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R. G. Nazmitdinov

Publications and source records attributed to R. G. Nazmitdinov.

At least 73 records · Page 4Linked to original sources
arXiv2002

Statistical Fluctuations of Electromagnetic Transition Intensities and Electromagnetic Moments in pf-Shell Nuclei

We study the fluctuation properties of $ΔT=0$ electromagnetic transition intensities and electromagnetic moments in $A \sim 60$ nuclei within the framework of the interacting shell model, using a realistic effective interaction for $pf$-shell nuclei with a $^{56}$Ni core. The distributions of the transition intensities and of the electromagnetic moments are well described by the Gaussian orthogonal ensemble of random matrices. In particular, the transition intensity distributions follow a Porter-Thomas distribution. When diagonal matrix elements (i.e., moments) are included in the analysis of transition intensities, we find that the distributions remain Porter-Thomas except for the isoscalar $M1$. The latter deviation is explained in terms of the structure of the isoscalar $M1$ operator.

nucl-th↗
arXiv2001

Semiclassical analysis of a two-electron quantum dot in a magnetic field: dimensional phenomena

While the dynamics for three-dimensional axially symmetric two-electron quantum dots with parabolic confinement potentials is in general non-separable we have found an exact separability with three quantum numbers for specific values of the magnetic field. Furthermore, it is shown that the magnetic properties such as the magnetic moment and the susceptibility are sensitive to the presence and strength of a vertical confinement. Using a semiclassical approach the calculation of the eigenvalues reduces to simple quadratures providing a transparent and almost analytical quantization of the quantum dot energy levels which differ from the exact energies only by a few percent.

cond-mat.mes-hall↗
arXiv2001

Conductance of Open Quantum Billiards and Classical Trajectories

We analyse the transport phenomena of 2D quantum billiards with convex boundary of different shape. The quantum mechanical analysis is performed by means of the poles of the S-matrix while the classical analysis is based on the motion of a free particle inside the cavity along trajectories with a different number of bounces at the boundary. The value of the conductance depends on the manner the leads are attached to the cavity. The Fourier transform of the transmission amplitudes is compared with the length of the classical paths. There is good agreement between classical and quantum mechanical results when the conductance is achieved mainly by special short-lived states such as whispering gallery modes (WGM) and bouncing ball modes (BBM). In these cases, also the localization of the wave functions agrees with the picture of the classical paths. The S-matrix is calculated classically and compared with the transmission coefficients of the quantum mechanical calculations for five modes in each lead. The number of modes coupled to the special states is effectively reduced.

cond-mat.mes-hall↗
arXiv2001

Dynamical moment of inertia and quadrupole vibrations in rotating nuclei

The contribution of quantum shape fluctuations to inertial properties of rotating nuclei has been analysed within the self-consistent one-dimensional cranking oscillator model. It is shown that in even-even nuclei the dynamical moment of inertia calculated in the mean field approximation is equivalent to the Thouless-Valatin moment of inertia calculated in the random phase approximation if and only if the self-consistent conditions for the mean field are fulfilled.

nucl-th↗
arXiv2001

Signature inversion in axially deformed $^{160,162}$Tm

The microscopic analysis of experimental data in $^{160,162}$Tm is presented within the two-quasiparticle-phonon model. The model includes the interaction between odd quasiparticles and their coupling with core vibrations. The coupling explains naturally the attenuation of the Coriolis interaction in rotating odd-odd nuclei. It is shown that the competition between the Coriolis and neutron-proton interactions is responsible for the signature inversion phenomenon.

nucl-th↗
arXiv2001

Whispering gallery modes in open quantum billiards

The poles of the S-matrix and the wave functions of open 2D quantum billiards with convex boundary of different shape are calculated by the method of complex scaling. Two leads are attached to the cavities. The conductance of the cavities is calculated at energies with one, two and three open channels in each lead. Bands of overlapping resonance states appear which are localized along the convex boundary of the cavities and contribute coherently to the conductance. These bands correspond to the whispering gallery modes appearing in the classical calculations.

cond-mat.mes-hall↗
arXiv2000

Octupole deformations in actinides at high spins within the cranking Skyrme-Hartree-Fock approach

The cranked Skyrme III effective Hamiltonian is applied for the analysis of the rotational dependence of the quadrupole and octupole moments in Ra, Th, and U isotopes. A comparison of the intrinsic electric dipole moments calculated in the model with available experimental and theoretical values is presented. It is found that the non-axial octupole deformation $Y_{32}$ becomes favorable at high spins for the actinide nuclei.

nucl-th↗
arXiv2000

Tilted Rotation and Wobbling Motion in Nuclei

The self-consistent harmonic oscillator model including the three-dimensional cranking term is extended to describe collective excitations in the random phase approximation. It is found that quadrupole collective excitations associated with wobbling motion in rotating nuclei lead to the appearance of two- or three-dimensional rotation.

nucl-th↗
arXiv1999

Tri-axial Octupole Deformations and Shell Structure

Manifestations of pronounced shell effects are discovered when adding nonaxial octupole deformations to a harmonic oscillator model. The degeneracies of the quantum spectra are in a good agreement with the corresponding main periodic orbits and winding number ratios which are found by classical analysis.

nucl-th↗
arXiv1999

Electromagnetic Modes in Deformed Nuclei

A strength function method is adopted to describe a coupling between electric and magnetic modes of different multipolarity. The collective vibrations are analysed for a separable residual interaction in the framework of the random-phase approximation. The coupling between $M2$ and $E1$ giant resonances is considered as an illustrative example.

nucl-th↗
arXiv1999

Analytic solutions to the problem of Coulomb and confining potentials

The oscillator representation method is presented and used to calculate the energy spectra for a superposition of Coulomb and power-law potentials and for Coulomb and Yukawa potentials. The method provides an efficient way to obtain analytic results for arbitrary values of the parameters specifying the above-type potentials. The calculated energies of the ground and excited states of the quantum systems in question are found to comply well with exact results.

quant-ph↗
arXiv1999

Integral representation of the RPA correlation energy

Using the spectral function F'(z)/F(z) the RPA correlation energy and other properties of a finite system can be written as a contour integral in a compact way. This yields a transparent expression and reduces drastically the numerical efforts for obtaining reliable values. The method applied to pairing vibrations in rotating nuclei as an illustrative example.

nucl-th↗
arXiv1999

Ground State Spin Oscillations of a Two-Electron Quantum Dot in a Magnetic Field

Crossings between spin-singlet and spin-triplet lowest states are analyzed within the model of a two-electron quantum dot in a perpendicular magnetic field. The explicit expressions in terms of the magnetic field, the magnetic quantum number $m$ of the state and the dimensionless dot size for these crossings are found.

cond-mat.mes-hall↗
arXiv1998

Orbital Magnetism in Small Quantum Dots with Closed Shells

It is found that various kind of shell structure which occurs at specific values of the magnetic field leads to the disappearance of the orbital magnetization for particular magic numbers of small quantum dots with an electron number $A < 30$.

cond-mat↗
arXiv1998

Statistical Fluctuations of Electromagnetic Transition Intensities in pf-Shell Nuclei

We study the fluctuation properties of E2 and M1 transition intensities among T=0,1 states of A = 60 nuclei in the framework of the interacting shell model, using a realistic effective interaction for pf-shell nuclei with a Ni56 as a core. It is found that the B(E2) distributions are well described by the Gaussian orthogonal ensemble of random matrices (Porter-Thomas distribution) independently of the isobaric quantum number T_z. However, the statistics of the B(M1) transitions is sensitive to T_z: T_z=1 nuclei exhibit a Porter-Thomas distribution, while a significant deviation from the GOE statistics is observed for self-conjugate nuclei (T_z=0).

nucl-th↗
arXiv1997

Electronic shell structure of large metallic clusters in the modified harmonic oscillator

Shell structure in the single particle spectrum of deformed harmonic oscillator potentials when a term proportional to $(\vec L)^2$ is added is analyzed for a large particle number. A scaling law which gives a dividing line between regular and chaotic behavior in terms of energy, deformation and strength of the $(\vec L)^2$ term has been found. According to this law, shell structure survives for higher particle numbers only with lesser deformation.

cond-mat↗
arXiv1997

Shell Effects in Mesoscopic Systems

The main aim of the results presented here is to demonstrate and analyse the importance of shell effects in nuclei, metallic clusters and quantum dots.

nucl-th↗