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

à XK(α) =exp−iτ i (E γ )x i (α)!(2.68)where the summation extends over various absorbers and the p-core. The Q k factors, resulting from 2.66,have to be evaluated numerically. In order not to repeat this procedure for every γ energy of interest, it ispractical to fit a simple analytic function describing the energy dependence, as discussed in section 4.To reproduce the experiment one should, in addition to the effects discussed in previous sections, includethe integration of 2.33 over the particle detection solid angle and, at least for the long-lived states, includethe correction due to in-flight decay, i.e. the time-dependent change in the angular position and the solidangle of a detector as seen by the decaying nucleus. These effects are treated numerically in GOSIA, thealgorithms used being presented in Chapter 4.2.2.4 Internal ConversionThe electromagnetic radiation field for a nuclear transition can lead to the ejection of a bound atomicelectron, or the creation of an electron-positron pair if the transition energy exceeds 2m e c 2 . The totalinternal conversion coefficient c(λ) is defined as the ratio of the internal conversion decay probability tocorresponding γ-ray decay probabilityc(λ) = Γ ic(2.69)Γ γwhere the total internal conversion coefficient is the sum of internal conversion for all atomic shells plusinternal pair conversion. Internal conversion opens additional decay paths populating a given state byunobserved cascade feeding from above. Fortunately the total decay width for any transition is increased byjust a multiplicative factor times the γ-ray decay probability. That is,Γ(I,I f ) total = Γ(I,I f ) γ (1 + c(λ)) (2.70)which is easy to handle using the concept of a conversion coefficient as illustrated by equation 2.44.Electric monopole, E(0), transitions are forbidden by single-photon decay, but they can decay by emissionof an internally converted electron or by internal pair creation. Double photon decay is an allowed higherorderprocess which is 10 3 to 10 4 times weaker than E(0) internal conversion and thus can be neglected.The concept of an E0 conversion coefficient is not useful since Γ(E0) γ =0. The E(0) internal conversiontransition probability is defined as∙ ¸2Γ(E0) = (δ 0 ) 2 =eR 2 (Ω ic + Ω π ) (2.71)where Ω ic and Ω π are the electronic factors defined by Church and Weneser[CHU56] and are in units of s −1 .The other terms are the reduced E0 matrix element, ,the electron charge e, and nuclearradius which is taken to be R =1.2A 1 3 fm. The firstterminequation2.71oftenisexpressedintermsofthedimensionless parameterρ(E0) ≡ eR 2 (2.72)The electric monopole conversion term can be included in the cascade feeding equation equation 2.44 byincluding λ =0in the summation with the conversion coefficient c(0) = 0.The National Nuclear Data Center, NNDC, at Brookhaven maintains an Evaluated Nuclear StructureData File, ENSDF, that includes a new internal conversion coefficient database, called BrIcc[KIB08]. Thisdatabase integrates a number of tabulations of internal conversion electron coefficients, ICC, and electronpositronpair conversion coefficients, IPC, as well as Ω(E0) electronic factors for E(0) conversion. The defaultICC tables are based on Dirac-Fock calculations, which use the "Frozen orbital" approximation, to take intoaccount the effect of atomic vacancies created in the conversion process. The tables do not take into accountthe partial ionization and the influence of the highly excited atomic shells of the excited nuclear ion recoilingin vacuum. The recoil velocities encountered in heavy-ion Coulomb excitation, when performed at safebombarding energy, produce only partial ionization and the decay times for the inner-bound atomic shells25