coulomb excitation data analysis codes; gosia 2007 - Physics and ...

Figure 2: The orbital integrals R 20 and R 2±1B(λ, I k → I f )=12I k +1 2 (2.29)for all cases in which the one-step excitation assumption can apply. In addition to their direct applicabilityto weak Coulomb excitation processes, the orbital integrals R give some general idea about the relationshipsbetween different modes of excitation. As an example, Fig. 2 shows the quadrupole orbital integrals R 20and R 2±1 as functions of ξ for θ cm = 180 o and θ cm = 120 o . Note that R 20 is a maximum and R 2±1 vanisheswhen θ cm = 180 o while θ cm = 120 o is the optimum scattering angle for 4m = ±1 excitation.The applicability of first and second order perturbation theories is limited to light-ion induced Coulombexcitation, or for heavy-ion beams, to beam energies far below the safe bombarding energy. In the caseof a typical multiple Coulomb excitation experiment, the system of differential equations 2.17 must besolved numerically. It is, for example, estimated that the excitation probability of the first excited 2 + of248 Cm bombarded with a 641 MeV 136 Xe beam is still sensitive to the excitation modes involving 30 th orderproducts of the reduced matrix elements. This proves that the perturbation-type simplifications are generallynot feasible. An efficient fast approximation to the Coulomb excitation problem is presented in Chapter 3.17