What are the most sensitive emotions that rise during critical negotiations? How to deal with them?

In any negotiations the recognition of and the trigger for emotional outburst needs to be understood. As a negotiator your reaction to this will be important. In dealling with them, some of the questions you may ask your self are:

1. Do we need to have a break to allow emotions to be dealt with?
2. Have i presented my interests in the best way or do i need to reframe?
3. Have i appreciated the cultural differences that might be part of discussion?
4. Is the emotions a tactic  being employed by my opponent?
5. Can i use the emotions to focus my negotiations?

Without some sort of calm the chances of negotiating any issues in an emotions charged theatre would be remote. You need to recognise the emotions and have a means of dealing with them before you reach an agreement.

My simple rule is get the relationship right, charter of behaviour then deal with the technical issues. Without a cooperative or collaborative approach negotiations will be impeded. While people are talking you have a chance, when people stop talking your in trouble. 

Appreciate invitation.

There are two categories of emotions, positive and negative. The negative emotions, like sadness, disgust, anger or fear of losing the deal may rise in the situation when either party adopts extreme position  and take the negotiation toward "win-lose" position, not acceptable by the other party. Such emotional situation may rise also due to bad faith or losing face values for some reasons. These emotions are incidental. The effect of incidental emotions on the decision making is critical.

On the other hand there is a deliberate and self designed emotional action, sometimes applied as a strategy to bargain more in the negotiation process. Preference of fairness is often in conflict with self-interest.

Sometimes inter-cultural differences may also spoil a critical negotiation if not handled professionally. Therefore, in Commercial negotiation both the parties should be flexible specially when you are lacking of more options.

You should have good "Conflict Management Skills" to differentiate and handle such unpleasant incidents.

You should have ability to control "Emotional Intelligence", to recognize your own and other's emotions. This will help to adopt your behavior and be flexible in your approach to deal in tension, conflicts and disrespectful counterparts during negotiation.

Researchers have begun examining how specific emotions—anger, sadness, disappointment, anxiety, envy, excitement, and regret—can affect the behavior of negotiators. They’ve studied the differences between what happens when people simply feel these emotions and what happens when they also express them to the other party through words or actions. In negotiations that are less transactional and involve parties in long-term relationships, understanding the role of emotions is even more important than it is in transactional deal making.

The truth is that your passions matter in real-life deal making and dispute resolution. You need to understand, channel, and learn from your emotions in order to adapt to the situation at hand and engage others successfully. That means you need to be emotionally prepared to negotiate—even when you expect the process to go smoothly. Anxieties and petty resentments may lurk below the surface. If you let them fester, or if you inadvertently get under a counterpart’s skin, talks can go off the rails. You also need to sense the first stirrings of your own feelings so that you don’t tense up, tune out, or explode.

The ability to monitor one’s own and others’ feelings and emotions, to discriminate among them and to use this information to guide one’s thinking and actions.” Specifically, emotionally intelligent people have the capacity to:

• identify the emotions they and others are experiencing;

• understand how those emotions affect their thinking;

• use that knowledge to achieve better outcomes;

• productively manage emotions, tempering or intensifying them for whatever purpose.                                                                                                               Though the business world was quick to apply emotional intelligence to leadership development, team building, and people management, it’s gotten surprisingly little attention in the field of negotiation.

it's showed through eye contacts, facial expressions, and the way of sitting, looking to his watch, touching nose .......... etc

generally it depends on body language and the other party culture

It shows through gesture that the other party is frustrated or under pressure when you talk to them and you would feel from hands and eyes contacts that they want to end this.