научная статья по теме THE QUANTUM AND THERMODYNAMICAL CHARACTERISTICS OF FISSION TAKING INTO ACCOUNT ADIABATIC AND NONADIABATIC MODES OF MOTION Физика

Текст научной статьи на тему «THE QUANTUM AND THERMODYNAMICAL CHARACTERISTICS OF FISSION TAKING INTO ACCOUNT ADIABATIC AND NONADIABATIC MODES OF MOTION»

ЯДРА. Теория

THE QUANTUM AND THERMODYNAMICAL CHARACTERISTICS OF FISSION TAKING INTO ACCOUNT ADIABATIC AND NONADIABATIC MODES OF MOTION

© 2007 S. G. Kadmensky*

Voronezh State University, Russia Received October 31, 2006

In the framework of the quantum theory of spontaneous and low-energy induced fission the nature of quantum and thermodynamical properties of a fissioning system is analyzed taking into account adiabatic and nonadiabatic modes of motion for different fission stages. It is shown that due to the influence of the Coriolis interaction the states of the fissile nucleus and of primary fission products are cold and strongly nonequilibrium. The important role of superfluid and pairing nucleon—nucleon correlations for binary and ternary fission is demonstrated. The mechanism of pumping of high values of relative orbital momenta and spins of fission fragments for binary and ternary fission and the nonevaporation mechanism of formation of third particles for ternary fission are investigated. The anisotropies and P-odd, P-even, T-odd asymmetries for angular distributions of fission products are analyzed.

PACS: 24.75.+i

1. INTRODUCTION

The quantum theory of spontaneous and low-energy induced fission describes the nuclear fission phenomenon applying methods of stationary multi-particle nuclear reaction theories [1,2] and theories of proton, alpha, and cluster radioactivity. The theory operates with the notions of wave functions of a fissioning system and fission products, amplitudes of partial fission widths, and fission phases. The quantum theory of fission (QTF) develops the traditional theory of fission [3] and quantum-mechanical approaches [4—6].

The main goal of QTF developed for binary fission [7, 8] as well as for ternary fission [9—11] is the unified description of fission process and interference effects for angular distributions of fission products. QTF uses the main assumptions of the traditional fission theory:

(a) the fissile nucleus in the initial state and the most probable fission fragments are markedly deformed and can be described by the generalized nuclear model [3];

(b) the fissioning system conserves the axial symmetry at all fission stages.

QTF distinguishes and studies the following four fission stages:

first, the evolution of the fissile nucleus from the initial state to the scission point;

E-mail:kadmensky@phys.vsu.ru

second, the formation of primary fission products and their angular distributions;

third, the thermalization of nonequilibrium states of primary fission fragments;

fourth, the emission of prompt neutrons and y quanta by thermalized fission fragments and the formation of final fission fragments.

2. QUANTUM AND THERMODYNAMICAL CHARACTERISTICS OF THE FIRST STAGE OF BINARY FISSION AND CORIOLIS INTERACTION

At the first stage of a binary fission the adiabatic separation of collective rotational and internal (collective deformational and nucleonic) nuclear modes is realized. The wave function of the fissile nucleus can be presented in the generalized nuclear model as

J = (1 " Ko)\ljè[DJMK^)x*K (£,a) +

* (1) + (-1)J+KDM -k(u)x^K+

+ ôK,0\l-J+TDM0 Mx^o a),

where M and K are projections of spin J of a fissile nucleus onto the Z axis of laboratory coordinate frame and onto the nuclear symmetry axis; £ and

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a are the sets of collective deformation parameters and additional nucleon coordinates, respectively. For the main region of nuclear motion, for the first fission stage the adiabatic separation of collective deformational and nucleonic modes is realized and the deformation potential V(a) can be calculated within the liquid-drop model with shell corrections by V. Strutinsky. However, for some region near the scission point (nonadiabatic region) the velocities of changing collective deformation parameters a become markedly higher than nucleon velocities, and the adiabatic separation of nucleonic and collective deformational modes of motion is broken and the nucleonic subsystem transits to excited states. If the time to of this nonadiabatic region passing for the fissile nucleus is much more than the time Teq of the fissile nucleus transition to equilibrium states, the fissile nucleus near the scission point can be characterized by some temperature T. Many fission models, see, e.g., [12—14], that provide a reasonable description of mass and charge distributions of fission fragments use this approximation (to » Teq) with the result that the fissile nucleus in the vicinity of the scission point has the temperature T & 1 MeV which corresponds to the excitation energy E & 30 MeV for fissile nuclei with mass numbers A & 240.

It was shown [3, 11] that the anisotropies and P-odd, P-even, T-odd asymmetries for fission fragment angular distributions appear if the distributions of projections M and K of the fissile nucleus spin J near the scission point are not simultaneously uniform. This condition for M distribution is realized by an orientation of the fissile nucleus spin in laboratory coordinate frame. Analogous conditions for K distribution are realized, first, by the influence of A. Bohr transitional fission states formed at the outer saddle points of the deformed potential V(a) associated with cold states of the fissile nucleus and appearing as filters for selecting the most probable values of K and, second, by the conservation of projection K as integral of motion for all subsequent regions of the first stage of fission.

The main factor which destroys the conservation of projection K is the Coriolis interaction. The heating of an axially symmetric deformed nucleus to relatively high temperatures gives rise to a dynamical enhancement of the Coriolis interaction [15]. The inclusion of this effect leads to the uniform statistical mixing of all possible values of projections K. By way of example, this situation is realized for neutron resonance states in heavy compound nuclei (A & & 240) in the first well of the deformation potential. The excitation energies Eex and characteristic temperatures T for these states are Eex & 6 MeV and T & 0.4 MeV, respectively. Due to the Coriolis mixing of all possible projections K, this projection

K disappears as a good quantum number for Wigner ensembles that characterize the experimental distributions of energy spacing between the neighboring neutron resonances [3].

Since the anisotropies and P-odd, P-even, and T-odd asymmetries for the angular distributions of fission fragments are observed, it means that the Coriolis mixing of different K values for the fissile nucleus states near the scission point is very weak.

The only possibility to realize this situation with the Coriolis mixing for the excited states of the nucleon subsystem with excitation energy Eex > 6 MeV is that the time to of passing of the nonadiabatic region by the fissile nucleus is much less than the time Teq to undergo rearrangement of excited states of the fissile nucleus to equilibrium thermalized states. This immediately leads to the concept that because of a nonadiabatic character of a collective deformation motion of the fissile nucleus near the scission point the only type of doorway states of the nucleon subsystem, which are known in the nuclear reaction theory and characterized by a rather simple (few-quasiparticle) collective structure and by a rather low density on the energy scale, can be excited. For such doorway states one can disregard the effects of the Coriolis mixing and consider the projection K as an integral of motion.

Although the superfluid nucleon—nucleon correlations for the doorway states are slightly suppressed by the blocking effects caused by the appearance of the particle—hole pairs in doorway states these correlations may play an important role for dynamics of the formation of primary fission fragments.

By analogy with alpha decay of heavy nuclei [16] one can expect that favored fission transitions for which primary fission fragments are formed without breaking the Cooper pairs occurring in the prescis-sion configuration of the fissile nucleus will proceed with high probability. The superfluid classification of fission transitions makes it possible to explain even—odd effects observed experimentally for charge distributions of final fission fragments [ 17].

3. THE FISSION STAGE OF FORMATION OF PRIMARY BINARY FISSION FRAGMENTS

The second fission stage is connected with disintegration of the fissile nucleus and emission of two primary fission fragments. The primary fragments are formed in cold states that are, however, strongly nonequlibrium in energy and deformation parameters. This stage is characterized by the time t2 that is much shorter than the time necessary for the transition of the primary fission fragments to equilibrium thermal-ized states. For the condition ensuring the validity of

THE QUANTUM AND THERMODYNAMICAL CHARACTERISTICS

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the concept of A. Bohr transitional fission states to be met it is necessary that the angular distributions of primary fission fragments be fully formed within the time t2 in order that the subsequent stage connected to the thermalizaton of primary fragments could not change these angular distributions.

For this fission stage it is possible to include the fission channel functions UJM, which for binary fission read

(ii) the kinetic energy Ekin essentially surpasses the sum of rotational energies of fission fragments:

h2Ji (Ji + 1) , h2J2 (J2 + 1) h2J2

Ekin »

2-i

+

2-2

-i

(6)

where -i is the moment of inertia of the ith fragment;

(iii) the time t2 is markedly less than the period of rotation of fission fragments:

UCJM — {{JJ(ui,Zi)JMl(^2,Î2)]im1 x (2)

X iLYLML (Q)

JM

where channel multiindex c = a1 K1J1 a2K2J2IL and the wave functions of the fission fragments (i = 1,2) have the forms analogous to (1).

In QTF, the amplitude of partial fission width

\JrjKc and fission phase 5 JKc are defined as following:

jsJn

uj m

yJn

1 aKc

(f¿:(+)(R)y

(3)

R

H

JM aK

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