VOLUME65, NUMBER24 PHYSICAL REVIEW LETTERS 10 DECEMBER 1990 Low-Lying Magnetic Dipole Excitations in Actinide Nuclei Amand Faessler, Dao Tien Khoa, M. Grigorescu, (a) and R. Nojarov (b) Institut fur Theoretische Physik, Universitdt Tubingen, Aufder Morgenstelle 14, D-7400 Tubingen, Federal Republic of Germany (Received 18 June 1990) The M\ excitation of K nsBB \ + states in 232 Th and 238 U through inelastic electron scattering is studied within a quasiparticle random-phase-approximation approach with quadrupole-quadrupole, spin-spin, and rotational-vibrational interactions. The calculated distorted-wave Born approximation (e,e) form factors and the low-energy spectrum of 1 + states are in good agreement with the experimental data. The strongest experimentally observed 1 + states can be interpreted as isovector rotational vibrations, in which several quasiparticle pairs perform a scissors type of vibrational motion. PACS numbers: 25.30.Dh, 21.60.Jz, 27.90.+b The low-lying magnetic dipole excitations have been observed recently in high-energy-resolution inelastic electron scattering (e,e') and nuclear resonance fluores- cence 1 for the actinide nuclei 232 Th and 238 U. The mi- croscopic structure of such states in several lighter-mass regions has been successfully studied within a quasiparti- cle random-phase approximation (RPA), 2 ' 5 and it is natural to apply this approach to study the 1 + states in the actinide region. In the present work we perform the RPA calculations for the low-lying 1 + states in 232 Th and 238 U. Since the reliability of the model should be tested by comparison of both the calculated spectrum and (e,e r ) form factors with the experimental data, we also present here the results for (e,e') form factors calcu- lated within the distorted-wave Born approximation (DWBA) using the RPA transition densities for the con- sidered 1 * states. Note that a theoretical description of these states has been performed in Ref. 1 using the tran- sition current densities calculated in the interacting- boson approximation (IBA). 6 As there is a certain difference between the RPA and IBA interpretations of the microscopic structure of the 1 + states in deformed nuclei, 7 and moreover, the shape of the IBA form factors changed after the underlying formalism was revised re- cently, 8 realistic RPA calculations for these states in ac- tinide nuclei are of considerable interest. We employ a RPA Hamiltonian including quasiparti- cle mean-field //n, self-consistent quadrupole-quadrupole HSCQ, spin-spin 7/ss, and rotation-vibrational //RV resid- TABLE I. Parameters of the Woods-Saxon potential [/•„ —1.26 fm, r p = \.24 fm, /i&> = (50 MeV)/A l/3 ] and energy-gap values used in the BCS calculations. The definitions of these quantities can be found in Refs. 2, 5, and 9. Nucleus 232 Th 238TJ (MeV) -47.0 -46.7 v P (MeV) -60.5 -61.0 In 30 27 */> 25 23 a n (fm) 0.60 0.69 a p (fm) 0.60 0.65 An (MeV) 0.7 0.6 A P (MeV) 0.8 0.7 fr a 0.216 0.236 fa 0.06 b 0.05 c a The corresponding experimental quadrupole moments, extracted from the adopted B(E2) values of Ref. 10, are reproduced microscopically with these /3: values. b FromRef. 11. c From Ref. 12. ual interactions: //=//O + //SCQ + //SS + //RV. (1) The role of these interactions and other details of our formalism have been published elsewhere. 2-5 We only note here that by solving the usual RPA equations of motion [//,r + (vm)]=H^ v T + (vm), (2) [r(vm),r + (vm)]=l, (3) together with the requirement L/(m),r f W)]=0, (4) the rotational symmetry of the RPA Hamiltonian is re- stored and this guarantees the exact orthogonality of the RPA solutions with respect to the spurious isoscalar ro- tational state generated from the ground state by the to- tal angular momentum operator J f . Here F f (vm) is the phonon creation operator with m as signature index; W v is the excitation energy of the vth RPA solution. The coupling constants of the interactions in the RPA Hamiltonian (l) are determined in a self-consistent pro- cedure described in Refs. 2-5. The quasiparticle mean- field Ho is obtained by solving the standard BCS equa- tion with a single-particle basis generated by a deformed Woods-Saxon (WS) potential with parameters taken from Ref. 9. The parameters of the WS potentials, nu- clear deformations, and energy gaps used in the BCS calculations for 232 Th and 238 U are listed in Table I. 2978 © 1990 The American Physical Society