ISSN 1062-8738, Bulletin of the Russian Academy of Sciences: Physics, 2009, Vol. 73, No. 2, pp. 187–192. © Allerton Press, Inc., 2009. Original Russian Text © V.E. Bunakov, S.G. Kadmensky, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 198–203. 187 Rotation of Fissioning Nuclei in Reactions with Polarized Neutrons V. E. Bunakov a and S. G. Kadmensky b a St. Petersburg Nuclear Physics Institute, Gatchina, Russia e-mail: bunakov@vb3190.spbu.edu b Voronezh State University, Voronezh, Russia Abstract—Advantages and disadvantages of taking into account rotation of polarized nuclei in classical trajec- tory calculations of ternary fission are considered. Expressions for polarization of the fissioning deformed com- pound nucleus which allow for the quantum number K in the fission channel are derived. DOI: 10.3103/S1062873809020129 INTRODUCTION In our previous works [1–3] we developed a theory explaining the earlier observed (see, for example, [4]) T -odd correlation of the form in ternary fission induced by polarized neutrons. Here [ , and are the unit vectors of the neutron spin and wave vectors of the light fragment and the third particle (normally α) emitted in the ternary fission. This correlation, which experimenters usually call TRI effect, resulted in that the differential cross section for the ternary fission reac- tion had the form (1) The experimental geometry was usually chosen such that the directions of the vectors and were parallel to the y and z axes respectively, and the vector varied in the (x, z) plane. The measured effect was defined as (2) where σ + and σ – are the differential cross sections at the positive and negative helicity of the neutron beam respectively. The amount of the effect for the 233 U target was about 3 × 10 –3 . It is important that this value (and its sign) was practically independent of the angle θ between the vectors and in a wide range of angles around θ ≈ 90°. However, recent measurements [5] with the 235 U tar- get have revealed a new effect called ROT. Unlike TRI, this effect does not vary under inversion of the vectors and but reverses its sign near the angle θ ≈ 90°. s n s n k LF k α d 2 σ d Ω LF d Ω α ----------------------- B 0 D 1 s n k LF k α , [ ] . + = s n k LF k α D σ + σ – – σ + σ – + -----------------, = k LF k α k LF k α This effect is fairly well reproduced [6] by the classical trajectory calculations of the α particle emission in the Coulomb field of the rotating system of two fission fragments with the total angular momentum on the order of several units of  which is equal to the polar- ized component of spin of fissioning nucleus 236 U resulting from absorption of the polarized neutron by the target nucleus. The rotation of the α particles slightly lags behind the rotation of the divergence axis of the fragments (Coriolis force effect), which causes a shift of the entire angular distribution of the α particle with respect to this axis. A change in the neutron helic- ity leads to a change in the direction of spin and con- sequently in the rotation direction of the system of frag- ments. As a result, the angular distribution of the α par- ticle counted from the divergence axis shifts in the opposite direction. It is the difference in angular distri- butions for opposite helicities that leads to the observed effect. The order of magnitude of the effect is repro- duced when the system is rotated through the angle θ of about 0.2°. It is known that classical trajectory calculations of angular distributions of α particles in ternary fission without taking into account the rotation of the decaying system fairly well reproduce experimental data. The rotation of the system of diverging fragments was first taken into account in this kind of calculations in [6]. It is first of all surprising that the results of the classical approach are in conflict with the quantum-mechanical uncertainty relation between the angular momentum J of the system and the angle θ of its rotation in the plane perpendicular to it (3) In the case considered, the angular momentum of the nucleus was about several ; therefore, it should be expected that the uncertainty of the system rotation angle would be ∆θ ≈ 1 rad. As was already mentioned, J ∆ J ∆θ ⋅  . ≈