Relativistic corrections to the Zeeman effect in hydrogen-like atoms, positronium, and helium-like atoms

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1993

OSTI ID:6960659

Anthony, J M

An approximately relativistic theory of bound states which ensures the Poincare invariance of atomic systems to relative order (v/c)[sup 2] is used to derive the Zeeman interaction Hamiltonians correct to order [alpha][sup 3] and to all orders in m[sub e]/m[sub N] for arbitrary two body systems and three body systems. Previously neglected radiative corrections of order [alpha][sup 3] and recoil corrections of order [alpha][sup 3]m[sub 3]/m[sub N] are also included. For neutral systems, the linear Zeeman Hamiltonians are unitarily equivalent to the linear Zeeman Hamiltonians obtained by other authors in the past. Explicit analytic expressions for the g[sub J] and g[sub I] factors of hydrogen-like atoms are given and verify the results of Grotch and Kashuba. The positronium ground state g factor calculated here agrees exactly with previous calculations. The terms of order m[sub e]/m[sub N], [alpha][sup 2], [alpha][sup 3], and [alpha][sup 2]m[sub e]/M[sub N] of the three-body linear Zeeman Hamiltonian are used to calculate the g factors for n=2 [sup 4]He and [sup 3]He. The effect of the finite mass of the nucleus on the wavefunction is accounted for the work presented here. The 2[sup 3]S[sub 1] g[sub J] factor is in excellent agreement with the results of Grotch and Hegstrom and experimental results. It is the first time that corrections of order [alpha][sup 3] and [alpha][sup 2]m[sub e]/m[sub N] have been used to calculate the 2[sup 3]P[sub J] and 2[sup 1]P[sub 1] helium g factors. Three different wavefunctions are used to derive the 2[sup 3][sub J] and 2[sup 1]P[sub 1] g factors for [sup 4]He and [sup 3]He. The most accurate is a 125 term configuration interaction wavefunction utilizing 12 nonlinear parameters. The resulting g's factor agrees exactly with the results of Lewis and Hughes (to order [alpha][sup 2]). The g'[sub L] factor obtained is a significant improvement over the results of Lewis and Hughes.

• Research Organization: Massachusetts Univ., Lowell, MA (United States)
• OSTI ID: 6960659
• Country of Publication: United States
• Language: English

Related Subjects

664400* -- Experimentally Derived Information on Atomic & Molecular Properties-- (1992-)
664500 -- Special Atoms & Molecules-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
ELEMENTS
FLUIDS
GASES
HAMILTONIANS
HELIUM
HYDROGEN
MATHEMATICAL OPERATORS
NONMETALS
POSITRONIUM
QUANTUM OPERATORS
RARE GASES
ZEEMAN EFFECT