Convergence of the Marcus–Lushnikov Process

The Smoluchowski coagulation equation describes the concentration c(t,x) of particles of mass x [ 0,] at the instant t 0, in an infinite system of coalescing particles. It is well-known that in some cases, gelation occurs: a particle with infinite mass appears. But this infinite particle is inert, in the sense that it does not interact with finite particles. We consider the so-called Marcus–Lushnikov process, which is a stochastic finite system of coalescing particles. This process is expected to converge, as the number of particles tends to infinity, to a solution of the Smoluchowski coagulation equation. We show that it actually converges, for t [0,], to a modified Smoluchowski equation, which takes into account a possible interaction between finite and infinite particles.     

Study of the (d, α) reaction applied to 50Cr and 52Cr

The reactions ⁵⁰Cr(d, α)⁴⁸V and ⁵²Cr(d, α)⁵⁰V have been carried out at an incident deuteron energy of 15 MeV to investigate the structure of the low-lying levels of ⁴⁸V and ⁵⁰V in the light of shell model expectations. Excitation energies and angular distributions have been measured for states up to about 1.5 MeV. For all resolved and strongly excited levels angular momentum transfers could be assigned by comparison with DWBA calculations. For ⁵⁰V spectroscopic factors have been extracted in relative units assuming pure configurations for the transferred pair of nucleons. The results indicate the existence of seniority and configuration mixing in the level structure of the ⁴⁸V and ⁵⁰V isotopes. In both reactions some transitions show characteristic deviations from the direct reaction mechanism. These deviations cannot be reproduced by the DWBA calculations.