The effective interaction in a nuclear model

The effective interactionU belonging to a given subspace ofn unperturbed model functions can be related to the free nucleon-nucleon interaction by means of an exact integral equation. The conditions for a Born-v. Neumann expansion ofU and for an approximation by a slowly energy dependent interaction with adjustable parameters are investigated. It appears that effective interactions which have been used successfully in shell model calculations of bound state properties do not necessarily describe the actual dynamics of a nucleus.     

Coupled-cluster-equations for the local ansatz

A new approximation is presented for calculations within the Local Ansatz, a scheme that allows to perform ab-initio correlation calculations for solids. While the approximations made so far when using this method do not give a perfect treatment of long range screening, this modification is able to handle them well. In addition a few more strongly correlated cases than before can be accounted for, although one is still far from treating the strongly correlated limit in general. The approximation consists in solving the complete Coupled-Cluster-equations in the subspace of those local two-particle operators constructed by the Local Ansatz. Such a treatment does not require sizeable additional computational costs as compared with the approximation made so far.     

Dyson-type boson mapping and SU(6) boson model

The Dyson-type boson mapping is applied to realistic cases to show that it is a very promising method for describing nuclear collective motion. Eigenvectors are obtained in the corresponding hermitian boson theory from the results of right- and left-hand-side eigenvalue problems in the Dyson boson theory. The numerical results are compared with those of the SU(6) boson model and exact quasiparticle shell-model calculations within the multi-phonon subspace.     

An analytic Voigt profile escape probability approximation

An efficient analytic Voigt profile escape probability approximation is presented and compared to exact numerical calculations. Using this analytic approximation, the two-level-atom source function is also computed for optically thick media, which have been previously evaluated exactly by Avrett and Hummer. Comparison with a more realistic laboratory plasma case also validates the usefulness of the approximation for economical modeling of radiation transport in optically thick plasmas.     

Corrections to the theory of screening and antiscreening in collisions with hydrogen atoms

By comparing with exact plane-wave-Born calculations of K-shell ionization in H + H collisions, a proposed correction to the theory of electron screening and antiscreening using the closure approximation is investigated.     

Limitations of first-order approximations for calculations using intensity jnd's

The way in which the noninfinitesimal size of the intensity jnd affects calculations using power functions for pure-tone loudness and neural count is examined. The results of the commonly used first-order differential for representing the change in the power functions due to a jnd in intensity are compared with the second-order approximation and the exact formula. Examples are taken from a variety of psychophysical studies dealing with loudness and intensity discrimination. The second-order and exact formulas are shown to be more consistent with experimental data than the first-order differential.     

Shape mixing as an approximation to shell model24Ne

Band mixing calculations have been done for²⁴Ne including the two degenerate prolate and oblate Hartree-Fock states and also some particle-hole excited states in the projection formalism using an interaction obtained by Preedom and Wildenthal. The energy spectrum agrees very well with the experimental results as well as the exact shell model calculations. Thus the band mixing calculations provide a good approximation to the lengthy exact shell-model calcuations. In addition they offer a physical insight into the collective nature of the nucleus as nuclear states are described in terms of only a few ‘intrinsic’ states.     

A variational method for hydrogen chemisorption

Starting from the Hartree-Fock approximation a general variational ansatz for the ground state of the metal-hydrogen system is presented which properly describes the strong correlation effects occuring at larger distances from the surface. As a simple example the Anderson model is studied. The calculated ground state energies are in excellent agreement with exact model calculations.     

Error analysis of the adding/doubling method for radiative scattering in inhomogeneous media

The doubling method is a fast and exact procedure for calculating radiative transfer in a homogeneous, scattering, plane-parallel medium. It can also be used in the adding mode for an inhomogeneous medium that is approximated by a finite number of homogeneous sublayers with different radiative properties. The errors caused by this approximation are analyzed in this paper through comparison with invariant imbedding calculations that are slow but exact for inhomogeneous media. A procedure is developed so errors can be estimated and controlled when using the faster adding/doubling calculations.     

The possibility of describing a two-particle quantum system and interparticle correlations in the self-consistent field approximation

The possibility of determining the energy spectrum and the wave function structure of the stationary states of a model two-particle system is examined in the self-consistent field approximation. The results of exact calculations are compared with the data obtained in the self-consistent field approximation with the use of orthogonal and nonorthogonal orbitals. The possibility of using these approximations for describing the interparticle quantum correlations is discussed.     

Cross sections for the rotationally inelastic scattering of Ne + N2: application of the exponential semi-classical distorted wave approximation

Exact quantum-mechanical close-coupling and approximate calculations are presented for Ne + N₂ collisions using a model potential. The approximate calculations were performed using an exponential semi-classical distorted wave approximation (ESCDW) which is outlined in the paper. The ESCDW approximation involves the evaluation of the same integrals as the standard distorted wave approximation. The former method, however, in contrast to the latter, yields a unitary S matrix and therefore conserves particle flux. The exponentiation process is shown to lead to dramatic improvements in the calculated cross sections for the present system. Cross sections evaluated using the ESCDW approximation compare very well with exact ones over the entire range of thermally accessible energies. Total and differential rotationally inelastic cross sections are presented and their variation with energy is examined. The dependence of the cross sections on the number of coupled channels included in the calculations is also investigated and a sufficient number of channels are included to ensure convergence.     

投影后变分新方法对原子核低激发态的描述

对我们近几年发展的投影后变分（VAP）新方法做了比较全面的介绍。首先介绍了对JTA投影波函数的变分计算,指出自旋投影是获得很好壳模型近似的关键因素。基于这一结论,将VAP简化,并推广应用于所有晕态。即采用基于HF真空态的自旋投影波函数,通过变分,得到了与壳模型结果非常接近的VAP晕态能量及相应波函数。为进一步描述非晕态,依据柯西交错定理,可靠地对VAP低激发态能量之和进行最小化。如果这些能量值之和达到极小值,则与该极小对应的各态也就被确定下来。通过VAP计算,所得原子核非晕态能量与壳模型精确值非常接近。最近,在VAP计算中加入宇称投影,在psd模型空间中计算了12C的正负宇称晕态,同样得到了比较好的壳模型近似。值得指出的是,该方法具有普适性,可广泛应用于不同量子多体体系的低激发态研究中。We present a comprehensive introduction in our newly developed Variation After Projection (VAP) calculations for the low-lying nuclear states. First, we discussed the VAP calculation with a fully JTA-projected wavefunction for the ground state in even-even nucleus. This leads to the conclusion that the spin projection plays a key role in obtaining a good shell model approximation. With this conclusion, we simplified the VAP with a time-odd Hartree-Fock mean field, on which only spin projection is required. Due to the time reversal symmetry breaking, this VAP now can be applied to the yrast states in all kinds of nuclei. It turns out that our VAP yrast energies as well as the corresponding VAP wavefunctions are very close the exact ones from the full shell model calculations. Such good approximation encourages us to extend the VAP calculations further to the non-yrast nuclear states. For this purpose, we proposed a new algorithm in our VAP based on the Cauchy's interlacing theorem. This theorem ensures that the sum of the calculated lowest projected energies with the same quantum numbers can be safely minimized. After minimization, all the calculated states can be determined simultaneously. Again, all the calculated VAP energies are very close to the exact shell model results. Recently, we have added the parity projection into the VAP, and the yrast states with both parity in 12C have been calculated in the psd model space. This time, we still have good shell model approximation for both parity states. Finally, we should point out that the present algorithm should be applicable to the low-lying states in different quantum many-body systems.     

Dynamics of a two-level system coupled to a quantum oscillator: transformed rotating-wave approximation

For studying the dynamics of a two-level system coupled to a quantum oscillator we have presented an analytical approach, the transformed rotating-wave approximation, which takes into account the effect of the counter-rotating terms but still keeps the simple mathematical structure of the ordinary rotating-wave approximation. We have calculated the energy levels of ground and lower-lying excited states, as well as the time-dependent quantum dynamics. It is obvious that the approach is quite simple and can be easily extended to more complicated situation. Besides, the results are compared with the numerically exact ones to show that for weak to intermediate coupling and moderate detuning our analytic calculations are quantitatively in good agreement with the exact ones.     

标量衍射理论的非傍轴近似及其有效性

当光束束腰（或衍射孔孔径）可与波长相比拟或光束具有较大的发散角时,傍轴近似不再成立.在标量瑞利.索末菲衍射积分的基础上,进一步研究了衍射场的非傍轴近似解,并详细分析了解的有效性.以平面波圆孔衍射为例,对衍射场的精确解、非傍轴近似解以及菲涅耳近似解进行了详细的数值计算和比较研究.结果表明,非傍轴近似对微小孔衍射非常精确、有效.     

Image aberrations in an acousto-optical tunable filter

The problem of deformation of images due to diffraction from 3D diffraction gratings (in particular, the grating formed by an acoustic wave in an acousto-optical filter) is considered. For the first time, the exact solution is obtained without using the small birefringence approximation. The form of aberrations induced by main types of acousto-optical filters is analyzed and illustrated by calculations.     

Permanent dipole moments and multi-photon resonances

The effects of non-zero diagonal dipole matrix elements on multi-photon resonance profiles, for the interaction of molecules with a sinusoidal field, are discussed by using an expression for the profiles derived in the rotating wave approximation. The validity of this result is discussed with reference to exact two-level model calculations.     

Neutrino pair creation in a strong magnetic field

An expression for the probability of neutrino pair creation by an electron in an ultrastrong magnetic field is obtained. The calculations are done using the exact solutions of the Dirac equation in a magnetic field in the low energy approximation of the Weinberg-Salam model.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 39–41, September, 1982.