Are there different factors for access concentration depending on which jhana an individual is entering? I have heard that a practitioner does not go from first jhana directly to second jhana or from second jhana directly to third jhana and so on. Instead, they go through momentary and access concentration to get to first jhana; then they drop out of first jhana and go through momentary and access concentration to get to second jhana and so on. First of all, is this correct, am I totally wrong or is there debate with regards to this?

Secondly, do the factors of access concentration change depending on which jhana someone is trying to enter?
I can only answer first part of your question, i.e. if a meditator returns to access concentration between Jhana-states.
You are correct in that understanding. Here is a quote from the book &quot;Practicing The Jhanas&quot; by Tina Rasmussen and Stephen Snyder, which describes access concentration and that between entering the different Jhana-states the meditator returns to access concentration. Highlights in the quote are made by me:

ACCESS CONCENTRATION
Meditators can eventually attain access concentration using either type of momentary concentration practice—samatha or vipassanā. However, samatha practices are more likely to lead to access concentration because of their more stable nature. Access concentration is characterized by the significant reduction or complete dropping of the five hindrances and the arising and strengthening of the jhāna factors. For most people, a period of intensive practice is required to reach access concentration. In access concentration, the meditative experience becomes smoother, easier, and more pleasant because of this lessening of hindrances and the arising of the powerful and blissful sensations of the jhāna factors. This allows meditators to meditate longer and progress more easily in the practice.
It becomes a positive, self-reinforcing loop.It is easy to confuse momentary concentration with access concentration. One difference is that with access concentration, the meditator’s continuity with the object is much longer and more stable over time. Another difference is that with access concentration, the object is much more energized and “bright.”Most of the practices outlined in this book are samatha practices specifically designed to settle the mind and develop laserlike awareness, leading eventually to full absorption into the jhānas. Examples of samatha practices designed to develop access and absorption concentration are ānāpānasati meditation (as presented by the Venerable Pa Auk Sayadaw), the kasiṇas, thirty-two-body-parts meditation, skeleton meditation, and the bramavihāras (sublime abidings).
As access concentration develops, but prior to full absorption, it is also easy to confuse access with absorption concentration. In access concentration, the jhāna factors are present but insufficiently strong for full absorption into jhāna. (The differences between access and absorption are described below.) Even after a meditator has experienced full jhāna absorption and begins to move through the practice progression, access concentration continues to be used. With progression to each successive jhāna, the meditator first experiences access concentration as the awareness orients to the new experiences and increases in stability.
-- Practicing The Jhanas, p. 73-75