# Semantic Change Characterization with LLMs using Rhetorics

Jader Martins Camboim de Sá1,2, Cédric Pruski2, Marcos Da Silveira2
1FSTM - University of Luxembourg
2 place de l’Université, L-4365, Esch-sur-Alzette, Luxembourg,
2Luxembourg Institute of Science and Technology
5 avenue des Hauts-Fourneaux, L-4362, Esch-sur-Alzette, Luxembourg,
Correspondence<EMAIL_ADDRESS>
###### Abstract

Languages continually evolve in response to societal events, resulting in new
terms and shifts in meanings. These changes have significant implications for
computer applications, including automatic translation and chatbots, making it
essential to characterize them accurately. The recent development of Large
Language Models has notably advanced natural language understanding,
particularly in sense inference and reasoning. In this paper, we investigate
the potential of LLMs in characterizing three types of semantic change:
dimension, relation, and orientation. We achieve this by combining LLMs’
Chain-of-Thought with rhetorical devices and conducting an experimental
assessment of our approach using newly created datasets. Our results highlight
the effectiveness of LLMs in capturing and analyzing semantic changes,
providing valuable insights to improve computational linguistic applications.

Semantic Change Characterization with LLMs using Rhetorics

Jader Martins Camboim de Sá1,2, Cédric Pruski2, Marcos Da Silveira2 1FSTM -
University of Luxembourg 2 place de l’Université, L-4365, Esch-sur-Alzette,
Luxembourg, 2Luxembourg Institute of Science and Technology 5 avenue des
Hauts-Fourneaux, L-4362, Esch-sur-Alzette, Luxembourg, Correspondence:
<EMAIL_ADDRESS>

##  1 Introduction

Language, a tool humans acquired throughout evolution, remains a subject of
fascination and inquiry across diverse disciplines, including neuroscience,
psychology, philosophy Pinker (2003), and computational linguistics. Despite
this interdisciplinary interest, our understanding of language is often
superficial, with much to uncover regarding its intricacies Allan (2013);
Pinker and Bloom (1990). Among the many elements that shape language, a
central aspect in understanding dynamics in language development is how the
semantics of words change Allan (2013); Pinker and Bloom (1990). This
evolution is particularly intriguing in computational linguistics, as it
impacts applications such as automatic translation and chatbots Camboim de Sá
et al. (2024). While humans can rapidly adapt to changes using a lot of
contextual information and cognitive processes to grasp the senses of a
sentence or a word, it is complex to provide enough cultural knowledge and
nuances to machines. Consequently, machines lack the tools to adapt to these
variations and to perform effective communication Tahmasebi et al. (2018).
Therefore, in many modern Natural Language Processing (NLP) systems, we
observe the impacts of semantic change on end users, especially when the task
requires deep contextual dependency Camboim de Sá et al. (2024).

In the context where historical or domain-specific knowledge of meaning is
crucial, the Lexical Semantic Change (LSC) field emerged to gain deep
understanding of and detect these changes Tahmasebi et al. (2018). While a
significant body of work explores which words changed in different moments or
domains, there is still a need for further comprehension regarding the types
and implications of semantic changes in these systems Hengchen et al. (2021).
For instance, in sentiment analysis, being aware that the term ‘sick’ has
acquired a positive connotation could significantly alter the interpretation
of a sentence.

Theories to comprehend semantic change exist. One prominent typology, proposed
by Traugott (2017), categorizes change into broadening/narrowing (a word gains
or loses senses), amelioration/pejoration (a word is perceived more
positively/negatively), metaphorization and metonymization (the word is used
as a metaphor or metonymy respectively). We illustrate these types of change
in Table 1.

A child in dirty overalls. |
---|---
He used a dirty trick to win the competition. | pejoration
No other style of hat was acceptable with an evening dress. |
He took off his politician’s hat and talked frankly. | metaphorization
The diamond is currently set in the crown of the Queen. |
The colonies revolted against the crown. | metonymization

Table 1: Examples illustrating the characterization of types of change.

Previous works have only partially covered the typology of semantic change,
typically focusing on a few types Camboim de Sá et al. (2024). However, recent
advancements in Language Models (LLMs) have showcased capabilities in
executing complex linguistic tasks such as inference, association,
understanding, and common sense reasoning OpenAI (2023) via the Chain-of-
Thought ( Chain-of-Thougth (CoT)) technique Wei et al. (2022). These reasoning
abilities in LLMs mimic human-like processes for establishing connections and
relations in natural language Dasgupta et al. (2022).

Rhetorical devices, known for their role in building persuasive arguments and
reasoning, utilize cognitive processes to improve argumentation and
communication efficiency Lakoff and Johnson (2008). These devices facilitate
concise communication and also exhibit characteristics related to semantic
evolution over time. Hence, they have been extensively employed by human
evaluators to compare senses Kearns (2006); Steen et al. (2007). In this
process, evaluators use historical and cultural knowledge to explain
variations in semantic change through rhetorical argumentation.

Moreover, recent studies have found that LLMs encode extensive cultural
knowledge, including relationships, associations, and events Petroni et al.
(2019), making them suitable for automating the characterization of semantic
change. Building upon this insight, we propose leveraging rhetoric in natural
language to characterize semantic change within the proposed typology by
exploring LLMs “thought” processes to mimic human cognitive reasoning.
Following the outlined typology, our methodology aims to instruct LLM to
utilize rhetorical devices and characterize change within a comparative
framework. Our contributions are:

  * •

A new approach to semantic change characterization exploring “reasoning” and
rhetoric capabilities of LLMs.

  * •

The proposal of 3 new public datasets for evaluation of semantic change
characterization: dimension, orientation, and relation.

The paper is structured as follows: Section 2 presents related work of the
field semantic change characterization using LLMs. Section 3 details our
methodology for prompting models for semantic change identification and
characterization. Section 4 introduces the experimental settings, including
datasets and results. Section 5 discusses insight from the method. Finally,
Section 7 contains concluding remarks and outlines future work.

##  2 Related Work

Most of the papers in semantic change address the problem of identification,
i.e., detecting if the meaning of a word changed without inferring what type
of change occurred. In the context of Language Models some authors explore
these capabilities to track semantic change identification as a sequence-to-
sequence problem Lyu et al. (2022); Giulianelli et al. (2023), by first
prompting the model to disambiguate the word in context and then generating a
contextualized word representation.

In challenges for semantic change identification for Russian and Spanish
Pivovarova and Kutuzov (2021); Zamora-Reina et al. (2022), the best performing
methodologies were large cross-language models fine-tuned in Word Sense
Disambiguation (WSD) for English data to then fit a linear regression over the
contextualized embeddings to identify semantic change. Later, LLMs were
employed for this task Wang and Choi (2023); Periti et al. (2024), but using
only few-shot prompt or fine-tuning to the task.

Previous works on semantic change characterization relies on extracting word
representations for each corpus, and later compare them to capture possible
differences in usage Camboim de Sá et al. (2024). In the context of
broadening/narrowing Bochkarev et al. (2022) utilize a neural network to
determine if a word is employed as a named entity. This approach creates a
temporal perspective of a word’s usage and allows them to compare occurrences
of a word to see whether it has gained new usage in the corpus. For
metaphorization Maudslay and Teufel (2022) fine-tuned with supervision a BERT
model to classify contextualized words into metaphor and then analyzed
different corpus. Finally, in the amelioration/pejoration context Fonteyn and
Manjavacas (2021) measures polarity in the term ‘to death’ by calculating the
distance between the word vectors ‘good’ and ‘bad’.

Compared to previous works on semantic change, this is the first study to use
CoT for this task, with our approach being deeply motivated by linguistic
literature. In terms of semantic change characterization, this is the first
work that generalizes across all types of change Camboim de Sá et al. (2024),
has no dependency on training data, and can be used for every type of relation
e.g., metaphor and metonymy.

##  3 Methodology

###  3.1 Background

In this paper, we propose a method for automating the characterization of
semantic change across different corpora. To this end, we rely on the
following set of predominant typologies defined in the literature Traugott
(2017); Juvonen and Koptjevskaja-Tamm (2016):

  * •

Broadening: gaining a new meaning related or not to the previous meaning, such
that a word represents more concepts, e.g., ‘cloud,’ a computing
infrastructure.

  * •

Narrowing: restriction of meaning occurs when a symbol represents fewer
concepts than previously, e.g., ‘gay’ which historically meant festive or
happy, is now predominantly used to refer to homosexuality.

  * •

Amelioration: a word gains a more positive sense to the previous sense, nice,
‘foolish, innocent’ changed to ‘pleasant.’

  * •

Pejoration: the word is used with a worse connotation to the previous usage,
stincan, ‘smell (sweet or bad)’ changed to stink.

  * •

Metonymization: association between terms, e.g., board ‘table’, changed to
“people sitting around a table, governing body.”

  * •

Metaphorization: conceptualizing one thing in terms of another, e.g., ‘head of
the company’ the word ‘head’ conceptualizes “command or control.”

We used the same classification of typologies as presented by Camboim de Sá et
al. (2024), where the typologies can be regrouped into three poles, namely
Dimension, Relation, and Orientation (see Figure 1).

Figure 1: Taxonomy for the poles of Lexical Semantic Change Traugott (2017);
Juvonen and Koptjevskaja-Tamm (2016).

In the dimension pole, we compute the “number of senses” a word can have. This
pole is self-complementary as increasing represents broadening, and decreasing
represents a narrowing of senses. After identifying the number of senses, we
can compare the differences between corpora.

Metaphorical and metonymical changes are classified under the relation
category, as these changes enhance the connection between one sense of a word
and its other senses. In this framework, a word’s meaning relies on the link
established through either conceptual (abstract relation) or material
(physical association) similarity between concepts. We identify which senses
are used figuratively in relation to other senses of the same word.

The orientation pole regroups the process of amelioration or pejoration of a
meaning. In this pole, words are analyzed according to the contextual
sentiment captured from each corpus, and then we analyze how the sentiment
changes over corpora. In this study, we explore only positive, negative, and
neutral sentiment values for words.

###  3.2 Rhetorical Arguments as a Pragmatic Tool

LLMs have exhibited significant progress in natural language comprehension.
This includes reasoning by analogy Webb et al. (2022), understanding metaphors
Liu et al. (2022), argumentation Chen et al. (2023), and acquiring cultural
knowledge Petroni et al. (2019). Additionally, instructing an LLM to generate
a rationale, which is a natural language explanation for its reasoning
process, before providing an answer has been shown to improve performance on
many NLP tasks that require logical reasoning Wei et al. (2022); Kavumba et
al. (2023). This rationale generation step is believed to inject more
information retrieved from the LLM’s internal knowledge store into the prompt.
This enriched prompt allows the LLM to consider a broader range of knowledge
during the final decision-making process Dasgupta et al. (2022).

In this paper, we rely on its stored cultural knowledge to improve the context
for the task and work as an annotator in the framework proposed in the
previous subsection. The problem of characterizing LSC, identifying different
senses, figurative usage, and feelings, relies on building cognitive relations
between other senses that depend on human perception and culture Lakoff and
Johnson (2008). As language is the best tool to explain language Pinker
(2003), in our approach, we try to mimic this cognitive process Huang and
Chang (2023), using the human knowledge contained in LLMs and rationales as a
means to produce the same associations human perform Dasgupta et al. (2022);
Strachan et al. (2024).

Tracking word senses and comparing them is a complex task Kilgarriff (1997).
To address this problem, we approach it as a “comparative semantics” problem,
i.e., instead of extracting the meaning as a final objective, we rely on the
idea of relatedness and likeness of meaning to compute LSC. Similar to the
work of Schlechtweg et al. (2024), we compare word occurrences for the
characterization problem. However, in DUREL the annotator is prompted with two
sentences that share a particular word and the annotator has to classify the
level of similarity between contextual senses. In our approach, we use an LLM
instead of humans to annotate the relatedness between words, and we reduce it
to just ‘identical’ and ‘different’ classes.

We perform the characterization starting with a cognitive semasiological
comparative analysis of the word meaning Kilgarriff (1997), following the
Cambridge setting Tang et al. (2013). We first provide a context where the
word sense could be inferred (the Gracian approach Agirre and Edmonds (2007)),
to then decide via reasoning if the deduced senses are different to a class of
change Blank (2003).

This step is done by a LLM that acts like a judge/annotator using a special
type of CoT Wei et al. (2022) with detailed step-by-step reasoning Mitra et
al. (2023) to elicit models ability of word sense induction and comparative
semantics. Our approach exploits rhetorical techniques to produce ‘cognitive-
appealing’ arguments on how the senses are different.

For the first pole, dimension, we created a prompt requesting a word sense
differentiation, where the prompt ask if a word is used in an identical or
different sense. To perform the sense differentiation, we instruct the model
to use zeugma Kearns (2006) as a cognitive approach to identify identical
senses. If it can produce a consistent zeugma, the senses are identical.
Otherwise, it should assume the words are different.

Zeugma is a rhetorical device where a single word, typically a verb or an
adjective, governs or modifies two or more words in a sentence. This device
creates a clever or unexpected relationship between different sentence parts.
Zeugma often results in a play on words contributing to the overall impact of
the expression, and it adds a layer of complexity or humor to the language
used in a sentence and allows us to explore the sense usage difference Kearns
(2006). For example:

> (1) "He lost his keys."
> (2) "He lost his temper."
> (3) "He lost his keys and his temper." (?)

In sentence (3), the word “lost” is used to combine both sentences in a
related sense to describe both (1) losing physical objects (keys) and (2)
losing emotional control (temper). This zeugma creates a figurative and
compact expression that links two different related meanings of the word
‘lost’ in a single sentence, creating a bad pun Kearns (2006). This bad pun
comes because the second usage of ’lost’ does not preserve the same sense as
the first usage, indicating a difference in the meaning. In Figure 2, we
present part of the prompt employing zeugma for the dimension dataset. In
Appendix D, we share the complete prompt for the experiments.

Sense Differentiation […]. Follow these steps to complete the task: • Step 1.
Describe the meaning of the word in the first sentence. • Step 2. Describe the
meaning of the word in the second sentence. • Step 3. Write a sentence that
joins both using zeugma and the same shared word while preserving the same
sense. If the construction makes a bad pun, the words have a different sense.
• Step 4. Based on the previous reasoning, give your final answer: ’identical’
or ’different.’ [Few-shot examples.] Figure 2: Prompt for sense
differentiation in the dimension dataset.

This work proposes a computational instruction for figurative language
analysis. The instruction is based on a simplified version of the Metaphor
Identification Procedure (MIP) Steen et al. (2007). To distinguish between
metaphor and metonymy, the model is tasked with building a relation between
the concepts. This relation can be either abstract, suggesting a metaphorical
mapping between domains (evoking tropes), or material, if a physical
association exists between the concepts.

> (1) "The main objective of this forthcoming decision will be preparation for
> the winter."
> (2) "Winter can cause many disruptions for public transport."
> (3) "The word ’winter’ in the second sentence is associated with its
> problems, such as snow, making it a metonymy."

The provided examples showcase how simile act as a parsing mechanism for the
AI model. By leveraging similes, the model can reframe figurative language
based on the similarity or association it expresses between concepts. In
essence, a simile acts as a rhetorical device that explicitly compares two
entities to enhance explanation and detail the nature of that comparison. By
deciphering the figurative meaning within context, we aim to guide the model
towards extracting more information about the underlying semantic
relationship. This, in turn, allows the model to make a more accurate
prediction regarding the type of relation – whether it’s a metaphor or
metonymy. In Figure 3, we illustrate the prompt for obtaining the figurative
association between word usages.

Sense Figurativeness […]. Follow these steps to complete the task: • Step 1.
Describe the meaning of the word in the first sentence. • Step 2. Describe the
meaning of the word in the second sentence. • Step 3. Compare the usage,
determining if the second is related as a metaphor (where the word is used in
a similar but non-literal sense), as a metonymy (where the word represents
something closely related to or associated with it), or unrelated, used with a
different sense. • Step 4. Based on the third step, write the final answer,
’metaphor’, ’metonymy’, or ’unrelated.’ [Few-shot examples.] Figure 3: Prompt
for figurative sense in the relation dataset.

For orientation pole, the current state-of-the-art sense-level sentiment
analysis requires first a WSD step, then a sentiment analysis step Zhang et
al. (2023). Similar to the previous prompts and following the best practice,
we instruct the rationale to perform a textual sense disambiguation and then
differentiate the orientations between these senses Wiebe and Mihalcea (2006).
To differentiate orientation, we use antanagoge to compare senses’
positiveness (or negativeness) and to enrich contextual information on how
these senses can be perceived in the training data.

Antanagoge is a rhetorical device that involves responding to an accusation or
negative point with a counter-argument or positive point. It is used to
mitigate the impact of something negative by placing it alongside something
positive. We use the common sentence “I’d rather X than Y” as a few-shot
demonstration to instruct LLM to get the most probable contextual ordering. In
the example below exemplify the usage of antanagoge.

> (1) "A terrific presentation."
> (2) "A terrific storm."
> (3) "I’d rather have an terrific presentation than an terrific storm."

Sense Orientation […]. Follow this instructions to execute the task: • Step 1.
Describe the meaning of the word in the first sentence. • Step 2. Describe the
meaning of the word in the second sentence. • Step 3. Leverage the rhetorical
strategy of antanagoge, contrasting a negative with a positive, to weigh why
one meaning might be more favorable than the other, or if they stand neutral.
• Step 4. Based on the third step, write the final answer ’negative’,
’positive’, or ’neutral.’ [Few-shot examples.] Figure 4: Prompt for sense
orientation in the orientation dataset.

Further optimization can be done as in Schlechtweg et al. (2024). A graph of
occurrences can be build and clusterized to extract senses over time. These
clusters allows annotating semantic changes for each sense over time.

##  4 Experiments

In this section, we introduce the dataset produced to evaluate our annotation
method and measure the quality of our annotations for LSC.

###  4.1 Dataset for Lexical Semantic Change Characterization

From a semasiological perspective, words’ meaning could be inferred from the
context, for example, “He targeted me, after I didn’t agree with his
proposal.” or “The mustache guy, is coming today?”. We can deduce the meaning
of a word based on context and/or knowledge of the original meaning.

Lexical and Semantic Change (LSC) reflects how word meaning evolves. New
senses emerge when a word is used in a novel, non-standard way. Over time, if
this usage becomes widespread enough, it transitions from creative expression
to a conventional meaning.

The ideal approach to LSC detection should mimic this human capability. This
means employing unsupervised learning techniques, where the system infers the
evolving sense of a word solely based on its prior exposure to the language
and the contextual information within the data. In essence, the system learns
to identify semantic shifts without the need for pre-labeled data Schlechtweg
et al. (2020).

To evaluate our framework, we produce an LSC Characterization dataset
following the Cambridge setting described in Tang et al. (2013). The dataset
is composed of pairs of sentences sharing the same word (see the example with
the word ’lost’ from equation (1) and (2)). The first sentence expresses one
possible usage (e.g., original usage), while the second sentence express a
different usage. The task is to infer how the word’s meaning in each context
and compare them. We create three new datasets, one for each pole of change,
where the instance pairs present the type of change the LLM should
characterize in the pipeline.

In the dimension dataset, we curated the WiC data Pilehvar and Camacho-
Collados (2019) for getting a fraction of reliable and high-quality examples.
The original dataset only classified the word’s meaning as related or
unrelated. We adapted it according to the DUREL format. For this, the word’s
meanings are identical if the same meaning is observed when we merge the
sentences (see the ’lost’ example, equation (3)), i.e., a zeugma can be
performed between the two sentences, relabeling the sentences to this.

We define words as related if they have a direct relation (metaphor or
metonymy) for their usage, if the relation is not direct, we define this
senses as unrelated. For example, if ‘head’ is used figuratively in both
usages, the ‘head’ to represent the leader of a company and the ‘head’ to
represent the mind, we define them as unrelated as there is no direct
figurative usage between them. Finally, if not one of the cases above, we set
them as unrelated or keep the original annotation.

For the relation data, we collected examples from the metaphor detection
dataset Choi et al. (2021) to get literal and metaphorical usages and also
examples from the literature to increase the evaluation dataset size, the
sentences were manually collected using online dictionaries like
Linguee111www.linguee.com and Merriam-Webster222www.merriam-webster.com and
verified by 3 human annotators. To collect metonymies, we similarly used
examples in literature Lakoff and Johnson (2008) and retrieved sentences from
online sources.

The orientation data we created by getting sense pairs for the same word where
we had the greatest variance from these pairs by analyzing SentiWordNet
Baccianella et al. (2010). The sentence pairs were obtained from SemCor
Raganato et al. (2017) and WordNet Miller (1995) depending on how easy it is
to infer the sense given the sentence. Additionally, we transform the
sentences so that the sentiment of a word cannot be trivially detected from
the whole sentence, so the detector needs to comprehend the word-level
sentiment. In some cases, we modified the sentence to be negative while the
word meaning is positive.

Task | labels | Total
---|---|---
Dimension | Identical , Different | 260
Relation | Metaphor, Metonymy, Unrelated | 331
Orientation | Positive, Negative , Neutral | 262

Table 2: General view of the three datasets created for Semantic Change
Characterization.

In Table 2 we describe the number of instance pairs for each dataset we
produced.

###  4.2 Experimental results

We compare our approach with two baselines to evaluate how good LLMs and
rhetoric devices are for characterizing semantic change. The prompt is based
on CoT and a few-shot prompt with no CoT, where all prompts are provided with
the same 3-shot examples with the correct label and also the dictionary sense.
We took a special care to the difference in prompt be only the method and not
inserting ‘hack’ phrases333e.g. ”Please think carefully”, ”Take a deep
breath”, ”This is important for my career.” to improve model performance.

We selected LLaMA-3 and Phi-3 as the current state-of-the-art LLMs for the
instruction prompt. We sampled the models 5 times for each method with
temperature $\tau=0.7$, using the guidance444https://github.com/guidance-
ai/guidance/ library to control the generated layout. We report the mean and
standard deviation of the accuracy.

In Table 3, we present the results for the dimension dataset. We can observe
that the rhetoric method meaningfully improves the accuracy of Phi-3 and
LLaMA-3-70b over the baselines, while for LLaMA-3-8b, the best method is few-
shot prompt. While the data used for instruction tuning LLaMA-3 is not
publicly released, we believe it was fine-tuned in WiC data Pilehvar and
Camacho-Collados (2019), which could explain the improved accuracy.

Method | LLaMA-3-8b | LLaMA-3-70b | Phi-3
---|---|---|---
Few-Shot | .75$\pm$.00 | .76$\pm$.00 | .60$\pm$.00
CoT | .59$\pm$.02 | .75$\pm$.02 | .62$\pm$.01
Rhetoric (ours) | .68$\pm$.03 | .78$\pm$.01 | .71$\pm$.02

Table 3: Accuracy metrics for the Dimension dataset.

Table 4 shows our results for the relation dataset. For both models, the
rhetoric method improved significantly over the baselines. With LLaMA-3-70b
getting the overall best capabilities for recognizing figurative usage.

Method | LLaMA-3-8b | LLaMA-3-70b | Phi-3
---|---|---|---
Few-Shot | .38$\pm$.00 | .52$\pm$.00 | .49$\pm$.00
CoT | .45$\pm$.01 | .53$\pm$.01 | .51$\pm$.03
Rhetoric (ours) | .52$\pm$.02 | .59$\pm$.02 | .56$\pm$.01

Table 4: Accuracy metrics for the Relation dataset.

In Table 5, the accuracy is tied between few-shot and rhetoric for LLaMA-3-8b,
while for Phi-3 is 10 points better. This task is particularly more difficult
than the rest for LLMs.

Method | LLaMA-3-8b | LLaMA-3-70b | Phi-3
---|---|---|---
Few-Shot | .37$\pm$.00 | .36$\pm$.00 | .30$\pm$.00
CoT | .34$\pm$.03 | .35$\pm$.00 | .30$\pm$.02
Rhetoric (ours) | .37$\pm$.03 | .39$\pm$.01 | .40$\pm$.02

Table 5: Accuracy metrics for the Orientation dataset.

In Appendix C we provide a correlation plot across models and prompting
strategies, we can observe that the Rhetorics method generate the lowest
correlation between strategies. This evidence points out that the initial bias
of the model for inferring change in meaning is very different from the
current established methods in linguistic literature.

##  5 Discussion

In the boxes below, we present some cherry-picked cases of the reasoning
approach with rhetoric devices. This illustrates how the method can improve
over no reasoning.

Example #54 cup • He drank a cup of coffee. • He borrowed a cup of sugar. In
sentence 1, it is used with the sense of a container. — In sentence 2, it is
used with the sense of an amount. — "He drank a cup of sugar." Both sentences
use ’cup’ with different meanings. A: different

In the example above the CoT and rhetorics method inference ‘cup’ in the
second sentence is used for “an amount”, instead of “a container”. However,
the rhetorics method differs by generating a zeugma that helps make clear why
the senses don’t work, as drinking a cup of sugar sounds absurd.

Example #9 battle • During the course of this battle, four Canadian soldiers
were wounded. • I call on him not to let the battle of hierarchies within the
directorates-general prevent this from being implemented. In the first
sentence, ’battle’ is used literally, referring to a fight or conflict. — In
the second sentence, ’battle’ is used metaphorically to represent a struggle
or conflict between different groups or factions. — The word ’battle’ is
related to the first sentence as a metaphor. A: metaphor

For the figurative prompt, the Phi-3 model enriched the prompt with a
reasonable inference for the second sentence, with this information the model
could correctly relate the senses as a metaphorical variation.

Example #167 salt • She was salty because of what happened yesterday. • She
salts her lectures with jokes. In sentence 1, ’salty’ is used to describe
someone who is angry or upset. — In sentence 2, ’salts’ is used to describe
the act of adding flavor to something, in this case, a lecture. — I’d rather
have a lecture with jokes than be angry or upset. The second sense is more
positive. A: positive

The orientation prompt forces an order between the senses, making comparing
non-trivial perceptions of good and bad feasible. In the example above, the
model is instructed to use antanagoge and then impersonate a preference over
both scenarios; this allows it to correctly classify the second sense as more
positive.

The illustrative examples demonstrate that LLMs can retrieve stored cultural
knowledge and enrich prompts, allowing in-context learning to utilize more
information for decision-making. However, in some cases, they fail to
correctly manipulate senses to produce zeugma, and sometimes the conclusions
are inconsistent with the reasoning. We have detailed these failure cases in
Appendix A.

This observation aligns with well-documented phenomena: LLMs can hallucinate
and generate incorrect reasoning even if they arrive at the correct answer Ye
and Durrett (2022). Other failure cases may involve the leakage of evaluation
data and the confusion of generalization with memorization, as it is difficult
to verify whether an LLM-generated figurative usage explanation is novel or
directly derived from training data.

Meaning is a fundamental open question in NLP. While LLMs can often replicate
human-like behavior by relying heavily on form, they struggle with simpler
tasks that require basic understanding of meaning Berglund et al. (2023).
Understanding how models deal with meaning in controlled settings (such as
comparing a word with itself) is crucial for enabling models to generalize
beyond mere form.

While rhetorical devices are standard tools in linguistics, our understanding
of their cognitive and psychological effectiveness is still evolving. By using
LLMs, we can better test theories and explore how humans relate meanings
through language, further advancing our understanding in this area.

##  6 Limitations

Our sentences were carefully selected to enable a concrete understanding of
the word’s meaning in the context; if the method is applied in under-
contextualized sentences, it can result in wrong sense disambiguation, leading
to a bad overall performance. We evaluated our approach on LLMs optimized for
English; while the methodology applies to other languages, the quality of
characterization may differ. LLMs can hallucinate on generating explanations,
so the generated rationale may not reflect the correct cognitive likeness
between senses even when it correctly characterizes the change.

##  7 Conclusion

In this paper, we exploited the vast amount of cultural knowledge in LLMs to
relate and characterize the word’s meaning change for different contexts.
Hereafter, we experimentally observed that rhetoric devices can help LLMs to
mimic human meaning associations, enabling semantic change characterization.

LLMs has many rhetoric examples in its training data, which are not trivially
detected. In future works, we expect to explore in depth if LLMs can produce
new rhetoric associations or if it’s just reproducing its training data, this
task can be investigate through non conventionalized metaphor or
circumstantial metonymy.

Another important aspect to investigate is how to better prompt language model
for figurative reasoning if it can perform better by providing all forms of
metaphors (instrumentality, container, etc.) Lakoff and Johnson (2008) and
metonymies (part-whole, cause-effect, etc.) Lakoff and Johnson (2008) as
examples. We also expect to extend the DUREL approach to automatize the
characterization of semantic change.

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##  Appendix A Negative Examples

In this section, we present some examples where the model failed to produce
the correct form or to give an answer over the correctly produced reasoning.

###  A.1 Dimension

Below are some examples of dimension data:

Example #44 come • Come out of the closet! • He came singing down the road. In
sentence 1 it is used with the sense of emerge. — In sentence 2 it is used
with the sense of move in a certain direction. — "He came out of the closet
singing." The word ’come’ doesn’t make a bad pun, but it has different senses.
It is still different. A: different

In the example above, the zeugma was not correctly constructed, and it ignored
the instruction, which only makes sense if it makes a bad pun.

Example #67 do • All you ever do is surf the Internet. • A ’B’ grade doesn’t
suffice to get me into medical school. In sentence 1 it is used with the sense
of an action. — In sentence 2 is used with the sense of to suffice, to be
enough. — "A’ B’ grade does not suffice for me to do what I want." The word
’do’ makes a bad pun, so is different. A: different

In the example above, it failed to build a zeugma using both contexts, even
though the answer is correct.

###  A.2 Orientation

Below are some examples of orientation data.

Example #67 do • He do not resent they supervision or person ’s sometimes
tiring sympathy. • The group exhibit more concern over the possibility of the
abolitionist make a martyr of person than it do over the development of
sympathy for he. In the first sentence, ’sympathy’ is used in a negative
context, indicating annoyance or irritation. — In the second sentence,
’sympathy’ is used to express understanding or concern. — Expressing
understanding or concern (second sentence) is more positive than feeling
annoyed or irritated. A: positive

While the answer was correct, in the example above, the model didn’t use
antithesis for ordering senses.

##  Appendix B Inference Settings

Given hardware constraints, we used the gguf version of the models with
llama.cpp555https://github.com/ggerganov/llama.cpp library. In the Phi-3 (mini
version), we used the 4k context with fp16 quantization. LLaMA-3-8b we used
8bit quantization and LLaMA-3-70b, 2bit quantization. All model weights were
obtained from HuggingFace666https://huggingface.co/models.

We did all the experiments on a Tesla V100 with 32GB RAM. The inference for
all the models and prompts took less than four days.

##  Appendix C Correlation Across Prompt Strategies and Models

In this section, we present the correlation plot between judgments across
different models and different prompts.

Figure 5: Correlation for Few-shot prompting. Figure 6: Correlation for CoT
prompting across models. Figure 7: Correlation for Rhetorics prompting across
models. Figure 8: Correlation for Phi-3 model across strategies. Figure 9:
Correlation for LlaMA-3-8b model across strategies.

In Figure 10 we observe that few-shot and CoT approaches are highly
correlated.

Figure 10: Correlation for LlaMA-3-70b model across strategies.

##  Appendix D Detailed Prompts

In the figures below, we show the detailed prompt for each type of
characterization.

Sense Differentiation You are presented with two sentences that both contain a
specific word. Your task is to analyze how this word is used in each sentence
and determine if its usage in the second sentence represents the same sense
with respect to its use in the first sentence. Follow these steps to complete
the task: • Step 1. Describe the meaning of the word in the first sentence. •
Step 2. Describe the meaning of the word in the second sentence. • Step 3.
Write a sentence that joins both sentences using zeugma and the same shared
word while preserving the same sense. If the construction make a bad pun, the
words have different sense. • Step 4. Based on the previous reasoning give
your final answer: ’identical’ or ’different.’ [Few-shot examples.] Figure 11:
Prompt for sense differentiation in the dimension dataset. The model is
instructed to perform a zeugma association between senses to reason if it has
a identical or different sense Sense Figurativeness You are presented with two
sentences that both contain a specific word. Your task is to analyze how this
word is used in each sentence and determine if its usage in the second
sentence represents a metaphor or a metonymy with respect to its use in the
first sentence. Follow these steps to complete the task: • Step 1. Describe
the meaning of the word in the first sentence. • Step 2. Describe the meaning
of the word in the second sentence. • Step 3. Compare the uses, determining if
the second is related as a metaphor (where the word is used in a similar but
non-literal sense), as a metonymy (where the word represents something closely
related to or associated with it), or unrelated, used with a different sense.
• Step 4. Based on the third reasoning, write the final answer, ’metaphor’,
’metonymy’, or ’unrelated.’ [Few-shot examples.] Figure 12: Prompt for
figurative sense in the relation dataset. The model is instructed to relate
the meanings by association or similarity. Sense Orientation You will be
provided with two sentences that share a common word used with different
senses. Your task is to describe if the second sense for the word is more
positive then the first. Follow this instructions to execute the task: • Step
1. Describe the meaning of the word in the first sentence. • Step 2. Describe
the meaning of the word in the second sentence. • Step 3. Leverage the
rhetorical strategy of antithesis, contrasting a negative with a positive, to
weigh why one meaning might be more favorable than the other, or if they stand
neutral. • Step 4. Based on the third reasoning, write the final answer
’negative’, ’positive’, or ’neutral.’ [Few-shot examples.] Figure 13: Prompt
for sense orientation in the orientation dataset. By using antithesis the
model should order the senses polarity using ‘personal preference’
argumentation.

##  Appendix E Annotation

To obtain sentiment labels for the orientation data we relied on human
annotation from volunteer students from a University in Europe where students
have different backgrounds and different native language but English is used
as the main language in their studies. The annotations were anonymously
collected.

We first provided the annotators with the agreement terms: “This is a study on
sentiment perception of polysemous words. This data will be freely available
for research purposes. Inside you’ll be asked to rate how the feeling varies
for a word in different sentences. Your answers will be completely anonymous.
COMPANY will not collect your personal data through this questionnaire and
will not be able to identify you based on your answers. For more information
about COMPANY’s privacy notice please visit our webpage at: URL”

Then we presented a training screen in Figure 14.

Figure 14: Training screen

We prompted the annotators for sentiment analysis with screen Figure 15.

Figure 15: Annotation screen for sentiments.

##  Appendix F Ai Assistants In Research Or Writing

As our native language is not English, we used AI assistants like Grammarly,
ChatGPT, and Gemini to improve vocabulary, grammar, and readability of this
documents and the prompts. We also checked all generated text for
inconsistencies with the original intent and fixed them properly when
identified.

  *[LLMs]: Large Language Model
  *[NLP]: Natural Language Processing
  *[LSC]: Lexical Semantic Change
  *[CoT]: Chain-of-Thougth
  *[LLM]: Large Language Model
  *[WSD]: Word Sense Disambiguation


# Experimental balance energies and isospin-dependent nucleon-nucleon cross-
sections

Sanjeev Kumar  Rajni  Suneel Kumar<EMAIL_ADDRESS>School of Physics
and Materials Science, Thapar University, Patiala-147004, Punjab (India)

###### Abstract

The effect of different isospin-dependent cross-section on directed flow is
studied for variety of systems(for which experimental balance energies are
available) using an isospin-dependent Quantum Molecular Dynamic (IQMD) model.
We show that balance energies are sensitive towards isospin-dependent cross-
sections for light systems, while nearly no effect exist for heavier nuclei. A
reduced cross-section $\sigma=0.9\sigma_{NN}$ with stiff equation of state is
able to explain experimental balance energies in most of systems. A power law
behaviour is also given for the mass dependence of balance energy, which also
follow N/Z dependence.

###### pacs:

25.70.-z, 25.75.Ld

††preprint: APS/123-QED

##  I Introduction

The heavy-ion physics branch has been renewed interest very recently. This
ranges from the fusion probabilities Puri92  to symmetry energy dependence at
intermediate energies as well as fragmentation of colliding matter Singh00 .
One observable that has been used extensively for extracting information from
heavy-ion collisions is the collective in-plane flow of various particles
Pan93 ; Sorge97 ; Ollitrauet98 ; Westfall93 ; Pak96 ; Pak97 ; Li96 ; Sood04 ;
Leiwen98 . Apart from transverse in-plane flow, one has also proposed, e.g
differential Li99  and elliptical flow Zhang99  etc.
In general, collective flow in heavy-ion collisions is affected by both the
nuclear mean field potential and nucleon-nucleon (NN) cross-sections. One
should also keep in the mind that reaction dynamics depends also on the
incident energy as well as on the impact parameter of the reaction Westfall93
; Pak96 ; Pak97 ; Li96 ; Sood04 . At low incident energies, reaction dynamics
is dominated by the attractive nuclear mean field potential which results in
deflection to negative angle. Worth mention, at these enegies the phenomenon
fusion, and cluster radioactivity are dominated RGupta93 ; Puri92 . With
increasing incident energy, repulsive nucleon-nucleon scattering becomes
important and results in reduced negative flow caused by the attractive mean
field potential. As a result, at a certain incident energy, called the balance
energy, the in-plane flow vanishes as a result of cancellation between these
two competing effects [10-14]. The composite dependence of the $E_{bal}$ on
the mean field and nucleon-nucleon cross-sections ($\sigma_{NN}$) can be
sorted out by noticing the sensitivity of $E_{bal}$ on the system size, impact
parameter as well as isospin degree of freedom of the reaction [6-10].
Experimentally, balance energy is observed for different systems ranging from
${}^{12}C+^{12}C$ to ${}^{197}Au+^{197}Au$ Westfall93 ; Pak96 ; Pak97 ;
Sullivain90 ; Cussol02 . The very accurate measurement of the $E_{bal}$ in
${}^{197}Au+^{197}Au$ Cussol02  has generated a renewed interest in the field.
Unfortunately, these studies have not provided any significant contribution of
isospin effects towards the balance energy. Later on, Pak et al. Pak97
demonstrated the isospin effect on the collective flow and balance energy at
central and peripheral geometries. These findings were limited only for
${}^{58}Fe+^{58}Fe$ and ${}^{58}Ni+^{58}Ni$ systems. Theoretically, the
disappearance of directed flow is studied using the Boltzmann Uehling
Uehlenbeck (BUU) model. Westfall93 ; Pak96 ; Li99 ; Sullivain90  and Quantum
Molecular Dynamics (QMD) model [3-5,10-21]. Different theoretical attempts
considered either a stiff or soft equation of state along with a variety of NN
cross-sections. Very recently, Puri and co-workers Sood04 , conducted a very
detailed analysis on the balance energy over entire periodic table with masses
between 24 and 394. These study shed light on various aspect of nuclear
dynamics. Unfortunately, this study along with all other studies reported in
literature are limited to Central/Semi-Central Collisions only Sood04 .
Following this work, the detailed analysis on the the semi-central and
peripheral collision is performed by the Puri and co-workers in 2010 Chugh10 .
All these studies indicated enhanced cross-section of 40-55mb with stiff
equation of state to verify the balance energy in intermediate energy heavy-
ion collisions. All these studies were independent of isospin effects. The
first study showing the isospin effects on the collective flow and balance
energy was reported by Li et al.Li96  using the isospin dependent Boltzmann
Uehling Uehlenbeck (IBUU) model, where strong dependence of isospin effects
was observed. In another contribution Zhang99 , they suggested the demand of
reduced isospin dependent cross-section($\sigma=0.88\sigma_{NN}$) to better
explain the experimental data. Chen et al.Leiwen98  studied the effect of
isospin degree of freedom on the balance energy using isospin dependent
Quantum Molecular Dynamics (IQMD) model, which was an improved version of
original QMD model Sood04 ; Aichelin91 ; Singh00 . The calculated results were
found to differ from the data at all colliding geometries. Recently, Gautam et
al. Gautam10  also studied the isospin effect on the balance energy by using
IQMD model Hartnack98 , and also compared their findings with the other
theoretical and experimental findings. They demanded to take care the Gaussian
width(L) and cross-section ($\sigma=0.88\sigma_{NN}$), while studying the
isospin effects in intermediate energy heavy-ion collisions.
From the above, it is cleared that one is demanding an enhanced constant
cross-section Sood04  in QMD model. On the other hand, it is also observed
that the reduced isospin dependent cross-section is valid for the soft as well
as for soft momentum dependent equation of state Zhang99 ; Gautam10  within
IQMD or IBUU model. The systematic concept of enhanced and reduced isospin
dependent cross-sections in the presence of hard equation of state is missing
throughout the literature. Moreover, the effect of isospin dependent cross-
sections are studied on the limited systems experimentally as well as
theoretically Pak97 ; Li96 ; Leiwen98 ; Gautam10 ; Hartnack98 . We plan to
study the effect of enhanced (30 % of $\sigma_{NN}$) as well as reduced (30 %
of $\sigma_{NN}$) isospin dependent cross-sections in the presence of hard
equation of state on the systems for which the experimental finding energy is
predicted in the literature and then will compare the results with
experimental findings. For this study, we will employ isospin dependent
Quantum Molecular Dynamics(IQMD) model which is discussed in sec. II. The
results are discussed in sec. III, followed by conclusion in sec. IV.

##  II ISOSPIN-Dependent QUANTUM MOLECULAR DYNAMICS (IQMD) MODEL

The isospin-dependent quantum molecular dynamics (IQMD) Hartnack98  model
treats different charge states of nucleons, deltas and pions explicitly
Hartnack98 , as inherited from the VUU model Krus85 . The IQMD model has been
used successfully for the analysis of large number of observables from low to
relativistic energies Gautam10 . The isospin degree of freedom enters into the
calculations via symmetry potential, cross-sections and Coulomb interactions
Krus85 . The details about the elastic and inelastic cross-sections for
proton-proton and neutron-neutron collisions can be found in Ref. Hartnack98 .
These cross-sections follow the data published by particle data group (PDG)
for proton-neutron and proton-proton scattering Amsler08 . In this model,
baryons are represented by Gaussian-shaped density distributions

$f_{i}(\vec{r},\vec{p},t)=\frac{1}{\pi^{2}\hbar^{2}}\cdot
e^{-(\vec{r}-\vec{r_{i}}(t))^{2}\frac{1}{2L}}\cdot
e^{-(\vec{p}-\vec{p_{i}}(t))^{2}\frac{2L}{\hbar^{2}}}.$ (1)

Where L is the Gaussian Width. As mentioned in Ref. Hartnack98 , in IQMD the
value of Gaussian width L depends on the size of the system. This system size
dependence of L in IQMD has been introduced in order to obtain the maximum
stability of the nucleonic density profile. Therefore, in the present study,
by checking the stability, we have taken the value from 0.5L to L. Its earlier
version QMD has been very successful in explaining the multifragmentation
Gossiaux97 , temprature and density Khoa92 , flow Kumar98 , multifragments
Singh00  and particle production Huang93 .
Nucleons are initialized in a sphere with radius $R=1.12A^{1/3}$ fm, in
accordance with the liquid drop model. Each nucleon occupies a volume of
$h^{3}$, so that phase space is uniformly filled. The initial momenta are
randomly chosen between 0 and Fermi momentum($\vec{P}_{F}$). The nucleons of
target and projectile interact via two and three-body Skyrme forces, Yukawa
potential, Coloumb interactions. In addition to the use of explicit charge
states of all baryons and mesons a symmetry potential between protons and
neutrons corresponding to the Bethe- Weizsacker mass formula has been
included.
The hadrons propagate using Hamilton equations of motion:

$\frac{d\vec{r_{i}}}{dt}~{}=~{}\frac{d\it{\langle~{}H~{}\rangle}}{d{p_{i}}}~{}~{};~{}~{}\frac{d\vec{p_{i}}}{dt}~{}=~{}-\frac{d\it{\langle~{}H~{}\rangle}}{d{r_{i}}},$
(2)

with

$\displaystyle\langle~{}H~{}\rangle$ $\displaystyle=$
$\displaystyle\langle~{}T~{}\rangle+\langle~{}V~{}\rangle$ (3)
$\displaystyle=$
$\displaystyle\sum_{i}\frac{p_{i}^{2}}{2m_{i}}+\sum_{i}\sum_{j>i}\int
f_{i}(\vec{r},\vec{p},t)V^{\it ij}({\vec{r}^{\prime},\vec{r}})$
$\displaystyle\times
f_{j}(\vec{r}^{\prime},\vec{p}^{\prime},t)d\vec{r}d\vec{r}^{\prime}d\vec{p}d\vec{p}^{\prime}.$

The baryon-baryon potential $V^{ij}$, in the above relation, reads as:

$\displaystyle V^{ij}(\vec{r}^{\prime}-\vec{r})$ $\displaystyle=$
$\displaystyle V^{ij}_{Skyrme}+V^{ij}_{Yukawa}+V^{ij}_{Coul}+V^{ij}_{sym}$ (4)
$\displaystyle=$
$\displaystyle\left(t_{1}\delta(\vec{r}^{\prime}-\vec{r})+t_{2}\delta(\vec{r}^{\prime}-\vec{r})\rho^{\gamma-1}\left(\frac{\vec{r}^{\prime}+\vec{r}}{2}\right)\right)$
$\displaystyle+~{}t_{3}\frac{exp(|\vec{r}^{\prime}-\vec{r}|/\mu)}{(|\vec{r}^{\prime}-\vec{r}|/\mu)}~{}+~{}\frac{Z_{i}Z_{j}e^{2}}{|\vec{r}^{\prime}-\vec{r}|}$
$\displaystyle+t_{6}\frac{1}{\varrho_{0}}T_{3}^{i}T_{3}^{j}\delta(\vec{r_{i}}^{\prime}-\vec{r_{j}}).$

Here $Z_{i}$ and $Z_{j}$ denote the charges of $i^{th}$ and $j^{th}$ baryon,
and $T_{3}^{i}$, $T_{3}^{j}$ are their respective $T_{3}$ components (i.e. 1/2
for protons and -1/2 for neutrons). Meson potential consists of Coulomb
interactions only. The parameters $\mu$ and $t_{1},.....,t_{6}$ are adjusted
to the real part of the nucleonic optical potential. For the density
dependence of nucleon optical potential, standard Skyrme-type parametrization
is employed. The choice of equation of state (or compressibility) is still
controversial one. Many studies advocate softer matter, whereas, much more
believe the matter to be harder in nature Krus85 ; Mage00 . For the present
analysis, a hard (H) equation of state, has been employed along with standard
energy dependent cross-sections. Note that the relativistic effects are
neglisible at these enegies Lehmann93 .

##  III Results and Discussion

We study the directed flow using a stiff equation of state along with enhanced
and reduced isospin dependent cross-sections ($\sigma$= 0.7 to 1.3
$\sigma_{NN}$), by simulating various reactions. The time evolution of
reaction is follow upto 200 fm/c. This is the time at which transverse in-
plane flow saturates for lighter as well as for heavier systems. For this
study, the reactions of ${}^{12}C_{6}~{}+~{}^{12}C_{6}$ ($\hat{b}=0.4$,
L=0.5L) where L=8.66 $fm^{2}$, ${}^{20}Ne_{10}~{}+~{}^{27}Al_{11}$
($\hat{b}=0.4$, L=0.5L), ${}^{40}Ar_{18}~{}+~{}^{45}Sc_{21}$ ($\hat{b}=0.4$,
L=0.5L), ${}^{40}Ar_{18}~{}+~{}^{51}V_{23}$ ($\hat{b}=0.3$, L=0.5L),
${}^{86}Kr_{36}~{}+~{}^{93}Nb_{41}$ ($\hat{b}=0.4$, L=0.6L),
${}^{64}Zn_{30}~{}+~{}^{58}Ni_{28}$ ($\hat{b}=2fm$, L=0.6L),
${}^{93}Nb_{41}~{}+~{}^{93}Nb_{41}$ ($\hat{b}=0.3$, L=0.7L),
${}^{129}Xe_{54}~{}+~{}^{118}Sn_{50}$ ($\hat{b}=0-3fm$, L=0.7L),
${}^{139}La_{57}~{}+~{}^{139}La_{57}$($\hat{b}=0.3$, L=0.8L),
${}^{197}Au_{79}~{}+~{}^{197}Au_{79}$($\hat{b}=2.5fm$, L=L) are simulated. The
choice of impact parameter is guided by the experimentally extracted
information Westfall93 ; Pak96 ; Pak97 ; Sullivain90 ; Cussol02 . The above
reactions were simulated between 45 and 200 MeV/nucleon using the hard
equation of state along with different isospin dependent cross-sections. We
have attempted to fit the reduced isospin dependent cross-sections in the
presence of stiff equation of state with experimental findings, as is
performed in the literature with soft equation of state with and without
momentum dependent interactions.
There are two methods in the literature used to find the balance energy Sood04
. In the first case, the balance energy is extracted from the $\langle
P_{x}/A\rangle$ Plots, where $\langle P_{x}/A\rangle$ is to plotted as a
function of rapidity distribution $Y_{c.m.}$/$Y_{beam}$, which is given as.

$Y(i)=\frac{1}{2}~{}ln\frac{E(i)+P_{z}(i)}{E(i)-P_{z}(i)}$ (5)

where E(i) and $P_{z}(i)$ are respectively, the total energy and longitudinal
momentum of $i^{th}$ particle. Naturally, the energy at which this flow passes
through zero is called balance energy. The second method is to study the
incident energy dependence of the directed transverse in-plane flow $\langle
P_{x}^{dir}\rangle$, which is defined as Sood04

$\langle P_{x}^{dir}\rangle=\frac{1}{A}\sum_{i}^{A}sign\\{Y(i)\\}P_{x}(i)$ (6)

where Y(i) is the rapidity distribution as discussed above and $P_{x}(i)$ is
the transverse momentum of the $i^{th}$ particle in x-direction. This $\langle
P_{x}^{dir}\rangle$ is defined over entire rapidity region and therefore
expected to present an easier way of measuring the in-plane flow rather than
complicated $\langle P_{x}/A\rangle$ plots. In the present study, we have
tried to study the effect of isospin dependent cross-sections on the flow or
alternatively on the balance energy by using both of the parameter and then
the detailed study is extended with later one.

Figure 1: The averaged $\langle P_{x}/A\rangle$ as function of the rapidity
distribution. Here we display the result for Kr+Nb system at different
incident energies and different isospin-dependent cross-sections. Figure 2:
As in 1, but for different system and at particular cross-section
$\sigma=0.9\sigma_{NN}$. Diffrent panels are at diffrent incident energies.
Figure 3:  Time evolution of $\langle P_{x}^{dir}\rangle$ for different
systems at E=60 MeV/nucleon. The different lines in figure representing the
directed fow at different cross-sections. Figure 4:  Time evolution of
$\langle P_{x}^{dir}\rangle$ for different systems at E=200MeV/nucleon. The
different lines in figure representing the directed fow at different cross-
sections. Figure 5:  Energy dependence of the directed nuclear flow $\langle
P_{x}^{dir}\rangle$ for different systems. The lines have same meaning as that
in fig 3 and fig 4. Figure 6:  same as in fig 5, but for different systems.
Figure 7:  The shift in balance energy due to cross section as a function of
combined mass of the system. Figure 8:  Balance energy as a function of
combined mass of the system. The experimental points are represented with
stars, QMD+40mb with crossed triangle and present with solid square.  Figure
9:  N/Z dependence of balance energy at $\sigma=0.9\sigma_{NN}$ The curve is
parametrized with power law.

In Fig. 1, we display the change in the transverse momentum $\langle
P_{x}/A\rangle$ as a function of the rapidity distribution at different
incident energies from 60 to 200 MeV/nucleon for
${}^{86}Kr_{36}~{}+~{}^{93}Nb_{41}$ systems. The different lines in the figure
are showing the variation with different cross-section values. From the
figure, we see that slope becomes less negative or more positive with increase
in the incident energy. On the other hand, with reduction in the cross-section
($\sigma_{NN}$), slope is getting more negative or less positive, while,
becoming more positive with enhanced cross-section. This indicates that we see
a change in the slope with incident energy and reduced isospin dependent
cross-section. The figure is indicating two values of balance energy i.e.
E=80MeV/nucleon (at $\sigma=0.7\sigma_{NN}$) and around E=60MeV/nucleon (at
$\sigma=0.9\sigma_{NN}$) for ${}^{86}Kr_{36}~{}+~{}^{93}Nb_{41}$ system. As
the experimental balance energy for ${}^{86}Kr_{36}~{}+~{}^{93}Nb_{41}$ is in
the range of 55-60 MeV/nucleon, So one is expecting to follow the whole
dynamics at $\sigma=0.9\sigma_{NN}$.
Further, the detailed analysis of rapidity distribution of transverse momentum
$\langle P_{x}/A\rangle$ for different systems at different energies with
$\sigma=0.9\sigma_{NN}$ is displayed in Fig. 2. The slope is becoming more
positive or less negative with increase in the composite mass of system,
indicating that lighter systems remain in the environment of mean field
compared to NN collisions at any given incident energy. The contribution of
the mean field the and collisions is discussed in detail in Ref. Sood04 . One
also notice that a higher incident energy is needed in lighter cases to
balance the attractive and repulsive forces. This energy is supposed to
decrease with increase in the system mass. Similar findings are also published
by Puri and co-workerSood04 . Note that their study did not take isospin
effects into consideration.
Figures 3 and 4 are displaying the time evolution of the second parameter
$\langle P_{x}^{dir}\rangle$ below (60MeV/nucleon) and above (200MeV/nucleon)
the experimental balance energy, respectively. The results in the figure are
displayed for five different systems and at reduced as well as enhanced
isospin dependent cross-sections. The figures are indicating the similar
scenerio with $\langle P_{x}^{dir}\rangle$ as is depicted with $\langle
P_{x}/A\rangle$. Below the balance energy (in Fig. 3), the directed in-plane
flow is negative during the initial phase of reaction for all the systems
under consideration. This becomes positive at sufficient high incident energy
say E=200 MeV/nucleon (in Fig. 4). These results shows that interaction among
nucleons are attractive during the initial phase of the reaction, which turns
out to be repulsive with increase in the incident energy. These interactions
remain either attractive or repulsive throughout the time evolution depends on
the incident energy, isospin dependent cross-sections as well as composite
mass of the system. It is clear from the figure that directed flow is becoming
more positive or less negative with incident energy, isospin dependent cross-
sections as well as with size of system. There is a sharp transition for each
system from negative to positive directed flow at a particular cross-section.
This particular transition is not possible for ${}^{12}C_{6}~{}+~{}^{12}C_{6}$
system indicates the requirement of other variable like momentum dependent
interaction as well as enhancement in cross-section more then 30 %. If one
compares the figs. 1-4, the same physics of balance energy elaborates with the
$\langle P_{x}/A\rangle$ as well as with $\langle P_{x}^{dir}\rangle$. Out of
these, as discussed earlier, $\langle P_{x}^{dir}\rangle$ is the simple and
more useful quantity, because it is summed over entire rapidity distribution,
that is why, $\langle P_{x}^{dir}\rangle$ is elaborated in detail for the
further study.
To study the influence of reduced as well as enhanced cross-sections on
directed flow $\langle P_{x}^{dir}\rangle$ or alternatively on the balance
energy, in Figs 5 and 6, incident energy dependence of directed flow is
displayed for different systems. The different lines in figure represent the
variation with different cross-sections. The studies with enhanced and reduced
cross-sections are also available in the literature Sood04 ; Zhang99 ;
Gautam10 . The experimental data are represented by stars. The directed flow
goes from negative to positive value with increase in the incident energy.
This is the general trend and is explained many times in the litrature by
taking the concept of mean field and NN cross-sections. On the other hand, the
role of different cross-sections is consistent through the present mass range.
By finding the evidence of reduced cross-sections from Fig. 5, the results are
displayed between (0.7-0.9 $\sigma_{NN}$)values in Fig. 6. The enhanced cross-
section (1.3 $\sigma_{NN}$) gives more positive value followed by the cugnon
cross-section ($\sigma_{NN}$) towards the reduced cross-section (0.7
$\sigma_{NN}$). In other words, with increase in the cross-section value from
(0.7$\sigma_{NN}$-1.3$\sigma_{NN}$), the directed flow is becoming more
positive or less negative. This is due to the reason that with increase in the
cross-section value, probability of reaction to take place increases that
further results increase in the NN collisions and hence more positive value of
the directed flow. This is resulting decrease in the balance energy. The
balance energy is also found to decrease with increase in the composite mass
of the system. This is due to dominance of Coulomb repulsion with an increase
in the composite mass of system. Except for some lighter systems, the cross-
section $\sigma=0.9\sigma_{NN}$ is found to explain the experimental balance
energy nicely. Similar parametrization was also performed by Sood et al.
Sood04  within QMD model. They also found that enhanced cross-section
($\sigma=40mb$) can best explain the data. In contrary, calculation in IQMD
model demand reduced value of cross-sections. The difference is due to the
additional effect of isospin dependent cross-sections in IQMD model Hartnack98
, which were absent in QMD model. As in QMD model, the strength of nn, pp, pp
cross-section is taken equal, while in IQMD,
$\sigma_{np}~{}=~{}3\sigma_{pp}\approx 3\sigma_{nn}$ Hartnack98 . Due to the
different strength of np, pp, nn cross-section in IQMD, additional repulsion
is produced compared to QMD model. This addition repulsion will force the
directed flow to take earlier transition from negative to positive value and
hence will lower the balance energy in IQMD model as compared to QMD for same
cross-section value. That is why, the balance energy that was obtained with
QMD at $\sigma=40mb$ are at $\sigma=0.9\sigma_{NN}$ in IQMD model. This is
first ever parametrization of balance energy with hard equation of state in
the presence of reduced cross-sections with experimental available balance
energy.
By taking the Ref. Sood04  into account, which depicts, that for heavier
colliding nuclei $E_{bal}$ is independent of the cross-section one is
choosing, we have plotted in Fig. 7 the $\Delta E_{bal}$ =
$(E_{bal})_{0.7\sigma_{NN}}-(E_{bal})_{0.9\sigma_{NN}}$ with composite mass of
system. Our findings are also supporting the findings of Ref. Westfall93 ;
Li99 . $\Delta E_{bal}$ is maximum for lighter systems and it goes on
decreasing with system mass. It is also indicating theoretically that balance
energy is almost independent of the nucleon-nucleon cross-section for the
heavier system such as Au+Au, U+U etc.
In Fig. 8, we display the energy of vanishing flow or balance
energy($E_{bal}$) as a function of composite mass of system that ranges from
${}^{40}Ar_{18}+^{45}Sc_{21}$ to ${}^{197}Au_{79}+^{197}Au_{79}$. In this
figure, $E_{bal}$ is showed for the experimental data (open stars), QMD+40mb
(crossed triangle) and IQMD+0.9 $\sigma_{NN}$ (solid squares). All the curves
are fitted with power law of the form $C(A_{TOT})^{\tau}$. The experimental
data are fitted by $\tau=-0.33\pm 0.06$ The balance energy is found to
decrease with the composite mass of the system, which is a well known trend
discussed many times in literature Sood04 . The difference is in the $\tau$
values obtained by different theoretical model. The BUU model report $\tau$
between $-0.28\leq\tau^{th}\leq-0.32$. In another study Westfall93  again with
BUU model $\tau^{th}=-0.41\pm 0.03$. The present calculation depicts the
$\tau$ value $(-0.29\pm 0.06)$, which is close to the experimental $\tau$
value $(-0.33\pm 0.06)$ as compared to QMD+40mb calculation having $\tau$
value $(-0.27\pm 0.17)$. In other words, the present IQMD model with a stiff
equation of state along with $\sigma=0.9\sigma_{NN}$ can explain the data much
better than any other theoretical calculations. The $\sigma=0.9\sigma_{NN}$
explains the data for all nuclei, except for some lighter nuclei. The lighter
nuclei, when checked out, demand for an enhanced cross-sections Sood04 ;
Kumar10  along with momentum dependent interactions Gossiaux97 . Our
calculations about the strength of reduced NN cross-section is in agreement
with earlier calculation, where disappearance of transverse in-plane flow
Gautam10  as well as elliptical flow is parametrized with experimental data
Zhang99 .
We have also tried to fit the balance energy in terms of other parameter such
as the neutron to proton ratio of colliding nuclei. This attempt is shown in
Fig. 9, where balance energy is plotted as a function of N/Z. The $E_{bal}$ is
parametrized with power law of the form $(N/Z)^{\tau}$. The $\tau$ value in
N/Z dependence is $-2.39\pm 0.40$, while in $A_{TOT}$ dependence in Fig. 8 is
$-0.29\pm 0.06$. The $\tau$ value in this case is larger compared to the mass
dependence. The difference in the slopes may be due to different charge to
mass ratio in heavier colliding nuclei.

##  IV Conclusion

By using the IQMD model, we have studied the effect of reduced as well as
enhanced isospin dependent cross-sections on the directed flow and balance
energy. A large number of reactions were studied having mass range from 24 to
394, where experimental balance energy is available. Our calculation with
stiff equation of state and reduced cross-section ($\sigma=0.9\sigma_{NN}$)
are in good agreement with the experimental findings, except for
${}^{12}C_{6}+^{12}C_{6}$. The dependence of isospin dependent cross-sections
get weakens with increase in the size of system. The balance energy is
parametrized with N/Z ratio in terms of power law, which is to be quite
similar with the parametrization of composite mass of system, but the $\tau$
values are different in both of the cases. One could try the balance energy
prediction with enhanced isospin dependent cross-section in the presence of
momentum dependent interaction for ${}^{12}C_{6}+^{12}C_{6}$, which is earlier
studied by Sood et al. Sood04  by using QMD in the presence of momentum
dependent interactions.

###### Acknowledgements.

This work has been supported by the Grant no. 03(1062)06/ EMR-II, from the
Council of Scientific and Industrial Research (CSIR) New Delhi, Govt. of
India.

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