Z. Phys. A Atoms and Nuclei 304, 363-366 (1982) Zeitschrift ~ ~r~n"~ fLir Physik A r'M,~ll I IO and Nuclei 9 Springer-Verlag 1982 Isovector Magnetic Dipole Sum Rules in (ds)-Shell T.R. Halemane* Department of Physics and Astronomy, University of Rochester, Rochester, New York, USA and Serin Physics Laboratory, Rutgers - The State University, Piscataway, New Jersey, USA J.B. French Department of Physics and Astronomy, University of Rochester, Rochester, New York, USA Received August 12, 1981 Linear-energy weighted sum-rules (LEWSR) are calculated for isovector magnetic di- pole transitions from the ground state in some (ds)-shell nuclei. It is found that the well-known Kurath sum rule is inadequate to explain the experimental transition strengths in these nuclei. A significant contribution to the sum-rule is seen to arise from the two-body part of the Hamiltonian. The calculations are made using the spectral distribution methods. The linear-energy-weighted sum-rule (LEWSR) for excitations represented by an operator O from an initial state li> can be expressed [1] as an expec- tation value of the double commutator [O, [H, OJ] in the initial state. Here H is the Hamiltonian of the nucleus. When the excitation is of the isovector magnetic dipole type, the contribution to the double commutator from the one-body spin-orbit part of the Hamiltonian has been expressed [2] in a simple way in terms of occupancies and is known as the Kurath sum-rule. This Kurath sum-rule is often used [3J as a theoretical measure for isovector magnetic dipole transitions. However, from experimental measurements [4] in ds-shell nuclei one gets a value for the LEWSR that exceeds the Kurath value, in- dicating [5] that the latter is inadequate and that the contribution to the expectation value of the dou- ble commutator from the two-body part of H may be significant. We employ spectral distribution methods [-6, 7] to evaluate LEWSR using a (1 +2)- body realistic interaction Hamiltonian. The isovector magnetic dipole operator is O-MI(T=I)=|/~ ~{-liTi+(g,,-gp)s~zi. } (1) * Presented address: Department of Physics, SUNY college at Fredonia, Fredonia, NY 14063, USA Excitations induced by this operator are best studied by the 180~ electron scattering technique. The LE- WSR for excitations from the ground state lo> is [1 l defined by S = ~(E m-Eo) Iffl 0 Io> 12 (2) f _1 -7<ol [0, [H, 0]] Io>. (3) Kurath [2] made detailed studies of 1p-shell nuclei using the Hamiltonian H=~Ho(i)+a~l i .si+ ~ V(i,j) (4) i i i>j which is a harmonic oscillator shell-model with spin-orbit coupling and two-body interactions of a central force nature. The relative strength a/K (where K ~ 1 MeV is a representative integral of the two-body interaction) of spin-orbit coupling was va- ried to study the effects and determine the best fits. A value of a/K~3 in SBe and a/K~4.5-6 in 12C were needed for the theoretical estimates to fit with experimental strengths. The LEWSR for this model was then calculated by forming the double commutator between /-/ of (4) and MI(T= 1) of (1). The Ho(i ) term commutes with