Hi. I agree with you that its important to try to understand the archetypal core from which keywords/characteristics like 'intense' arise. Obviously we're dealing with the interaction of two archetypes here - that symbolised by the ascendant, and that symbolised by the zodiacal sign of Scorpio.
The Ascendant symbolises the experience of being an entity which can act upon its environment. It doesn't symbolise self-awareness in an objective or reflective manner, but rather the raw awareness of being a self at all. Other parts of the house cycle symbolise the various experiences through which we become more fully conscious of all that we are; the ascendant, as the beginning of the house cycle, gets the ball rolling by introducing an individual to the very fact of her or his existence. As with all cycles, the initial impulse which begins the house cycle resonates throughout the whole cycle, and every experience is coloured by the nature of the ascendant in the native's chart. In other words, every moment is a new beginning of one sort or another. So the ascendant is an interface between the native and life - and any archetype found 'on' the ascendant forms an inescapable image of what it is to be an individual. To develop the qualities of such an archetype is to enhance one's ability to 'deliver' (Rudhyar - The Astrological Houses) oneself into the world in a convincing and creative manner in each moment, and particularly in those moments which are particularly significant because they mark the beginning of some new venture or phase of life.
When differentiating between a point or stage of the house cycle, and a point or stage on the zodiacal cycle, it is important to note that where a house symbolises a particular category of experience - for example, the first house symbolises the experience of being an individual entity, and the second house symbolises the experience of drawing upon available resources to bolster one's individual existence - a zodiacal sign symbolises a particular type of life-giving fuel. Aries symbolises the fuel which enables us initiate new ventures and assert our right to be; Taurus symbolises the fuel which enables us to consolidate our position; and so on.
Besides the mode and element of a sign, it is important to note the position of a zodiacal sign in the zodiacal cycle. Scorpio is the fixed water sign. On the water 'plane' we connect with life in a way which is felt as either pleasant or unpleasant, and fixity focuses an element in a way which intensifies our experience of it. From this we can already produce a long list of keywords, but there is something missing from our understanding if we don't note that Scorpio's combining of water and fixity implies, and is implied by, Scorpio's position in the zodiacal cycle. In other words, the mode and element cycles could only produce that combination of water and fixity at that point of the cycle, and at that point in the cycle, only that combination could arise.
The first six signs are concerned with fuelling the development of the separate individual - the second six with fuelling the development of the larger collective of which the individual is part. In Libra, the tendency for individuals to come together as units of togetherness is new, although Virgoan service is a preparation for this, and Cancer and Leo can also be seen as prior stages in such preparation. Libra, as the cardinal air sign, and the sign which really gets collectivisation going, does so on a certain level - an intellectual level. Social etiquettes etc are laid out which will provide a basis on which individuals can co-exist in partnerships, communities, and so on. In Scorpio, the process of collectivisation is consolidated (just as the Arian impulse to exist was consolidated by Taurus). Where individuality is consolidated on the earth plane - an inherently boundaried plane - collectivisation is consolidated on the water plane - an inherently unboundaried plane where individuals can merge with one another and cement their communal ties (of whatever nature) at a deep feeling level.
The general thrust of the third quadrant of the zodiacal cycle is towards unquestioning collectivisation, but in Scorpio there is often hesitancy because the potential to experience painful feelings arises here to a much greater extent than in the signs of Libra and Sagittarius which are also found in this quadrant. But it is in the nature of Scorpio of merge individuals together.
Scorpio on the ascendant symbolises the fact that the native must use Scorpio fuel in all acts of 'self-delivery'. The native is motivated to act upon the world by opportunities to use Scorpio fuel, and opportunities to use Scorpio fuel are more readily noticed by the native as she or he surveys her or his surroundings. The individual is better able to function as an individual when there is sufficient trust to honour the deep connectedness which potentially exists between individuals - to share resources and participate with feeling in the various binding rituals which help to cement people into a society. Sexual intimacy is only one way in which people can experience that depth of connectedness.
Where such trust is lacking, the Scorpio rising native will hold back rather than risk painful feelings, having been taught in childhood that openness leads to humiliation, and investing of oneself leads to a poor return.
Well I ended up writing more than I intended, but its good to spend time collecting and organising thoughts when trying to learn about something as vast as astrology. Hopefully you'll get something from it too. If this kind of approach interests you, then the Rudhyar book mentioned above, and also his book, 'The Pulse of Life' are highly recommended, though need careful and patient reading.