Relativistic Self-Consistent-Field Calculations With Application to Atomic Hyperfine Interaction Part I: Relativistic Self-Consistent Fields Part Ii: Relativistic Theory of Atomic Hyperfine Interaction

Large multiconfigurational Hartree-Fock calculations on the hyperfine-structure constants of theLi72sCarlsson1, Jönsson2, Fischer3 1992Phys. Rev. A442170View full textAdd to dashboardCite

“…INTRODUCTION The hyperfine structure of the atomic energy levels is caused by the interaction between the electrons and the electromagnetic multipole moments of the nucleus. The contribution to the Hamiltonian can be represented by an expansion in multipoles of order K, where T' ' and M' ' are spherical tensor operators of rank I( in the electronic and nuclear space, respectively [1]. The For Li the electronic tensor operators are, in atomic units [1,2], The hyperfine interaction couples the electronic (J) and nuclear (I) angular momenta to a total angular momentum F=I+J.…”

“…The contribution to the Hamiltonian can be represented by an expansion in multipoles of order K, where T' ' and M' ' are spherical tensor operators of rank I( in the electronic and nuclear space, respectively [1]. The For Li the electronic tensor operators are, in atomic units [1,2], The hyperfine interaction couples the electronic (J) and nuclear (I) angular momenta to a total angular momentum F=I+J. In this representation the diagonal and off-diagonal hyperfine energy corrections are given by WM((J, J) = -, ' AJC, Wt(t((J, J -1) = -, ' &J J, [(K+1)(K -2F) (6) X (K -2I )(K -2J+ 1) ]'i, (7) by orbital motion of the electrons and is called the orbital term.…”

“…The For Li the electronic tensor operators are, in atomic units [1,2], The hyperfine interaction couples the electronic (J) and nuclear (I) angular momenta to a total angular momentum F=I+J. In this representation the diagonal and off-diagonal hyperfine energy corrections are given by WM((J, J) = -, ' AJC, Wt(t((J, J -1) = -, ' &J J, [(K+1)(K -2F) (6) X (K -2I )(K -2J+ 1) ]'i, (7) by orbital motion of the electrons and is called the orbital term. The second term represents the dipole field due to the spin motions of the electron and is called the spindipole term.…”

“…The nuclear tensor operators M'" and M' ' are related to the nuclear magnetic dipole moment pl and the electric quadrupole moment Q (assuming Mt =I) (4) 3 T(2) -y C(2)(~) -3 (3) (3/4C(C+ 1) -I(I+ 1)J(J + 1) 2I(2I -1)J(2J - 1) where gI=(1 -m, /7m )=0.99922 and g, =2.0023193…”

Construction of the energy matrix for complex atoms Part I: General remarks

“…The completeness of fs analysis requires including magnetic interactions of the kinds: orbit-orbit, spin-other orbit and spin-spin interactions. The forms of magnetic interaction operators were published in the papers [4,6,7,17]. The matrix elements for configurations d N were given by Judd [18] and Barnes [19].…”