Nucleus isospin

Consider the A = 14 isobars, 14C, 14N, and 140.14C and 140 are mirror nuclei and have ground states with T3 = + 1. As such they must be part of an isospin triplet with T = 1 (T3 = 0, +1). Thus, in the 7) = 0 nucleus, 14N, there must be a state with T= 1, r3 = 0 that is the analog of the 7) = 0 ground states of 14C and 140. (See Problems section for further details.) We expect the three members of this multiplet to have approximately the same energy levels after correction for the Coulomb effect and the neutron-proton mass difference. 

For an additional degree of freedom of a particle that defines one of the two possible states in which it exists, we shall apply now the concept of isospin (in analogy with the theory of the nucleus where the isospin doublet includes protons and neutrons, which are treated as two states of the same particle - the nucleon [122]). For a pair of states (a,/ ) we introduce the isospin operators... 

Let us substitute wave functions, Eqs. (A.9) and (A. 10), taking count of Eqs. (A.ll) and (A. 12), into the matrix element in the initial expression, Eq. (8) (Section II). The weak-interaction Hamiltonian Hfj acts on the charge (isospin) wave functions of the leptons and of the radioactive nucleus n, as... 

The reason we include in our discussion, is the fact that this nucleus with T =, the JT = 10 two-body matrix elements, discussed above in connection with the increased binding provided by a potential with a weak tensor force, come into play. For which has isospin T = 2, these matrix elements do not occur. It is therefore instructive to compare the spectra obtained with all three Bonn potentials for these two nuclei. 

For cases with two-body interactions which are dependent on the isospin of the target nucleons this substitution is not strictly correct. An exact treatment of this wiii introduce small isospin corrections to the second-order opticai potential. Analogous isospin corrections to the proton-and pion-nucleus KMT optical potentials occur in first order and are veiy smaii. 

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