Faculty of Physics
M.V.Lomonosov Moscow State University
Theoretical and mathematical physics

## Exact solutions of Dirac equation in strong external fields in $1+1$ dimensions

### O.F. Dorofeev, V.R. Khalilov

Moscow University Physics Bulletin 2001. 56. N 5. P. 1

Influence of a superstrong external magnetic field on the electron energy spectrum in a strong Coulomb field and on the value of nucleus critical charge has been studied. Investigation has been reduced to solving the problem in a cut-off Coulomb field in $1+1$ dimensions. The Dirac equation in $1+1$ dimensions in an external scalar Coulomb field is shown to have a zero-energy nondegenerate charge-self-conjugate solution, and hence, the vacuum of the model should acquire a fermion charge ${\pm 1/2}$.

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## The method of integral functionals

### V.V. Ternovskii, A.M. Khapaev

Moscow University Physics Bulletin 2001. 56. N 5. P. 5

A theory of induced radiation the foundations of which are laid in the work of I.M. Ternov is developed. An analytical solution to the problem about forced radiation of an ensemble of charged particles that interact with variable electromagnetic fields localized in a domain being a model of an open resonator has been obtained.

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## Neutron beta decay and lepton anomalous magnetic moment in an external field: from first studies to modern state

### A.I. Studenikin

Moscow University Physics Bulletin 2001. 56. N 5. P. 9

Two important problems are discussed that arise in the study of elementary particles interaction in external electromagnetic fields. It was in the 1960s that the first results were obtained by I.M. Ternov and his colleagues in their studies of the neutron beta decay and charged lepton anomalous magnetic moments in external fields, and even now, the two problems still attract much attention. A brief review of the subject is presented. New findings obtained recently provide evidence that the above problems are quite up to date.

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## A mixed boundary problem of magnetized semiconductor physics in interior of domain

### A.O. Chikilev, P.A. Krutitskii

Moscow University Physics Bulletin 2001. 56. N 5. P. 19

A mixed boundary problem has been considered for harmonic functions in a multiply connected interior of domain. Some boundary curves obey the Dirichlet condition, the rest of the boundary curves satisfying a condition with an oblique derivative. To find the solution, a uniquely solvable Fredholm integral equation of second kind has been obtained. As a result, the existence of the unique solution of the problem in the domain of continuous functions has been proved.

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## Dissipative terms in quasi-gas-dynamic equations and their effect on shock wave flow field

### T.G. Elizarova$^1$, M.E. Sokolova$^2$

Moscow University Physics Bulletin 2001. 56. N 5. P. 24

The general form of quasi-gas-dyn81Ilic equations has been presented, along with that of additional dissipative terms in cylindrical and rectangular Cartesian coordinates, and the effect of additional dissipation on gas flow par81Ileters in a shock wave has been demonstrated.

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## Real resonances in a waveguide with nonhomogeneous filling

### A.N. Bogolyubov,A.L. Delitsyn, M.D. Malykh

Moscow University Physics Bulletin 2001. 56. N 5. P. 29

Eigenvalues embedded in continuous spectra of spectral problems for acoustic and electromagnetic waveguides with filling have been considered. A criterion for the existence of an infinite sequence of eigenvalues for fillings of the insertion type has been given. In the case of fillings of the "simple insert" and "elbow" types, the eigenvalues have been found as roots of transcendental equations.

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## Some mathematical models of immunology and their computer testing

### A.A. Volodin, V.B. Glasko, E.A. Rovenskaya, S.V. Rodionov

Moscow University Physics Bulletin 2001. 56. N 5. P. 33

Two quasi-equilibrium immunology models are considered. The problem of the uniqueness of a solution of respective inverse problems is studied for one of the models. Results of mathematical experiments and obtainable accuracy estimate are presented.

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## On resonance quantum limit for interference gravitational antenna

### A.M. Chebotarev, A.V. Churkin, G.V. Ryzhakov, A.M. Sinev

Moscow University Physics Bulletin 2001. 56. N 5. P. 38

In quantum measurement theory, the sensitivity of a measuring instrument is bounded below by the standard quantum limit (SQL). The expression for SQL obtained by the authors for an exactly solvable problem on a gravitational-wave interference detector enables the estimation of the minimum metric curvature in a periodic gravitational wave in the resonance and nonresonance cases. The authors consider the dependence of SQL on the selection of an observable quantity and on the intensity of a laser beam for the exponential distribution of the number of photons.

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## Determination of discrete spectrum of radial Schr$\stackrel{..}{o}$dinger equation with arbitrary attracting potential

### O.S. Pavlova, A.R. Frenkin

Moscow University Physics Bulletin 2001. 56. N 5. P. 44

The method of integral transforms related to the study of the Laplace images of wave functions is applied to find the discrete spectrum of the radial Schr$\stackrel{..}{o}$dinger equation with short- and long-range attracting potentials of general form. The summation of the series has been performed in matrix elements of the characteristic equation, which are represented as formal expansions in inverse powers of the energy. The possibilities of the method have been demonstrated on the example of the $S$-state of the Schr$\stackrel{..}{o}$dinger equation with the Huelten potential. The suggested method can also be successfully used for other potentials.

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Atomic and nuclear physics

## A method of measuring proton and helium nuclei energy by specific energy release in the maxima of hadronic cascades in dense matter

### I.D. Rapoport, A.N. Turundaevsky, V.Ya. Shestoperov

Moscow University Physics Bulletin 2001. 56. N 5. P. 50

A method is suggested for determining the energy of protons and He nuclei (in the energy range over 1 TeV) based on measuring the energy release in the maxima of hadronic cascades induced by these particles in dense matter. The accuracy attainable in energy measurements has been evaluated, and comparison is made between model results and the results obtained in the experiment "Sokol-2".

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## Antarctic balloon experiment on measuring cosmic rays of ultimate energies

### R.A. Antonov$^1$, L.A. Kuzmichev$^1$, M.I. Panasyuk$^1$, D.V. Chernov$^1$, S.I. Nikolsky$^2$, T.I. Sysoyeva$^2$

Moscow University Physics Bulletin 2001. 56. N 5. P. 55

The paper describes an antarctic experiment planned to be performed on the basis of a modernized SFERA balloon setup. A long-term flight in a closed circumpolar path at an altitude of 30-40 km can help to measure the energy spectrum of cosmic rays in the energy region between $10^{18}$ and $(3-5)\cdot10^{20}$ eV. Such an experiment has a number of advantages over the satellite experiments being planned.

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Optics and spectroscopy

## Raman spectroscopy of an agglutinin ricin aqueous solution in the presence of guanidine chloride

### N.N. Brandt$^1$, O.V. Voronina$^1$, Yu.A. Savochkina$^2$, A.I. Sotnikov$^1$, A.G. Tonevitsky$^3$, A.Yu. Chikishev$^1$

Moscow University Physics Bulletin 2001. 56. N 5. P. 59

Partial denaturation of agglutinin ricin - ribosome-inactivating protein - under the effect of guanidine chloride (a cellular membrane-interaction model) results in a rearrangement of its secondary structure, which manifests itself in the form of changes in the amide III and presumably amide IV bands. The conformation-sensitive bands corresponding to the vibrations of tryptophan and disulfide bridges undergo no changes.

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Solid state physics

## Focusing point defect generation wave along crystallographic axes in crystals under the action of Gaussian laser beam

### V.I. Emel'yanov, A.V. Rogacheva

Moscow University Physics Bulletin 2001. 56. N 5. P. 65

We have theoretically studied the spatial self-organization of a point defect generation wave in laser-excited crystal semiconductors and dielectrics and demonstrated that owing to the elastic anisotropy of the crystals and the Gaussian intensity distribution of the exciting laser radiation, the wave proves to be focused along the crystallographic axes of the crystals.

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## Exchange effects in a two-dimensional electron gas in a semiconductor at finite temperatures

### A.G. Mironov

Moscow University Physics Bulletin 2001. 56. N 5. P. 73

The exchange energy of electrons of the size quantization subzone in a narrow quantum well has been calculated at arbitrary electron concentrations and temperatures. Conditions have been determined for the transition of a two-dimensional electron system into a spin-polarized state owing to the gain in the exchange contribution to a free energy. It has been demonstrated that in a certain electron concentration region two transitions, first into a polarized and then into an unpolarized state, can consecutively take place under changes of temperature.

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Astronomy

## Electric fields in stars

### V.I. Grigor'ev, V.S. Rostovskii

Moscow University Physics Bulletin 2001. 56. N 5. P. 78

Physical factors responsible for electric fields inside stars and the run of their intensity are discussed within the electron-proton equilibrium model of stars with allowance made for the Pauli principle; numerical estimates for the Sun are given.

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Theoretical and mathematical physics

## Effective transformation of optical noise into monochromatic radiation and generation of squeezed states in media with cubic nonlinearity

### Yu.E. D'yakov

Moscow University Physics Bulletin 2001. 56. N 5. P. 82

An exact solution of a statistical problem on the passage of a signal-cum-noise mixture through a medium with cubic nonlinearity has been obtained. It has been demonstrated that there can take place an effective (up to 34$\%$) energy transfer from the noise component to the monochromatic one of radiation. The distribution of the degree of squeezing of the noise field over the length of the nonlinear medium has been found, and the possibility has been noted of an abrupt squeezing jump at the beginning of the propagation region.

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