Some properties of the two-body effective interaction in the 208Pb region

The (3He,d) and (4He,t) single proton transfer reactions on 208Pb and 209Bi were studied using 30 and 40 MeV He beams from the Princeton Cyclotron Laboratory. The outgoing d and t were detected by a position sensitive proportional counter in the focal plane of a Q-3D spectrometer. The resolution varied between 10 and 14 keV (FWHM). Using the ratio of the cross-sections for the (3He,d) and (4He,t) reactions to determine the magnitude of the angular momentum transfers, the spectroscopic factors for the reaction on 209Bi have been measured relative to the transitions to the single particle states in these reactions on 208Pb. Sum rules as developed by Bansal and French are used to study the configurations vertical bar h/sub 9/2 x h/sub 9/2/>, vertical bar h/sub 9/2/ x f/sub 7/2/>, vertical bar h/sub 9/2 x i/sub 13/2/>, vertical bar h/sub 9/2/ x f/sub 5/2/>and part of vertical bar h/sub 9/2/ x p/sub 3/2/> and vertical bar h/sub 9/2/ x p/sub 1/2>. Using the linear energy weighted sum rule, the diagonal matrix elements of the effective interaction between valence protons around the 208Pb core are deduced. The matrix elements obtained from a simple empirical interaction V/sub I//sup T=1/ of a pure Wigner type are compared to the extracted matrix elements. The interaction is characterized by an attractive short-range (0.82j and a repulsive long-range (8.2fm) potential: V/sub I//sup T = 1/ (MeV =-/96 e/sup - (r/0.82) 2/ + 0.51 e/sup -(r/8.2)2. The core polarization is studied using the experimental static electric quadrupole and magnetic dipole moments of the nuclei in the 208Pb region. In general, the magnetic moments of multiple valence nucleon nuclei are well predicted by simple rules of Racah algebra. The three and four valence proton spectra (211At and 212Rn) calculated with the experimental two particle matrix elements agree well with the experimental spectra