Is there a pali term for "natural concentration"? In the book, "Handbook for mankind" Buddhadhasa Bikkhu describes two types of concentration:


One "as a result of organized practice", which he refers to as vipassana-dhura, and is mentioned in post-tipitaka commentaries.
One that "come about naturally".


In the text, there are no pali words given for the latter, and the only reference given is that it is described in the Tipitaka. 

My questions are, 


Is there a name in pali for the latter type?
Are there specific descriptions of the second type of concentration somewhere in the tipitaka or elsewhere?


(Please note that i'm not asking for the correctness, efficacy, or other evaluations of the statements above. This is primarily a reference request).
I used to study Ajahn Buddhadasa very comprehensively. However, Handbook For Mankind was a book I was never partial towards. While it contains many basic teachings, I always found the verbal style of delivery difficult or abrasive to read. However, merely browsing and offering an answer: 


The book is from 1956 lectures the Venerable Buddhadasa Bhikkhu gave to a group of prospective judges. Therefore, the two chapters on meditation are addressed to laypeople. 
The chapter on "Nature Method" concludes: "Summing up, natural concentration and insight, which enable a person to attain the Path and the Fruit, consist in verifying all day and every day the truth of the statement that nothing is worth getting or being."
The statement: "nothing is worth getting or being" essentially comes from MN 37. It is a statement of Right Understanding: Samma Ditthi. 
In his book Heartwood From The Bo Tree, Bhikkhu Buddhadasa said about concentration: "As for samadhi, an empty mind is the supreme samadhi, the supremely focused firmness of mind. The straining and striving sort of samadhi isn't the real thing and the samadhi which aims at anything other than non-clinging to the five khandas is micchasamadhi (wrong or perverted samadhi). You should be aware that there is both micchasamadhi and sammasamadhi (right or correct samadhi). Only the mind that is empty of grasping at and clinging to 'I' and 'mine' can have the true and perfect stability of sammasamadhi. One who has an empty mind has correct samadhi."
To conclude, the teachings above by Bhikkhu Buddhadasa accord with the following sutta teachings about samadhi: 


sattahaṅgehi cittassa ekaggatā parikkhatā sammādiṭṭhi pubbaṅgamā: mind with single intent equipped with seven factors in use where right view is the leader (MN 117)
samādhindriyaṃ vossaggārammaṇaṃ: faculty of concentration reliant upon letting go (SN 48.10) 
samādhisambojjhaṅgaṃ vivekanissitaṃ virāganissitaṃ nirodhanissitaṃ vossaggapariṇāmiṃ: concentration factor of enlightenment that relies on solitude, dispassion &amp; cessation maturing as letting go (MN 118).  

In summary, "natural concentration" means "concentration without craving".