M2L8o.txt

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Let's now talk about the volume effect.
If we would look at the charge distribution
in the nucleus as a function of R. If we go from one isotope
to an heavier isotope with more neutrons,
the nuclear radius becomes larger.
And the charge becomes more spread out.
So if I plot now the electrostatic potential--
the electrostatic potential is, of course, the Coulomb
potential, 1 over R, until we enter the charge distribution.
And then, as you know from electrostatic,
it continues-- this is one over R--
and then it's flattened off.
It continues quadratically.
For the heavier-- oops, I wanted to change color--
for the heavier nucleus, it is like this.
And for the lighter nucleus, it like this.
So in other words, the finite size of the nucleus
is cutting off the Coulomb potential
where it is strongest.
And this happens the earlier, the larger,
or the heavier the nucleus is.
So therefore, what you obtain is, you obtain in perturbation
theory, a level shift.
Since it only affects the electron when
it's very close to the origin, this level shift
is, as other effects we have discussed today,
proportional to the probability of the electron
to be at the center.
Only S electrons are affected.
And well what is the effect in terms of energy?
Well it's clear, the Coulomb potential is weakened.
Therefore, this effect, the volume effect, weakens - decreases the binding energy of the electron.