Effects of pairing correlation on neutron drop

In this work, the effects of the pairing correlation on the properties of neutron drops N=6-50 trapped in a harmonic oscillator potential with ω = 10 Me V are investigated by comparing the results given by the Skyrme Hartree-Fock and Hartree-FockBogoliubov theories with the density-dependent delta interaction(DDDI) pairing force. The results showed that the pairing correlation slightly made the neutron drops more bound, and increased the central neutron density, the spin-orbit and pseudo spin-orbit splittings. Thus, the pairing correlation must be accounted for to improve the Skyrme functional compared with the ab initio calculations. Furthermore, although the single-particle energy gaps with or without pairing were similar, the shell closures varied due to pair scattering. Here, the shell closures in neutron drops using the Sk M* parameter set and DDDI pairing force were found at N=8, 16, and 32.     

Orbital fractional parentage coefficients for the harmonic oscillator shell model

The Hamiltonian ofn particles moving in a common harmonic oscillator potential has as its symmetry group the unitary groupU(3n) in 3n dimensions,n particle states of the harmonic oscillator shell model can be characterized as bases of irreducible representations (BIR) of the groupU(3n) and of certain subgroups of this group. Use is made of these subgroups for the factorization and calculation of 2, 3, and 4 particle fractional parentage coefficients (fpc) of the harmonic oscillator shell model. Recoupling coefficients for subgroup chains of the symmetric groupS (n) appear as factors in the fpc. These coefficients are analyzed and calculated explicitly. The 2, 3 and 4 particle fpc of the 1s 1p shell configuration are obtained as products of these recoupling coefficients with known reduced Wigner coefficients of the unitary groupU(3) in 3 dimensions. Possible applications are indicated.     

Macroscopic-microscopic theory of semi-spheroidal atomic cluster

The macroscopic-microscopic method is adapted to atomic clusters deposited on a surface. Analytical relationships for the deformation-dependent liquid drop model (LDM) energies of oblate and prolate semi-spheroidal atomic clusters have been obtained. A superdeformed prolate semi-spheroid is the most stable semi-spheroidal shape within LDM. It is also the shape with maximum degeneracy of quantum states of the semi-spheroidal harmonic oscillator used to compute the shell and pairing corrections. The microscopic corrections as well as total deformation energy show parabolic valley and ridges of the potential energy surfaces in the plane (deformation, number of atoms). The ground state and isomeric state deformation of clusters of various sizes depends on the interplay between the minima of LDM and shell correction energies.     

自相似结构壳模型

为了扩展以简谐振子为基矢的常规壳模型（ＳＭ）计算到晕核，提出了自相似结构壳模型（ＳＳＭ）．通过对简谐振子动能项和势能项的重度规以及单粒子平均场模拟，可以得到ＳＳＭ中的单粒子轨道有态相关的圆频率，在ＳＳＭ中，晕核大的均方根半径、厚的中子皮以及Ｂｏｒｒｏｍｅａｎ晕核和的束缚态性质能够再现出来。     

Self-Similar Strcture Shell Model

In Order to extend the conventional shell model(SM) calculation with harmonic oscillator bases to halo nuclei, a self-similar, structure shell model(SSM) is proposed. The SSM is achieved by a rescaling of both the Kinetic and potential energy term of the harmonic oscillator and a mean field imitation, so that the single particle orbit in SSM has state (orbit) -dependent frequency. The large r. m. s. radius and the thick neutron skin for halo nuclei as well as the bound state properties of Borromean nuclei such as ⁶He, ¹¹Li and ¹⁴Be can be reproduced.     

Thermodynamic anomalies in the presence of general linear dissipation: from the free particle to the harmonic oscillator

A free particle coupled to a heat bath can exhibit a number of thermodynamic anomalies like a negative specific heat, reentrant classicality or a nonmonotonic entropy. These low-temperature phenomena are expected to be modified at very low temperatures where finite-size effects associated with the discreteness of the energy spectrum become relevant. In this paper, we explore in which form the thermodynamic anomalies visible in the specific heat and the entropy of the free damped particle appear for a damped harmonic oscillator. Since the discreteness of the oscillator’s energy spectrum is fully accounted for, the results are valid for arbitrary temperatures. As expected, they are in agreement with the third law of thermodynamics and indicate how the thermodynamic anomalies of the free damped particle can be reconciled with the third law. Particular attention is paid to the transition from the harmonic oscillator to the free particle when the limit of the oscillator frequency to zero is taken.     

Penetration depth anisotropy in d-density wave scenario

We discuss thermalization of a test particle schematized as a harmonic oscillator and coupled to a Boltzmann heat bath of finite size and with a finite bandwidth for the frequencies of its particles. We find that complete thermalization only occurs when the test particle frequency is within a certain range of the bath particle frequencies, and for a certain range of mass ratios between the test particle and the bath particles. These results have implications for the study of classical and quantum behaviour of high-frequency nanomechanical resonators.     

Nuclear level densities in self-consistent field approximation

The effect of two-body nature of the nuclear shell model potential on the recent numerical calculations of the nucleai level density has been examined. For the two most widely used single particle energy level schemes based on harmonic oscillator and Woods-Saxon potential, this effect is shown to significantly modify the excitation energy dependence of the level densisties.     

A unified model description of mobile and localized adsorption: I. MFA with nonadditive lateral interactions — an application to disordered adsorbed monolayer on a structureless substrate

A simple model is used to treat mobile adsorption on a structureless substrate. The influence of temperature on the state of motion of adsorbed particles is described by means of an interpolation formula used earlier in the theory of hindered rotation, whereas the influence of the nearest-neighbour potential with varying degree of coverage is accounted for in terms of a “free area”, available for individual particle motion, for which a simple analytical expression, based on an harmonic oscillator approximation, is obtained. An irregularity in the long range order of the adsorbed monolayer is introduced in terms of “varying distances”, resp. of varying energy bonds between the particles in dependence of the number of nearest neighbours actually present in the first coordination sphere of each particle (nonadditivity of the bonds).     

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.     

Structure of Light Nuclei on Neutron Drip Line

In order to extend the conventional shell model (SM) calculation with harmonic oscillator bases to light nuclei on neutron drip line, a self-similar-structure shell model (SSM) is proposed. We do this by a rescaling of both the kinetic and potential energy terms of the harmonic oscillator so that the single-particle orbit in SSM has its own state(orbit)-dependent frequency. Meanwhile, a new method to imitate the Woods-Saxon potential with harmonic oscillator potential is introduced. By the rescaling method and imitation procedure, all light exotic nuclei together with the light stable nuclei are studied in a unified way. The results are in good agreement with experimental data. Furthermore, the puzzle of the unexistence of ⁵He, ^{10Li and 13B is naturaUy explained in SSM.}     

一维线性谐振子哈密顿量改写中的非幺正变换

通过引入一非幺正算符实现了对一维线性谐振子系统哈密顿量的从坐标、动量表象(Q,P)到占有数表象(a,a+)的改写.     

Pseudospin symmetry and the relativistic ring-shaped non-spherical harmonic oscillator

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The eigenfunctions and eigenenergies are obtained for the ring-shaped non-spherical harmonic oscillator by solving Dirac equation with equal mixture of vector and scalar potentials in opposite signs, for which pseudospin symmetry is exact. Several particular cases such as the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.     

The relativistic bound states for a new ring-shaped harmonic oscillator

In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.     

Einfluß der Schalenstruktur und der Paarung auf die Dichte der Energiezustände von Atomkernen

The density of nuclear single particle states is calculated within the framework of the spherical oscillator model including spinorbit and pairing interactions. The use of the oscillator energies leads to a strong influence of shell-effects on the level density which are slightly reduced, if pairing interactions are taken into account.     

Energy basis via decoherence

The question of the emergence of a preferred basis which is generally understood as that basis in which the reduced density matrix is driven to a diagonal (classically interpretable) form via environment induced decoherence is addressed. The exact solutions of the Caldeira-Leggett Master Equation are analyzed for a free particle and a harmonic oscillator system. In both cases, we see that the reduced density matrix is driven diagonal in the energy basis, which is momentum for the free particle and the number states for the harmonic oscillator. This seems to single out the energy basis as the preferred basis which is contrary to the general notion that it is the position basis which is selected since the coupling to the environment is via the position coordinates     

Formation and application of correlated states in nonstationary systems at low energies of interacting particles

We consider prerequisites and investigate some optimal methods for the formation of a correlated coherent state of interacting particles in nonstationary systems. We study the influence of the degree of particle correlation on the probability of their passage through the Coulomb barrier for the realization of nuclear reactions at low energies. For such processes, the tunneling probability and, accordingly, the probability of nuclear reactions can grow by many orders of magnitude (in particular, the barrier transparency increases from D _{r = 0} ≈ 10⁻⁴² for an uncorrelated state to D _{|r| = 0.98} ≈ 0.1 at a correlation coefficient |r| ≈ 0.98). The formation of a correlated particle state is considered in detail for different types of monotonic decrease in the frequency of a harmonic oscillator with the particle located in its parabolic field. For the first time, we have considered the peculiarities and investigated the efficiency of the creation of a correlated state under a periodic action on a harmonic oscillator. This method is shown to lead to rapid formation of a strongly correlated particle state that provides an almost complete clearing of the potential barrier even for a narrow range of oscillator frequency variations.