grigorenko2001
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TWO-PROTON RADIOACTIVITY AND THREE-BODY . . .
FIG. 9. Case of 48Ni at E51.39 MeV. Stability of width as a function of box radius rbox for different boundary conditions at rmax5200 fm. Solid line corresponds to Eq. ~18!, while dashed line to Eq. ~20!.
Eq. ~20!, the results are very stable ~within approximately 1%!.
IV. CONCLUSION
In this paper we address a range of theoretical problems that exist in the studies of the three-body decays and in particular in the studies of the two-proton radioactivity. We limit our studies to nuclear systems where three-body channel is the only ~or dominating! decay channel. We discuss the relevant experimental information and classify the decays. We examine existing qualitative models ~e.g., diproton model, direct decay to continuum! of the phenomenon, give corresponding estimates, discuss problems they are facing, and consider the feasibility of the suf®ciently precise quasiclas-
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sical approach in general. We demonstrate that the attempts to ®nd adequate quasiclassical description of three-body decay process fail and a more complete quantum mechanical few-body treatment is required.
We develop a three-body model for studies of two-proton radioactivity and three-body decays that is free of most of the uncertainties typical for quasiclassical estimates. This model employs various forms of approximate boundary conditions at large hyper-radius r for the three-body Coulomb problem. The sensitivity of the results to the choice of different boundary conditions, as well as other parameters of the model, has been demonstrated. The results of the calculations show a high stability of obtained decay widths and spatial distributions.
This model has already been applied to the studies of two-proton radioactivity for the ground states of 19Mg and 48Ni in Ref. @13#. In the forthcoming papers we will apply this model for the detailed theoretical studies of some nuclei from Tables I and II, which are under experimental investigation now.
ACKNOWLEDGMENTS
The authors thank B. V. Danilin, N. B. Shul'gina, N. K. Timofeyuk, and V. A. Ziman for valuable discussions. L.V.G. is grateful for support from Royal Swedish Academy of Science and hospitality of Chalmers University of Technology, where part of this work was done. I.G.M. acknowledges the support by the German Federal Minister for Education and Research ~BMBF! under Contract No. 06 DA 915I. We acknowledge the support of EPSRC Grant No. GR/M82141 and RFBR Grant No. 00-15-96590.
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