using the above definition to define the proton and neutron unpolarized structure function :

The above is true within the framework of the constituent quark model when in the valence quark region where the more massive quarks are ignored as well as anti-quarks

Using Isospin symmetry

and

The unpolarized structure functions for the proton and neutron may be written as

similarly for the polarized structure function

In the non-relativistic constituent quark model

<ref>https://arxiv.org/abs/hep-ph/9809255 PHYSICAL REVIEW D, VOLUME 59, 034013 Valence quark spin distribution functions Nathan Isgur , https://arxiv.org/abs/hep-ph/0411005 The Spin Structure of the Proton Steven D. Bass Rev.Mod.Phys.77:1257-1302,2005</ref>

One can use the two equations above and solve for the polarized quark distributions assuming the unpolarized are known and get , for example

Then using the above approximation for A_1

<ref> Eq. 28 from https://arxiv.org/abs/1505.07877 which is based on https://arxiv.org/abs/0809.4308</ref>

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