(a) The structure of atomic nuclei is shown to be dramatically modified by strong magnetic fields relevant for supernovae and neutron stars. We demonstrate that within the mean-field treatment such a modification can be viewed as a relative shift of nucleon levels governed by projections of respective magnetic moments on the field axis. The shell-effects of nuclides give rise to magnetic response anomalies which resemble the behavior associated with magnetic phase transitions. These anomalies are argued to give rise to erratic jumps in the neutron star crust magnetodynamics. Such a noise originates from magnetic avalanches and shows intensity and statistical properties which are favorably compared to the burst activity of Soft Gamma Repeaters.

(b) Particle-accompanied fission was discovered in 1946. Different types of such processes were detected, in which the light particle is a proton, deuteron, triton, 3-6,8He, 6-11Li, 7-14Be, 10-17B, 13-18C, 15-20N, 15-22O, as well as a series of heavier isotopes of F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, Ca. The higher yield is obtained for a-accompanied fission. This rare phenomenon was initially detected with photographic plates or ionization chambers. New decay modes (a and 10Be accompanied cold (neutron-less) fission) as well as double fine structure and triple fine structure in binary and ternary fission were discovered during last years with GAMMASPHERE. Also, a possible new quasimolecular state, detected in Darmstadt and Nashville will be presented and discussed within a phenomenological three-center model. Half-lives of quasimolecular states which could be formed in 10Be or 12C accompanied fission of 252Cf were roughly estimated.