Calculating the mass of isotopes

zincshow

The spin values of each isotope of carbon are given on wiki here.

When showing nuclear spin values the notation (1/2+)# is used.

I dont understand what the () brackets and # hashtag are for?

At the bottom of the page, they clarify it by saying:

"Values marked # are not purely derived from experimental data, but at least partly from systematic trends. Spins with weak assignment arguments are enclosed in parentheses."

Are these values not specifically calculated from first principles or do we depend on "systematic trends" to predict them?

mfb

Calculating systems with ~10 nucleons from first principles is tricky (even the mass of a single proton is hard to evaluate in QCD). I would expect that some assumptions or simplified models are used to calculate those properties.