Angular and energy dependence of (e, e′) cross sections for orbital 1+ excitations

Abstract

The main features of the (e, e ′ ) cross sections of low-lying orbital excitations with K π = 1 + in heavy deformed nuclei are studied in RPA on the example of 156 Gd.The dependence of the DWBA E2 and M1 cross sections on the scattering angle 0 • < θ < 180 • and incident electron energy E i < 210 MeV is analyzed in PWBA.The cross section is larger for M1 than for E2 transitions at any angle if E i < 30MeV. The longitudinal (Coulomb) C2 excitation dominates the E2 response for 5 • < θ < 170 • . Only transverse M1 and E2 excitations compete for θ > 175 • and the former one is dominant for q < 1.2 fm −1 . The M1 response is almost purely orbital up to q = 1.4 fm −1 even in backward scattering. Qualitative PWBA estimates based on the q-dependence of the form factors alone are not able to predict some important features of the (e, e ′ ) cross sections stemming from the strong magnetic and orbital character of the studied 1 + excitations. The expectation for M1 over E2 dominance in backward scattering should not be extended to higher momentum transfers and incident energies.The backward inelastic electron scattering has established itself in the last 30 years as one of the main tools for the experimental study of nuclear magnetic excitations. The attention was focused in the past mainly on spherical nuclei, as it can be seen, e.g., from the review articles [1,2]. The detailed study of low-lying magnetic dipole (M1) excitations in heavy deformed nuclei started with (e, e ′ ) experiments at the linear accelerator in Darmstadt [3], reviewed recently in [4]. Most of the data were collected at a backward scattering angle θ = 165 • , where one expects a strong damping of electric excitations. This can be understood from qualitative considerations [5, 6] in the plane wave Born approximation (PWBA). The (e, e ′ ) cross section can be decomposed in this case into longitudinal (Coulomb) and transverse (electric and magnetic) terms, multiplied by corresponding kinematic factors. The longitudinal kinematic factor V ℓ (θ) vanishes for θ = 180 • and only transverse multipoles are excited in backward scattering [5]. Among those with the same multipolarity, the magnetic excitation is dominant over the electric transverse one [6]. This qualitative estimate is obtained in the long-wave limit qR ≪ 1, or small momentum transfer q in comparison with the radius R of the target nucleus. Magnetic dominance was found at backward angle also in [1] by assuming a purely spin-flip transition. The more realistic distorted wave Born approximation (DWBA) [7] leads to important corrections especially in heavy nuclei with a strong Coulomb field (a large charge number Z). But this approach is not suitable for simple qualitative predictions, since the longitudinal and transverse electric contributions to the (e, e ′ ) cross section interfere with each other in DWBA. Moreover, their separation would be meaningless when the longitudinal and transverse electric contributions are related in the DWBA formalism [8, 9] through the continuity equation.In contras...