THE SHAPE TRANSITION IN ROTATING NUCLEI F. Ivanyuk 1, K. Pomorski 2 and J.Bartel 3 1 Institut for Nuclear Research, Kiev, Ukraine 2 Theoretical Physics Division, UMCS, Lublin, Poland 3 Institute Pluridisciplinaire Hubert Curien, Strasbourg University, Strasbourg, France Introduction The Strutinsky‘s procedure for the shape of fissioning nuclei The shape transition in axially symmetric rotating charged liquid drop The shape of triaxial rotating drop Summary and outlook

Strutinsky‘s optimal shapes V.M.Strutinsky et al, Nucl. Phys. 46, 659 (1963)

Optimal shapes of fissioning drop

The deformation energy F. Ivanyuk, Int. J. Mod. Phys. E18 (2009) 130

The shape of axially symmetric rotating drop J. Bartel, F. Ivanyuk and K.Pomorski, Int. Jour. Mod. Phys. E19 (2010) 601

The energy and shape transition in axially symmetric rotating drop

The deformation energy of rotating drop

The energy and shape transition in axially symmetric rotating drop

The shape transition in rotating drop

The energy and shape transition in axially symmetric rotating drop

The critical rotational velocities

The non-axial rotating drops K. Pomorski, F. Ivanyuk and J. Bartel, Acta Phys. Polon. B42 (2011) 455 A. May, K. Mazurek, J. Dudec, M. Kmiecik and D. Rouvel, Int. J. Mod. Phys. E19 (2010) 532

The equations for

The shape of axially non-symmetric rotating drop

The energy of axially non-symmetric rotating drop

The comparison with ellipsoidal shapes

The effective ellipsoids

The effective ellipsoids, the energy

The limiting values of rotational velocity

Summary and outlook Within a liqiud drop model we have developed a method for the calculation of optimal shape of the surface within a broad region of rotational velocitiy and fissility parameter We have found out that sharp Jacobi transition from oblate to triaxiall ellipsoides is the result of limitation imposed by the assumption of the ellipsoidal shape For the more flexible shape parmeterisation the Jacobi transition gets smoothed For the drops with the fissility parameter x LD >0.612 the fission takes place before the Jacobi transition The investigation of Poincare instability will be the subject of future studies

Thank you for attention

The barrier heights, topographical theorem W. D.Myers and W. J. Swiatecki, Nucl. Phys. A601, 141 (1996): the “barrier will be determined by a path that avoids positive shell effects and has no use for negative shell effects. Hence the saddle point energy will be close to what it would have been in the absence of shell effects, i.e., close to the value given by the macroscopic theory!” F.A.Ivanyuk and K.Pomorski, Phys: Rev. C 79, (2009)