Bare soil index in not name of the index but it is the index prepared for analyzing bare soils as bare-soil plays an important role by being  the reason of dust storms. this index was prepared to study the deltas and to improve the land use classification through remote sensing 

the give article may help you to understand more.

Dear Salamma,

Can you explain why it is not the name of the index?

I think, because the index used for analysis of bare soil. I have gone through the paper attached here and I suggest you to please go through the article. You can find more details of bare soil index in the attached research article. 

http://dx.doi.org/10.5194/isprsarchives-XL-4-139-2014

Yeah.  I have gone through that. Rather it was a derived index from T-cap. Im searching on the Bare soil index using: 

( ( (float(b1)+float(b2)) - (float(b3)+float(b4)) ) / ( (float(b1)+float(b2)) + (float(b3)+float(b4)) ) )

b1 = L5

b2 = L3

b3 = L4

b4 = L1