Matrix elements charge-current operator

The spinor product ipl pk represents the charge density associated with the four-spinor ipk, while c aqtpk represents the g-component of the current. The matrix elements of these operators may be reduced to elementary G-spinor integrals of the form... 

Both the NDDO and the CNDO assumptions apply only to matrix elements involving the charge density operator. Other arguments have to be used for matrix elements of other operators, such as the kinetic energy and the current density. 

The redistribution of charge in the system during the tunneling transition is described in terms of current density J (f, t) and its spatial distribution J (f), which is given by the matrix element between states A and D of the current density operator (this is the so-called transition current) ... 

The matrix elements of r, and a are of rank-one, r is the exact analogue of the isospin-changing El operator and the conserved-vector-current (CVC) theorem can be invoked to relate the matrix element of a to that of r. Further, [r, spin-dipole operator. The helicity operator 75 is the time-like component of the rank-zero axial current - also known as the axial charge - discussed in Section 1. We thus have five independent matrix elements, two each of rank zero (RO) and rank one (Rl) and one of rank two (R2) which we denote as... 

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