Charge Independence of Nuclear Forces

Example Problem Consider the mirror nuclei 25Mg and 25Al. What is the energy difference between their ground states  

Solution Note the conversion of 25Mg into 25A1 will involve the change of one neutron into one proton. The neutron and proton have slightly different masses, of course. The extra proton will interact electromagnetically with the other 12 protons giving a second tenn in the energy difference  

So we would expect the ground state of 25Al to be 5.128 MeV above the ground state of 25Mg. 

The observation of the masses of mirror nuclei suggests the strong or nuclear force between a neutron and a proton is the same. This equivalence leads naturally to considering the neutron and the proton as corresponding to two states of the same particle, the nucleon. (A similar simation holds for the it meson, where the it0, tt+, 

A Nucleus Total Binding Energy (MeV) Coulomb Energy (MeV) Net Nuclear Binding Energy (MeV) 

---

Ladungsinvarianz der Kernkrafte, charge independence of nuclear forces 486. 

This property, the charge independence of nuclear forces, can he described conveniently by the isospin formalism introduced by W. Heisenberg. The isospin formalism is completely analogous with the quantum-mechanical formalism of spin 1/2 particles. In the case of a many-nucleon system the total isospin (T) is defined as a sum of the nucleonic isospins ... 

A considerable amount of evidence indicates that nuclear forces are charge-independent, i.e, the neutron-neutron, neutron-proton, and proton-proton forces are identical. The meson theory of nuclear forces, originated by Yukawa, postulates the atomic nucleus being held together by an exchange force in which particles, now called mesons, are exchanged between individual nucleons within the nucleus. 

An example of the energy level matching in the mirror pair 17F, 170 is shown in Figure 6.7. The agreement of the levels is quite remarkable and can be taken as strong evidence for the charge independence of the nuclear force, that is, the protons and neutrons move in essentially identical but separate orbitals in the nucleus. 

The operator for total isotopic spin T and that for its resolved part commute with the nuclear Hamiltonian for charge independent forces. Both T and should be conserved in a nuclear reaction if this may be regarded as a small perturbation produced by a charge independent interaction. The evidence for conservation of total isotopic spin in nuclear reactions has been summarised in several articles. Isotopic spin conservation may fail, as discussed by Lane and Thomas [i9], when a nuclear reaction passes through a long lived state in which the Coulomb perturbation has time to mix wave functions of different T. 

The similarity of level systems in some light nuclei and also the scattering experiments indicate that the nuclear forces are almost frilly independent of the electric charge of nucleons. 

---