The lack of the stabilization of quasi-stationary electron states in a strong magnetic field

Rodionov, V. N.; Kravtsova, G. A.; Mandel, A. M.

doi:10.1134/1.1519315

Cited by 8 publications

(9 citation statements)

References 2 publications

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“…But this is not always the case for a strong magnetic field, as shown in [3], [4]. We note that efforts to analyze spin effects in the nonrelativistic approximation were made many times.…”

Section: Introductionmentioning

confidence: 99%

Wave function and the probability current distribution for a bound electron moving in a uniform magnetic field

2010

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We study the effects of electromagnetic fields on nonrelativistic charged spinning particles bound by a short-range potential. We analyze the exact solution of the Pauli equation for an electron moving in the potential field determined by the three-dimensional δ-well in the presence of a strong magnetic field. We obtain asymptotic expressions for this solution for different values of the problem parameters. In addition, we consider electron probability currents and their dependence on the magnetic field. We show that including the spin in the framework of the nonrelativistic approach allows correctly taking the effect of the magnetic field on the electric current into account. The obtained dependences of the current distribution, which is an experimentally observable quantity, can be manifested directly in scattering processes, for example.

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“…But this is not always the case for a strong magnetic field, as shown in [3], [4]. We note that efforts to analyze spin effects in the nonrelativistic approximation were made many times.…”

Section: Introductionmentioning

confidence: 99%

Wave function and the probability current distribution for a bound electron moving in a uniform magnetic field

2010

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“…Such investigations are becoming increasingly relevant both because ever stronger electromagnetic fields are being created in laboratory conditions and because theoretical methods for studying quantum processes whose descriptions lie beyond the frames of the standard theory of perturbations in an external field are being improved. For instance, this pertains to studying nonlinear phenomena in strong fields of involved configurations, which has attracted much interest recently [8]- [12], [16]- [18]. In particular, the joint action of strong constant electric and magnetic fields on the process of atomic particle ionization was studied in detail [16].…”

Section: The Problem Settingmentioning

confidence: 99%

“…The process of the interaction of laser radiation with a negative ion in a strong constant electric field was thoroughly analyzed in [17], [18]. The analogous nonlinear processes of ionization in a laser radiation field in the presence of a strong magnetic field 1 was studied in [8], [9], [11], [12].…”

Section: The Problem Settingmentioning

confidence: 99%

Equation for the Complex Energy of a Bound Particle in a Laser Radiation Field in the Presence of Strong Constant Electromagnetic Fields

2005

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We construct exact solutions of the Schrödinger and Pauli equations for charged particles in the external field of the Redmond generalized configuration. We calculate the Green's functions of scalar and spinning particles in this field. Using them, we calculate the equations for the complex quasienergy of a bound particle (bound by a short-range potential) two different ways. In the example of an external constant electric field, we discuss the applicability domain of the obtained equations and the differences between their solutions. The problem settingStudying the processes of the nonlinear ionization of atoms and their ions by a strong low-frequency electromagnetic radiation field, which began almost immediately after lasers were invented, is known to be one of the most rapidly developing branches of atomic physics [1]- [16]. It was based on the already known laws of the process of ionization by a constant electric field and of the one-photon ionization reaction. In particular, it was already shown in the first papers on this subject that in the case where the photon energy is below the ionization potential, the multiphoton ionization effects and the tunneling effects occur, highly similar to processes in a constant field. We mention that the theoretical study of multiphoton processes was based on nonperturbative methods from the very beginning. In this respect, we note that the basic results of the nonperturbative approach to studying nonlinear ionization by constant and variable fields were obtained based on a short-range atomic potential model. Such investigations are becoming increasingly relevant both because ever stronger electromagnetic fields are being created in laboratory conditions and because theoretical methods for studying quantum processes whose descriptions lie beyond the frames of the standard theory of perturbations in an external field are being improved. For instance, this pertains to studying nonlinear phenomena in strong fields of involved configurations, which has attracted much interest recently [8]- [12], [16]-[18]. In particular, the joint action of strong constant electric and magnetic fields on the process of atomic particle ionization was studied in detail [16]. The process of the interaction of laser radiation with a negative ion in a strong constant electric field was thoroughly analyzed in [17], [18]. The analogous nonlinear processes of ionization in a laser radiation field in the presence of a strong magnetic field 1 was studied in [8], [9], [11], [12].

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“…But this is not always the case for a strong magnetic field, as shown in [16], [30]. We note that efforts to analyze spin effects in the nonrelativistic approximation were made many times.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…But because mathematical estimates are complicated in the case of spinning particles, the obtained conclusions are not always sufficiently convincing. In our opinion, the papers [27], [30], [32], where the effects of the field on the behavior of spinning and scalar particles were compared, are most correct from the standpoint of the necessity to take particle spins into account. For these purposes, the solutions of the Pauli equations, together with the solutions of the Schrödinger equation, were also used in the indicated papers.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

The energy level shifts, wave functions and the probability current distributions for the bound scalar and spinor particles moving in a uniform magnetic field

Rodionov

Kravtsova

2011

Phys. Part. Nuclei

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We discuss the equations for the bound one-active electron states based on the analytic solutions of the Schrodinger and Pauli equations for a uniform magnetic field and a single attractive δ(r)-potential. It is vary important that ground electron states in the magnetic field differ essentially from the analogous state of spin-0 particles, whose binding energy was intensively studied more than forty years ago. We show that binding energy equations for spin-1/2 particles can be obtained without using the language of boundary conditions in the δ-potential model developed in pioneering works. We use the obtained equations to calculate the energy level displacements analytically and demonstrate nonlinear dependencies on field intensity. We show that the magnetic field indeed plays a stabilizing role in considered systems in a case of the weak intensity, but the opposite occurs in the case of strong intensity. These properties may be important for real quantum mechanical fermionic systems in two and three dimensions. We also analyze the exact solution of the Pauli equation for an electron moving in the potential field determined by the three-dimensional δ-well in the presence of a strong magnetic field. We obtain asymptotic expressions for this solution for different values of the problem parameters. In addition, we consider electron probability currents and their dependence on the magnetic field. We show that including the spin in the framework of the nonrelativistic approach allows correctly taking the effect of the magnetic field on the electric current into account. The obtained dependencies of the current distribution, which is an experimentally observable quantity, can be manifested directly in scattering processes, for example.

show abstract

The lack of the stabilization of quasi-stationary electron states in a strong magnetic field

Cited by 8 publications

References 2 publications

Wave function and the probability current distribution for a bound electron moving in a uniform magnetic field

Wave function and the probability current distribution for a bound electron moving in a uniform magnetic field

Equation for the Complex Energy of a Bound Particle in a Laser Radiation Field in the Presence of Strong Constant Electromagnetic Fields

The energy level shifts, wave functions and the probability current distributions for the bound scalar and spinor particles moving in a uniform magnetic field

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