[Article] Group Epitope Mapping by Saturation Transfer by M. Mayer, B. Meyer

By M. Mayer, B. Meyer

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The second peak, corresponding to the Gamow energy, moves according to the temperature. From these considerations, and except in the temperature range where both peaks overlap, the resonant reaction rate can be split in two terms NA < σv >≈ NA < σv >R + NA < σv >T , (13) where NA < σv >R corresponds to the maximum at E = ER . For a narrow resonance, we have 3 2 2π ER 2 , ωγ exp − NA < σv >R = NA μmN kB T kB T where the resonance strength ωγ is defined by 2JR + 1 Γ 1 Γ2 ωγ = , (2I1 + 1)(2I2 + 1) Γ1 + Γ2 (14) (15) (Γ1 , Γ2 ) being the partial widths at E = ER .

In the 16 O(α, γ)20 Ne reaction for example, the 0+ 1 ground + + 16 state and the 0+ 4 broad resonance are well described by an α+ O structure, but the 02 and 03 resonances would require other configurations, such as α+16 O∗ or p+19 F. This problem is more and more frequent as the level density increases. 4 The phenomenological R-matrix method The R-matrix method is well known in atomic and nuclear physics [10De0A]. The basis idea is to divide the space in two regions: the internal region (with radius a), where the nuclear force is important, and the external region, where the interaction between the nuclei is governed by the Coulomb force only.

If phase shifts are available, they can be used to determine the initial potential. Frequently used nuclear terms are the WoodsSaxon potential VN (ρ) = V0 , 1 + exp((ρ − ρ0 )/a) (22) or the Gaussian potential VN (ρ) = V0 exp(−(ρ/a)2 ). (23) Additional terms, such as the spin-orbit or the tensor forces can be introduced without loosing generality. 1007/978-3-642-22930-5 3 c Springer-Verlag Berlin Heidelberg 2012 Excited Nuclear States 8 In this simple model, the capture cross section (1) is deduced from integrals involving scattering J π functions g JiiIπi (ρ) at energy E, and bound-state wave functions g ffI f (ρ).

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