For a given isotope, does the nuclear binding energy per nucleon depend on the presence of electrons? For instance, if an electron was excited by an incoming photon and jumps to a different orbital, will the nuclear binding energy change?
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asked May 25, 2015 at 0:43
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$\begingroup$ Yes, but very weakly. There are tiny chemical modulations of nuclear energies, so in theory nuclear decays and reactions are susceptible to chemical composition, temperature, pressure etc.. but the effects are so small that they can be neglected for all purposes as far as I know. $\endgroup$– CuriousOneCommented May 25, 2015 at 1:41
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$\begingroup$ Like what CuriousOne said, yes. Think of hydrogen. You've got one nucleon, a proton. You've also got an electron. The binding energy is -13.6keV. An incoming photon comes along, the electron jumps to a different orbital, and the binding energy has changed. $\endgroup$– John DuffieldCommented May 25, 2015 at 7:39
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$\begingroup$ Why would hydrogen have a binding energy? en.wikipedia.org/wiki/Hydrogen_atom Wikipedia says the binding energy of hydrogen is exactly 0? $\endgroup$– QCD_IS_GOODCommented May 25, 2015 at 7:41
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$\begingroup$ @JoshuaLin The nuclear binding energy of hydrogen is zero. The hydrogen atom in its ground state has a binding energy of 13.6 eV. It is bound because it has a binding energy. Can you be clearer in your question about what definition of binding energy you want to know about. $\endgroup$– ProfRobCommented May 25, 2015 at 8:46
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$\begingroup$ Sorry, I meant the nuclear binding energy $\endgroup$– QCD_IS_GOODCommented May 25, 2015 at 8:48
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1 Answer
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In an answer to another question I made reasonable estimate of the amount of electron charge that's contained within the nucleus. (Actually for that question I used a volume somewhat larger than the nucleus, but the method is there.) To first approximation, all the electronic charge within the nuclear volume comes from the two $1s$ electrons. The distribution of a full $p$-wave or higher shell is spherically symmetric. By the shell theorem, a spherically symmetric shell of charge does not affect the energy levels of systems inside.
Since the nuclear interaction is mostly blind to electric charge, and the charge within the nucleus is always a tiny correction to the proton charge, the effect on nuclear structure due to electronic charges must be very small.
