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

Abstract

The mass-velocity term, Hmv = –p4/8m3ec2, of the Breit-Pauli Hamiltonian is studied for its range and capability in providing relativistic corrections to the nonrelativistic kinetic energy, Hke = p2/2me. For this purpose, after a brief critical review of the characteristics of Hmv, the expectation values (Hkr), (Hmv), and (H0) are presented for a series of ground-state neutral atoms (Z = 1–92), where H0 is the relativistic kinetic energy, mec2[(1 + p2/m2ec2)1/2 – 1]. All expectation values are with respect to nonrelativistic wavefunctions. As expected, (Hke) has a larger value than (H0) for all atoms considered, whereas the mass velocity–corrected kinetic energy, (Hke) + (Hmv), is always (i.e., for all values of Z) smaller than (H0), even for the hydrogen atom. Our results also indicate that the efficiency of Hmv in bringing about relativistic corrections to (Hke), 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 Hmv in the relativistic Hamiltonian produces more error than correction.