^{*}

nazaruk@inr.ru

^{3}.

Particle oscillations in absorbing matter are considered. The approach based on the optical potential is shown to be inapplicable in the strong absorption region. Models with Hermitian Hamiltonian are analyzed. They give an increase of the process width in comparison with the model based on the optical potential.

In-particle oscillations in the medium absorption can play an important role, for example, in

In the standard approach (later referred to as a

The results are compared in Sec.

In Sec.

We consider process

In the lowest order in

The optical model was developed for the Schrödinger-type equations. The physical meaning of

To get

The structure and

The interaction Hamiltonian of process

The

The general definition of the antineutron annihilation amplitude

The amplitude of process

In the lowest order in

(a)

When dealing with infrared singularity, for solving the problem a field-theoretical approach with a finite-time interval has been proposed

Starting from

The process width

We return to process

The process width

The amplitude

First, I compare the potential model with the model with a dressed propagator. In

The same conclusion has been done in Ref.

As proved earlier, the model with dressed propagator is unjustified. Nevertheless, the correction of the type

In

Therefore,

If

The difference in the results is seen from the ratio

To conclude: (1) The smaller the

For the realistic parameters

Finally, in the strong absorption region the model with an optical potential is inapplicable. In the models I calculate directly the off-diagonal matrix element. The optical potential is not used. (Note that in the case of Hermitian Hamiltonian the optical theorem is applicable.)

The model based on the optical potential compared with direct calculation of off-diagonal matrix element. The potential model is applicable only in the case of slight absorption.

If absorption is strong, then the potential model is inapplicable: (1) It contains double counting. (2) The

The field-theoretical approach is free from drawback mentioned above. Two variants of the models have been considered: the model with bare and dressed propagators. (In the latter case I come to the

The chief drawback in the model with a dressed propagator is that the procedure of separation of

In my opinion the model with a bare propagator is preferable. The model with the dressed propagator has been considered for the study of the process since the problem is of a great importance. It also gives the conservative limit

In the oscillation of other particles the difference between