14.9 Nucleon separation energies

Nucleon separation energies are the equivalent of atomic ionization energies, but for nuclei. The proton separation energy is the minimum energy required to remove a proton from a nucleus. It is how much the rest mass energy of the nucleus is less than that of the nucleus with one less proton and a free proton.

Figure 14.3: Proton separation energy. [pdf]
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Figure 14.4: Neutron separation energy. [pdf]
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Similarly, the neutron separation energy is the energy needed to remove a neutron. Figures 14.3 and 14.4 show proton and neutron separation energies as grey tones. Note that these energies are quite different from the average binding energy per nucleon given in the previous subsection. In particular, it takes a lot of energy to take another proton out of an already proton-deficient nucleus. And the same for taking a neutron out of an already neutron deficient nucleus.

In addition, the vertical striping in 14.3 shows that the proton separation energy is noticeably higher if the initial number of protons is even than if it is odd. Nucleons of the same kind like to pair up. If a proton is removed from a nucleus with an even number of protons, a pair must be broken up, and that requires additional energy. The neutron separation energy 14.4 shows diagonal striping for similar reasons; neutrons too pair up.

There is also a visible step down in overall grey level at the higher magic numbers. It is not dramatic, but real. It illustrates that the nucleon energy levels come in shells terminated by magic numbers. In fact, this step down in energy defines the magic numbers. That is discussed further in section 14.12.

Figure 14.5: Proton pair separation energy. [pdf]
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Figure 14.6: Neutron pair separation energy. [pdf]
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Figures 14.5 and 14.6 show the energy to remove two protons, respectively two neutrons from even-even nuclei. This show up the higher magic numbers more clearly as the pairing energy effect is removed as a factor.