Effective electro-magnetic operators of 50Ti investigated with the (e, e′) reaction

Abstract

Cross sections have been measured for inelastic electron scattering from 50 Ti. Magnetic form factors have been deduced for the J π = 5 + level at E x = 4.884(5) MeV, and for the levels with J π = 4 − at E x = 7.293(10) MeV, J π = 8 − at E x = 8.755(7) MeV, J π = 3 + at 9.061 (12) MeV, J π = 5 + at E x = 9.188(15) MeV and J π = 8 − at E x = 9.442(10) MeV. Charge form factors have been deduced for the yrast J π = 2 + , 4 + and 6 + levels. The form-factor data have been compared with shell-model and core-polarization calculations, emphasizing the radial shape of the model wave function in comparison with the q -dependence of the data. All observed magnetic form factors show a q -dependence corresponding to an up to 15% larger value of the Woods-Saxon radial parameter than in the single-particle model approximation. The radial effect is explained in detail by configuration mixing and core-polarization calculations. The form-factor data for excitation of the yrast J π = 2 + , 4 + and 6 + states show — almost independently of the multipole order — a q -dependence corresponding to a 10% larger value of the Woods-Saxon radial parameter than in the (1 f 7 2 ) 2 model approximation. The polarization charges deduced from the data are decreasing as a function of the multipole order but are still positive for the J π = 6 + level. Neither of the present calculations is able to reproduce these results. On the contrary, both the form factors calculated in the shell model and in the core-polarization model correspond to a radial behaviour close to that for the (1 f 7 2 ) 2 form factor. From the C6 form-factor data the radial extension of the 1 f 7 2 proton orbit has been deduced. The corresponding r.m.s. value is found to be (5 ±2)% larger than the r.m.s. value deduced from high- q M7 elastic magnetic electron scattering from the neighbour nucleus 51 V. A possible explanation for this effect is discussed in terms of collective effects in the inelastic charge form factors.