# In War and Peace:
The Impact of World Politics on Software Ecosystems

Raula Gaikovina Kula  Nara Institute of Science and Technology, Japan
<EMAIL_ADDRESS>and  Christoph Treude  University of Melbourne, Australia
<EMAIL_ADDRESS>
(2022)

###### Abstract.

Reliance on third-party libraries is now commonplace in contemporary software
engineering. Being open source in nature, these libraries should advocate for
a world where the freedoms and opportunities of open source software can be
enjoyed by all. Yet, there is a growing concern related to maintainers using
their influence to make political stances (i.e., referred to as protestware).
In this paper, we reflect on the impact of world politics on software
ecosystems, especially in the context of the ongoing War in Ukraine. We show
three cases where world politics has had an impact on a software ecosystem,
and how these incidents may result in either benign or malignant consequences.
We further point to specific opportunities for research, and conclude with a
research agenda with ten research questions to guide future research
directions.

Libraries, Software Ecosystem, Protestware, Supply Chain Attacks

††conference: Submitted ACM Joint to the European Software Engineering
Conference and Symposium on the Foundations of Software Engineering; 14 - 18
November, 2022; Singapore††copyright: acmcopyright††journalyear: 2022††doi:
XXXXXXX.XXXXXXX††price: 15.00††isbn: 978-1-4503-XXXX-X/18/06

##  1\. Introduction

Contemporary software is not built in isolation. With the emergence of third-
party libraries, and massive software repositories, now more than ever
developers are able to quickly adopt functionality into their applications,
avoiding the time-consuming and error-prone task of writing and testing from
scratch.

The success of these libraries is made possible through the concept of Open
Source Software (OSS). OSS allows software to be free for anyone to use, which
is incorporated into everything from independent projects to mainstream,
proprietary consumer software. Being OSS, libraries are typically maintained
by one or a handful of volunteers, and they benefit from having further
volunteer contributors, as generally the developers in a software ecosystem
should be able to help each other by pointing out issues and contributing new
features. Libraries harness the power of distributed peer review and
transparency of process, promising higher quality, better reliability, greater
flexibility, and lower cost. Projects build reputation over time, with
developers gaining trust in using these libraries. Each ecosystem has their
own culture of maintainers, who are empowered to approve and publish
contributed code changes. Evidence of the impact of libraries is seen with the
growing size of NPM with more than one million packages (Mujahid et al.,
2022), for example, and the growing support for these ecosystems, e.g.,
GitHub’s 2020 acquisition of NPM.111https://github.blog/2020-03-16-npm-is-
joining-github/

Problems arise when a maintainer feels empowered to sabotage their own
projects, thus weaponizing their library as protestware, e.g., with the
intention to make users of their library aware of some political stance, or
situation. Responses from practitioners to such protestware have been mixed.
According to a developer blog that was later republished by the IEEE Computer
Society (Benischke, 2022), practitioners have expressed their concerns,
stating that “It’s ill-considered and user-hostile, and can trivially go
wrong. Weaponizing open source to inject malware, no matter how well
intentioned, is still injecting malware”. Others question whether this is Open
Source anymore, as a OSS licence clearly states that there should be “No
Discrimination Against Persons or Groups. The license must not discriminate
against any person or group of persons” (Initiative, 2007). The official
statement from the Open Source Initiative (OSI) community lays the
responsibility to maintainers, stating that “Protest is an important element
of free speech that should be protected. Openness and inclusivity are
cornerstones of the culture of open source, and the tools of open source
communities are designed for global access and participation. Instead of
malware, there are so many outlets for open source communities to be creative
without harming everyone who happens to load the update. Longer term, the
downsides of vandalizing open source projects far outweigh any possible
benefit, and the blowback will ultimately damage the projects and contributors
responsible. Use your power, yes—but use it wisely” (on Protestware, 2007).

The purpose of this article is to point the software engineering research
community to open questions regarding how researchers can investigate,
address, and regulate such kinds of protestware. In light of the War in
Ukraine, we present three motivating scenarios where world politics has had
impact on software ecosystems, highlighting the side affects, and then present
an agenda on how to dissect and respond to such behaviour during software
engineering practices. Another blog (Sharma, 2022) raises growing concerns
within an ecosystem: “Protestware can deliver similar anti-war messages, but
within the open-source community there are worries that the possibility of
sabotage — especially if it goes further than simple anti-invasion messaging
and starts destroying data — can undermine the open-source ecosystem. Although
it is less well known than commercial software, open-source software is
enormously important to running every facet of the internet”. Our vision is
that the lines of research outlined in this article can contribute towards
building resilient and yet open software ecosystems.

In the remainder of the paper, we first introduce three motivating scenarios
related to the War in Ukraine in Section 2 before we briefly discuss
protestware in other contexts in Section 3. Section 4 presents the research
agenda on dissecting the status quo of protestware, increasing open-source
supply chain resilience, and managing trust and responsibiliy in software
ecosystems, and we conclude the paper in Section 5.

##  2\. Motivating Cases

In this section, we discuss three cases where protestware has had an impact on
a software ecosystem. Specifically, we focus on the War in Ukraine, and three
different effects that resulted from maintainers making a political stance.
The first case involves the malignant effects of protestware. The second case
is a benign case where protestware had no malicious intent to harm the users
of a library. In the last case, we take a look at a case where sanctions were
placed on accounts that were related to world politics.

###  2.1. Case 1: Malignant Protestware

A developer of the JavaScript library node-ipc (Web, 2022f), which is used by
the popular vue.js framework, deliberately introduced a critical security
vulnerability that, for some netizens, would destroy their computers’ files.
The library is fetched about a million times a week from the NPM registry, and
is described as an “inter-process communication module for Node, supporting
Unix sockets, TCP, TLS, and UDP”. Seemingly, the maintainer intentionally
changed his code to overwrite the host system’s data, then changed the code to
display a message calling for world peace, as a protest against Russia’s
invasion of Ukraine. GitHub declared this a critical vulnerability, which was
tracked as CVE-2022-23812 (Web, 2022a).

The malicious code was intended to overwrite arbitrary files dependent upon
the geo-location of the user’s IP address, attacking software in specific
locations. Concretely, the affected versions 10.1.1 and 10.1.2 of the library
check whether the host machine has an IP address in Russia or Belarus, and if
so overwrites every file it could with a heart symbol. Version 10.1.3 was
released soon after without this destructive functionality, while 10.1.1 and
10.1.2 were removed from the NPM registry.

There was a strong response from the community, including frustrations that
led to insightful discussions. One example from a contributor on the GitHub
Discussions channel is shown below (Web, 2022b):

> I’m very happy to see that the principles and character of many in tech
> (FOSS especially) remain clear enough to recognize how completely wrong this
> was. Of course, if the marketplace of current things keeps hammering away at
> this, it will benefit a small number of corporate giants (misplaced
> trust/safety). I hope we all start seeing these patterns as we grapple with
> a general blurring of lines between tools for marketing and weaponry. It’s
> essential to ask: what’s the outcome and who benefits? I like to ask the
> faux ideologues “who agrees with you?” “Isn’t it strange how well aligned
> you are with a small number of very visible, influential, and powerful
> organizations?” “What’s the fight and who is on which side, again?” It’s
> about competency, not power. Power feeds and is fueled by egocentrism
> (plainly, weak vanity). Competency comes from discovering your natural gifts
> and applying them.

Another user from that Github Discussion quoted how this affected the Open
Source Community (Web, 2022b):

> The trust factor of open source, which was based on goodwill of the
> developers is now practically gone, and now, more and more people are
> realizing that one day, their library/application can possibly be exploited
> to do/say whatever some random dev on the internet thought was ‘the right
> thing to do’.

The maintainer defended his module on GitHub, saying “this is all public,
documented, licensed and open source”. Earlier, there were more than 20 issues
flagged against node-ipc about its behavior. Some of the comments referred to
the creation as “protestware, while others might call it malware”.

###  2.2. Case 2: Benign Protestware

We present two cases where the protestware does not have malicious intent, but
aims at increasing awareness. For the first case, the same maintainer of the
node-ipc library then created the peacenotwar library (Web, 2022h). As
explained by the maintainer, it serves as a non-violent protest against
Russia’s aggression. Instead of malicious deletion of files, the module adds a
message of peace on users’ desktops (Web, 2022i). The maintainer was quoted in
the README file222https://github.com/RIAEvangelist/peacenotwar:

> I pledge that this module, to the best of my knowledge and skills, does not
> do any damage to anyone’s data. If you do not like what this module does,
> please just lock your dependencies to any of my work or other’s which
> includes this module, to a version you have code reviewed and deemed
> acceptable for your needs. Also, please code-review your other modules for
> vulnerabilities.

When accepted, this code was included:

⬇

1

variable ”putin_khuylo”{

3 description = ”Do you agree that Putin doesn’t respect Ukrainian sovereignty
and territorial integrity? More info:
https://en.wikipedia.org/wiki/Putin_khuylo!”

type = bool

5 default = true}

Another example is given by a maintainer of the terraform modules for AWS who
added their own protest in the licence file, with “Additional terms of use for
users from Russia and Belarus” (Web, 2022j):

> By using the code provided in this repository you agree with the following:
> \- Russia has illegally annexed Crimea in 2014 and brought the war in Donbas
> followed by full-scale invasion of Ukraine in 2022.
> \- Russia has brought sorrow and devastations to millions of Ukrainians,
> killed hundreds of innocent people, damaged thousands of buildings, and
> forced several million people to flee.

These two libraries are examples of protestware that are not intended to be
malignant, compared to the case described in the previous section.

###  2.3. Case 3: Developer Sanctions

The third case is not related to a single library maintainer, but affects a
software ecosystem more broadly. We report two instances. The first is the
decision of MongoDB not to sell its products to Russian buyers (Zhluktenko,
2022), using the following statement:

> The breadth of the new sanctions from the US and internationally is
> unprecedented, and MongoDB has taken action to comply with them. We will not
> sell our cloud services to customers in Russia and Belarus and we will not
> sell any more MongoDB software to customers in Russia or Belarus.

MongoDB’s decision appears to hinge on an interpretation of Western sanctions
that say SaaS subscriptions represent a sale. In order to comply with
sanctions, MongoDB decided it should not continue to offer its wares, not even
as a service. Interestingly, Oracle also stated on
Twitter333https://tinyurl.com/8admb86d that it is ending support for Russian
users, Even Microsoft joined Apple and SAP in suspending sales in
Russia.444https://www.siliconrepublic.com/enterprise/microsoft-sales-russia-
ukraine-cyberattacks

In another instance of developer sanctions, at first GitHub suspended Russian
accounts. According to a blog post from a developer (Web, 2022e), “suspending
an account” on GitHub meant deleting all activity for a user—which results in
(1) every pull request from the suspended account being deleted, (2) every
issue opened by the suspended account being deleted, and (3) every comment or
discussion from the suspended account being deleted. In effect, the user’s
entire activity and history evaporated. The bigger issue was that GitHub had
not provided any warning to the library maintainers. As explained by a
maintainer in a blog post (Web, 2022e):

> I recently took over as a lead maintainer for two popular projects in the
> Apple developer community, Quick and Nimble. I just released version 5.0 of
> Quick a few days ago. During the week leading up to the release, I was
> reviewing and merging many pull requests. But when it came time to write the
> release notes, I noticed very bizarre behavior. Mysteriously, some pull
> requests were deleted. Poof. Gone. Then I realized that an entire
> contributor’s presence had disappeared — all of their comments on issues
> were missing, all of the issues they opened were gone, all of the pull
> requests they opened had vanished. Every piece of activity related to the
> user was gone.

GitHub later reached out to this maintainer, letting them know that it had
restored the missing pull requests, issues, comments, etc. from the Russian
developers whose accounts had been suspended. User profiles were also
restored, although GitHub did not specifically mention that the accounts had
been suspended (Web, 2022d).

##  3\. Other Maintainer Stances

The War in Ukraine is not the first time that open-source maintainers have
used their open source libraries as a platform for protest. For example,
Faker.js555https://fakerjs.dev/ and Colors.js666https://colorjs.io/ created
problems for users of Amazon’s Cloud Development Kit. Big companies, critics
have long said, benefit from open source ecosystems without adequately
compensating developers for their time. In turn, developers responsible for
the software are unfairly strained. The maintainer of these two JavaScript
libraries with more than 21,000 dependent apps and more than 22 million weekly
downloads, intentionally released an update that produced an infinite loop
that caused dependent apps to spew gibberish, prefaced by the words “Liberty
Liberty Liberty”. His stance was made clear in the README file: “Take this as
an opportunity to send me a six-figure yearly contract or fork the project and
have someone else work on it” (Web, 2022c).

These cases show that protestware is not only relevant in the context of
political conflicts, but has a long history of capturing and communicating the
opinions of open source maintainers.

##  4\. Research Agenda

In this section, we present our research agenda. We have presented three
motivating scenarios where world politics has had an impact on a software
ecosystem. These cases form initial evidence on the current state of practice,
and how the nature of open source software and protestware will affect the
software supply chain, trust, and resilience within an ecosystem. In this
context, a software supply chain attack occurs when a compromised library
distributes malicious code to applications that depend on
it.777https://capec.mitre.org/data/definitions/437.html

As discussed in Section 3, there is anecdotal evidence from blogs and
developer discussions on the topic, yet there have been very few research
studies that articulate the impact of protestware on software engineering.
From these motivating cases, the following questions about the possible
implications have emerged. We discuss each of these potential implications
below in turn, and suggest ten research questions that could form the basis of
future research projects.

###  4.1. Dissecting the status quo of protestware

Evidence from this paper shows the thin line that exists between protestware
and malware. As mentioned by the OSI community, protest is an important
element of free speech, with openness and inclusivity being cornerstones of
the culture of open source. However, vandalizing open source projects
threatens any possible benefit, and might damage the projects and contributors
responsible. Our first four research questions target the potential of
protestware.

  1. (1)

How effective is protestware at communicating political messages?

  2. (2)

What is the immediate impact of protestware on a software ecosystem?

  3. (3)

Who is affected by protestware, and what relationship do they have with the
protestware maintainer, if any?

  4. (4)

What mitigation strategies do projects use for securing or repairing their
supply chains, and how effective are those mitigation strategies?

Through in-depth studies of cases such as the ones introduced in Section 2, we
propose research questions aimed at understanding the status quo of
protestware, to build the foundations for further work on increasing
resilience and trust in software ecosystems. We propose to survey developers
that rely on the modified projects to determine whether protestware managed to
achieve its goals of political messaging. Maintainers interested in taking
political action are confronted with dilemmas of instrumental vs. value
rationality, i.e., selecting the most effective and efficient means to reach
given ends (instrumental rationality) or acting without considering the
foreseeable consequences in the service of conviction (value rationality)
(Rutgers and Schreurs, 2006; Oakes, 2003). Is the creation of protestware a
legitimate means to pursue a political agenda? Answers to such questions lie
beyond traditional software engineering research, but we can investigate
whether the message is received as intended, and what its immediate
consequences are. Who is affected? A small number of developers who have a
working relationship with the acting maintainer (e.g., through reciprocal
contributions to each others’ code), or an entire ecosystem? Using case
studies, we can further investigate which strategies other players in a
software ecosystem have employed to work around protestware and/or mitigate
its impact, with the ultimate goal of learning how to increase resilience in
the future.

###  4.2. Increasing supply chain resilience

In response to the attacks on supply chains, the Linux Foundation’s partner
group – Open Source Security Foundation (OpenSSF), Google, and Microsoft
joined forces to work with security experts and use automated security testing
to improve open-source security in a project called the Alpha-Omega Project
(Web, 2022g). This is a global effort to secure code, and has sparked other
efforts such as weak links analysis (Zahan et al., 2022). Hence, our next
three research questions are related to the supply chain.

  1. (5)

How effective are redundancies in supply chains at increasing resilience?

  2. (6)

How do changes which turn libraries into protestware differ from other
software evolution?

  3. (7)

How accurately can we automatically detect protestware?

Efforts to increase supply chain resilience could form a spectrum from manual
efforts to minimise the impact of protestware by reducing the reliance on
external libraries (Xu et al., 2020) or introducing redundancies into supply
chains (Gherbi et al., 2011) to automated tools for protestware detection and
mitigation, similar to vulnerability detection (Li et al., 2016). To pave the
way for automated detection and mitigation, we propose research questions
related to unique characteristics of patches which turn a library into
protestware (e.g., are such patches ‘surprising’ to a language model trained
on past patches? (Caddy et al., 2022)) as well as automated prediction,
borrowing methods from the defect prediction literature (Wan et al., 2018).

###  4.3. Managing trust and responsibility

Prior work has established that the success of a library is based on the
library itself, which involves the assumption of a module’s functional and
non-functional correctness. For instance, system maintainers need to trust the
reliability of non-functional attributes such as security and stability of an
adopted library (Kula et al., 2015). This trust in components is well-known in
other fields, such as Dependable and Secure Computing (Guha et al., 2004;
Hasselbring and Reussner, 2006; Yan and Prehofer, 2011). However, we argue
that trust also falls back on the maintainer. The final three research
questions are aimed at maintainers and their role in an ecosystem as a whole.

  1. (8)

What are the responsibilities of maintainers, as perceived by other
stakeholders in a software ecosystem?

  2. (9)

How does protestware affect trust into a library and entire ecosystems?

  3. (10)

How is protestware regulated at ecosystem level?

Recent anecdotes, such as a Fortune-500 company unabashedly requesting a curl
maintainer’s immediate response about the Log4J vulnerability (Stenberg,
2022), highlight the current confusion about what exactly are the
responsibilities of a great open-source maintainer (Dias et al., 2021). The
recent emergence of protestware only adds to this confusion—do maintainers act
irresponsibly if they use open source for political action? We propose to
capture the perceptions of different players in a software ecosystem about
these responsibilities and how protestware can affect trust in single
libraries or entire ecosystems. It is important that software ecosystems are
resilient to threats against their culture, thus becoming sustainable (Kula
and Robles, 2019). As mentioned in Section 1, open source licences contain
statements about discrimination (Initiative, 2007), but they are not explicit
about protestware. We also propose to investigate how codes of conduct
(Tourani et al., 2017) at project and ecosystem level can play a role in
regulating the management of protestware.

##  5\. Discussion and Conclusion

Protests are a powerful way for people to make their voices heard. They can be
used to call attention to injustices, and to demand change. In the world of
open source software, protests take the form of “protestware”. This is
software that is released in protest against a particular decision or action
by an open source project. In highly inter-connected and large software
ecosystems, where the average package can directly depend on more than five
other packages (NPM (Kula et al., 2017)), the impact of protestware on the
entire ecosystem can be devastating, especially if it is malignant in nature.
Using the context of the ongoing War in Ukraine, we have argued how and why
protestware does have an impact on software ecosystems, and we have outlined a
comprehensive research agenda for understanding and addressing protestware and
its implications on ecosystem resilience, trust, and responsibility.

To answer the research questions posed above, we need a systematic research
approach. To confirm the anecdotal evidence, we need methods to define and
detect different forms of protestware. Perceptions of developers as well as
viewpoints of large Fortune-500 companies would need to be sought, e.g., via
surveys or interviews. Furthermore, political stances can become a sensitive
topic, so care needs to be taken in the design on how to effectively gather
and interpret our results.

Our hope is that answering these questions will help us understand how to
sustain and build resilient software ecosystems.

## Acknowledgement

This work is supported by Japanese Society for the Promotion of Science (JSPS)
KAKENHI Grant Numbers 20K19774 and 20H05706.

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# Analysis of 2-Body Central Events for ${}^{129}Xe+^{nat}Sn$ from $8A$ $MeV$
up to $18A$ $MeV$ and for ${}^{129}Xe+^{197}Au$ at $15A$ $MeV$ and $18A$
$MeV$.

L. Manduci  Ecole des Applications Militaires de l’Energie Atomique, BP 19
50115, Cherbourg Armées, France  Normandie Univ, ENSICAEN, UNICAEN,CNRS/IN2P2,
LPC Caen, 14400 Caen, France  O. Lopez, D. Durand, R. Bougault, E. Vient
Normandie Univ, ENSICAEN, UNICAEN,CNRS/IN2P2, LPC Caen, 14400 Caen, France  M.
Pârlog  Normandie Univ, ENSICAEN, UNICAEN,CNRS/IN2P2, LPC Caen, 14400 Caen,
France  ”Horia Hulubei” National Institute of Physics and Nuclear Engineering
(IFIN-HN), RO-077125 Bucharest Magurele, Romania  B. Borderie  Université
Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France  I. Lombardo  INFN
Sezione di Catania, via Santa Sofia 64, I-95123 Catania, Italy  G. Verde
Laboratoire des 2 Infinis - Toulouse (L2IT - IN2P3), Universit de Toulouse,
CNRS, UPS, F-31062 Toulouse Cedex 9 (France)  INFN Sezione di Catania, via
Santa Sofia 64, I-95123 Catania, Italy

(April 2022)

###### Abstract

Background

Study of medium-mass heavy-ion reactions leading to two fragments in the exit
channel from barrier to 18A MeV.

Purpose

A special focus is made on fission and quasi-fission for events with two
fragments ($Z\geq 10$) in the exit channel selected with a specific
observable.

Method

Reactions induced by ${}^{129}Xe$ projectiles on ${}^{nat}Sn$ and on
${}^{197}Au$ at energies ranging from $8A$ MeV to $18A$ MeV were analyzed.
Using the fragment ($Z\geq 10$) multiplicity equal to 2 and the requirement
that the total detected charge to be $90\%$, fission and quasi-fission events
were studied for the lowest beam energies using the fission fragment charge
distributions, the total kinetic energy distribution (TKE) and its standard
deviation $\sigma_{TKE}$.

Results

For the lighter system it is still possible to observe fission events from
incomplete fusion. At variance, for the heavier system, Xenon on gold target
only quasi-fission is evidenced.

Conclusions

The study of the events characterized by two fragments in the final channel
shows that fission, related to fusion in the entrance channel, disappears
around 20A MeV for both systems. At lower energies (8A, 12A and 15A MeV) for
the Sn target, an evolution with increasing energies towards an asymmetric
fission mode is displayed in the fragment charge distributions. This trend can
be attributed to the increasing angular momentum as indicated by the out-of-
plane angular distribution for light charged particles. The same effect is
also observed in the case of the gold target at 15A MeV. However, for this
heavier system, a strong memory of the entrance channel leading to quasi-
fission is evidenced. A comparison with the Viola systematics, moreover, shows
a deviation, greater for the heavier system than for ${}^{129}Xe+^{nat}Sn$
system. For this latter, at the lower beam energies (8A MeV and 12A MeV) the
average Total Kinetic Energy (TKE) shows a behavior close to the Viola
systematics, despite the high excitation energies reached in these reactions
compared with the ones in previously published studies. The TKE dispersion
$\sigma^{2}_{TKE}$ as well shows the same trend. A complete understanding of
the above results would certainly require precise model calculations at these
energies.

##  I Introduction

The present work concentrates on events with two fragments in the exit
channel. It continues the study on the reaction mechanisms of the nearly
symmetric system ${}^{129}Xe+^{nat}Sn$ at incident energies 8A, 12A, 15A, 18A
MeV based on the selection with the variable $E_{Iso}^{Max}$ discussed in
reference PRC_Manduci .

The basic assumption made here is the formation of a composite system through
a fusion (or incomplete fusion) reaction and its subsequent de-excitation by
particles and intermediate mass fragments evaporation or fission for energies
lower than 20 A MeV.
Following the Bohr hypothesis bohr , the two processes can be decoupled :
compound nucleus formation and compound nucleus decay once the excitation
energy has been distributed to all degrees of freedom. This scenario is
observed at low bombarding energies, i.e. close to the barrier. Due to the
involved scale, the composite system does not retain any memory of the
entrance channel with the exception of the excitation energy and the angular
momentum. When it undergoes fission, two fragments are then emitted. These
latter may be of nearly equal size. In this case, the macroscopic Liquid Drop
Model (LDM) Wei  accounts for their formation. In the description of the
nucleus as a classical and incompressible liquid drop, the repulsive Coulomb
interaction and the attractive surface energy of the two fragments create a
smooth Potential Energy Surface (PES). Here, the deformed and excited system
can just follow one trajectory : the one towards a break up into two equal
fragments. However, most of the time these fragments are different in size
(asymmetric fission) and the LDM alone can not explain this mass asymmetry.
The description of the asymmetric fission needs the inclusion of microscopic
effects, such as shell effects or pairing, to consider the influence of the
neutron and proton shell closures. These corrections create a PES with
different valleys (depending on the entrance energy, the asymmetry and the
total mass of the initial system) that the system may follow giving as final
state a symmetric or/and an asymmetric fission karpov . However there is
evidence that shell effects are negligible for higher excitation energies
because the PES reverts to a smooth surface with a symmetric fission as in the
case of the LDM potential and the compound nucleus will fission mostly
symmetrically andreyev .

For medium-heavy systems ($Z_{P}Z_{T}<1600$, where $Z_{P}$ and $Z_{T}$ are,
respectively, the projectile and the target atomic number) at energies above
the Coulomb barrier, a compound nucleus is easily formed. For heavier systems,
instead, the Coulomb repulsion is responsible for the re-separation process
with a large probability. In this process, an important nucleonic transfer
occurs between the two colliding nuclei and they finally re-separate without
forming a compound nucleus. This process is called quasi-fission (QF) and is
in competition with the fusion-fission process. It becomes the dominant
mechanism for very heavy systems for which the product of the projectile
charge multiplied by the target charge exceeds $Z_{P}Z_{T}>1600$ (toke -hagino
). In this regard, the ”orientation effect” may determine the final products
of the collision : because of the static deformation of the two nuclei (or of
just one of them) there is a variation in the Coulomb barriers whether if the
collision occurs as ”equatorial-side” (higher Coulomb barrier) or ”pole-
side”(lower Coulomb barrier) contact; in this case it is enhanced in a
collision with a heavy deformed prolate nucleus. In the first case the
reaction may result in symmetric fission while in the second case quasi-
fission (QF) sets up giving asymmetric mass distributions nishio .

For this study, to better understand the role of the system mass, we also
studied the heavier system ${}^{129}Xe+^{197}Au$ at 15A and 18A MeV. For the
system ${}^{129}Xe+^{nat}Sn$ the product of the atomic charges of the
projectile ($Z_{P}$) and the target ($Z_{T}$) is $Z_{P}Z_{T}=2700$ and for the
system ${}^{129}Xe+^{197}Au$ is $Z_{P}Z_{T}=4266$ are larger than the quasi-
fission threshold value. This means that these systems should present features
typical of the quasi-fission. In the framework of the extra-push model, Bass
gave the expression of the fissility effective parameter, $x_{eff}$, which is
linked to the entrance channel and is a measure of the competition between the
Coulomb interaction to the nuclear potential bass , swiat . If this parameter
is greater than 1 no fusion pocket exists and the compound nucleus cannot
therefore be formed. For reactions with the $Sn$ target this parameter is
$x_{eff}^{Sn}=0.898$ while for the $Au$ target its value is
$x_{eff}^{Sn}=1.116$. In the first case the fusion pocket can exists, while in
the second one fusion is disfavoured. In a recent study by R. du Rietz rietz
an average fissility parameter ($x_{m}=0.75x_{eff}+0.25x_{CN}$ where $x_{eff}$
is the Bass effective fissility parameter and $x_{CN}$ is the fissility
compound nucleus for complete fusion) was proposed. For values $x_{m}>0.68$ QF
sets on while for values $x_{m}>0.765$ QF dominates. Since for
${}^{129}Xe+^{nat}Sn$, $x_{m}^{Sn}=0.676$ and for ${}^{129}Xe+^{197}Au$,
$x_{m}^{Au}=0.840$, we expect that quasi-fission dominates for the heavier
system. Another criterion, such as the comparison of the entrance channel
asymmetry (which is correlated with the fusion probability) for both systems
compared with the Businaro-Gallone mass asymmetry busi , goes in the same
direction : the presence of quasi-fission.

In the following, after a short presentation on the experiment and on the
INDRA multidetector, we will discuss the observable used to select the events
and in the fourth paragraphe we will discuss the events with two fragments in
the final state and compare the two systems.

##  II The Experiment

$E_{Beam}/A$ $(MeV)$ |  $E_{c.m.}$ $(MeV)$ | $E_{c.m.}/V_{C}$ | $v_{Lab}$ | $v_{c.m.}$ | $\Theta_{gr}^{\circ}$
---|---|---|---|---|---
$8$ | $494.6$ | 1.8 | $3.90$ | $2.04$ | $22.13$
$12$ | $741.6$ | 2.7 | $4.77$ | $2.50$ | $12.84$
$15$ | $926.6$ | 3.4 | $5.32$ | $2.79$ | $9.79$
$18$ | $1111.5$ | 4.0 | $5.81$ | $3.05$ | $7.91$
$20$ | $1234.6$ | 4.5 | $6.12$ | $3.21$ | $7.02$
Table 1:  Kinematic characteristics for the ${}^{129}Xe+^{nat}Sn$ system at different incident energies. The laboratory velocity $v_{Lab}$ and the center mass velocity $v_{c.m.}$ are in $(cm/ns)$. $E_{Beam/A}$ $(MeV)$ |  $E_{c.m.}$ $(MeV)$ | $E_{c.m.}/V_{C}$ | $v_{Lab}$ | $v_{c.m.}$ | $\Theta_{gr}^{\circ}$
---|---|---|---|---|---
$15$ | $1167.3$ | 2.9 | $5.32$ | $2.12$ | $14.98$
$18$ | $1400.3$ | 3.4 | $5.81$ | $2.33$ | $12.02$
Table 2:  Kinematic characteristics for the ${}^{129}Xe+^{197}Au$ system at
different incident energies. The laboratory velocity $v_{Lab}$ and the center
mass velocity $v_{c.m.}$ are in $(cm/ns)$.

The present study concerns the analysis of the data recorded during the
$5^{th}$ INDRA campaign for reactions induced by ${}^{129}Xe$ projectiles on
self-supporting (350 $\mu g/cm^{2}$ thick) ${}^{nat}Sn$ targets at different
beam energies $E_{Beam}/A$ = 8, 12, 15, 18 MeV with trigger multiplicity
$M_{trig}=1$. We will use also the data from the reactions induced by
${}^{129}Xe$ on gold target at E/A = 15, 18 MeV ($M_{trig}=1$) for comparisons
with an heavier and asymmetric system. The apparatus covered angles are from
$3^{\circ}$ to $180^{\circ}$.

The experiment was performed at GANIL (Caen, France). The description of the
experiment and the apparatus may be found in references pouthas1 ; pouthas2 ;
tabacaru ; parlog1 ; parlog2 ; tassan ; oli .

INDRA can measure ion charge and energy in a wide range and can resolve masses
up to $Z=4$. Unit charge resolution was obtained up to $Z=20$ for heavy
products stopping in the ion chamber-silicon-CsI telescopes, less than 5 units
for $Z=80$. The energy identification threshold is $\simeq 1$ MeV/nucleon for
light fragments and $1.5-1.7$ MeV/nucleon for fragments of $Z=50$.

Tables 1 and 2 display the kinematical characteristics of both systems,
${}^{129}Xe+^{nat}Sn$ and ${}^{129}Xe+^{197}Au$ respectively, at the different
beam energies . The Coulomb barrier, calculated with the Bass formula Bass ,
for the Sn target at interaction radius amounts $V_{C}\simeq 275$ MeV whereas
for the ${}^{197}Au$ target it is $V_{C}\simeq 406$ MeV. As it appears from
the ratio of the available energy in the centre of mass $E_{c.m.}$ to the
Coulomb barrier $E_{c.m.}/V_{C}$, in the third column of both tables 1 and 2,
the reactions are always produced above Coulomb barrier.

##  III Event selection

Figure 1: Second heavier fragment parallel velocity to the beam direction in
the centre of mass frame for incident energies from 8A to 20A MeV for events
selected with both conditions : complete events and $E_{Iso}^{Max}\leq 0$ for
the system ${}^{129}Xe+^{nat}Sn$.

In order to select events with marked fusion characteristics, the kinematical
global observable $E_{Iso}^{Max}$ (PRC_Manduci ) in term of the velocity
components of the heaviest fragment in the event, was used. This observable is
defined as :

$E_{iso}^{max}=V_{\parallel,max}^{2}-0.5V_{\perp,max}^{2}(1+sin2\phi)$ (1)

where $V_{\parallel,max}$ and $V_{\perp,max}$ are the velocity components of
the heaviest fragment in the centre of mass (CM) parallel and orthogonal to
the beam direction and $\phi$ is its azimuthal angle.
In reference PRC_Manduci , the $E_{Iso}^{Max}$ observable was used to select
fusion events and to estimate the fusion cross section for each beam energy.
It was shown that the condition $E_{Iso}^{Max}\leq 0$ selects one half of the
events with marked fusion and incomplete fusion characteristics.
The condition $E_{Iso}^{Max}\leq 0$ alone does not provide a well selected
event sample. In fact, when summing up the events for computing the cross
section it is reasonable to accept a broader sample constitued also by
incomplete events. The above condition on $E_{Iso}^{Max}$ selects also events
which had been only partially measured in charge and momentum, i.e. events for
which some fragments or particles were not detected.
The additional constraint on the total detected charge ensures that the events
are well detected. The selected events therefore will satisfy both
requirements : ”Complete Events and $E_{Iso}^{Max}\leq 0$ ”.
By ”Complete Events ” we mean all the events for which nearly the whole
charges produced and their energies were correctly measured. They will be
selected by imposing that :

  * 1)

the total event charge $Z_{tot}$ (sum of all the charges of the particles and
fragments belonging to the event) is larger than $90\%$ of the initial
channel.

  * 2)

the total event pseudo-momentum parallel to the beam direction component :

$P_{Tot}=\sum_{i}Z_{i}V^{\parallel}_{i}>80\%$ (2)

where $i$ runs over the detected nuclei.

In this way most of the charge and the linear momentum have been correctly
measured and only few light charged particles or one intermediate mass
fragment (with $Z<10$) were lost.
To support the statement that the selected events are ”truly fusion or quasi-
fusion events”, we display, in figure 1 and for the system
${}^{129}Xe+^{nat}Sn$, the parallel velocity (with respect to the beam
velocity component) of the second heavier fragment charge for the events
selected using both conditions : complete events plus $E_{Iso}^{Max}\leq 0$.
The choice for the second heavier fragment, rather than the heaviest one, is
due to the fact that this latter is used for the event selection in equation 1
and therefore its velocity distribution will be, by definition, centred around
the centre of mass velocity. As one may see in figure 1, from 8 A MeV till 20A
MeV, the centre of mass velocity distributions show a peak, which broadens for
increasing beam energies, around zero. For these lower beam energies we can
deduce that the fusion-evaporation or fusion-fission could be the dominant
mechanism. Already at 18A MeV the peak is very large and at 20A MeV it is
rather a plateau. Starting from this last incident energy, if ”fusion” and
quasi-fusion are still present, the decay mechanism is not any longer
evaporation and fission (as already shown in abdou  and diego ) but other
decay processes which appear to be dominant. This gives rise to forward and
backward velocity distributions for the second heavier fragment which at 20 A
MeV are still very close. This is why in the study of the events with two
fragments in the output channel the highest beam energy considered will be 18A
MeV.

Figure 2: Second heavier fragment parallel velocity to the beam direction for
Incident energies 15A and 18A MeV for events selected with both conditions :
complete events and $E_{Iso}^{Max}\leq 0$ for the system
${}^{129}Xe+^{197}Au$.

In short, for the ${}^{129}Xe+^{nat}Sn$ system, both constraints select, with
good efficiency and for beam energies lower than 20 A MeV, fusion or
incomplete fusion events.
Concerning the system ${}^{129}Xe+^{197}Au$ we applied the same constraints as
for the Sn target. Figure 2 shows, as in the figure 1, the parallel velocity
distributions for 15A MeV and 18A MeV for the second heavier fragment. We
observe a velocity distribution centred around the centre of masse without the
side contributions seen for the ${}^{129}Xe+^{nat}Sn$ at 15A MeV and 18A MeV.

##  IV Two-fragment multiplicity events

In this section, we study ”fusion” events characterized by two fragments
($Z\geq 10$) in the final state, i. e. the fission of the composite system.
Such events were selected requiring, as previously discussed,
$E_{Iso}^{Max}\leq 0$ and complete events.

Fission has been largely studied in the context of the binary break-up of
actinides at low energy. Most of the theoretical and experimental data were
typically produced up to few tens MeV of excitation energy. Experiments
performed on spontaneous or thermal neutron induced fission on heavy actinides
have provided a large body of data: fission fragment yields and prompt neutron
multiplicities which are among the most important variables to elaborate
models describing the fission process schmidt , andreyev .

In the present work, fission events were induced in heavy-ion collisions at
low and intermediate energies (well above the Coulomb barrier), leading to
excitation energies from 1.5 MeV/nucleon up to 4-5 MeV/nucleon and possibly to
large internal angular momenta. As INDRA can only measure charged particles
and provides (with the lowest threshold of about 1 MeV/nucleon) kinetic
energies and particle charges, no neutrons spectra are available and no
nuclear masses can be identified for the fragments. However, some interesting
results can be shown and could trigger phenomenological studies.

###  IV.1 Fission fragment charge, relative velocity and angle distributions,
TKE in function of the fragment charge

Figure 3: Fission fragment charge distributions for beam energies 8A to 18A
MeV for the system ${}^{129}Xe^{nat}Sn$.

The FFCD (Fission Fragment Charge Distribution) and the TKE (Total Kinetic
Energy in the center of mass) are among the most illustrative variables to
study fission schmidt .
A global view of fission fragment charge distributions is shown in figure 3
for the system ${}^{129}Xe+^{nat}Sn$ at beam energies from 8A to 18A MeV. A
smooth transition from symmetric to asymmetric partition is observed. For the
lowest energy at 8A MeV, a typical symmetric fission pattern could be
described by the Liquid Drop Model (LDM), since shell effects do not dominate.
The fragment distribution is peaked around $Z\simeq 46$. However the
distribution is not gaussian : small bumps on both the sides indicate a
coexistence with an asymmetric fission mode. For increasing beam energies, one
assists to the transition towards a double humped distribution where the two
gaussians are so close to give nearly a plateau distribution. The transition
occurs smoothly; in fact, at the beam energy of 12A MeV, one sees that a
double asymmetric bump starts to delineate indicating the presence of the
asymmetric fission mode. Such a transition is possibly due to the increase of
angular momentum transferred to the fissioning systems, as discussed in
section IV.3.

Figure 4: Fission fragment charge distributions for beam energies 15A and 18A
MeV for the system ${}^{129}Xe+^{197}Au$.

Figure 4 displays the FFCD for the ${}^{129}Xe+^{197}Au$ system. Here a clear
double humped structure appears which could be originated by fission. However,
in the case of such a heavy system, what is observed could be rather quasi-
fission with a strong memory of the entrance channel.

Table 3 gives the order of magnitude of the mean excitation energy total and
per nucleon (evaluated by calorimetry kaliveda ) for the two systems at the
different incident energies. As already mentioned, these values are just a
rough estimate because of the uncertainties which could affect Vient .

Target |  $E_{beam}/A$ (MeV) |  $<\epsilon>$ MeV/nucleon |  $<E^{*}>$ MeV
---|---|---|---
Sn | 8 | 1.24 | 287
Sn | 12 | 2.22 | 513
Sn | 15 | 2.83 | 652
Sn | 18 | 3.43 | 788
Au | 15 | 2.16 | 633
Au | 18 | 2.63 | 773
Table 3: Mean values of the excitation energy (per nucleon and total) for the
two systems and different incident energies.

Figure 5: Upper panel : Relative velocity distributions between the two
fission fragments for beam energies from 8A to 18A MeV. The arrow indicate the
Viola velocity.
Lower panel : Relative emission angle distributions between the two fission
fragments for beam energies from 8A to 18A MeV. The distributions are
normalized to the number of events. System ${}^{129}Xe+^{119}Sn$.

Figure 6: Upper panel : Relative velocity distributions between the two
fission fragments for beam energies at 15A MeV and 18A MeV for the system
${}^{129}Xe+^{197}Au$. The arrow indicate the Viola velocity.
Lower panel : Relative emission angle distributions between the two fission
fragments at 15A MeV and 18A MeV for ${}^{129}Xe+^{197}Au$. The distributions
are normalized to the number of events.

We display in figure 5 the relative two-fragment velocity distributions (upper
panel) and the folding angle distributions for the considered incident
energies for the system ${}^{129}Xe+^{119}Sn$. The arrow shows the Viola
systematics value (i.e. $V_{rel}^{Viola}\simeq 2.7cm/ns$ viola ) for ”fully
damped” reaction in the sense of Bohr loss of memory of the entrance channel
for the final state. As one may see, for the lowest incident energy, 8A MeV,
the mean velocity value is very close to Viola’s, while, for increasing beam
energies, there is a progressive gaussian broadenning with a sensible
displacement towards higher values of the most probable value. This departure
from Viola value in the velocity distributions may be understood as a smooth
transition with increasing available energy from a dominant mechanism of
fusion (or incomplete fusion) with subsequent fission towards a mechanism
which is different from pure fission and where the available energy is not
completely relaxed so that the system shows a memory of the entrance channel.
This could be interpreted as a signature of quasi-fission, where the two
nuclei do not form a composite (or compound) system in the very short
($t\simeq 10^{-21}$ s) time in which they enter in contact exchanging few
nucleons before re-separating in fission-like fragments. While the presence of
quasi-fission, as it will be shown later, is not dominant for the lowest
incident energy (8A MeV), it starts to become sizeable as the beam energy
increases.

The lower panel of figure 5 shows the relative emission angle distributions
for each incident energy in the center of mass. The relative angle, in the
center of mass, is equal or larger than $160^{\circ}$ which means that the
fragment were emitted ”back-to-back” in a fusion-fission (or quasi-fission)
fashion with a full momentum transfer signature violajr  at the lowest energy.

Figure 7: TKE (Total Kinetic Energy) profiles in function of the fragment
charge for both systems and for all incident energies.

Figure 6 shows the same as figure 5 for the ${}^{129}Xe+^{197}Au$ system. In
this case the velocity distributions, for both beam energies, depart from the
Viola systematics (upper panel) while the folding angle distributions (lower
panel) are quite similar to the case of the Sn target. The departure from
Viola value in the velocity distributions is more evident than in the Sn
target case as expected for heavier systems for which the Coulomb repulsion
inhibits the formation of a compound system and so the quasi-fission mechanism
is more favoured.

Figure 7 shows the Total Kinetic Energy (TKE) in the center of mass in
function of the fragment charge. The difference in the behavior of the two
systems is quite evident : while for ${}^{129}Xe+^{119}Sn$, at all incident
energies, the TKE values superpose and have nearly the same trend (in
particular, at 8A MeV, the trend is very close to the Viola symmetric split
values). For ${}^{129}Xe+^{197}Au$ (at incident energies as same as the
lighter system, i.e. tin target) the TKE values are as higher as roughly 100
MeV, indicating a definite variation in the mechanism of production of the two
final fragments. This difference in the TKE value is consistent with the
higher mean values of the relative velocity distribution shown in figures 5
and 6, already discussed.

###  IV.2 Fission Fragment Charge Distributions per $Z_{12}^{Red}$ bins

To study the role of excitation energy, angular momentum and the competition
between symmetric vs asymmetric fission, we define the global variable,
$Z_{12}^{Red}$, as follows :

$Z_{12}^{Red}=\frac{Z_{12}}{Z_{proj}+Z_{target}}$ (3)

where $Z_{12}=Z_{1}+Z_{2}$ is the sum of the fragment charges (where $Z_{1}$
is the heaviest one).
Table 4 gives the different bins labelled $Tzi$, $i=1,...5$ for the
$Z_{12}^{Red}$ reduced sum parameter and the corresponding fragment charge sum
for each target. Each bin is 5 units charge wide.

Figures 8, 9, 10 for the Sn target and figure 11 for the gold target display,
respectively, the evolution of the fission fragment charge distributions for
bins of the $Z_{12}^{Red}$ $Tzi$, $i=1,...5$, starting from the top of the
figures. For each $Tzi$ bin, are also reported the average excitation energies
per nucleon deduced from calorimetry kaliveda . Note that their order is
decreasing, i.e., the highest value of the excitation energy corresponds to
the $Tz1$ bin.
The average excitation energies values, altogether with the uncertainties, are
listed in the tables 5 and 6 for both systems at the beam energies of
interest. The assumption that for more central collisions correspond events
with larger excitation energy and lower angular momentum transfer is supported
by the evolution of the fission fragment charge distributions in the figures,
where the mean excitation energy per bin decreases with the increasing values
of the charge sum $Z_{12}$. An higher excitation energy is therefore needed to
break down the system in two fragments with a smaller size and a larger
emission of light charged particles and intermediate mass fragments. In fact,
the light charged particle and intermediate mass fragment multiplicities
decrease for decreasing excitation energies as expected.

Bins | $Z_{12}^{Red}$ | $Z_{12}^{Sn}$ | $Z_{12}^{Au}$
---|---|---|---
Tz1 | $\leq 0.70$ | $\leq 72.8$ | $\leq 93.1$
Tz2 | $(0.70,0.75]$ | $(72.8,78]$ | $(93.1,99.7]$
Tz3 | $(0.75,0.80]$ | $(78,83.2]$ | $(99.7,106.4]$
Tz4 | $(0.80,0.85]$ | $(83.2,88.4]$ | $(106.4,113]$
Tz5 | $>0.85$ | $>88.4$ | $>113$
Table 4:  $Z_{12}^{Red}$ bins, first column. In the second and third columns are reported the intervals in $Z_{12}$ for the tin and the gold target (event by event), respectively. See text for the variables definition. Figure 8: Fragment charge distributions for bins of $Z_{12}^{Red}$ at 8A MeV for ${}^{129}Xe+^{119}Sn$. Only the last three bins (Tz3, Tz4, Tz5) are shown because of the low statistics of the first two ones. For each bin is reported the average excitation energy per nucleon.  Figure 9: Fragment charge distributions for bins of $Z_{12}^{Red}$ at 12A MeV for ${}^{129}Xe+^{119}Sn$. For each bin is reported the average excitation energy per nucleon.  $<\epsilon*>$ | 8A MeV | 12A MeV | 15A MeV | 18A MeV
---|---|---|---|---
Tz1 | - | $2.92\pm 0.34$ | $3.07\pm 0.28$ | $3.54\pm 0.31$
Tz2 | $1.95\pm 0.23$ | $2.59\pm 0.35$ | $2.92\pm 0.29$ | $3.37\pm 0.31$
Tz3 | $1.71\pm 0.27$ | $2.35\pm 0.30$ | $2.76\pm 0.29$ | $3.18\pm 0.32$
Tz4 | $1.60\pm 0.24$ | $2.14\pm 0.27$ | $2.56\pm 0.30$ | $2.96\pm 0.34$
Tz5 | $1.21\pm 0.27$ | $1.91\pm 0.27$ | $2.33\pm 0.34$ | $2.92\pm 0.28$
Table 5:  Mean excitation energy per nucleon (MeV/A) obtained by calorimetry for each bin of the $Z_{12}^{Red}$ variable for the system ${}^{129}Xe+^{119}Sn$ at the beam energies 8A, 12A, 15A an 18A MeV. $<\epsilon*>$ | 15A MeV | 18A MeV
---|---|---
Tz1 | $2.48\pm 0.27$ | $2.80\pm 0.28$
Tz2 | $2.35\pm 0.28$ | $2.65\pm 0.30$
Tz3 | $2.19\pm 0.28$ | $2.52\pm 0.30$
Tz4 | $1.99\pm 0.29$ | $2.35\pm 0.33$
Tz5 | $1.73\pm 0.28$ | $1.90\pm 0.18$
Table 6:  Mean excitation energy per nucleon (MeV/A) obtained by calorimetry
for each bin of the $Z_{12}^{Red}$ variable for ${}^{129}Xe+^{197}Au$ at 15A
MeV and 18A MeV.

For the system ${}^{129}Xe+^{nat}Sn$, in each figure, a slow evolution with
the beam energy and with the $Z_{12}^{Red}$ variable is observed.
At 8A MeV (figure 8), the distributions (which start from the third bin of
$Z_{12}^{Red}$ because of the low statistics in the first two bins) show a
symmetric fission mode. In the last bin of $Z_{12}^{Red}$, however, the
distribution broadens and departs from a gaussian mode as if an asymmetric
fission mode starts to set on. At 12A MeV (figure 9) the first bin still shows
a symmetric fission mode. Then, for increasing values of $Z_{12}^{Red}$, an
increase in the asymmetric fission mode is observed, till the last bin in
which both modes coexist.
At 15A MeV and 18A MeV (figure 10) the symmetric fission mode disappeared and
a plateau is observed. For increasing $Z_{12}^{Red}$ values peaks appear which
testify the presence of both modes.
On the basis of the observation, in figure 5, of a slight deviation in the
mean relative velocity of the two fragments from the Viola systematics, one
could wonder if what appears in the last bins at 12A MeV, 15A MeV and 18A MeV
could be therefore interpreted as quasi-fission. For example, in the last bin
at 15A MeV, the extreme two peaks are, respectively, centered around $Z\simeq
25$ and $Z\simeq 65$ while the central peak, for symmetric fission, is
centered on $Z\simeq 50$. They could have been produced in both mechanisms :
asymmetric fission or quasi-fission.

For the heavier system ${}^{129}Xe+^{197}Au$ (figure 11) the behavior is
different : for each bin of $Z_{12}^{Red}$, at both energies (15A and 18A MeV)
two peaks appears starting from the first bin of $Z_{12}^{Red}$ which becomes
more well marked in the last bins. These two peaks could rather be quasi-
fission for this heavier system. We already saw how the relative mean
velocities depart from Viola systematics in a greater extent.

Figure 10: Fragment charge distributions for bins of $Z_{12}^{Red}$ at 15A MeV
(upper panel) and at 18A MeV (lower panel) for the system
${}^{129}Xe+^{nat}Sn$. For each bin is reported the average excitation energy
per nucleon.

Figure 11: Fragment charge distributions for bins of $Z_{12}^{Red}$ at 15A MeV
(upper panel) and at 18A MeV (lower panel) for the system
${}^{129}Xe+^{197}Au$. For each bin is reported the average excitation energy
per nucleon.

The excitation energy decreases from the first to the fifth bin and what
changes is the global system size : for higher excitation energies the system
evaporated more particles and intermediate mass fragments so that the two
fragments, after mass equilibration, have lower mean charge values than the
projectile and the target. At variance, in the last Tz5 bin, where the
excitation energy is lower, their mean charge is close to the projectile and
the target ones. This behaviour was already observed, for very low energies,
in Leguillon ,nishio , Nishio2 , Nishio3 ,Katsuhisa  where the asymmetric
distribution is interpreted as quasi-fission.

###  IV.3 Light Charged Particle Angular Distributions

Figure 12: Cosine out-of-plane distributions for protons (left) and alpha
(right) for the system ${}^{129}Xe+^{nat}Sn$ at 8A, 12A, 15A and 18A MeV and
for the system ${}^{129}Xe+^{197}Au$ at 15A MeV and 18A MeV.

In order to put in evidence the possible role of angular momentum, we present
the out-of-plane angular distributions of protons and alpha emitted in
coincidence with the two fission fragments. First, the reaction plane is
defined by the two following vectors: the beam direction and the relative
velocity of the two fragments. The out-of-plane angle, $\Theta_{out-of-
plane}$, is thus the angle with respect to a vector perpendicular to the
reaction plane. The in-plane angle, $\Theta_{in-plane}$, is the angle between
the beam direction and the reconstructed center-of-mass velocity. These
observables are very sensitive to the rotational energy, i.e. the spin and to
the temperature moretto ; colin ; steck . Figure 12 displays the out-of-plane
cosine distributions of protons and alpha for 8A, 12A, 15A and 18A MeV
incident energies for $Xe+Sn$. For the alphas, the distributions are mostly
peaked around $0$ suggesting that most alphas are emitted in the reaction
plane as it should be due to angular momentum effect. A small dip around $0$
(i.e. $\Theta_{out-of-plane}=90^{\circ}$) is however observed: this could be
due to final state interaction (Coulomb interaction) of the particles with the
fission fragments. This ’ejection’ process from the reaction plane suggests a
rather fast emission and could be used as a clock. For protons, this effect is
even more pronounced and the distributions are not anymore peaked around $0$:
it is well known that $\alpha$ are much more sensitive to angular momentum
than protons. Such findings deserve further analyses based on phenomenological
models. However, the general evolution of the distributions with beam energies
suggest an increase of the transferred angular momentum with beam energies and
probably a shortening of the emission times as expected.

###  IV.4 TKE results: comparison with the Viola systematics

To better compare to low energy data Itkis , we study the mean value of TKE as
a function of the fissility parameter $Z^{2}_{CN}/(A_{CN})^{1/3}$, where the
charge and the mass of the compound nucleus were estimated as the sum of the
charges and the masses (assuming that the ratio $N/Z$ of the fragments is the
same as the compound system since masses are not measured) of the two fission
fragments, respectively.

Figure 13: Upper panel : average values of TKE as a function of the fissility
parameter $Z^{2}_{CN}/(A_{CN})^{1/3}$ for ${}^{129}Xe+^{nat}Sn$ at 8A, 12A,
15A and 18A MeV and ${}^{129}Xe+^{197}Au$ at 15A and 18A MeV. Lower panel :
TKE variance $\sigma_{TKE}$ as a function of the fissility parameter for the
two systems as explained above.

Figure 13 shows in the upper panel the mean TKE values for
${}^{129}Xe+^{nat}Sn$ at 8A, 12A, 15A and 18A MeV and for
${}^{129}Xe+^{197}Au$ at 15A and 18A MeV. The line represents the Viola
systematics ($0.1071Z^{2}/A^{1/3}+22.2$). As one may see, the experimental
results are above the Viola systematics as an indication that at those
energies we do not find pure fission but a combination of fission and quasi-
fission which tends, as the incident energy increases and as the system is
heavier, to go more and more towards quasi-fission. The closest data to the
systematics are those of Xe+Sn at 8A MeV. Slighty above, and starting for
lower fissility parameter (i.e. lower composite size), follow those for 12A
MeV. Data for the incident energy at 15A MeV for the Sn target overlap to
those for 12A MeV till roughly $Z^{2}_{CN}/(A_{CN})^{1/3}\simeq 1300$ and then
set above deviating of about $\Delta(TKE)\simeq 50$ MeV. Finally, always for
the Sn target, the data for 18A MeV are very close to both 12A MeV and 15A MeV
and they depart for increasing fissility parameters.
For ${}^{129}Xe+^{197}Au$, for both incident energies, starting from
$Z^{2}_{CN}/(A_{CN})^{1/3}\simeq 1500$, the data set definitively above and
diverge more and more.
Globally, as the incident energy increases and the system is heavier, the
departure from the Viola systematics is larger. For a single beam energy one
may see that data depart slightly from the Viola line with increasing
composite size, especially for the tin target. Due to pre-equilibrium
fluctuations the size of the fissioning system may vary. For lower fissioning
system size, the colliding nuclei may reach the potential pocket for fusion
and this composite system successively undergoes fission. This would be in
agreement with the fact that smaller sizes have greater excitation energy. As
the colliding nuclei keep a memory of the entrance channel, the fragments have
a larger mass : few nucleons have been exchanged during a very short contact
time and then they re-separate. This is quasi-fission marked by a gradual but
constant deviation from the Viola line, for both systems but with a more
marked trend for gold.
Therefore, in the case of the gold target, the behavior is in agreement with
the fact that we do not anylonger expect standard fission in the final state
but rather quasi-fission for both incident energies. For the Sn target, while
for lower energies and, especially for the lowest at 8A MeV, data are closer
to the systematics, we may still expect fusion/fission. However, for the
higher beam energy the departure from the systematics increases the presence
of quasi-fission.
The dispersion $\sigma_{TKE}$ is usually linked to the dynamics of the system
moving from the saddle to the scission point Itkis , Itkis1 . From the
experimental data appears that it is constant for compound nuclei with
$Z^{2}_{CN}/(A_{CN})^{1/3}$ lower than 1000 and for values greater than 1300
it starts to increase linearly. This behaviour is not explained by the Liquid
Drop Model (LDM). In the present case one can see that, for the system
${}^{129}Xe+^{nat}Sn$ at 12A and 15A MeV, the trend is the one predicted while
the behaviour of the 8A MeV approach the LDM. However for the system with the
gold target the behaviour does not follow neither the systematics nor the
other beam energies.

##  V Conclusion

This work focused on central events for two systems (${}^{129}Xe+^{nat}Sn$ and
${}^{129}Xe+^{197}Au$) at different incident energies from 8A MeV up to 18A
MeV. Events with two heavy fragments in the output channel were studied in
order to investigate fusion-fission and quasi-fission, in the case of two
different systems and for energies exceeding the excitation energies of 100
MeV, typically reached in published studies concerning fusion/fission and
quasi-fission at low energy.

From FFCD, we saw that, for the quasi-symmetric system ${}^{129}Xe+^{nat}Sn$
there is an evolution with increasing beam energies from dominant symmetric
fission mode at 8A MeV towards more asymmetric fission consistent with the
increasing influence of angular momentum as testified by the angular
distributions of the associated light charged particles. For larger sizes of
the fissioning system (at lower excitation energies) the symmetric and
asymmetric fission modes coexists and the asymmetric mode associated to quasi-
fission increases as the incident energy increases. On the other hand, for the
heavier system ${}^{129}Xe+^{197}Au$, the FFCD, at both beam energies, show
asymmetric fragment distributions suggesting a strong memory of the entrance
channel. This fact is confirmed by the subsequent relative fragment velocity
distributions in which it is possible to observe a departure from the Viola
velocity which increases with the system mass and with increasing beam
energies. As already discussed, this was interpreted as dominant fusion-
fission at the lowest beam energy (8A MeV), consistent with Viola systematics.
For increasing available energy and pre-equilibrium emission this decay mode
is more and more contaminated by quasi-fission decay mode.
Therefore, while for the Sn target there is at least an evolution towards more
and more quasi-fission, for the gold target, already at 15A MeV the asymmetric
fragment distribution has a memory of the entrance channel, as discussed for
the relative fragment velocities.
When studying the evolution with the size of the compound undergoing fission,
we observe an evolution towards coexistence of both fission modes for the Sn
target as the system ($Z_{12}^{Red}$) is heavier, till the emergence of three
peaks : asymmetric and symmetric mode altogether. For the gold target, the
evolution is towards a definitevely asymmetric (quasi-fission) split.
When comparing the Total Kinetic Energy (TKE) in function of the fissility
parameter for the both systems with the Viola systematics, one see a clear
deviation from the systematics as the incident energy and the size of the
fissioning system increase in the case of the tin target. For the gold target
system (i.e. the heavier one) this deviation is more evident as the composite
system increases in size. For the lighter system (tin target), here again, the
lowest energy is the closest to the systematics. Data for increasing beam
energies are close to the Viola line only for smaller composite system sizes,
where an increasing pre-equilibrium left a fissioning system such that it
could partially fuse (reaching the potential pocket) and then fission. The
progression of the departure from the systematics is therefore two fold : in
beam energies and in system size.
The behaviour of the $\sigma^{2}_{TKE}$ dispersion shows a trend similar to
previous studies reported in literature for the Xe+Sn system (especially for
8A MeV), while for the Xe+Au system a completely different behaviour is
observed.
We are not aware of fission modelisation at such high energies as studied
here. Fission dynamics involved in the case of heavy ion reactions at these
energies are different from the studied dynamics close to the Coulomb barrier.
To deeply understand the behaviour discussed above, it would be useful to
develop systematic microscopic model calculations to be compared with our
results.

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