# CAMS: An Annotated Corpus for Causal Analysis
of Mental Health Issues in Social Media Posts

###### Abstract

Research community has witnessed substantial growth in the detection of mental
health issues and their associated reasons from analysis of social media. We
introduce a new dataset for Causal Analysis of Mental health issues in Social
media posts (CAMS). Our contributions for causal analysis are two-fold: causal
interpretation and causal categorization. We introduce an annotation schema
for this task of causal analysis. We demonstrate the efficacy of our schema on
two different datasets: (i) crawling and annotating $3155$ Reddit posts and
(ii) re-annotating the publicly available SDCNL dataset of 1896 instances for
interpretable causal analysis. We further combine these into the CAMS dataset
and make this resource publicly available along with associated source code:
https://github.com/drmuskangarg/CAMS. We present experimental results of
models learned from CAMS dataset and demonstrate that a classic Logistic
Regression model outperforms the next best (CNN-LSTM) model by 4.9% accuracy.

Keywords: clinical depression, clinical psychology, intent classification,
suicidal tendency

languageresourceLanguage Resources

CAMS: An Annotated Corpus for Causal Analysis
of Mental Health Issues in Social Media Posts

Muskan Garg1,7, Chandni Saxena2, Veena Krishnan3, Ruchi Joshi5,
---
Sriparna Saha4, Vijay Mago6, Bonnie J Dorr7
1Thapar Institute of Engineering & Technology, India,
2The Chinese University of Hong Kong, Hong Kong SAR,
3University of Petroleum And Energy Studies, India 4Indian Institute of
Technology, Patna,
5Amity University Rajasthan, India, 6Lakehead University, Canada, 7University
of Florida, USA.
{muskangarg<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>

Abstract content

##  1\. Introduction

With substantial growth in digitization of psychological phenomena, automated
Natural Language Processing (NLP) has been applied by academic researchers and
mental health practitioners to detect, classify or predict mental illness on
social media. However, there is a critical need for identifying underlying
causes of mental illness in the face of dire outcomes. For example, a person
commits suicide every 11.1 minutes in the US111https://suicidology.org/wp-
content/uploads/2021/01/2019 datapgsv2b.pdf and 23% of deaths in the world are
associated with mental disorders according to the World Health Organization.
The pandemic lockdown has heightened the mental health crisis in UK [Pierce et
al., 2020] and US [McGinty et al., 2020].

In this context, people with mental disorders who decide to visit mental
health practitioners for social well-being may face difficulty due to social
stigma or unavailability of mental health practitioners, leaving those most in
need to be neglected by the community. As a result, sufferers of mental health
conditions are unable to take necessary steps for their treatment.
Unfortunately, 80% of those with mental health conditions do not undergo
clinical treatment and about 60% of those who take their own lives previously
denied having any suicidal thoughts [Sawhney et al., 2021]. Accordingly,
social media platforms (e.g., Reddit, Twitter) are important resources for
investigating the mental health of users based on their writings.

###  1.1. Motivation

The research community has witnessed tremendous growth in the study of mental
health classification on social media since 2013 [Garg, 2021]. However, there
is minimal automation for identifying potential causes that underlie mental
illness. Online users suffering from depression may express their thoughts and
grievances on social media unintentionally, for instance, the post $(P)$.

> $P$: I cannot deal with this breakup anymore and want to finish my life

The reason behind depression in $P$ is clearly interpreted from the word
breakup, which serves as an indicator of a cause related to the notion of
relationship. Through the application of automatic causal analysis, underlying
reasons of this type may be extracted and potentially leveraged to address
mental health problems.

Figure 1: The intent-cause analysis of mental health on social media Dataset |  Details |  Task |  Avail.
---|---|---|---
CLPsych [Coppersmith et al., 2015] |  Three types of annotated information: Depression-v-Control [DvC], PTSD-v-Control [PvC], and Depression-v-PTSD [DvP] |  Suicide risk detection |  S
MDDL [Shen et al., 2017] |  300 million users and 10 billion tweets in D1: Depression D2: Non-depression, D3: Depression candidate |  Depression detection |  A
RSDD [Yates et al., 2017] |  Reddit dataset of 9210 users in depression and 1,07,274 users in control group |  Depression detection |  ASA
SMHD [Cohan et al., 2018] |  Reddit dataset for multi-task mental health illness |  Mental health classification |  ASA
eRISK [Losada et al., 2018] |  Early risk detection by CLEF lab about problems of detecting depression, anorexia and self-harm |  Depression detection |  A
Pirina18 [Pirina and Çöltekin, 2018] |  Acquired filtered data from Reddit |  Depression detection |  A
Ji18 [Ji et al., 2018] |  Reddit: 5,326 suicide risk samples out of 20k; Twitter: 594 tweets out of 10k |  Suicide risk detection |  AR
Aladag18 [Aladağ et al., 2018] |  10,785 posts were randomly selected and 785 were manually annotated as suicidal v/s non-suicidal |  Suicide risk detection |  AR
Sina Weibo [Cao et al., 2019] |  3,652 (3,677) users with (without) suicide risk from Sina Weibo |  Suicide risk detection |  AR
SRAR [Gaur et al., 2019] |  Posts from 500 Redditors (anonymized) & annotated by domain expert |  Suicide risk detection |  ASA
Dreaddit [Turcan and McKeown, 2019] |  190K Reddit posts of 5 different categories |  Stress detection |  A
GoEmotion [Demszky et al., 2020] |  Manually annotated 58k Reddit comments for 27 emotion categories |  Emotion detection |  A
UMD-RD222The University of Maryland Reddit Dataset [Shing et al., 2020] |  11,129 users who posted on r/SuicideWatch and 11,129 users who did not |  Suicide risk detection |  ASA
SDCNL [Haque et al., 2021] |  Reddit dataset of 1895 posts of depression and suicide |  Suicide v/s depression classification |  A
CAMS (Ours) |  Interpretable causal analysis of mental illness in social media (Reddit) posts |  Causal analysis |  A
Table 1: Different mental health datasets and their availability. A:
Available, ASA: Available via Signed Agreement, AR: Available on Request for
research work

Social, financial and emotional disturbances have a huge impact on the mental
health of online users. Here, we consider three levels of mental disorder
analysis from automation to latent cause as shown in Figure 1. We identify the
intent (level 0 task) of a user by mental illness prediction and
classification of social media posts. We further automate the process of
identifying and categorizing the direct cause (level 1) that a user may
mention in the post. In the future, causal analysis may discern crucial
protective factors for mental health and address some important societal
needs. Domain experts refer to level 1 as a  direct cause mentioned by a user,
often accompanied by a latent cause (Level 2) when they are posted on social
media. In this work, we focus on automation by introducing a dataset for level
1: interpretable causal analysis.

###  1.2. Challenges and Contributions

Mental health illness detection and analysis on social media presents many
linguistic, technical and psychological challenges. Among many under-explored
dimensions, some substantial research gaps are addressed as follows:

  1. 1.

Social media posts are first-hand user-generated data containing informal and
noisy text. The nature of the text in a post may vary for different platforms.

  2. 2.

Dataset availability may be limited due to the sensitive nature of personal
information.

  3. 3.

There are many existing level 0 studies for mental health detection but no
substantial study for Level 1, e.g., in-depth causal analyses of disorders.

To address these challenges, we introduce the task of causal analysis. We
first introduce an annotation scheme for causal analysis. The dataset
annotations are carried out in two ways: (i) crawling and annotation of the
Reddit dataset (ii) re-annotation of the existing SDCNL dataset [Haque et al.,
2021] for the proposed task of Causal Analysis of Mental health on Social
media (CAMS). There are no existing studies for this task as observed from
Table 1. To the best of our knowledge, our work is the first to address causal
analysis and to provide a publicly available dataset for this purpose. Our
major contributions are:

  1. 1.

Definition of Interpretable Causal Analysis and construction of an annotation
schema for this new task.

  2. 2.

Annotated web-crawled Reddit dataset of 3362 instances using our annotation
schema.

  3. 3.

Re-annotation of the existing SDCNL dataset as a robustness test for our
annotation schema.

  4. 4.

Combination of the datasets above and introduction of our new, publicly
available CAMS dataset.

  5. 5.

Demonstration of the performance of machine learning and deep learning models
using CAMS.

Below we discuss relevant background (Section 2) and introduce the annotation
scheme for causal analysis (Section 3). Section 4 presents our new CAMS
resource, annotation, and validation. Annotations are verified by experts
(clinical psychologist and rehabilitation counselor) and validated using
statistical testing of Fleiss’ Kappa agreement [Falotico and Quatto, 2015]. We
further use existing multi-class classifiers for interpretable causal analysis
in Section 5. Section 6 provides concluding remarks and future research
directions.

##  2\. Background

Reddit has become one of the most widely used social media platforms. ?) use
two subreddits $r/depression$ and $r/suicidewatch$ to scrape the SDCNL data
and to validate a label correction methodology through manual annotation of
this dataset for depression versus suicide. They also address ethical issues
impacting dataset availability and make their dataset publicly available. In
this section, we discuss the evolution of mental health studies and the
historical perspective of causal analysis.

###  2.1. Evolution of Mental Health Studies

Many machine learning researchers have identified mental health disorders for
social media posts [De Choudhury et al., 2013]. ?) examines the evolution of
suicidal tendencies from historical posts of users (longitudinal studies).
Figure 2 highlights recent developments in analysis of mental health disorders
from social media.

Figure 2: Evolution of studies for mental health detection on social media

New NLP questions have emerged from investigations into predicting depression
[De Choudhury et al., 2013] and suicidal tendencies [Masuda et al., 2013].
Researchers consider users’ profiles [Conway and O’Connor, 2016] to introduce
the CLPsych shared task dataset [Coppersmith et al., 2015] for solving the
problem of Mental Illness Detection and Analysis on Social media (MIDAS).
MIDAS has further benefited from exploiting social network features
[lin2017detecting], attention mechanisms [Nam et al., 2017], handling
imbalanced dataset [Cong et al., 2018], and explainability [Cao et al., 2019].

Additional research directions have emerged from the use of knowledge graphs
[Cao et al., 2020], feature optimization techniques [Shah et al., 2020],
longitudinal studies [Sawhney et al., 2021], and handling noisy labels [Haque
et al., 2021]. The 3-step theory (3ST) [Klonsky et al., 2021] of suicide
supports the argument of gradual development of suicidal tendencies (over
time) associated with a range of potential causes.

###  2.2. Historical Perspective: Causal Analysis on Social Media

Our work is relevant to causal analysis of human behavior on social media.
Recent approaches are developed to study ‘why online users post fake news’
[Cheng et al., 2021], beliefs and stances behind online influence [Mather et
al., 2022], and causal explanation analysis on social media [Son et al.,
2018]. The work of ?) is the closest to ours in that it detects a connection
between two discourse arguments to extract a causal relation based on
annotated Facebook data. However, the dataset is limited and is not publicly
available; thus, no recent developments are observed. To address this issue,
we annotate the Reddit dataset (the nature of Reddit data is different from
that of Facebook) and further categorize causal explanations.

##  3\. Annotation Scheme

###  3.1. Inferences from Literature

Potential reasons behind mental illness may be detected in posts that refer to
insomnia, weight gain, or other indicators of worthlessness or excessive or
inappropriate guilt. Underlying reasons may include: bias or abuse [Radell et
al., 2021], loss of jobs or career [Mandal et al., 2011], physical/emotional
illness leading to, or induced by, medication use [Smith, 2015, Tran et al.,
2019], relationship dysfunction, e.g., marital issues [Beach and Jones, 2002],
and alienation [Edition and others, 2013]. This list is not exhaustive, but it
is a starting point for our study, giving rise to five categories of reasons
(plus ‘no reason’) for our automatic causal analysis: no reason, bias or
abuse, jobs and careers, medication,333We recognize ‘medication’ as both an
indicator of physical/emotional illness (e.g., an intent to alleviate illness)
and a potential cause of illness (e.g., medication-induced depression).
relationship, and alienation.

###  3.2. Annotation Task

Table 2 presents examples of data annotation involving the labeling of direct
causes of mental health disorders in social media posts. There are two types
of annotations: cause category and Inference. The Inference column contains
textual data which represents the actual reason behind mental disorders. This
inferred reason is further classified as one of the six different causal
categories.

Figure 3: Architecture of the causal analysis for mental health in social media posts Text |  Cause |  Inference
---|---|---
That’s all I can really say. Nothing is worth the effort… I don’t think I am capable of taking steps to improve my life, because I just don’t even fucking care. Whatever I’m doing, wherever I go in my life, I’ll find a way to be miserable. Why try… I just… ugh… |  Alienation |  Nothing is worth the effort
Does anyone feel like the only person that could understand your depression would be someone else that was depressed? But also feel like if they were to date someone who was depressed they couldn’t handle it because it might suck you into a place that you don’t want to be in again. |  No reason |  -
God help me…. I know I should go to the hospital. I know I have to keep fighting….if only to prove to my children, cursed with these genetic tendencies of mine, that life is worth living. I made my son promise at Christmas to get help, and he did and he is thriving. My life long battle is starting to wear on this old soul of mine. It feels like the same pattern over and over, no matter how many variables I change. I am a very hard person to love. My scars and cynicism are just a little too hard for anyone who tries to stay around too long. |  Medication |  go to the hospital, scars and cynicism, genetic tendencies
I hate my job .. I cant stand living with my dad.. Im afraid to apply to any developer jobs or show my skills off to employers..I dont even have a car rn… I just feel like a failure..Im really lonely.. I feel like everything is getting worse and worse.. maybe I should start taking anti depressant medication.. |  Jobs and Careers |  hate my job, feel like failure, really lonely
it doesn’t make any sense. can figure out what i may have done to trigger it, but 5 of my closest friends from high school have stopped responding to my calls or texts. i thought it was just a phone issue at first, but it is too unlikely of just coincidence. |  Relationships |  5 of my closest friends, stopped responding
I was with a group of friends last night, and another friend started talking to another friend about how many girls secretly liked him and stuff. It was crazy, because no one has ever talked to me about things like that. Then, on the way to the pub, a group of girls basically called me unattractive. Funny how girls are never shy about calling me ugly, but they’re apparently too shy to “approach me”. |  Bias or Abuse |  girls call me unattractive
Table 2: Sample of the CAMS dataset for causal analysis Range |  Interpretation
---|---
$<0$: |  Less than chance agreement
0.01–0.20: |  Slight agreement
0.21– 0.40: |  Fair agreement
0.41–0.60: |  Moderate agreement
0.61–0.80: |  Substantial agreement
0.81–0.99: |  Almost perfect agreement
Table 3: Interpretation of resulting values of Fliess’ Kappa agreement study.

###  3.3. Problem Formulation

The architecture for our automatic causal analysis is shown in Figure 3.
Social media text is provided to prediction/classification algorithms that
filter out non-mental disorder from posts. The remaining mental disorder posts
are then analyzed to detect reasons behind users’ depression or suicidal
tendencies. Finally, the reasons are classified into 5 causal categories and
one ‘no reason’ category.

More formally, we introduce the problem of Causal Analysis of Mental health on
Social media (CAMS) as a multi-class classification problem. We extract a set
of social media posts as $p={p_{1},p_{2},p_{3},...,p_{n}}$ for $n$ number of
posts. We interpret the cause for every $i^{th}$ post $p_{i}$ as $C_{p_{i}}$
and classify it into one of the predetermined categories
$y={y_{0},y_{1},y_{2},y_{3},y_{4},y_{5}}$ where $y_{0}$: ‘no reason’, $y_{1}$:
‘bias or abuse’, $y_{2}$: ‘Jobs and careers’, $y_{3}$: ‘Medication’, $y_{4}$:
‘Relationship’, and $y_{5}$: ‘Alienation’ as $y_{p_{i}}$.

###  3.4. Guidelines for Annotation

Our professional guidelines support annotation of the post $p_{i}$ with causal
inference $C_{p_{i}}$ and class $y_{p_{i}}$. The guidelines are developed
through collaborative efforts with a clinical psychologist and a
rehabilitation counselor. Student annotators label posts with their causal
inference and causal class. The latter are annotated as follows:

  1. 1.

No reason: When there is no reason that identifies the cause of mental
disorder in the post.

> $C_{y_{0}}$: [“I just want to die”, “Want to end my life”.]

  2. 2.

Bias or abuse: A strong inclination of the mind or a preconceived opinion
about something or someone. To avoid someone intentionally, or to prevent
someone from taking part in the social activities of a group because they
dislike the person or disapprove of their activities. It includes body
shaming, physical, sexual, or emotional abuse.

> $C_{y_{1}}$: [“No one speak to me because I am fat and ugly.”, “It has been
> 5 years now when that horrible incident of ragging shattered down all my
> confidence”.]

  3. 3.

Jobs and careers: Financial loss can have catastrophic effects on mental
illness, relationships and even physical health. Poor, meaningless and
unmanageable education, unemployment, un-affordable home loans, poor financial
advice, and losing a job are some of the major concerns. It includes gossiping
and/or social cliques, aggressive bullying behavior, poor communication and
unclear expectations, dictatorial management techniques that don’t embrace
employee feedback. The educational problems like picking up courses under some
external pressure and poor grades are also part of this category.

> $C_{y_{2}}$: [“cant afford food or home anymore”, “I do not want to read
> literature but my parents forced me to do so. Not happy with my grades”]

  4. 4.

Medication: The general drugs and other antiviral drugs can increase the risk
of depression. The habit of using substances and alcohols can aggravate the
problem of mental disorders. Moreover, medical problems like tumors, cancer,
and other prolonged diseases can boost the presence of mental depression.

> $C_{y_{3}}$: [“I am chain smoker, want to quit, but I cant. My life is
> mess”, “tried hard to leave drugs but this dire craving is killing me..”]

  5. 5.

Relationships: When two people or a group of people fight, it may lead to a
relationship or friendship drifting apart, for example, regular fights,
breakups, divorce, mistrust, jealousy, betrayal, difference in opinion,
inconsistency, conflicts, bad company, non-commitment, priority, envy.
Problems like bad parenting and childhood trauma are also part of this
category.

> $C_{y_{4}}$: [“Cannot deal with this breakup anymore”, “He dumped me and its
> killing me”]

  6. 6.

Alienation: Alienation is the feeling of life being worthless even after doing
everything. There may be indicators of meaninglessness, loneliness, tired of
daily routines, powerlessness, normlessness, isolation, and cultural
estrangement.

> $C_{y_{5}}$: [“I don’t know why am I living, everything seems to be
> meaningless”]

The student annotators were trained by experts (clinical psychologist and
rehabilitation counselor) to pick those words and/ or phrases through which
they have identified the $y_{p_{i}}$ of the post $p_{i}$, and rank them. The
student annotators followed these guidelines thoroughly.

###  3.5. Annotation Perplexity

The judgement of reasons behind online users’ intentions is a complex task for
human annotators, generally due to mentions of multiple reasons or the
presence of ambiguity in human interpretations. Causal analysis can be viewed
as a multivariate problem, resulting in multiple labels. The annotation scheme
is not sophisticated enough to capture all the aspects of this phenomenon. We
thus propose perplexity guidelines to simplify the task and facilitate future
annotations. Our mental health therapists and social NLP practitioners have
constructed perplexity guidelines to handle the trade-off between task
complexity and simplicity of the annotation scheme. The perplexity guidelines
are:

  1. 1.

Multiple reasons in the post: There are some posts with multiple reasons for
conveyed feelings. To resolve this, annotators must find a root cause among
the direct causes mentioned by the user.

> Example 1: I was of 11 years since when i realized and facing constant
> ignorance of my parents. 8 yrs later i lost my first girlfriend and
> alcoholic since then. My beer belly and obesity has made people biased
> towards me. I have lost everything and want to end up now.

In Example 1, the root cause of the mental disorder is  negligence of parents.
Thus, this post is assigned the Relationship category. That is, we handle
multiple causes by prioritizing the root cause or the most emphasized reason
by the user. This perplexity guideline reduces annotation ambiguity and helps
develop better models for automation of this task in the near future.

  2. 2.

Ambiguity in human interpretations: The subjective nature of causal analysis
makes this task even more complicated for human annotators. The six different
causes are not atomic in nature. The human interpretation of the same post and
the same inference may vary, even among experts.

> Example 2: I wish I could stay alone somewhere and cry my self to sleep. I
> wish i won’t wake up.

Example 2 contains some important words like alone and cry which convey the
category as Alienation. However, two out of three annotators considered this
to be the No reason category. As this is the subjective decision of every
human annotator, we leave it at their discretion. However, the final category
assigned by the human expert (following human annotation) is based on
“majority rules,” in this case, ‘no reason.’

  3. 3.

Subject of intent in the post: Many posts refer to the depression of loved
ones and other acquaintances. Given that the goal of this task is to identify
the cause behind mental depression of online users, experts agree that such
posts are candidates for causal analysis.

> Example 3: I love to do prepare meals for my cousin because I think he is
> suffering from depression due to his car accident last month.

In Example 3, the user is talking about their cousin who is purportedly
suffering from depression. This text is passed through classification to
detect depression; however, the third person usage precludes detection of a
reason behind this condition. Although the user presents their own perspective
on the reason for their cousin’s condition (car accident), the input must
include self-reported evidence for the reason. Thus, this example is annotated
as No reason.

The professional training and guidelines are supported by perplexity
guidelines. We have further deployed student annotators to label the dataset
after they annotate the first $25$ posts under the supervision of experts.

##  4\. CAMS Dataset

We introduce a new language resource for CAMS and elucidate the process of
data collection (4.1) and data annotations (4.2). We further discuss the
challenges and discuss future research directions (4.3). We make our dataset
and the source code publicly available for future use.

###  4.1. Overview of Data Collection

We demonstrate the efficacy of our annotated scheme as follows:

  1. 1.

We collect $3362$ Reddit posts which are available with subreddit r/depression
using Python Reddit API Wrapper (PRAW). Experts remove empty and irrelevant
instances from the crawled dataset resulting in $3155$ samples.

  2. 2.

We leverage the existing SDCNL dataset comprised of $1,896$ posts: $1517$
training samples and $378$ testing samples, assumed as the cleaned dataset.

  3. 3.

We combine these two corpora, introducing them as the CAMS dataset, which is
further annotated by our trained student annotators.

  4. 4.

We consult mental health practitioners, a clinical psychologist and a
rehabilitation counselor, to verify the combined dataset.

Class | Crawled corpus | SDCNL Training data | SDCNL Test data
---|---|---|---
| Min | Max | Avg | Min | Max | Avg | Min | Max | Avg
No reason | 1 | 508 | 59.78 | 1 | 1785 | 68.58 | 1 | 1562 | 84.85
Bias or Abuse | 6 | 2109 | 347.48 | 5 | 4378 | 227.24 | 6 | 578 | 149.80
Jobs and career | 13 | 2258 | 228.28 | 17 | 2771 | 255.70 | 20 | 1481 | 206.95
Medication | 5 | 1552 | 213.83 | 3 | 3127 | 205.86 | 11 | 1124 | 165.60
Relationship | 2 | 3877 | 229.35 | 14 | 2739 | 240.08 | 9 | 756 | 202.56
Alienation | 3 | 1592 | 153.86 | 1 | 899 | 147.01 | 12 | 683 | 145.67
Table 4: Word length variation in posts across causal classes for each
dataset.

###  4.2. Dataset Annotations

After verification of the dataset by experts, three duly trained student
annotators manually annotate the data in the format: $<$text, cause,
inference$>$ as shown in Table 2. In this section, we discuss the annotation
process, verification by experts, and validation using statistical tests.

Annotation is carried out manually by annotators who are proficient in the
language. They work independently for each post and follow the given
guidelines. Each annotator takes one hour to annotate about $15-25$ Reddit
posts and $180$ and $90$ hours to annotate the crawled and existing dataset,
respectively. The annotations are obtained as three separate files.

Several challenges have emerged during the annotation process, e.g., a
countable ($<10$) set of non-English posts. For such cases, augmented
guidelines instruct the annotator to mark the post as No reason. We recommend
the removal of non-English posts as the CAMS dataset is proposed for English
only. The annotated files are verified by a clinical psychologist and a
rehabilitation counselor. This verification is performed over the annotations
given by our trained annotators without bringing this to their knowledge and
experts have given the final annotations.

We further validate three annotated files using Fliess’ Kappa inter-observer
agreement study. The agreement study for the crawled dataset is found to be
$64.23\%$. We also study the inter-agreement annotations for the existing
dataset as $73.42\%$ and $60.23\%$ for testing and training data of SDCNL,
respectively. The trained annotators agree with $61.28\%$ agreement among the
annotators for the CAMS dataset. The resulting values are interpreted as per
Table 3. Despite the increased subjectivity of the task, the student
annotators substantially agree with their judgements.

###  4.3. Discussion

Existing work on causal analysis is associated with finding discourse
relations among words and identifying the segments that represent the reason
behind the intended information. We extend this work to find the category of
the cause using these interpreted segments. Since we are extending the causal
interpretations to automatic categorization, our work is not directly
comparable to any of the existing works. However, we glean insights into the
characteristics of the CAMS dataset through further analysis. This section
examines the word length of posts in the dataset (4.3.1) and varying number of
instances in each class (4.3.2). Additionally, we discuss the social nature of
the dataset (4.3.3).

####  4.3.1. Length of the Posts

The length of posts varies from a few characters to thousands of words. One of
the major challenges for automation is the construction of a multi-class
classifier that is suitable for posts of varying word lengths. One of the
possible solutions to this challenge is to extract the inference from the post
and classify it using the inference text. We choose to explore this in the
near future. Table 4, shows that, although there is consistency in the average
number of words among all the classes, there is a huge variation in the word
counts across posts. This shows that the data is unstructured and to handle
this kind of text, we need handcrafted features or other semantic measures for
causal analysis.

####  4.3.2. Imbalanced Dataset

Table 5 shows that the number of posts for every cause varies widely, perhaps
signifying that causes of mental health disorders are not well-distributed in
society.

Cause |  CC |  Train_S |  Test_S |  CAMS
---|---|---|---|---
No reason |  292 |  332 |  70 |  694
Bias or abuse |  122 |  194 |  35 |  351
Jobs/careers |  399 |  181 |  48 |  628
Medication |  410 |  170 |  43 |  623
Relationship |  956 |  297 |  91 |  1344
Alienation |  976 |  340 |  92 |  1408
Total |  3155 |  1517 |  379 |  5051
Table 5: Sample distribution of the CAMS dataset for different causes where CC
is Crawled Corpus, Train_S is the Training data of SDCNL dataset, Test_S is
the Test data of SDCNL dataset, and CAMS column contains the total number of
samples in the dataset for each cause.

In the crawled corpus, the highest number of samples is observed for the
Relationship and Alienation causal categories, which is perhaps an indicator
that our society is less equipped to deal with issues pertaining to ‘near &
dear ones’ and ‘loneliness / worthlessness’, respectively. The number of posts
with ‘no reason’ is smaller in the crawled corpus due to the cleaning of the
dataset. Interestingly, there are fewer posts assigned ‘Bias or abuse’—less
than half of each of the two additional categories: ‘Jobs and careers’ and
‘Medication’.

####  4.3.3. Social nature of the dataset

Our expert clinical psychologists have explored the social nature of the
dataset, in light of our analysis above. During re-annotation of existing
dataset, the prevalence of some causes, e.g., Alienation and Relationship,
point to the importance of the ability to take a societal pulse on a regular
basis, especially in these unprecedented times of pandemic-induced distancing
and shut-downs. Other problems, e.g., Jobs and careers and bias and abuse
depend upon good governance. The problem of medication depends upon
technological/medical advances and accessible healthcare, or lack thereof.
Additionally, online users often feel depressed but do not address any
specific reason behind it, indicating that inferring relevant causes is a
challenge if one uses NLP alone.

###  4.4. Ethical Considerations

We emphasize that the sensitive nature of our work necessitates that we use
the publicly available Reddit dataset [Haque et al., 2021] in a purely
observational manner[Broer, 2020]. We claim that the given dataset does not
disclose the user’s personal information or identity. We further acknowledge
the trade-off between privacy of data and effectiveness of our work
[Eskisabel-Azpiazu et al., 2017]. We ensure that our CAMS corpus is shared
selectively and is subject to IRB approval to avoid any misuse. Our dataset is
susceptible to the biases and prejudices of annotators who were trained by
experts. There will be no ethical issues or legal impact with this causal
analysis of mental illness.

Classifier | F1: C0 | F1: C1 | F1: C2 | F1: C3 | F1: C4 | F1: C5 | Accuracy
---|---|---|---|---|---|---|---
LR | 0.63 | 0.28 | 0.54 | 0.46 | 0.46 | 0.53 | 0.5013
SVM | 0.54 | 0.23 | 0.56 | 0.44 | 0.48 | 0.45 | 0.4670
LSTM | 0.54 | 0.27 | 0.52 | 0.46 | 0.42 | 0.51 | 0.4595
CNN | 0.56 | 0.27 | 0.51 | 0.42 | 0.46 | 0.38 | 0.4378
GRU | 0.51 | 0.27 | 0.54 | 0.47 | 0.48 | 0.42 | 0.4541
Bi-LSTM | 0.55 | 0.12 | 0.41 | 0.23 | 0.44 | 0.50 | 0.4351
Bi-GRU | 0.57 | 0.14 | 0.55 | 0.46 | 0.49 | 0.39 | 0.4568
CNN+GRU | 0.51 | 0.14 | 0.49 | 0.36 | 0.27 | 0.45 | 0.4027
CNN+LSTM | 0.54 | 0.22 | 0.54 | 0.47 | 0.54 | 0.47 | 0.4778
Table 6: Experimental results with CAMS dataset. F1 is computed for all six
causal classes: ‘No reason’ (C0), ‘Bias or abuse’ (C1), ‘Jobs and careers’
(C2), ‘Medication’ (C3), ‘Relationship’ (C4), ‘Alienation’ (C5).

##  5\. Corpus Utility for Machine Learning

We include traditional multi-class classifiers trained on CAMS training
dataset and evaluate it on the CAMS test data. We choose the following
Recurrent Neural Network (RNN) architectures: Long Short Term Memory (LSTM)
model, Convolution Neural Network (CNN), Gated Recurrent Unit (GRU),
Bidirectional GRU/LSTM (Bi-GRU/Bi-LSTM) and other hybrid models. In this
section, we discuss the experimental setup (5.1) and analyze the results
(5.2).

###  5.1. Experimental Setup

We use the existing re-annotated SDCNL dataset for experimental results and
analysis. We clean the dataset, pre-process the posts and then use
GloVe444https://nlp.stanford.edu/projects/glove/ word embedding with 100
dimensions trained on Wikipedia for each token. We further set up RNN
architectures with default settings
($lr=0.001,\beta_{1}=0.9,\beta_{2}=0.999,\epsilon=1e-08$) for the batch-size
of 256. The categorical Cross Entropy loss function and the ADAM optimizer are
used to perform the back-propagation learning on $20$ epochs.

The number of samples for three classes of the existing SDCNL dataset (‘Bias
or abuse’, ‘Jobs and careers’, and ‘Medication’) are very few in comparison to
the other three classes. We add $120+120+120$ samples from the crawled corpus,
to help balance the number of instances across the classes. As a result, the
number of training samples increases from $1517$ to $1877$. We use these
training data to build and validate the multi-class classifier. We test this
classifier on the $379$ sample test data and analyze the results. The
evaluation metrics used for this task are F1-measure and Accuracy.

###  5.2. Results and Discussion

We use multi-class classifiers to find causal categories and obtain the
results reported in Table 6. We test our performance with both machine
learning and deep learning approaches. The two top-performing machine learning
algorithms are based on Logistic Regression and Support Vector Machine.
Whereas the former outperforms all existing techniques, the latter shows
comparative results with deep learning models.  The hybrid model, CNN-LSTM,
attains the best performance among all deep learning mechanisms with $47.78\%$
accuracy. The CNN+GRU model performs the worst with $40.27\%$ accuracy on test
data. It is interesting to observe that the results are consistent for all the
classifiers with few exceptions for classes Bias or abuse and Medication. We
further analyze the best performing deep-learning classifier (CNN+LSTM) below.

####  5.2.1. Error Analysis

The accuracy of multi-class classification is found to be around $40\%$ to
$50\%$. We undertake a comprehensive error analysis to explore the intricacies
of our task.

  1. 1.

Cause classification error: We obtain the confusion matrix for CNN+LSTM as
shown in Figure 4. We highlight the cells with more than $40\%$ incorrect
predictions. The predictions for Alienation and Relationship are incorrect and
overlap with Bias or Abuse and Medication. This is due to complex
interactions, as illustrated in the following perceivable overlap between Bias
or Abuse and Relationship:

> Example 4: My friends are ignoring me and I am feeling bad about it. I have
> lost all my friends.

Example 4 is associated with biasing and friendship, in a case where someone
feels ostracized by their friends. The emphasis on friends tips the balance in
favor of the class Relationship. However, the major challenge is to train the
model in such a way that it understands the inferences and then chooses the
most emphasized causal category using optimization techniques. We view this
challenge as an open research direction.

  2. 2.

Overlapping class: The overlapping problem of classes is observed with
ambiguous results for samples, e.g., for Relationship and Alienation. This
class representation problems can be resolved with data augmentation [Ansari
et al., 2021] and demarcation of boundaries among classes. In a real-time
scenario, demarcation of fixed boundaries is not possible due to subjectivity
of the task. We recommend the approximation of a newly built model over
handcrafted / automated features accordingly.

  3. 3.

Uncertainty: Related to the overlapping class issue above, all learning-based
models obtain low performance for class 1 (‘Bias or abuse’) due to annotators’
perceived overlap with classes 4 and 5 (‘Relationship’ and ‘Alienation’).
Future work is needed to mitigate such uncertainty. For example, delineation
of discourses within the text would support a more definitive interpretation
and reliable annotation.

  4. 4.

Semantic Parsing: In a multi-class classification task, as the length of posts
varies over a wide range, one may choose to summarize every post before
applying a classifier. Our experiments with YAKE [Campos et al., 2020] for
keyword extraction yielded results that are further deteriorated. From this we
determine that it is important to identify the causal interpretation from the
full text in order to perform multi-class classification. A future avenue of
research involves the exploration of discourse relations to identify segments
that represent independent causes that underlie mental health disorders.

####  5.2.2. Implications and Limitations

The CAMS dataset provides a means for exploring the identification of reasons
behind mental health disorders of online users. The notion of causal
categorization is defined and used to proactively identify cases where users
are at potential risk of mental depression and suicidal tendencies. The
results of this work may be employed to explore the impact of unemployment,
low grades, etc. Our analysis may also be useful for the study of online
behavior. A major limitation of the CAMS dataset is that the users may
intentionally post their intent of mental disorder on social media, e.g., for
deliberately making new friends. In this work, we have assumed that the data
has no such biasing.

Figure 4: Confusion matrix of CNN+LSTM model on test data

##  6\. Conclusion

This paper introduces the task of causal analysis to identify the reasons
behind mental depression and suicidal tendencies (intent). We have introduced
CAMS: a dataset of 5051 instances, to categorize the direct causes of mental
disorders through mentions by users in their posts. We transcend the work of
Level 0 studies, moving to the next level (Level 1) for causal analysis. Our
work is the combined effort of experts in the field of Social Natural Language
Processing (Social NLP), including a rehabilitation counselor and clinical
psychologists (CPsych). We have further implemented machine learning and deep
learning models for causal analysis and found that Logistic Regression and
CNN+LSTM gives the best performance, respectively. In the future, we plan to
extend the problem of causal analysis of mental health detection on social
media as a multi-task problem. Another major future challenge for this work is
the generation of explanations for multi-class classification, by leveraging
causal analysis within the CAMS framework.

##  7\. Acknowledgement

We acknowledge our three student annotators: Simran jeet Kaur, Astha Jain and
Ritika Bhardwaj. We also acknowledge Amrith Krishna for his kind support and
for proofreading this manuscript. Publication costs are funded by NSERC
Discovery Grant (RGPIN-2017-05377), held by Vijay Mago, Department of Computer
Science, Lakehead University, Canada.

##  8\. References

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# Production of heavy and superheavy nuclei in massive fusion reactions

Zhao-Qing Feng1111Corresponding author.
_E-mail address:_<EMAIL_ADDRESS>Gen-Ming Jin1, Jun-Qing Li1, Werner
Scheid2

1 _Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China_

2 _Institut für Theoretische Physik der Universität, 35392 Giessen, Germany_

Abstract

Within the framework of a dinuclear system (DNS) model, the evaporation-
residue excitation functions and the quasi-fission mass yields in the 48Ca
induced fusion reactions are investigated systematically and compared with
available experimental data. Maximal production cross sections of superheavy
nuclei based on stable actinide targets are obtained. Isotopic trends in the
production of the superheavy elements Z=110, 112-118 based on the actinide
isotopic targets are analyzed systematically. Optimal evaporation channels and
combinations as well as the corresponding excitation energies are proposed.
The possible factors that influencing the isotopic dependence of the
production cross sections are analyzed. The formation of the superheavy nuclei
based on the isotopes U with different projectiles are also investigated and
calculated.
_PACS:_ 25.70.Jj, 24.10.-i, 25.60.Pj
_Keywords:_ DNS model; evaporation-residue excitation functions; 48Ca induced
fusion reactions; isotopic trends

##  1 Introduction

The synthesis of heavy or superheavy nuclei is a very important subject in
nuclear physics motivated with respect to the island of stability which is
predicted theoretically, and has obtained much experimental research with the
fusion-evaporation reactions [1, 2]. The existence of the superheavy nucleus
(SHN) ($Z\geq 106$) is due to strong binding shell effects against the large
Coulomb repulsion. However, the shell effects get reduced with increasing the
excitation energy of the formed compound nucleus. Combinations with a doubly
magic nucleus or nearly magic nucleus are usually chosen owing to the larger
reaction $Q$ values. Reactions with 208Pb or 209Bi targets were first proposed
by Oganessian et al. to synthesize SHN [3]. Six new elements with Z=107-112
were synthesized in cold fusion reactions for the first time and investigated
at GSI (Darmstadt, Germany) with the heavy-ion accelerator UNILAC and the SHIP
separator [1, 4]. Recently, experiments on the synthesis of element 113 in the
70Zn+209Bi reaction have been performed successfully at RIKEN (Tokyo, Japan)
[5]. However, it is difficulty to produce heavier SHN in the cold fusion
reactions because of the smaller production cross sections that are lower than
1 pb for $Z>113$. Other possible ways to produce SHN are very needed to be
investigated in experimentally and theoretically. Recently, the superheavy
elements Z=113-116, 118 were synthesized at FLNR in Dubna (Russia) with the
double magic nucleus 48Ca bombarding actinide nuclei [6, 7, 8]. New heavy
isotopes 259Db and 265Bh have also been synthesized at HIRFL in Lanzhou
(China) [9]. Further experimental works are necessary in order to testify the
new synthesized SHN. A reasonable understanding of the formation of SHN in the
massive fusion reactions is still a challenge for theory.

In accordance with the evolution of two heavy colliding nuclei, the dynamical
process of the compound nucleus formation and decay is usually divided into
three reaction stages, namely the capture process of the colliding system to
overcome the Coulomb barrier, the formation of the compound nucleus to pass
over the inner fusion barrier, and the de-excitation of the excited compound
nucleus by neutron emission against fission. The transmission in the capture
process depends on the incident energy and relative angular momentum of the
colliding nuclei, which is the same as that in the fusion of light and medium
mass systems. The complete fusion of the heavy system after capture in
competition with quasi-fission is very important in the estimation of the SHN
production. The concept of the ”extra-push” energy explains for the fusion of
two heavy colliding nuclei in the macroscopic dynamical model [10, 11]. At
present it is still difficult to make an accurate description of the fusion
dynamics. After the capture and the subsequent evolution to form the compound
nucleus, the thermal compound nucleus will decay by the emission of light
particles and $\gamma$ rays against fission. The three stages will affect the
formation of evaporation residues observed in laboratories. The evolution of
the whole process of massive heavy-ion collisions is very complicated at near-
barrier energies. Most of the theoretical methods on the formation of SHN have
a similar viewpoint in the description of the capture and the de-excitation
stages, but there are different description of the compound nucleus formation
process. There are mainly two sorts of models, depending on whether the
compound nucleus is formed along the radial variable (internuclear distance)
or by nucleon transfer in a touching configuration which is usually the
minimum position of the interaction potential after capture of the colliding
system. Several transport models have been established to understand the
fusion mechanism of two heavy colliding nuclei leading to SHN formation, such
as the macroscopic dynamical model [10, 11], the fluctuation-dissipation model
[12], the concept of nucleon collectivization [13] and the dinuclear system
model [14, 15]. Recently, the improved isospin-dependent quantum molecular
dynamics (ImIQMD) model was also proposed to investigate the fusion dynamics
of SHN [16, 17]. With these models experimental data can be reproduced to a
certain extent, and some new results have been predicted. However, these
models differ from each other, and sometimes different physical ideas are
used.

Further improvements of these models have to be made. Here we use a dinuclear
system (DNS) model [15, 18], in which the nucleon transfer is coupled with the
relative motion by solving a set of microscopically derived master equations,
and a barrier distribution of the colliding system is introduced in the model.
We present a new and extended investigation of the production of superheavy
nuclei in the 48Ca induced fusion reactions and in other combinations.

In Section 2 we give a simple description on the DNS model. Calculated results
of fusion dynamics and SHN production are given in Section 3. In Section 4
conclusions are discussed.

##  2 Dinuclear system model

The dinuclear system [19] is a molecular configuration of two touching nuclei
which keep their own individuality [14]. Such a system has an evolution along
two main degrees of freedom: (i) the relative motion of the nuclei in the
interaction potential to form the DNS and the decay of the DNS (quasi-fission
process) along the R degree of freedom (internuclear motion), (ii) the
transfer of nucleons in the mass asymmetry coordinate
$\eta=(A_{1}-A_{2})/(A_{1}+A_{2})$ between two nuclei, which is a diffusion
process of the excited systems leading to the compound nucleus formation. Off-
diagonal diffusion in the surface $(A_{1},R)$ is not considered since we
assume the DNS is formed at the minimum position of the interaction potential
of two colliding nuclei. In this concept, the evaporation residue cross
section is expressed as a sum over partial waves with angular momentum $J$ at
the centre-of-mass energy $E_{c.m.}$,

$\sigma_{ER}(E_{c.m.})=\frac{\pi\hbar^{2}}{2\mu
E_{c.m.}}\sum_{J=0}^{J_{max}}(2J+1)T(E_{c.m.},J)P_{CN}(E_{c.m.},J)W_{sur}(E_{c.m.},J).$
(1)

Here, $T(E_{c.m.},J)$ is the transmission probability of the two colliding
nuclei overcoming the Coulomb potential barrier in the entrance channel to
form the DNS. In the same manner as in the nucleon collectivization model
[13], the transmission probability $T$ is calculated by using the empirical
coupled channel model, which can reproduce very well available experimental
capture cross sections [13, 15]. The $P_{CN}$ is the probability that the
system will evolve from a touching configuration into the compound nucleus in
competition with quasi-fission of the DNS and fission of the heavy fragment.
The last term is the survival probability of the formed compound nucleus,
which can be estimated with the statistical evaporation model by considering
the competition between neutron evaporation and fission [15]. We take the
maximal angular momentum as $J_{max}=30$ since the fission barrier of the
heavy nucleus disappears at high spin [20].

In order to describe the fusion dynamics as a diffusion process in mass
asymmetry, the analytical solution of the Fokker-Planck equation [14] and the
numerical solution of the master equations [21, 22] have been used, which were
also used to treat deep inelastic heavy-ion collisions [23]. Here, the fusion
probability is obtained by solving a set of master equations numerically in
the potential energy surface of the DNS. The time evolution of the
distribution function $P(A_{1},E_{1},t)$ for fragment 1 with mass number
$A_{1}$ and excitation energy $E_{1}$ is described by the following master
equations [18, 21],

$\displaystyle\frac{dP(A_{1},E_{1},t)}{dt}=\sum_{A_{1}^{\prime}}W_{A_{1},A_{1}^{\prime}}(t)\left[d_{A_{1}}P(A_{1}^{\prime},E_{1}^{\prime},t)-d_{A_{1}^{\prime}}P(A_{1},E_{1},t)\right]-$
$\displaystyle\left[\Lambda^{qf}(\Theta(t))+\Lambda^{fis}(\Theta(t))\right]P(A_{1},E_{1},t).$
(2)

Here $W_{A_{1},A_{1}^{\prime}}$ is the mean transition probability from the
channel $(A_{1},E_{1})$ to $(A_{1}^{\prime},E_{1}^{\prime})$, and $d_{A_{1}}$
denotes the microscopic dimension corresponding to the macroscopic state
$(A_{1},E_{1})$. The sum is taken over all possible mass numbers that fragment
$A_{1}^{\prime}$ may take (from $0$ to $A=A_{1}+A_{2}$), but only one nucleon
transfer is considered in the model with $A_{1}^{\prime}=A_{1}\pm 1$. The
excitation energy $E_{1}$ is the local excitation energy
$\varepsilon^{\ast}_{1}$ with respect to fragment $A_{1}$, which is determined
by the dissipation energy from the relative motion and the potential energy of
the corresponding DNS and will be shown later in Eqs.(8) and (9). The
dissipation energy is described by the parametrization method of the classical
deflection function [24, 25]. The motion of nucleons in the interacting
potential is governed by the single-particle Hamiltonian [15, 21]:

$H(t)=H_{0}(t)+V(t)$ (3)

with

$\displaystyle H_{0}(t)$ $\displaystyle=$
$\displaystyle\sum_{K}\sum_{\nu_{K}}\varepsilon_{\nu_{K}}(t)a_{\nu_{K}}^{{\dagger}}(t)a_{\nu_{K}}(t),$
$\displaystyle V(t)$ $\displaystyle=$
$\displaystyle\sum_{K,K^{\prime}}\sum_{\alpha_{K},\beta_{K^{\prime}}}u_{\alpha_{K},\beta_{K^{\prime}}}(t)a_{\alpha_{K}}^{{\dagger}}(t)a_{\beta_{K^{\prime}}}(t)=\sum_{K,K^{\prime}}V_{K,K^{\prime}}(t).$
(4)

Here the indices $K,K^{\prime}$ $(K,K^{\prime}=1,2)$ denote the fragments $1$
and $2$. The quantities $\varepsilon_{\nu_{K}}$ and
$u_{\alpha_{K},\beta_{K^{\prime}}}$ represent the single particle energies and
the interaction matrix elements, respectively. The single particle states are
defined with respect to the centers of the interacting nuclei and are assumed
to be orthogonalized in the overlap region. So the annihilation and creation
operators are dependent on time. The single particle matrix elements are
parameterized by

$u_{\alpha_{K},\beta_{K^{\prime}}}(t)=U_{K,K^{\prime}}(t)\left\\{\exp\left[-\frac{1}{2}\left(\frac{\varepsilon_{\alpha_{K}}(t)-\varepsilon_{\beta_{K^{\prime}}}(t)}{\Delta_{K,K^{\prime}}(t)}\right)^{2}\right]-\delta_{\alpha_{K},\beta_{K^{\prime}}}\right\\},$
(5)

which contain some parameters $U_{K,K^{\prime}}(t)$ and
$\Delta_{K,K^{\prime}}(t)$. The detailed calculation of these parameters and
the mean transition probabilities were described in Refs. [15, 21].

The evolution of the DNS along the variable R leads to the quasi-fission of
the DNS. The quasi-fission rate $\Lambda^{qf}$ can be estimated with the one-
dimensional Kramers formula [26, 27]:

$\Lambda^{qf}(\Theta(t))=\frac{\omega}{2\pi\omega^{B_{qf}}}\left(\sqrt{\left(\frac{\Gamma}{2\hbar}\right)^{2}+(\omega^{B_{qf}})^{2}}-\frac{\Gamma}{2\hbar}\right)\exp\left(-\frac{B_{qf}(A_{1},A_{2})}{\Theta(t)}\right).$
(6)

Here the quasi-fission barrier is counted from the depth of the pocket of the
interaction potential. The local temperature is given by the Fermi-gas
expression $\Theta=\sqrt{\varepsilon^{\star}/a}$ corresponding to the local
excitation energy $\varepsilon^{\star}$ and level density parameter $a=A/12$
$MeV^{-1}$. In Eq.(6) the frequency $\omega^{B_{qf}}$ is the frequency of the
inverted harmonic oscillator approximating the interaction potential of two
nuclei in R around the top of the quasi-fission barrier, and $\omega$ is the
frequency of the harmonic oscillator approximating the potential in R around
the bottom of the pocket. The quantity $\Gamma$, which denotes the double
average width of the contributing single-particle states, determines the
friction coefficients:
$\gamma_{ii^{\prime}}=\frac{\Gamma}{\hbar}\mu_{ii^{\prime}}$, with
$\mu_{ii^{\prime}}$ being the inertia tensor. Here we use constant values
$\Gamma=2.8$ MeV, $\hbar\omega^{B_{qf}}=2.0$ MeV and $\hbar\omega=3.0$ MeV for
the following reactions. The Kramers formula is derived with the quasi-
stationary condition of the temperature $\Theta(t)<B_{qf}(A_{1},A_{2})$.
However, the numerical calculation in Ref. [27] indicated that Eq.(6) is also
useful for the condition of $\Theta(t)>B_{qf}(A_{1},A_{2})$. In the reactions
of synthesizing SHN, there is the possibility of the fission of the heavy
fragment in the DNS. Because the fissility increases with the charge number of
the nucleus, the fission of the heavy fragment can affect the quasi-fission
and fusion when the DNS evolves towards larger mass asymmetry. The fission
rate $\Lambda^{fis}$ can also be treated with the one-dimensional Kramers
formula [26]

$\Lambda^{fis}(\Theta(t))=\frac{\omega_{g.s.}}{2\pi\omega_{f}}\left(\sqrt{\left(\frac{\Gamma_{0}}{2\hbar}\right)^{2}+\omega_{f}^{2}}-\frac{\Gamma_{0}}{2\hbar}\right)\exp\left(-\frac{B_{f}(A_{1},A_{2})}{\Theta(t)}\right),$
(7)

where the $\omega_{g.s.}$ and $\omega_{f}$ are the frequencies of the
oscillators approximating the fission-path potential at the ground state and
on the top of the fission barrier for nucleus $A_{1}$ or $A_{2}$ (larger
fragment), respectively. Here, we take
$\hbar\omega_{g.s.}=\hbar\omega_{f}=1.0$ MeV, $\Gamma_{0}=2$ MeV. The fission
barrier is calculated as the sum of a macroscopic part and the shell
correction energy used in Refs. [15, 28]. The fission of the heavy fragment
does not favor the diffusion of the system to a light fragment distribution.
Therefore, it leads to a slight decrease of the fusion probability.

In the relaxation process of the relative motion, the DNS will be excited by
the dissipation of the relative kinetic energy. The excited system opens a
valence space $\Delta\varepsilon_{K}$ in fragment $K(K=1,2)$, which has a
symmetrical distribution around the Fermi surface. Only the particles in the
states within this valence space are actively involved in excitation and
transfer. The averages on these quantities are performed in the valence space:

$\Delta\varepsilon_{K}=\sqrt{\frac{4\varepsilon^{\ast}_{K}}{g_{K}}},\varepsilon^{\ast}_{K}=\varepsilon^{\ast}\frac{A_{K}}{A},g_{K}=\frac{A_{K}}{12},$
(8)

where the $\varepsilon^{\ast}$ is the local excitation energy of the DNS,
which provides the excitation energy for the mean transition probability.
There are $N_{K}=g_{K}\Delta\varepsilon_{K}$ valence states and
$m_{K}=N_{K}/2$ valence nucleons in the valence space $\Delta\varepsilon_{K}$,
which gives the dimension $d(m_{1},m_{2})=\left(\begin{array}[]{c}N_{1}\\\
m_{1}\end{array}\right)\left(\begin{array}[]{c}N_{2}\\\
m_{2}\end{array}\right)$. The local excitation energy is defined as

$\varepsilon^{\ast}=E_{x}-\left(U(A_{1},A_{2})-U(A_{P},A_{T})\right).$ (9)

Here the $U(A_{1},A_{2})$ and $U(A_{P},A_{T})$ are the driving potentials of
fragments $A_{1}$, $A_{2}$ and fragments $A_{P}$, $A_{T}$ (at the entrance
point of the DNS), respectively. The detailed calculation of the driving
potentials can be seen in Ref. [18]. The excitation energy $E_{x}$ of the
composite system is converted from the relative kinetic energy loss, which is
related to the Coulomb barrier $B$ [29] and determined for each initial
relative angular momentum $J$ by the parametrization method of the classical
deflection function [24, 25]. So $E_{x}$ is coupled with the relative angular
momentum.

After reaching the reaction time in the evolution of $P(A_{1},E_{1},t)$, all
those components on the left side of the B.G. (Businaro-Gallone) point
contribute to the formation of the compound nucleus. The hindrance in the
diffusion process by nucleon transfer to form the compound nucleus is the
inner fusion barrier $B_{fus}$, which is defined as the difference of the
driving potential at the B.G. point and at the entrance position. Nucleon
transfers to more symmetric fragments undergo quasi-fission. The formation
probability of the compound nucleus at the Coulomb barrier $B$ (here a barrier
distribution $f(B)$ is considered) and angular momentum $J$ is given by

$P_{CN}(E_{c.m.},J,B)=\sum_{A_{1}=1}^{A_{BG}}P(A_{1},E_{1},\tau_{int}(E_{c.m.},J,B)).$
(10)

Here the interaction time $\tau_{int}(E_{c.m.},J,B)$ is obtained using the
deflection function method [30], which means the time duration for nucleon
transfer from the capture stage to the formation of the complete fused system
with the order of 10-20 s. We obtain the fusion probability as

$P_{CN}(E_{c.m.},J)=\int f(B)P_{CN}(E_{c.m.},J,B)dB,$ (11)

where the barrier distribution function is taken in asymmetric Gaussian form
[13, 15]. So the fusion cross section is written as

$\sigma_{fus}(E_{c.m.})=\frac{\pi\hbar^{2}}{2\mu
E_{c.m.}}\sum_{J=0}^{\infty}(2J+1)T(E_{c.m.},J)P_{CN}(E_{c.m.},J).$ (12)

The survival probability of the excited compound nucleus cooled by the neutron
evaporation in competition with fission is expressed as follows:

$W_{sur}(E_{CN}^{\ast},x,J)=P(E_{CN}^{\ast},x,J)\prod\limits_{i=1}^{x}\left(\frac{\Gamma_{n}(E_{i}^{\ast},J)}{\Gamma_{n}(E_{i}^{\ast},J)+\Gamma_{f}(E_{i}^{\ast},J)}\right)_{i},$
(13)

where the $E_{CN}^{\ast},J$ are the excitation energy and the spin of the
compound nucleus, respectively. The $E_{i}^{\ast}$ is the excitation energy
before evaporating the $i$th neutron, which has the relation

$E_{i+1}^{\ast}=E_{i}^{\ast}-B_{i}^{n}-2T_{i},$ (14)

with the initial condition $E_{1}^{\ast}=E_{CN}^{\ast}$. The energy
$B_{i}^{n}$ is the separation energy of the $i$th neutron. The nuclear
temperature $T_{i}$ is given by $E_{i}^{\ast}=aT_{i}^{2}-T_{i}$ with the level
density parameter $a$. $P(E_{CN}^{\ast},x,J)$ is the realization probability
of emitting $x$ neutrons. The widths of neutron evaporation and fission are
calculated using the statistical model. The details can be found in Ref. [15].
The level density is expressed by the back-shifted Bethe formula [31] with the
spin cut-off model as

$\rho(E^{\ast},J)=K_{rot}K_{vib}\frac{2J+1}{24\sqrt{2}\sigma^{3}}a^{-1/4}(E^{\ast}-\Delta)^{-5/4}\exp[2\sqrt{a(E^{\ast}-\Delta)}]\exp[-\frac{(J+1/2)^{2}}{2\sigma^{2}}],$
(15)

where the $K_{rot}$ and $K_{vib}$ are the coefficients of the rotational and
vibrational enhancements. The pairing energy is given by

$\Delta=\chi\frac{12}{\sqrt{A}}$ (16)

in MeV($\chi$=-1, 0 and 1 for odd-odd, odd-even and even-even nuclei,
respectively). The spin cut-off parameter is calculated by the formula:

$\sigma^{2}=T\zeta_{r.b}/\hbar^{2},$ (17)

where the rigid-body moment of inertia has the relation
$\zeta_{r.b}=0.4MR^{2}$ with the mass $M$ and the radius $R$ of the nucleus.
The level density parameter is related to the shell correction energy
$E_{sh}(Z,N)$ and the excitation energy $E^{\ast}$ of the nucleus as

$a(E^{\ast},Z,N)=\tilde{a}(A)[1+E_{sh}(Z,N)f(E^{\ast}-\Delta)/(E^{\ast}-\Delta)].$
(18)

Here, $\tilde{a}(A)=\alpha A+\beta A^{2/3}b_{s}$ is the asymptotic Fermi-gas
value of the level density parameter at high excitation energy. The shell
damping factor is given by

$f(E^{\ast})=1-\exp(-\gamma E^{\ast})$ (19)

with $\gamma=\tilde{a}/(\epsilon A^{4/3})$. All the used parameters are listed
in Table 1. In Fig.1 we give the level density parameters of different
nuclides at the ground state calculated by using Eq.(18) and compared them
with two empirical formulas $a(A)=A/8$, and $A/12$. It can be seen that the
strong shell effects appear in the level density.

With this procedure introduced above, we calculated the angular momentum
dependence of the capture, fusion and survival probabilities as shown in Fig.2
for the reaction 48Ca+208Pb at incident energies 172.36 MeV and 192.36 MeV,
respectively. The values of the three stages decrease obviously with
increasing the relative angular momentum. So in the following estimation of
the production cross sections, we cut off the maximal angular momentum at
$J_{max}=30$, which is taken as the same value that used in the cold fusion
reactions [18].

##  3 Results and discussions

###  3.1 Fusion-fission reactions and quasi-fission mass yields

As a test of the parameters for the estimation of the transmission of two
colliding nuclei and the de-excitation of the thermal compound nucleus, we
analyzed the fusion-fission reactions for the selected systems shown in Fig.3
assuming $P_{CN}=1$. The capture and evaporation residue cross sections are
compared with the available experimental data [32, 33, 34, 35]. For these
systems the quasi-fission does not dominate in the sub-barrier region, which
also means that $P_{CN}\sim 1$. The evaporation residues are mainly determined
through the capture of the light projectile by the target nucleus and the
survival probabilities of the formed compound nucleus. The experimental data
can be reproduced rather well within the error bars. Some discrepancies may
come from the quasi-fission in the above barrier region and from the input
quantities, such as the neutron separation energy, shell correction and mass.
The rotational and the vibrational enhancement in the level density can also
affect the survival probabilities of the excited compound nucleus [36]. Here
we take unity for both coefficients as shown in Table 1 because the height of
the fission barrier is also sensitive to the survival of the compound nucleus
by fitting the experimental evaporation residue excitation functions in the
fusion-fission reactions.

Since the electrostatic energy of the composite systems formed by two heavy
colliding nuclei is very large, so although the two nuclei may be captured by
the nuclear potential, they almost always separate after mass transfer from
the heavier nucleus to the lighter one rather fusing. This process is called
quasi-fission [37, 38], which is the main feature in the massive fusion
reactions and can inhibit fusion by several degree of freedom. Recently,
experiment has performed nice works by measuring the quasi-fission and fusion-
fission mass yields [39]. In the DNS model, the quasi-fission mass yields are
expressed as [26]

$Y_{q-f}(A_{1})=\sum_{J=0}^{J_{max}}\int_{0}^{\tau_{int}}P(A_{1},E_{1},t)\Lambda^{qf}(\Theta(t))dt.$
(20)

In Fig.4 we show a comparison of the calculated quasi-fission mass yields and
the experimental data for the two 48Ca induced reaction systems. The trends of
the distribution can be reproduced by the DNS model. At the domain of the
medium-mass fragments A1=ACN/2-30$\sim$ACN/2+30, The experimental data are
higher than the calculated values, which may be come from the contribution of
the fusion-fission fragments.

###  3.2 Evaporation residue cross sections

The evaporation residues observed in laboratories by the consecutive $\alpha$
decay are mainly produced by the complete fusion reactions, in which the
fusion dynamics and the structure properties of the compound nucleus affect
their production. Within the framework of the DNS model, we calculated the
evaporation residue cross sections producing SHN Z=110, 112, 113, 115 with
232Th, 238U, 237Np and 243Am targets in the 48Ca induced reactions as shown in
Fig.5, and compared them with the Dubna data [7, 40, 41] as well as with the
recent GSI data [42] for 238U targets in the 3n channel. Compared with the
Dubna data for the system 48Ca+238U, the GSI results show that the formation
cross sections in the 3n channel have a slight decrease at the same excitation
energy, which is in a good agreement with our calculated results. The
calculations were carried out before getting the experimental data [41] for
the reaction 48Ca+237Np, and a good agreement with the data is also found
[43]. The excitation energy of the compound nucleus is obtained by
$E^{\ast}_{CN}=E_{c.m.}+Q$, where the $E_{c.m.}$ is the incident energy in the
center-of-mass system. The $Q$ value is given by $Q=\Delta M_{P}+\Delta
M_{T}-\Delta M_{C}$, and the corresponding mass excesses $\Delta M_{i}$
($i=P,T,C$) are taken the data from Ref. [44] for the projectile, target and
compound nucleus denoted with the symbols $P$, $T$ and $C$, respectively.
Usually, the neutron-rich projectile-target combinations are in favor of
synthesizing SHN experimentally, which can enhance the survival probability
$W_{sur}$ in Eq.(1) of the formed compound nucleus because of the smaller
neutron separation energy. Differently to the cold fusion reactions [18], the
maximal production cross sections from Ds to 115 especially in the 2n-5n
channels are not changed much although the heavier SHNs are synthesized.
Within the error bars the experimental data can be reproduced rather well.
With the same procedure, we analyzed the evaporation residue excitation
functions with targets 242,244Pu and 245,248Cm that are used to synthesize the
superheavy elements Z=114 and 116 in Dubna [40, 45] (Fig.6). Our calculations
show that the target 244Pu has a larger production cross section than 242Pu
because of the larger survival probability. In Fig.7 we also calculated the
evaporation residue excitation functions to synthesize superheavy elements
Z=117-120 using the actinide isotopes with longer half-lives 247Bk, 249Cf,
254Es and 257Fm. The 3n evaporation channel with an excitation energy of the
formed compound nucleus around 30 MeV is favorable to produce SHN with
Z$\geq$117 by using the actinide targets. Within the error bars, the positions
of the maximal production cross sections are in good agreement with the
available experimental results. Similar calculation of the evaporation residue
excitation functions was also reported in Ref. [46]. The spectrum form of
evaporating neutrons is mainly determined by the survival probability, in
which the neutron separation energy and the shell correction play a very
important role in the determination of the value. We considered the angular
momentum influence in the calculation of the level density, but did not
include it in the estimation of the fission barrier of the thermal compound
nucleus. As pointed out in section 1, the fission barrier of SHN decreases
rapidly with increasing excitation energy of the compound nucleus, where the
rotation of the system affects the height of the barrier and also influences
other crucial quantities such as the level density etc.

In Fig.8 we show a comparison of the calculated maximal production cross
sections of superheavy elements Z=102-120 in the cold fusion reactions by
evaporating one neutron, in the 48Ca induced reactions with actinide targets
by evaporating three neutrons, and the experimental data [1, 2, 4, 47]. The
production cross sections decrease rapidly with increasing the charge number
of the synthesized compound nucleus in the cold fusion reactions, such as from
0.2 $\mu b$ for the reaction 48Ca+208Pb to 1 pb for 70Zn+208Pb, and even below
0.1 pb for synthesizing Z$\geq$113 [18]. It seems to be difficult to
synthesize superheavy elements Z$\geq$113 in the cold fusion reactions at the
present facilities. The calculated results show that the 48Ca induced
reactions have smaller production cross sections with 232Th target, but are in
favor of synthesizing heavier SHN (Z$\geq$113) because of the larger cross
sections. The experimental data also give such trends. In the DNS concept, the
inner fusion barrier increases with reducing mass asymmetry in the cold fusion
reactions, which leads to a decrease of the formation probability of the
compound nucleus. However, the 48Ca induced reactions have not such increase
of the inner fusion barrier for synthesizing heavier SHN. Because of the
larger transmission and the higher fusion probability, we obtain larger
production cross sections for synthesizing SHN (Z$\geq$113) in the 48Ca
induced reactions although these reactions have the smaller survival
probability than those in the cold fusion reactions. It is still a good way to
synthesize heavier SHN by using the 48Ca induced reactions. Of course, further
experimental data are anticipated to be obtained in the future. However, the
actinide targets are difficulty to be handled in experiments synthesizing
heavier SHN.

###  3.3 Isotopic dependence of the production cross sections

Recent experimental data show that the production cross sections of the SHN
depend on the isotopic combination of the target and projectile in the 48Ca
induced fusion reactions. For example, the maximal cross section in the 3n
channel is $3.7\pm^{3.6}_{1.8}$ pb for the reaction 48Ca+245Cm at the
excitation energy 37.9 MeV; however, it is $1.2$ pb for the reaction
48Ca+248Cm although the later is a neutron-rich target [8, 40]. The isotopic
trends of the production cross sections were also observed and investigated in
cold fusion reactions [48, 18]. Further investigations on the isotopic trends
in the 48Ca induced reactions are very necessary for predicting the optimal
combinations, excitation energies (incident energies) and evaporation channels
in the synthesis of SHN. In Fig.9 we show the calculated isotopic trends in
producing superheavy elements Z=110, 112 with the isotopic actinides Th and U
in the 3n channels, and compare them with the available experimental data
performed in Dubna [40] (squares with error bars) and at GSI [42] (circles
with error bars). The results show that the targets 230Th in the 4n channel
and 235,238U in the 3n channel have the largest cross sections. The isotopic
trends in synthesizing Z=113-116 with the actinide targets Np, Pu, Am and Cm
are also calculated systematically, and compared with the existing data
measured in Dubna [7, 40, 45] and the results of Adamian et al. [49] for the
Pu isotopes as shown in Fig.10 and Fig.11. The isotopes 237Np, 241Pu,
242,243Am and 245,247Cm in the 3n channels, and 244Pu in the 4n channel as
well as the isotope 250Cm are suitable for synthesizing SHN. Except for the
244Pu, our calculated cross sections are smaller than the ones of the Adamian
et al. In the DNS model, the isotopic dependence of the production cross
sections is mainly determined by both the fusion and survival probabilities.
Of course, the transmission probability of two colliding nuclei can also be
affected since the isotopes have initial quadrupole deformations. With the
same procedure, we analyzed the dependence of the production cross sections on
the isotopes Bk and Cf in the 3n channels for synthesizing the superheavy
elements Z=117, 118 and compared them with the available experimental data [8]
shown in Fig.12. The results show that the targets 248,249Bk and 251,252Cf are
favorable for synthesizing the superheavy elements Z=117 and 118. The
corresponding excitation energies are also given in the figures.

In Fig.13 we show the dependence of the inner fusion barrier, the fission
barrier of the compound nucleus, and the neutron separation energies of
evaporating 3n and 4n on the mass numbers of the isotopic targets Cm in the
48Ca induced reactions. It is obvious that the combinations with the isotopes
245,247Cm have smaller inner fusion barriers, higher fission barriers and
smaller 3n separation energies, which result in larger production cross
sections producing the superheavy element Z=116. Although the lower fission
barrier for the isotope 250Cm, it gives the smaller inner fusion barrier and
neutron separation energies, which also leads to the larger cross sections in
the 3n and 4n channels as shown in Fig.11. The shell correction and the
neutron separation energies are taken from Ref. [44]. When the neutron number
of the target increases, the DNS gets more asymmetrical and the fusion
probability increases if the DNS does not consist of more stable nuclei (such
as magic nuclei) because of a smaller inner fusion barrier. A smaller neutron
separation energy and a larger shell correction lead to a larger survival
probability. The compound nucleus with closed neutron shells has a larger
shell correction energy and a larger neutron separation energy. The neutron-
rich actinide target has larger fusion and survival probabilities due to the
larger asymmetric initial combinations and smaller neutron separation
energies. But such actinide isotopes are usually unstable with smaller half-
lives. With the establishment of the high intensity radioactive-beam
facilities, the neutron-rich SHN may be synthesized experimentally, which
approaches the island of stability.

###  3.4 238U based reactions

The uranium is the heaviest element existing in the nature. It has a larger
mass asymmetry constructed as a target in the fusion reactions with the
various neutron-rich light projectiles. The isotope 238U is the neutron-
richest nucleus in the U isotopes and often chosen as the target for
synthesizing SHN. In Fig.14 we give evaporation residue excitation functions
of the reactions 40Ar, 50Ti, 54Cr, 64Ni+238U in the 2n-5n channels. The
results show that the 4n channel in the reaction 40Ar+238U has the larger
cross sections with 2.1 pb at an excitation energy 42 MeV. This reaction is
being used to synthesize the superheavy nucleus Ds with HIRFL accelerator at
Institute of Modern Physics in Lanzhou. The reactions 50Ti, 54Cr, 64Ni+238U
lead to the cross section smaller than 0.1 pb. The isotopic trends based on
the U isotopes are also investigated using the DNS model as shown in Fig.15.
Calculations show that the isotopes 235U and 238U are favorable in producing
SHN. The cross sections are reduced with increasing the mass numbers of the
projectiles. Other reaction mechanisms to synthesize SHN have to be
investigated with theoretical models, such as the massive transfer reactions,
and the complete fusion reactions induced by weakly bound nuclei. Work in
these directions is in progress within the framework of the DNS model.

##  4 Conclusions

Using the DNS model, we systematically investigated the production of
superheavy residues in fusion-evaporation reactions, in which the nucleon
transfer leading to the formation of the superheavy compound nucleus is
described with a set of microscopically derived master equations that are
solved numerically and include the quasi-fission of the DNS and the fission of
the heavy fragments. The fusion dynamics and the evaporation residue
excitation functions in the 48Ca fusion reactions are systematically
investigated. The calculated results are in good agreement with the available
experimental data within the error bars. Isotopic trends in the production of
superheavy elements are analyzed. It is shown that the isotopes 235,238U,
237Np, 241,244Pu, 242Am and 245,247,250Cm, 248,249Bk and 251,252Cf in the 3n
channels, and 230Th, 244Pu, 248,250Cm in the 4n channels are favorable for
producing the superheavy elements Z=110, 112 and 113-118, respectively. The
evaporation residue excitation functions of the reactions 40Ar, 50Ti, 54Cr,
64Ni+238U in the 2n-5n channels and the isotopic trends with 40Ar, 48Ca, 50Ti,
54Cr, 58Fe and 64Ni bombarding U isotopes are also studied.

##  5 Acknowledgement

One of us (Z.-Q. Feng) is grateful to Prof. H. Feldmeier, Dr. G.G. Adamian and
Dr. N.V. Antonenko for fruitful discussions and help, and also thanks the
hospitality during his stay in GSI. This work was supported by the National
Natural Science Foundation of China under Grant No. 10805061, the special
foundation of the president fellowship, the west doctoral project of Chinese
Academy of Sciences, and major state basic research development program under
Grant No. 2007CB815000.

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Table 1: Parameters used in the calculation of the level density.

$K_{rot}$ $K_{vib}$ $b_{s}$ $\alpha$ $\beta$ $\epsilon$ 1 1 1 0.114 0.098 0.4

Figure 1: Calculated values of the level density parameters as a function of
the atomic mass. Figure 2: Calculated capture, fusion and survival
probabilities as functions of the relative angular momenta in the reaction
48Ca+208Pb at excitation energies of the compound nucleus of 20 MeV and 40
MeV, respectively. Figure 3: Comparison of the calculated fusion-fission
excitation functions and the available experimental data for the reactions
16O+208Pb, 16O+238U, 36Ar+148Sm and 26Mg+238U. Figure 4: Calculated quasi-
fission mass yields for the reactions 48Ca+244Pu and 48Ca+248Cm at excitation
energies of the compound nuclei 42 MeV and 33 MeV, respectively, and compared
them with the available experimental data [39]. Figure 5: The calculated
evaporation residue excitation functions with 232Th, 238U, 237Np and 243Am
targets in 48Ca induced reactions, and compared with the available
experimental data [7, 40, 41]. Figure 6: The same as in Fig.5, but for the
targets 242,244Pu and 245,248Cm to produce superheavy elements Z=114 and 116.
Figure 7: The same as in Fig.5, but for the targets 247Bk, 249Cf, 254Es and
257Fm to synthesize superheavy elements Z=117-120. Figure 8: Maximal
production cross sections of superheavy elements Z=102-120 in cold fusion
reactions based on 208Pb and 209Bi targets with projectile nuclei 48Ca, 50Ti,
54Cr, 58Fe, 64Ni, 70Zn, 76Ge, 82Se, 86Kr and 88Sr, in 48Ca induced reactions
with actinide targets by evaporating 3 neutrons, in comparison with available
experimental data [1, 2, 4, 47]. Figure 9: Isotopic dependence of the
calculated maximal production cross sections in the 3n evaporation channel and
the corresponding excitation energies in the synthesis of superheavy elements
Z=110 and 112 for the reactions 48Ca+ATh and 48Ca+AU, and compared with the
experimental data [40, 42]. Figure 10: The same as in Fig.9, but for isotopic
targets Np and Pu to produce superheavy elements Z=113 and 114. Figure 11: The
same as in Fig.9, but for isotopic targets Am and Cm to synthesize superheavy
elements Z=115 and 116 in 3n and 4n channels. Figure 12: The same as in Fig.9,
but for isotopes Bk and Cf in 48Ca induced reactions. Figure 13: (a) the inner
fusion barrier, (b) the fission barrier of the compound nucleus and (c) the
neutron separation energy as a function of the mass numbers of the isotopic
targets Cm in the reactions 48Ca+ACm. Figure 14: The evaporation residue
excitation functions in the reactions 40Ar, 50Ti, 54Cr, 64Ni+238U. Figure 15:
The production cross sections in the 3n channels as a function of the mass
number of the isotopic targets U with projectiles 40Ar, 48Ca, 50Ti, 54Cr, 58Fe
and 64Ni.