Validity of the mass‐velocity term in the Breit‐Pauli hamiltonian

The mass‐velocity term, H mv = – p 4/8 m 3 e c 2 , of the Breit‐Pauli Hamiltonian is studied for its range and capability in providing relativistic corrections to the nonrelativistic kinetic energy, H ke = p 2 /2 m e . For this purpose, after a brief critical review of the characteristics of H mv , the expectation values ( H kr ), ( H mv ), and ( H 0 ) are presented for a series of ground‐state neutral atoms ( Z = 1–92), where H 0 is the relativistic kinetic energy, m e c 2 [(1 + p 2 / m 2 e c 2 ) 1/2 – 1]. All expectation values are with respect to nonrelativistic wavefunctions. As expected, ( H ke ) has a larger value than ( H 0 ) for all atoms considered, whereas the mass velocity–corrected kinetic energy, ( H ke ) + ( H mv ), is always (i.e., for all values of Z ) smaller than ( H 0 ), even for the hydrogen atom. Our results also indicate that the efficiency of H mv in bringing about relativistic corrections to ( H ke ), decreases linearly as a function of the atomic number, Z . This efficiency starts at 98.41% for Z = 1 (hydrogen) and decreases to 0.639% for Z = 60 (neodymium), beyond which the efficiency is negative and the inclusion of H mv in the relativistic Hamiltonian produces more error than correction.