I know there is a multiplier factor by using Sm (ppm) results from bulk-rock geochemical data in igneous rocks that roughly evaluate if these rocks are or not from crustal/mantle origin. Do anyone know about that?
This sounds a bit confused - you can calculate the 147Sm/144Nd ratio based on the Sm and Nd concentration data from a whole rock analysis - but that is something you would only really need if you also have the 143Nd/144Nd ratio so you can calculate an initial ratio at a certain age, to comapre to the mantle at that age. By itself the 147Sm/144Nd, or simply the Sm/Nd ratio does not tell you much about mantle or crustal origin. Rocks with a low Sm/Nd ratio can either have crustal origin, or represent a small-degree melt from the mantle, or a high-degree melt from enriched mantle. Of course samples with a very flat REE , or LREE-depleted pattern are more likely to be mantle-derived than those with an LREE-enriched pattern, but this is most easily assessed in a normalised REE diagram.
both answers above agree with what I know about isotope geochemistry- there is no way to use whole rock geochemistry to infer isotopic characteristics. As for a mantle origin, if you have basic rocks, Ni and Cr contents are quite useful to infer how close your rock (melt) is to a mantle derived magma.
I am also unsure whether I understand the question. To calculate E(Nd) for any rock one needs to know (1) The 143Nd/144Nd of the rock; (2) The age of the rock so that one can calculate the initial 143Nd/144Nd of the rock and CHUR at that age; (3) 147Sm/144Nd which can be obtained by measurement or calculated from Sm and Nd concentration data provided one knows the 143Nd/144Nd. The interpretation of E(Nd) in terms of mantle or crustal derivation is also not that straightforward. Very young mantle-derived CRUSTAL rocks may have negative (mantle-like) E(Nd) and many mantle-derived igneous rocks (some basalts, lamproites, some kimberlites) have positive (crustal-like) E(Nd). I agree with all the responses you have had from others
I am also agree with all above answers. You should take care when using epsilon Nd to evaluate the origin of the rocks. It is better to use the isotopic data with other whole rock geochemical data especially the REEs to study the petrogenesis of your rocks.
probably this spreadsheet can help you to clarify some basic concepts on epsilon values (both for Sr and Nd isotopes, but it can be exported also for other isotope systematics). This is part of the homework I give to my graduate students.