452 Progress of Theoretical Physics Supplement No. 146, 2002 Isovector Mixing in Inelastic Scattering Induced by the Radioactive Beams Dao T. Khoa ∗) Institute for Nuclear Science & Technique, VAEC, P. O. Box 5T-160, Nghia Do, Hanoi, Vietnam (Received December 15, 2001) The folding model for the nucleon-nucleus inelastic form factor is applied to study in- elastic scattering of 18,20 O isotopes on proton target. A realistic density dependent M3Y interaction, well tested in the folding analysis of nucleus-nucleus scattering, is used as effec- tive NN interaction. The nuclear ground state and transition densities (for the low-lying 2 + and 3 - states in the oxygen isotopes) are obtained in the Hartree-Fock-BCS and generalized Bohr-Mottelson approach, respectively. Strong isovector mixing has been observed in the 2 + inelastic channel of the 20 O+p system. The isovector strength of the form factor, implied by the inelastic 20 O+p data at 43A MeV, gives a ratio of transition moments M n 2 + /M p 2 + ≃ 4.3 for the lowest 2 + excitation in 20 O. §1. Introduction Although the isospin dependence of the nucleon-nucleus optical potential or the so-called Lane potential 1) has been studied since a long time, no systematic study has been made for the isospin effects in various inelastic scattering channels. The neutron and proton contributions to the structure of the low-lying nuclear excitations are known to be very different, 2) and the inelastic nuclear form factor contains, therefore, an isospin dependence which determines the degree of the isovector mixing in the inelastic scattering that induces the excitation. Similar to the Lane potential, the isospin dependent term of the inelastic form factor should be proportional to the scalar product of the projectile and target isospins (T p T t ). For the nucleus-nucleus interaction, this term has been shown 3) to be negligible and the total scattering cross section is predominantly determined by the isoscalar part of the nucleus-nucleus potential. In the proton-nucleus optical potential U (R)= U IS (R) - εU IV (R),ε =(N - Z )/A, (1 . 1) the strength of the Lane potential (εU IV ) is known to amount up to about 10 ∼ 15% of the total potential U . Using standard ‘deformed-potential’ (DP) approach, one can obtain the transition form factor for the inelastic proton-nucleus scattering (leading to a 2 λ -pole excited state of the target) as δ λ dU (R) dR = δ (0) λ dU IS (R) dR - εδ (1) λ dU IV (R) dR . (1 . 2) Second term in (1 . 2) gives the degree of isovector mixing in the inelastic scattering. 4) The isovector deformation length δ (1) λ can be determined, in principle, from the (p,n) ∗) E-mail: khoa@mail.vaec.gov.vn Downloaded from https://academic.oup.com/ptps/article-abstract/doi/10.1143/PTPS.146.452/1863128 by guest on 14 June 2020