Electron scattering from some even fp- and N50-shell nuclei with implanting the influence of short-range correlation functions

The influence of two body short range correlations on elastic electron scattering charge form factors, charge densities as well as root mean square charge radii of some fp-shell nuclei (for example, ⁴⁸Ca, ⁵⁰Cr, ⁵⁴Fe, ⁵⁸Ni, ⁷⁰Ge and ⁷⁴Se) and some N50-shell nuclei (for example, ⁸⁸Sr and ⁹⁰Zr) is analyzed using the one- and two-body terms in the cluster expansion together with the single particle harmonic oscillator wave functions. The Jastrow-type correlation function is utilized to embed the effect of short range correlations into elastic charge form factors F(q) and charge densities ρ(r). Both F(q) and ρ(r) depend upon the harmonic oscillator parameter b and the correlation parameter β (which initiates from the Jastrow correlation function). Here, the parameters b and β are determined via the fitting to the measured charge form factors. The embedding of short range correlations imitates the measured charge form factors at the high momentum transfers (q ≥ 2 fm⁻¹). It is noticed that the implanting of short range correlations is required for obtaining a remarkable alteration in the computed elastic charge form factors which in turn leads to explain the data of electron scattering astonishingly throughout the entire range of considered momentum transfers.     

Propagator for the Chebyshev q object

We propose an alternative role of the harmonic oscillator algebra. Observing that the q-deformed harmonic oscillator algebra defines the Chebyshev q object, we show that the q-free particle and the pulsed oscillator are special cases of the Chebyshev q object, characterized by a common deformation parameter q and reduced to a usual free particle as q tends to unity. For the deformed free particle, q is a real number, whereas for the pulsed oscillator it belongs to S ¹. Then, we derive the propagator for the Chebyshev q object, from which we obtain the propagators for the deformed free particle and the pulsed oscillator.     

An application of a new harmonic-oscillator basis to the calculation of trinucleon ground-state observables

A new harmonic-oscillator basis for trinucleon ground-state calculations is introduced, featuring different oscillator radii for the two intrinsic variables. This basis allows charge-dependent interactions to be handled and seems to yield a better convergence with respect to the previously used oscillator bases. A test calculation with the Reid soft-core interaction is presented. The resulting (extrapolated) triton binding energy is 7.3 ± 0.2 MeV, and the first minimum in the ³He charge form factor occurs at q² = 13.1 fm^?2.     

Charge and mass radii of the tin isotopes

Data on the isotope shift of the nuclear charge densities of the tin isotopes and of their mean square charge radii are considered from the viewpoint of the Hartree-Fock and Droplet Models. Attention is paid to the electromagnetic corrections of order 1/m². Through a leptodermous analysis of charge and matter densities we find: (i) differences of m.s. charge radii are mainly sensitive to the external region, (ii) the electromagnetic corrections are important in that region, (iii) despite different leptodermous properties, forces Ska and GO-P lead to the same neutron skin thickness. The average rate of variation of the proton m.s. radius is interpreted as favouring either a low valueQ≈30 MeV for the droplet model asymmetry parameter, or a zero value for the saturation asymmetry parameterL.     

The solutions of the generalized classical and quantum harmonic oscillators with time dependent mass, frequency, two-photon parameter and external force: The squeezing effects

The exact analytical solutions of a generalized classical harmonic oscillator with time dependent mass, frequency, two-photon parameter and external forces are obtained. By using the invariance property of the scaled Wronskian, these solutions are used to obtain the solutions of the quantum mechanical counterpart of the oscillator under Heisenberg picture. In order to discuss the applications of these solutions of the quantum mechanical oscillator, we calculate the exact analytical expressions for the second order variances of both the canonically conjugate quadratures in terms of the time dependent mass, frequency and two-photon parameter. However, these variances calculated in terms of the initial coherent state do not depend on the time dependent driven terms. We argued that the time dependent frequency is on the way of the exact analytical solutions and hence it is kept constant throughout the investigation. We, however, discuss few situations of physical interest where the mass is varying in time. The special circumstance where all the parameters are time independent is used to discuss the squeezing effect in both the quadratures. It is seen that the parameter g involving the two-photon interaction term produces squeezing effects. With the increase of interaction time, the squeezing in both the quadrature components exhibit collapse and revival phenomena for g < ω (frequency of the oscillator). The squeezing of X-quadrature is completely ruled out for g > ω. However, the squeezing for P-quadrature is possible for small interaction time. The squeezing patterns of the X and P-quadratures are also discussed for pulsating mass, and for mass increasing with time. The squeezing is also discussed when the mass is increasing exponentially in time. It is envisage that the solutions could be used in the investigation of quantum statistical properties of the radiation field coupled to the said oscillator.     

Quartic oscillator potential in the γ-rigid regime of the collective geometrical model

A prolate γ-rigid version of the Bohr-Mottelson Hamiltonian with a quartic anharmonic oscillator potential in β collective shape variable is used to describe the spectra for a variety of vibrational-like nuclei. Speculating the exact separation between the two Euler angles and the β variable, one arrives at a differential Schrödinger equation with a quartic anharmonic oscillator potential and a centrifugal-like barrier. The corresponding eigenvalue is approximated by an analytical formula depending only on a single parameter up to an overall scaling factor. The applicability of the model is discussed in connection to the existence interval of the free parameter, which is limited by the accuracy of the approximation, and by comparison with the predictions of the related X(3) and X(3)-β ² models. The model is applied to qualitatively describe the spectra for nine nuclei which exhibit near-vibrational features.     

The spin-wave resonance spectrum and the structure of cermet Fe - SiO films

The results of electron-microscopic investigation of the structure and spin-wave resonance of thin ferromagnetic Fe_100-x(SiO)_x films are presented in the paper. The correlation radii of fluctuations of the exchange interaction parameter are determined from the analysis of the experimental results of spin-wave resonance. These radii are compared with characteristic sizes of the structural clusters in the films.     

Description of the smooth rms charge radius surface R(N, Z) and prediction of neutron skin by a two-liquid drop model

The smooth N and Z dependence of nuclear rms charge radii is interpereted by a two-liquid drop model with ?_p+?_n=?₀=const. Proton and neutron radii R _p and R _n are given in closed form. In addition to rms charge radii, the model yields the nucleon number dependence of the skin thickness, s, e.g. ds=0.00124×dA for Sn isotopes, in agreement with experimental results and theoretical calculations. A strong correlation between the two global parameters of the model — including s _stthe skin thickness of the stable isotope — is established. If s _stis taken from experiment, the other parameter is also fixed; this parameter (m) characterizes the restoring force responsible for the skin thickness. Its value m=2.2 suggests that — in addition to the number of nucleons in the skin — the skin thickness also influences the distribution of “surplus” nucleons between volume and skin.     

Anyons,deformed oscillator algebras and projectors

We initiate an algebraic approach to the many-anyon problem based on deformed oscillator algebras. The formalism utilizes a generalization of the deformed Heisenberg algebras underlying the operator solution of the Calogero problem. We define a many-body Hamiltonian and an angular momentum operator which are relevant for a linearized analysis in the statistical parameter ν. There exists a unique ground state and, in spite of the presence of defect lines, the anyonic weight lattices are completely connected by the application of the oscillators of the algebra. This is achieved by supplementing the oscillator algebra with a certain projector algebra.     

Nonextensive thermostatistics and deformed structures

We obtain a generalized Planck law within the framework of nonextensive statistics making use of a deformed oscillator system. Our results are used to fit the data from the COBE (Cosmic Background Explorer) satellite. Best fit values for the entropy parameter q, the deformation parameter r and for the temperature are found.     

The formation of correlated states and the increase in barrier transparency at a low particle energy in nonstationary systems with damping and fluctuations

We consider peculiarities in the formation of a coherent correlated state (CCS) of a particle in a periodically modulated harmonic oscillator with damping for various types of stochastic perturbation. It is shown that in the absence of stochastic perturbation, an optimal relation exists between the damping parameter (damping coefficient) and the modulation depth, for which the ??extrinsic?? characteristics of the oscillator (amplitudes of ??classical?? oscillation and the momentum of a particle) remain unchanged, while the correlation coefficient rapidly increases from |r| = 0 to |r|_max ?? 1; this corresponds to a completely correlated coherent state. Under nonoptimal conditions, the formation of the CCS with a simultaneous increase in is accompanied by damping or excitation of the oscillator. It is shown that for a certain relation between the damping coefficient and the modulation depth, the presence of a stochastic external force acting on the nonstationary oscillator does not prevent the formation of a CCS with |r|_max ?? 1. A fundamentally different effect is observed under a stochastic influence on the nonstationary frequency of the oscillator; this effect always limits the value of |r| at a level |r|_max < 1; a CCR cannot be formed with an unlimited increase in its intensity, and |r|_max ?? 0. The influence of the CCS formation on the averaged probability ??D?? of the tunnel effect (transparency of the potential barrier) is considered for a particle in an oscillator with damping both in the absence and in the presence of a stochastic force. It is shown using a specific example that complete clearing of the potential barrier and the increase in the barrier transparency from the initial value ??D _r=0?? = 10^?80 to ??D?? ?? 1 can occur over a comparatively short time interval in both these cases. These effects can be used to obtain highly efficient nuclear fusion at a low energy of interacting particles.     

Nonlinear optical properties in a quantum well with the hyperbolic confinement potential

We have performed theoretical calculation of the nonlinear optical properties in a quantum well (QW) with the hyperbolic confinement potential. Calculation results reveal that the transition energy, oscillator strength, second-order nonlinear optical rectification (OR), geometric factor and nonlinear optical absorption (OA) are strongly affected by the parameters (α,σ) of the hyperbolic confinement potential. And an increment of the parameter α reduces all these physical quantities, while an increment of the parameter σ enhances them, but not for geometric factor. In addition, it is found that one can control the optical properties of QW by tuning these parameters.     

Constrained variational calculations of closed shell nuclei with the reid potential

Lowest-order constrained variational calculations with harmonic oscillator wave functions are carried out for ⁴He, ¹⁶O, and ⁴⁰Ca nuclei with the Reid potential. The results obtained with this simple method are in very close agreement with those obtained by renormalized Brueckner-Hartree-Fock theory with orthogonalized plane wave intermediate states. The A-dependence of the difference between the experimental and calculated binding energies for A = 2, 3, 4, 16, 40 and ∞ can be explained by a three-body cluster term coming either from a wrong off-energy-shell behavior of the Reid potential or a three-body force. The calculated radii of ¹⁶O and ⁴⁰Ca are ≈ 10% too small, indicating that the Reid potential may not be very realistic.     

Oscillator strengths and polarizabilities of the hot-dense plasma-embedded helium atom

The effect of weakly coupled hot plasma environment on the oscillator strengths of the ultraviolet and visible series and the polarizabilities of helium has been investigated using variational highly correlated wave functions within the non-relativistic framework. The Debye shielding approach that admits a variety of plasma conditions is used to simulate the plasma effects. For each shielding parameter, dipole oscillator strengths are calculated for the 1 ¹S-n¹P (n=2, 3), 2 ¹S-2 ¹P, 2 ³S-n³P (n=2, 3) and 2 ^1,3P-n^1,3D (n=3, 4) transitions. The dipole and quadrupole polarizabilities for the ground He (1s²¹S) state are also reported for each screening parameter. Results obtained are useful in plasma diagnostic purposes besides several other applications.     

Toroidal p-branes, anharmonic oscillators and (hyper)elliptic solutions

Exact solvability of brane equations is studied, and a new U(1)×U(1)×?×U(1) invariant anzats for the solution of p-brane equations in D=(2p+1)-dimensional Minkowski space is proposed. The reduction of the p-brane Hamiltonian to the Hamiltonian of p-dimensional relativistic anharmonic oscillator with the monomial potential of the degree equal to 2p is revealed. For the case of degenerate p-torus with equal radii it is shown that the p-brane equations are integrable and their solutions are expressed in terms of elliptic (p=2) or hyperelliptic (p>2) functions. The solution describes contracting p-brane with the contraction time depending on p and the brane energy density. The toroidal brane elasticity is found to break down linear Hooke law as it takes place for the anharmonic elasticity of smectic liquid crystals.     

Nonclassical properties of a particle in a finite range trap: The f-deformed quantum oscillator approach

A particle bounded in a potential with finite range is described by using an f-deformed quantum oscillator approach. Finite range of this potential can be considered as a controllable deformation parameter. The nonclassical quantum statistical properties of this deformed oscillator can be manipulated by nonlinearities associated to the finite range.     

Properties of lead isotopes in the vicinity of the neutron drip line

On the basis of the Hartree-Fock method with Skyrme forces of the Ska, SkM*, and Sly4 type, the position of the neutron drip line and the properties of neutron-rich lead isotopes are studied with allowance for deformations. It is shown that, in extremely neutron-rich nuclei, the neutron and proton density distributions are characterized by an anomalously large deformation parameter of β ～ 0.6. Also, nuclei of superdeformed lead isotopes have anomalously large root-mean-square radii. The existence of the isotopes ^266–288Pb, which are stable to the emission of one neutron, is predicted.     

Nuclear charge radii of Al and Si from elastic electron scattering between 25 and 60 MeV

Elastic electron scattering cross sections of²⁷Al and Si (natural isotopic mixture) have been measured relative to carbon. The rms charge radiiR _m , deduced with partial wave calculations, are (3.01±0.05) fm for²⁷Al and (3.06±0.05) fm for Si, in good agreement with results from muonic X-ray energies. The values given are those for a Fermi charge distribution with skin thickness 2.5 fm; harmonic oscillator shell model distributions yield radii smaller by 0.03 fm. The ratioR _m (²⁷Al)/R_m(Si) is 0.984±0.016.     

Charge radii of high-spin isomers measured using laser spectroscopy methods

The overview of experimental data on charge radii differences between the ground and the high-spin isomeric states is presented. Methods of high-resolution laser spectroscopy were used for measurements. Charge radii differences obtained in two ways are compared: from measurements of isomeric shifts of atomic levels of nuclei under study and from measurements of quadrupole moments in both states under the assumption that the radii differences are determined by the difference of their quadrupole deformations. Isomers formed at a rupture of one or several nucleon pairs and isomers with the configuration of the odd neutron 1h _11/2 for the nuclear region Cd-Ba and 1i _13/2 for the region Hg-Pb are considered. Observed deviations of the above charge radii differences for isomeric states of a different nature are discussed.     

Elastic scattering of 32S on 24Mg, 27Al and 40Ca and the effect of nuclear forces on the grazing collision

Elastic scattering of ³²S ions on ²⁴Mg, ²⁷Al and ⁴⁰Ca has been measured at energies between 67 MeV and 120 MeV. Angular distributions were analyzed with the optical model with Woods-Saxon potentials. Strong absorption radii are extracted with and without consideration of the nuclear interaction at the surface. The nuclear potential decreases the otherwise anomalously large strong absorption radii which can then be described by a radius parameter of r₀ = 1.41 fm.