ЯДЕРНАЯ ФИЗИКА, 2011, том 74, № 7, с. 979-985
= ЯДРА
PROMPT RADIATION AS A PROBE FOR FISSION DYNAMICS
©2011 F. F. Karpeshin*
University of Buenos Aires, Argentina; Saint Petersburg State University, Russia Received January 29, 2010; in final form, October 11, 2010
It is shown that the Strutinsky—Denisov induced polarization mechanism leads to the appearance of the prompt electric dipole radiation from fission fragments of 235 U by thermal neutrons in the domain of around 5 MeV. The probability of the radiation is at the level of 0.001 per fission, which is in agreement with experiment. The angular distribution exhibits left—right asymmetry with respect to the direction of the neutron polarization axis. That means that the emission of gamma quanta at the given angle depends on the neutron polarization. The asymmetry is at the level of 10~3. The study of this effect will give a direct information about the scission configuration, nuclear viscosity, and dissipation properties of the collective energy of the surface vibration in fragments with large amplitude. This will give a complete picture of the process of snapping back the nuclear surface.
1. INTRODUCTION
Nuclear fission is a unique process of the collective motion with an extremely large amplitude. From this viewpoint, fission is of great interest. Developing, this complex process goes through a number of stages: prefission vibration, formation of the fragments, the neck rupture and separation of the nascent fragments, their acceleration and thermolization of their deformation energy, evaporation of neutrons in flight and gamma quanta by stopped fragments, and so on (e.g., [1] and references cited therein). Correspondingly, the dynamics of fission from the beginning to the formation of the final fragments has many facets. At the same time, basic characteristic features of this complicated process, such as the time scale as well as the scission configuration and dynamics, are not fairly clear. Thus, information about the time scale in the fusion—fission theory is usually obtained by studying prefission neutrons or gamma quanta emitted from hot compound systems. Contrary, in the case of neutron-induced fission, in spite of well decades of search for, detection of prompt, or prefis-sion neutrons remains a challenging, but not solved problem (e.g., [2]). Actually, the prefission scenario is mastered by the viscosity of nuclear matter. Small viscosity leads to a more prolonged shapes of the nascent fragments and larger distance between them at the moment of scission, which is compensated by a higher initial velocity. High viscosity will be characterized by a shorter scission distance and lower velocity of the nascent fragments, which may result in the same total kinetic energy of the fragments at infinity (e.g., [3] and references therein). It is only the
E-mail: fkarpeshin@ya.ru
muon distribution of prompt fission in muonic atoms which shed light on the viscosity strength, giving an experimental evidence in favor of a rather compact scission configuration [1, 3—6]. Even less is known about prompt gamma rays, though the nonstatistical contribution to the hard domain of the spectrum, detected in [7], can be of this kind.
Herein, we investigate a possibility of radiation which arises as a result of contraction of the nuclear matter after scission. We show that appearance of the Electric Dipole Moment (EDM) in the fragments gives rise to the nonstatistical prompt radiation. We consider fission of 235U induced by thermal neutrons.
Such a possibility of emitting prompt gamma quanta due to snapping back the nuclear surface was noted yet in [8]. Estimations were made in [9]. The study of this effect will present invaluable information on the dynamics of this process, providing a direct confirmation of this phenomenon. The radiation arises before the neutron evaporation. Therefore, that bares information about this very early stage of fission. Moreover, we will show that the magnitude of the effect depends on the scission configuration and therefore it also bares information on the viscosity of the nuclear matter, in view of what is said above. We will estimate the energy and consider the angular distribution of the prompt part of the radiation. Its energy appears to be MeV. This is in the same region as that observed in [7]. Moreover, we will show that the angular distribution of these gamma rays will not be invariant with respect to the polarization of the fissile nucleus, and estimate the parameter of the left—right asymmetry. Current experiments [2, 10— 12] where similar effects in the angular correlations of the emitted alphas, neutrons, and usual gammas
The collective rotation of the fissile nucleus of 236 U caused by the polarization of the captured neutron (a, curved arrow), and the resulting rotation of the fission fragments (b). The captured neutron was polarized opposite to the z axis in the laboratory frame. z' is the symmetry axis of a representative fragment in the intrinsic coordinate system. The rotation angle of the fragment 3 = ut (Eq. (11)).
from fission are under investigation, increase interest in the calculations at the contemporary stage of investigation. Present results can be useful for better understanding the results of these experiments.
2. PHYSICAL PREMISES 2.1. Polarization of the Fragments
The first premise comes from the shake effects brought about by the neck rupture. From mathematical viewpoint, the rupture means breakdown of the analyticity of the Hamiltonian with respect to time. At the moment of scission, the nascent fragments have a pear-like form with the noses directed towards the point of the rupture. The sharpened noses cause appearance of the induced EDMs in the fragments (see the figure). The rupture starts the snapping-back of the nuclear surface [8]. This snapping-back may give rise to the oscillation of the surface. This oscillation smears out in time, depending on the dissipation. The induced EDM of the fragments also oscillate, following the oscillations of the shape of the fragments. The oscillations of the EDM generate electromagnetic field in space, changing with time. This manifests itself as the electric dipole radiation, which may also lead to internal conversion. In the case of muon-induced prompt fission, this mechanism was proved to manifest itself in muon shake-off, which direct process is observed on the background of the regular muonic conversion spectrum. The calculated probability agrees with the experiment [13, 14]. The oscillations of the induced EDM of the fragments
occurs along its symmetry axis, whereas the resulting radiation is directed perpendicularly to the symmetry axis of the fragment.
The appearance of the induced EDM was predicted in nuclei by Strutinsky [15] in the case of superposition of even and odd harmonics (E2 and E3) in the decomposition of the shape of the nuclear surface. Therefore, this is an effect of the second order in deformation. This effect received a substantial attention (e.g., [16—18] and references therein). It was shown that the induced EDM is responsible for the enhanced E1 intraband transitions in heavy-ion collisions [19]. Furthermore, the induced EDM is responsible for many phenomena related to the space parity violation ([18] and references cited therein). The anapole nuclear moment was calculated in terms of the induced EDM [20]. An analytical expression was given for the amplitude of the induced EDM by Denisov [17].
2.2. The Collective Rotation of the Fissile Nucleus and the Fragments
The second premise concerns the angular distribution and its asymmetry related to the polarization of the fissile nucleus. That is the ordered collective rotation of the fissile nucleus which is brought about by the neutron polarization. Fission is facilitated by the rotation in the direction perpendicular to the rotation axis (see the figure). This rotation is due to the well-known fact that the fissile nucleus is cold at the scission point. Otherwise, the angular moment could be distributed among the individual nucleons, without appearance of the collective rotation. Recent experiments showing the effect of rotation of the fission axis in ternary fission after scission [11] clearly confirms this picture. The measured angle of the rotation is 0.003, which fairly coincides with a simple solid-state estimate. This is the most impressive lesson of the study of this phenomenon.
Evidently, this rotation is transferred to the fragments. Again, simple solid-state estimations show that the fraction of the primary angular momentum, which is transferred to each of the fragments, depends on the shape of the fragments at scission. It varies within 6 to 11% per fragment under various suppositions about the shape. The smaller the neck radius at scission, the smaller is the fraction of the angular momentum transferred. In turn, the probability of the prompt radiation per fission, as well as the magnitude of the left—right effect is proportional to the momentum transferred. Therefore, these values are very sensitive to its variation, and may be used as a probe of the fission dynamics. The remaining 80% of the primary momentum contribute to relative angular momentum of the fragments. Thus the fragments
a
y
b
x
У
z
remember the direction of the primary polarization of the fissile nucleus. And the directivity diagram of the electric dipole radiation, which is at first perpendicular to the fission axis, rotates together with the fragment. Reversal of the neutron polarization causes the reciprocal reversal of the direction of the rotation. This will manifest itself as the left—right effect in the angular distribution of the radiation with respect to the plane perpendicular to the neutron polarization (see the figure).
The polarization of the neutron beam naturally defines the quantization axis z in the laboratory frame. In [10] fission fragments and gammas were detected in the
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