9100(230) | $(7/2\sim 11/2)$ | 0.3(1) | 5.8(2)
133mIn | 3621(19) | $(3/2^{+})$ | 32.5(12) | 5.5(1)
| 3794(23) | $(1/2^{+})$ | 11.9(5) | 5.9(1)
| 4098(30) | $(1/2^{+},~{}3/2^{+})$ | 13.6(5) | 5.8(1)
| 4464(44) | $(1/2^{+},~{}3/2^{+})$ | 0.9(2) | 6.8(1)
| 4639(49) | $(1/2^{+},~{}3/2^{+})$ | 0.9(2) | 6.8(1)
| 5142(62) | $(1/2^{+},~{}3/2^{+})$ | 4.3(2) | 6.0(1)
| 5604(78) | $(1/2^{+},~{}3/2^{+})$ | 11.7(5) | 5.5(1)
| 6210(100) | $(1/2,~{}3/2)$ | 1.4(3) | 6.3(1)
| 6500(110) | $(1/2,~{}3/2)$ | 5.7(4) | 5.6(1)
| 6800(120) | $(1/2,~{}3/2)$ | 2.3(2) | 5.9(1)
| 7200(140) | $(1/2,~{}3/2)$ | 1.1(2) | 6.1(1)
| 8110(180) | $(1/2,~{}3/2)$ | 0.6(2) | 6.1(1)
| 9450(250) | $(1/2,~{}3/2)$ | 0.5(2) | 5.7(1)
Figure 3:  Constructed decay schemes of 133gIn ($9/2^{+}$) and 133mIn
($1/2^{-}$) between $S_{\mathrm{n}}=2.399$ MeV Wang  _et al._ (2021) and
$E_{ex}=6.0$ MeV, where isolated resonances were observed in 133Sn. Decays
associated with the ground state and isomer are differentiated in blue and
red, respectively. The states below the neutron separation energy are included
for completeness Piersa  _et al._ (2019); Allmond  _et al._ (2014). Half-lives
and neutron-emission probabilities ($P_{n}$) in 133In are taken from Refs.
Piersa  _et al._ (2019); Benito  _et al._ (2020). The excitation energy of the
$1/2^{-}$ isomer is from Ref. Izzo  _et al._ (2021). The states with a solid
spin-parity assignment are highlighted by “$\ast$” on their excitation
energies.

The results from a $\chi^{2}$-fitting analysis in Fig. 2 (b, f) are summarized
in Table 1 and Fig. 3. The numbers of peaks in the response function to fit
the ground-state and isomeric decays were 18 and 13, respectively. All the
ground-state peaks were included in the analysis of isomeric decay due to
contamination. Their contributions, as illustrated by the blue peaks in Fig. 2
(f) (and Fig. 2 (g)), were determined by fixing their relative intensities to
the strongest peak at 41 ns with the ratios obtained from the ground-state
decay. The neutron peaks associated with the isomeric decay were drawn in red
in Fig. 2 (f) (and Fig. 2 (g)) to be differentiated from the ground-state
peaks. The excitation energies $E_{ex}$ were derived by summing the neutron
kinetic energy, corrected by recoil energy, with the neutron separation energy
$S_{\mathrm{n}}=2.399(3)$ MeV in 133Sn Wang  _et al._ (2021). The experimental
error combined the uncertainty in neutron TOF centroid, flight distance, and
neutron separation energy. In this analysis, the number of detected $\beta$
decays $N_{\beta}$ was estimated from the number of detected neutrons divided
by the $\beta$-delayed neutron emission probability ($P_{\mathrm{n}}$), which
is 90(2)% and 93(2)% for 133gIn and 133mIn respectively Benito  _et al._
(2020). Then, the decay probability $I_{\beta}$ of the state was calculated by
normalizing the neutron intensity to $N_{\beta}$. In cases where there were
$\gamma$ decays competing with neutron emissions, which will be discussed in
more detail later, $I_{\beta}$ included the contribution from $\gamma$ decays.
It is noted that all the $I_{\beta}$ in Table 1 were calculated from the
neutron emissions directly feeding the 132Sn ground state. It is strictly
correct for the states below 6.44 MeV in 133Sn. For the states above 6.44 MeV,
where the neutron-$\gamma$ cascade is energetically possible, these
$I_{\beta}$ should be regarded as the lower limits. The ground-state
(isomeric) decay $\mathrm{log}ft$ values were extracted using the $I_{\beta}$
in Table 1, the $\beta$-decay half-life of 133gIn (133mIn) from Ref. Piersa
_et al._ (2019), and the $Q_{\beta}=13.2$ MeV (13.8 MeV) from the atomic mass
difference between 133gIn (133mIn) Izzo  _et al._ (2021) and 133Sn Wang  _et
al._ (2021).

A high-energy part of the neutron spectra in Figs. 2 (b, f), i.e., $E_{n}>4$
MeV and TOF$<40$ ns, is more likely due to a continuum of strength
distribution rather than due to isolated resonances. There, a peak in the
response function should be regarded as a neutron quasi resonance Madurga  _et
al._ (2016). The distribution of transitions in the continuum was inferred by
increasing the energy threshold of INDiE, resulting in better resolving power
in the TOF spectrum than the previously quoted values. For instance, Figs. 2
(d, g) present the spectra with 1-MeVee energy threshold for the 133g,mIn
decays, respectively, showing better resolution for the high-energy neutron
peaks than Fig. 2 (b, f). The centroids of the high-energy neutron peaks were
determined in Fig. 2 (d, g) before they were fixed in the fit of Fig. 2 (b, f)
to extract intensities together with lower-energy neutron peaks.

Figure 4: Portion of $\gamma$-ray spectra measured in coincidence with the
ground-state decay of 133In. The candidate $\gamma$ deexcitations from the
133Sn neutron-unbound states are marked by “$\bullet$”, to be distinguished
from the $\gamma$ decays in 132Sn. SE stands for single-escape peak. See text
for details.

The observations of $\gamma$ decay from neutron-unbound states were reported
previously in 133Sn Piersa  _et al._ (2019); Vaquero  _et al._ (2017); Benito
_et al._ (2020). Therefore, both $\gamma$ and neutron intensities were
measured in this work to ensure no strength was missing in $I_{\beta}$. In the
133gIn decay, five $\gamma$ peaks at 3564, 3928, 4110, 6018, and 6088 keV were
found to have half-lives and energies consistent with the corresponding
neutron peaks in Table 1. These observed $\gamma$ rays agree with the previous
$\beta$-decay study of 133In using pure $\gamma$-ray spectroscopy Piersa  _et
al._ (2019); Benito  _et al._ (2020). Figure 4 shows portions of $\gamma$-ray
spectra in the relevant energy ranges. Statistically, none of these $\gamma$
transitions were in coincidence with any other $\gamma$ rays nor neutron
emissions, suggesting they were single-$\gamma$ transitions from a neutron
unbound state to the ground state. For the transitions at 3564, 3928, and 4110
keV, their $\gamma$ intensities were added to the $I_{\beta}$ of 3561-, 3919-,
and 4092-keV states in Table 1, respectively. Regarding the two $\gamma$
transitions around 6 MeV, their separation is only 70 keV, too close to be
resolved by our neutron detectors. Instead, a neutron peak was observed at
$E_{n}=3642$ keV ($E_{ex}=6068$ keV) with TOF$\sim$39.5 ns, see Fig. 2(d).
Thus, it was presumed that the neutron peak consists of an unresolved doublet
at 6018 and 6088 keV, respectively. The $I_{\beta}$ of the 6068-keV state
corresponds to the sum of the doublet. In contrast, no neutron-$\gamma$
competition was identified following the 133mIn decay. Below 6-MeV excitation
energy, where $\beta$ feedings are strong, the $1/2^{-}$ isomer is expected to
populate low-spin positive-parity states in 133Sn via FF transitions. From
those states, the electromagnetic (EM) $E2$/$M1$ transitions to the $7/2^{-}$
ground state in 133Sn are forbidden, and higher-order EM transitions
($M2$/$E3$) are too slow to compete with neutron emissions. From a low-spin
negative-parity state fed by GT transitions at higher energy, the
neutron-$\gamma$ competition is in principle possible, similar to 133gIn as
discussed above. However, no such candidates were found due to the combined
effect of smaller $\beta$ feeding and a limited number of implanted samples.

Figure 5:  The experimental $\beta$-decay strength distribution (in
$S_{\beta}=1/ft$ Duke  _et al._ (1970)) of the 133In ground state (blue) and
isomer (red) between $E_{ex}=2.5$ and 11 MeV.

Figure 5 presents the extracted $\beta$-strength distribution, in the form of
$S_{\beta}=1/ft$ Duke  _et al._ (1970), of the 133g,mIn decays with an energy
interval of 200 keV. The distributions include the states listed in Table 1
and the decay strengths associated with the neutron emissions feeding the
132Sn excited states, which is around 7% of total neutron emissions as
discussed above. For these minor strengths, the neutron-$\gamma$ coincidence
analysis was needed to correct the excitation energies of the neutron-unbound
states in 133Sn. This can be easily applied to the neutron emissions that feed
the $2^{+}$, $3^{-}$, or $4^{+}$ states in 132Sn due to their relatively
strong neutron-$\gamma$ cascades. Additionally, Piersa et al. and Benito et
al. observed weak neutron emissions feeding the states higher than the $4^{+}$
state in 132Sn Piersa  _et al._ (2019); Benito  _et al._ (2020). Their
observations were confirmed in our measurement, but the associated $\gamma$
decays were generally too weak to perform credible neutron-$\gamma$
coincidence analysis for the energy correction. To simplify the analysis and
include their contribution in Fig. 5, two extreme cases were considered.
First, the strength distribution was calculated assuming those weak neutron
emissions only fed the lowest $2^{+}$, $3^{-}$, or $4^{+}$ states around 4 MeV
in 132Sn. Second, the calculation was repeated with the 132Sn state shifted to
6.5 MeV, the highest observed state in the $\beta$-delayed neutron emissions
of 133g,mIn Benito  _et al._ (2020). The final results shown in Fig. 5 are the
average between the two calculations, with the error bars covering their upper
and lower limits.

##  IV Spin and parity assignments

Before this work, the only state known to have a neutron-hole configuration in
133Sn was the $11/2^{-}$ state at 3564 keV Hoff  _et al._ (1996); Piersa  _et
al._ (2019); Vaquero  _et al._ (2017). Its wavefunction is dominated by a
neutron 2p-1h configuration, in which a neutron hole at $h_{11/2}$ couples to
two neutron particles above $N=82$. In the 133gIn decay, the same state was
observed at $E_{ex}=3561(18)$ keV, in good agreement with the literature
value. It is the lowest neutron unbound state seen in the experiment (see Fig.
3). In an intuitive picture, the decay is associated with a FF transition $\nu
h_{11/2}\rightarrow\pi g_{9/2}$, during which the two neutron particles
outside $N=82$ persist as a spin $J=0$ pair in the initial and final states.
Fogelberg et al. observed the analogous transition without the neutron pair in
131In$\rightarrow^{131}$Sn with a $\mathrm{log}ft>5.6$ Fogelberg  _et al._
(2004). According to the odd-mass tin isotopes with $N<82$, there are two
extra neutron orbitals $d_{3/2}$ and $s_{1/2}$ close to $h_{11/2}$, giving
rise to three neutron 2p-1h states at similar excitation energy in 133Sn.
Indeed, two states were observed in the isomeric decay at excitation energies
of 3.62 and 3.79 MeV. Following the systematics, the lower state
($\mathrm{log}ft=5.4$) was assigned $I^{\pi}=3/2^{+}$, and the upper state
($\mathrm{log}ft=5.8$) $I^{\pi}=1/2^{+}$. Their underlying transitions are
$\nu d_{3/2}\rightarrow\pi p_{1/2}$ and $\nu s_{1/2}\rightarrow\pi p_{1/2}$,
respectively, both of which are FF transitions. The most important neutron-
hole orbital involved in the 133In decay is the deeply bound $\nu g_{7/2}$
because it determines the GT strength of 133gIn. In Fig. 5, one can see a
remarkable strength at $E_{ex}=5.92$ MeV exclusive to the 133gIn decay. Its
$I_{\beta}$ gives a $\mathrm{log}ft=4.7$, which is significantly stronger than
any other feeding in the decay. Thus, the state was assigned $I^{\pi}=7/2^{+}$
originating from $\nu g_{7/2}^{-1}$. The newly determined GT strength of $\nu
g_{7/2}\rightarrow\pi g_{9/2}$ in 133gIn has a similar $\mathrm{log}ft$ as in
the 131gIn decay (=4.4 Fogelberg  _et al._ (2004)). It is noted that this
assignment is different from that in Ref. Piersa  _et al._ (2019) suggesting
the 6088-keV state to be populated via the dominant GT decay.

Figure 6: Reduced level schemes of 131Sn and 133Sn. Each group of states is
labeled by the dominant neutron $\mathit{p\mathchar 45\relax h}$ configuration
in the wave functions. Information in 131Sn is taken from Refs. Fogelberg  _et
al._ (2004); Kozub  _et al._ (2012). In 133Sn, the spins, parities, and
excitation energies of the $\nu$1p-0h states are taken from Refs. Piersa  _et
al._ (2019); Allmond  _et al._ (2014), while those of $\nu$2p-1h are from this
work. The dashed lines connect groups of states with the same odd-even
combination of neutron p-h configuration.

The result enables a complete comparison between 131Sn and 133Sn, see Fig. 6.
Before this work, the neutron 1p-2h states in 131Sn and the neutron 1p-0h
states in 133Sn had revealed remarkable similarity in neutron transfer
reactions Jones  _et al._ (2010); Kozub  _et al._ (2012). Similarly, if one
moved down the neutron 2p-1h states in 133Sn and aligned the lowest $11/2^{-}$
state to the ground state in 131Sn, the level scheme constructed in this work
is analogous to that of the 0p-1h states in 131Sn Fogelberg  _et al._ (2004),
supporting our spin-parity assignment discussed previously.

Besides, one notices strong $\beta$ feedings at $E_{ex}\sim 5$ MeV in Fig. 5
in both ground-state and isomeric decays. At this excitation energy, it is
possible to break the proton $Z=50$ core and populate the proton 1p-1h excited
states in 133Sn. From the low-lying states in odd-mass antimony isotopes
($Z=51$) around $N=82$, $\pi g_{7/2}$ and $\pi d_{5/2}$ are expected to be the
lowest two proton orbitals outside $Z=50$. Thus, the lowest proton core
excited states observed in the 133In decay should be dominated by either
$\pi(g^{-1}_{9/2}\ g_{7/2})\times\nu f_{7/2}$ or $\pi(p^{-1}_{1/2}\
g_{7/2})\times\nu f_{7/2}$, depending on where the proton hole is in the
initial state, i.e., whether the ground-state or isomeric decay. Both
scenarios are carried by the FF transition $\nu f_{7/2}\rightarrow\pi
g_{7/2}$. At slightly higher excitation energy, states with the
$\pi(g^{-1}_{9/2}\ d_{5/2})\times\nu f_{7/2}$ or $\pi(p^{-1}_{1/2}\
d_{5/2})\times\nu f_{7/2}$ configuration should also be accessible via $\nu
f_{7/2}\rightarrow\pi d_{5/2}$. Benito et al. observed analogous transitions
in the decay from 132In to 132Sn at similar excitation energy Benito  _et al._
(2020). The $I^{\pi}$ of those states were assigned based on the $\beta$-decay
selection rules of non-unique FF transitions: $\Delta I=0$ or 1 and
$\Delta\pi=-1$. The unique FF transitions with $\Delta I=2$ were not
considered in the present spin assignment due to their significantly larger
$\mathrm{log}ft$ and smaller intensities Singh  _et al._ (1998). For example,
the neutron $d^{-1}_{5/2}$ state in 131Sn is populated in the isomeric decay
of 131In ($\nu d_{5/2}\rightarrow\pi p_{1/2}$) with a $\mathrm{log}ft=9.5$
Fogelberg  _et al._ (2004), of which the feeding probability is far below our
sensitivity.

Above the $7/2^{+}$ state at 5.92 MeV, no isolated resonances were seen with
strong feeding strength in either of the 133g,mIn decay. The spectra follow a
continuous distribution, which was attributed to the high level density and
limited resolving power. In this energy region, $\beta$ decay can populate
both positive- and negative-parity states via GT or FF transitions. The GT
transitions are favored because of their more significant matrix elements.
Following the selection rule, the states with $E_{ex}>6$ MeV were assigned the
spin $I=(7/2,~{}9/2,~{}11/2)$ in the ground-state decay and $(1/2,~{}3/2)$ in
the isomeric decay.

##  V Summary and conclusions

In this work, the $\beta$-decay properties of 133g,mIn were studied at IDS.
With the use of $\beta$-delayed $\gamma$ and neutron spectroscopy, their major
components in the decay-strength distribution were located above the neutron
separation energy in the daughter 133Sn. The strong GT transformation $\nu
g_{7/2}\rightarrow\pi g_{9/2}$ was observed in the 133gIn decay, feeding a
$7/2^{+}$ state at 5.92 MeV in 133Sn. Besides, many neutron-unbound states
originating from neutron or proton $\mathit{p\mathchar 45\relax h}$
excitations were found at lower energies following the FF decays of 133g,mIn.
The spins and parities of those states were assigned tentatively based on the
$\beta$-decay selection rules, the extracted $\mathrm{log}ft$ values, and
systematics along the isotopic chain.

The experimental findings greatly extend our knowledge of the 133In decay from
previous works Hoff  _et al._ (1996); Piersa  _et al._ (2019); Benito  _et
al._ (2020), providing the $\beta$-strength distribution southeast of 132Sn.
The results are crucial to benchmark $\beta$-decay theories and will serve as
a bridge to understand the decay properties of more neutron-rich nuclei, e.g.,
those $r$-process waiting-point nuclei near the $N=82$ shell closure.

###### Acknowledgements.

We acknowledge the support of the ISOLDE Collaboration and technical teams.
This project was supported by the European Unions Horizon 2020 research and
innovation programme Grant Agreements No. 654002 (ENSAR2), by the Office of
Nuclear Physics, U.S. Department of Energy under Award No. DE-FG02-96ER40983
(UTK) and DE-AC05-00OR22725 (ORNL), by the National Nuclear Security
Administration under the Stewardship Science Academic Alliances program
through DOE Award No. DE-NA0002132, by the Romanian IFA project CERN-
RO/ISOLDE, by the Research Foundation Flanders (FWO, Belgium), by the
Interuniversity Attraction Poles Programme initiated by the Belgian Science
Policy Office (BriX network P7/12), by the German BMBF under contracts
05P18PKCIA and 05P21PKCI1 in Verbundprojekte 05P2018 and 05P2021, by the UK
Science and Technology Facilities Research Council (STFC) of the UK Grant No.
ST/R004056/1, ST/P004598/1, ST/P003885/1, ST/V001027/1, and ST/V001035/1, by
National Natural Science Foundation of China under Grant No. 11775316, by the
Polish National Science Center under Grants No. 2019/33/N/ST2/03023, No.
2020/36/T/ST2/00547, and No. 2020/39/B/ST2/02346, by Spanish MCIN/AEI
FPA2015-65035-P, PGC2018-093636-B-I00, RTI2018-098868-B-I00,
PID2019-104390GB-I00, PID2019-104714GB-C21, and IJCI-2014-19172 grants, by
Universidad Complutense de Madrid (Spain) through Grupo de Física Nuclear
(910059) and Predoctoral Grant No. CT27/16-CT28/16.

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