_{1}

^{*}

Models of the pointed interactions approximately describing real interactions of nuclear particles in quantum mechanics are considered. The concept of “a dot cluster”—a complex of charges which at the zero size create possibility of localization of a trial particle in the field of the final size is entered. States in one-dimensional systems, and also in three-dimensional systems with “a local isotropy” are studied. The conditions of dot systems characterized by the nonzero, including fractional, orbital moment were studied.

For the model description of nuclear processes extensive literature―see, for example, [

We will consider, at first, the one-dimensional system described by Schrödinger’s equation of the following look:

where

where

there are also conditions of dispersion which are in detail studied in [

where the

charge of a cluster q is equal to zero―the dipolar moment is also equal to zero―

deduction of charged particle (electron) in limited area existence of a charge of an opposite sign in the center of system isn’t obligatory―the electron can be localized if it interacts with the dot cluster characterized by a zero charge, but having the square moment, other than zero. At this field of a cluster everywhere, except the vicinity of a point

We will consider a situation when there are two δ―the center, i.e. potential has an appearance:

The solution of the stationary equation of Schrödinger characterized by level depth

Substituting (5) in (1) taking into account (4) we will receive system:

Here a, b―constants. From a condition of existence of the nonzero decision of this system for a, b it is possible to receive a ratio for size

In a case when

that

We will consider, further, impact of a field of the electron connected by two centers on these centers―dot clusters. The full force operating on a cluster is calculated as integral of the following look:

where

This equation corresponds to symmetric distribution of electronic density,

The derivative of integrand function has a gap in a point near which the cluster is loclized:

The difference between values on the right and to the left of a point

In the absence of symmetry of system for forces operating on clusters it is possible to receive:

We will note here that consideration of the real work makes sense at

positive. If

The symmetric equation of Schrödinger stationary spherically at zero orbital quantum number has an appearance:

If the potential created by third-party charges has an appearance:

Charge density in a spherical cluster is defined from the equation:

will notice that two separate clusters, “locally” spherically symmetric, located in different points, don’t influence at each other. Also it is necessary to notice that the determined higher than a potential doesn’t determine depth of the connected level, the equation is satisfied at any

Let δ―the centers be located at

where

We will substitute these expressions in (10), considering that

Equating of coefficients at

The condition of existence of the nonzero decision of this system has an appearance:

The type of a ratio (13) is similar (6). (See also works [

If the orbital quantum number

We will make replacement in the Equation (14), including:

At

that the first addresses in zero at

Due to these circumstance we will consider the Equation (14) in conditions when divergence of a charge of an electron at is absent. The solution of the Equation (14) with zero right part has an appearance:_{2} equality follows: _{2} is equal

In summary, we will notice that in work problems of the theoretical description of systems with dot potentials in symmetric systems one-dimensional and three-dimensional spherically are considered.

AlexanderChikhachev, (2015) Interaction of Dot Clasters. Journal of Modern Physics,06,1642-1646. doi: 10.4236/jmp.2015.611165