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The cross sections for inelastic neutron scattering and radiative capture in the field of a light wave

The mixing of the levels of a compound nucleus in the field of a high-intensity light wave is considered. The cross sections for inelastic neutron scattering and radiative capture are computed with allowance for this effect. The effect of the electron shell on the effective charge for the dipole interaction between the neutron + nucleus system and the external electromagnetic field is taken into consideration.


INTRODUCTION
The effect of resonance excitation of atoms in a laser radiation field has been fairly well studied from both the theoretical and experimental points of view [1]. In the case of a nucleus the resonance excitation of the levels near the ground state was accomplished with the aid of the Mossbauer effect. There are only incoherent-radiation sources for this energy region. The situation is different when the levels of a compound nucleus are excited, e.g., in reactions with neutrons. In the case of heavy nuclei (the rare earths, the actinides), for excitations corresponding Preprint submitted to Physics of Atomic Nuclei to the binding energy of the neutron, the distance between the levels of the compound nucleus is close in order of magnitude to the energies of laser-light quanta. Therefore, we can, in principle, raise the question of resonance transitions between two levels of a compound nucleus, one of which is excited in the course of the neutron capture. In this case levels with opposite parities, which may differ significantly in the partial nuclear decay probabilities associated with them, will, as a rule, be mixed in an external resonance electromagnetic field.
In earlier papers [2,3] was attempted to estimate the probability for mixing of the levels of a compound nucleus in the presence of an external electromagnetic field. There was assumed that the electron shell of the atoms had no effect on the probability for resonance mixing of the levels of a compound nucleus, i.e., that the frequency of the electromagnetic field was not equal to the electron-transition frequency. Furthermore, the spin of the neutron was assumed to be equal to zero. These two assumptions are rather far removed from what the real situation is, especially, the neglect of the effect of the electron shell. It had been shown earlier in another connection [4] that, in the case of electric dipole nuclear transitions with low frequency ( nucl el   the electron -transition frequency) ), the electron shell of the atom has an appreciable effect on the nucleartransition probabilities.
In the present paper we investigate the role of the electron shell in the processes of resonance mixing of the levels of a compound nucleus, and also compute the probability for this mixing.

EFFECT OF THE ELECTRON SHELL
The Hamiltonian of an atom + neutron system in an external electromagnetic field has the form where m and M are respectively the electron and neutron masses, We transform to a system of coordinates fixed to the nucleus; to do this, we introduce the relative coordinates and the coordinate of the center of gravity: 1 ,, After simple transformations, the Hamiltonian can be written in the form where oa H and on H are respectively the Hamiltonians of the atom and neutron + nucleus system in the absence of an external electromagnetic field, and for the operator V we obtain the following expression: Here the first term describes the interaction of the electrons with the external electromagnetic field, the summation being over all the electrons in the atom (Z '  Z ); the second term describes the interaction of the system neutron + nucleus with the A field; and the third term describes the correlation between the motion of the electron + nucleus system and that of the neutron. This interaction is the result of the separation of the center of mass of the atom + neutron system and the going over to the coordinates of the neutron and the electrons relative to the nucleus. In [4] a similar interaction between the nucleons of the nucleus and the electron shell arises from the Coulomb energy as a result of an expansion in powers of the small parameter / nucl el rr Therefore, this interaction is proportional to the square of the charge, but the interaction considered in the present paper does not depend on the charge at all.
The quantity Ze/A should be interpreted as the effective charge for the electric dipole transitions in the neutron-+ nucleus system. If the effect of the electron shell is insignificant, then only this charge needs to be considered. Let us consider the effect of the electron shell on the effective charge. To do this, let us compute the matrix element of the transition between the compound-nucleus level for the s neutron and the corresponding p level with emission or absorption of a quantum of the external electromagnetic field. We shall assume that the electron shell of the atom remains in the process in the ground state. Then we obtain in the lowest orders of perturbation theory the expression Here, for simplicity, we consider the case in which the z axis is oriented along the vector 0 E . Let us transform the expression in the round brackets. Let us separate out in this expression the independent term, and, using the well-known sum rule for the square of the matrix element of the dipole operator [5] reduce it to the ratio Z '/Z, where Z ' is the number of electrons in the atom (ion) and Z is the nuclear charge. Let us express the other term, which is proportional to 2  , in terms of the dipolar polarizability of the atom (ion) [ Estimates of the second term in (9) in the static limit yield a value of 4 10  for non alkali neutral atoms and a value roughly an order of magnitude higher for the alkali atoms. When allowance is made for the  dependence of the dynamica1 polarizability, the corresponding term can be much greater than the term in the static case. Thus, for example, for the cesium atom and a neodymium laser the value of the polarization term can be as high as

PROBABILITY FOR MIXING OF THE LEVELS OF A COMPOUND NUCLEUS
For the subsequent calculations it is convenient to express the nuclear transition operator in (9) in terms of the spherical harmonics ( , ) lm Y  : is over all the final states. In the case of slow-neutron scattering by nuclei we can limit ourselves in the initial state to the consideration of the s and p waves. We shall assume that the target nucleus has zero spin; then the initial-state wave function in the region n rR  (the nuclear radius) will have the form (we assume, for simplicity, that the neutron is a spineless particle) Thus, as follows from a comparison of the formulas (19) and (20), in the second case (transition from the p into the s state) the total cross section depends on the angle 0  between the vectors 0 k and 0 E and, when 0 /2