RealQM vs StdQM: Binding Energy of 4He

This is a clarification of recent posts on RealQM vs StdQM for small nuclei.

To determine the binding energy of the 4He nucleus built from 2 protons and 2 neutrons is an elementary exercise in high school physics: Compute the mass defect as the difference in mass of 2 free protons 2 + 2 free neutrons and the mass of 4He determined experimentally to be with c2 the speed of light squared:

• mass of a free proton $m_p= 938.272$ MeV/c2
• mass of a free neutron $m_n= 938.565 MeV/c2
• mass of nucleus 4He  $m_{4He}= 3727.38$ MeV/c2

and compute using Einstein's E=mc2 to find the binding energy BE as

• BE = $2m_p+2m_n-m_{4He} = 26.289$ MeV or 7.1 MeV per nucleon.

This value stands out as very large compared to 2.2 for 2H (Deuteron), 2.8 for 3H (Tritium) and 2.6 for  3He MeV per nucleon. It is explained as an expression of a doubly magic number present in the 2 protons and 2 neutrons of 4He. 

Is it possible that the BE for 4He determined from mass defect using E=mc2 as above, does not represent true physics? Is it possible that the rationalisation with reference to magic numbers is not real physics? 

Note that there is a gap in the above mass defect computation in the sense that the mass of the protons and neutrons inside the nucleus is not available to measurement and they enter into an energy budget required to break the nucleus apart. If the protons and neutrons in fact take on bigger mass inside the nucleus than outside then the binding energy will shrink maybe towards normality. The above high-school energy computation may reflect rather a convention than reality.

We compare with the BE about 1.7 MeV/nucleon for 4He computed by RealQM as a parameter free mathematical model without experimental input assuming a change of scale of $10^5$ between atom and atomic nucleus. Changing the scale a little then gives BE of about the same size as those above for 2H, 3H and 3He. 

Let us see what StdQM has to offer. We thus ask chatGPT if it is possible to determine BE without experimental input from the Standard Model (QCD) as the present mathematical model of atomic nuclei within StdQM.  Here is what chatGPT delivers as a conclusion of a lengthy report:

• A fully QCD-derived prediction of ⁴He’s binding energy without any experimental input is not yet realized, but current methods are closing in, and future simulations at physical quark masses are expected to reach this goal.

Summary: RealQM delivers BE for 4He in the range 2-3 MeV/nucleon with only experimental input the change of scale between nucleus and atom. StdQM struggles to deliver a result. The list value of 7.1 MeV/nucleon stands out as 2-3 times too large.