转动原子核的对关联变化

利用粒子数守恒方法,在i=11/2壳中精确处理了推转壳模型和粒子转子模型。研究了转动原子核对关联随角动量的变化情况。且通过对上述两种模型给出的对关联、能谱,顺排角动量和seniority结构的分析和比较,还对推转壳模型的可靠性进行了估价。 关键词：     

原子核高角动量激发

用推转壳模型计算研究了原子核的高速转动运动及其结构特性.讨论了A～50区核的转动特性;A～80$区(N=Z)核的形状共存问题; A～110$区丰中子核的扁椭球形变的稳定性. 基于壳模型理论, 我们用限制组态绝热堵塞方法计算讨论了A～130, 180和超重核区的高角动量同核异能态,系统预言了高角动量多准粒子态的存在, 并指出这些核态可以有较长的寿命, 这对于不稳定核的研究是很有帮助的. 计算解释了不少典型的实验观测, 一些理论预言已经被最近的实验证实.     

164Er96与166Er98核推转壳模型波函数的K结构新探

在一组新的表象空间中,对轴对称变形核¹⁶⁴Er₉₆与¹⁶⁶Er₉₈的推转壳模型(CSM)波函数的K结构进行了分析,随转动角频率ω增大,CSM波函数不再具有单一的K结构,原子核逐渐偏离轴对称,计算表明,¹⁶⁴Er₉₆与¹⁶⁶Er₉₈的晕带K结构极其相似,但第一激发带的K结构却有较大不同。 关键词：     

自旋-轨道耦合系统的电子涡旋

在轨道角动量守恒的无自旋-轨道耦合系统中存在带轨道角动量量子数的电子涡旋波解,研究了存在自旋-轨道耦合,轨道角动量不守恒的系统,发现携带总角动量量子数的电子旋量波函数也有涡旋波解,表现为自旋波函数和涡旋波波函数的纠缠波函数.以中心力场中的电子为例,构建了自旋-轨道耦合导致的轨道角动量不守恒但总角动量守恒的情况下,携带固定总角动量量子数的电子沿z轴传播的涡旋波旋量波函数结构.对自旋-涡旋纠缠中相应的电子涡旋波进行了微扰求解,并结合Foldy-Wouthuysen变换,说明了在相对论情况下,中心力场中携带固定总角动量量子数的电子沿z轴传播时也确实存在四分量旋量的涡旋解,从而为有自旋-轨道耦合导致的轨道角动量不守恒但总角动量守恒的系统提供了存在涡旋结构的理论支持.     

角动量投影HF方法中的电磁跃迁

本文讨论了严格的角动量投影形变哈特里-福克(PDHF)波函数用于研究原子核性质的一般问题.给出了多粒子体系的单体张量算符在PDHF波函数中的矩阵元公式.计算了偶钛核低激发态间的γ跃迁B(E2)值,找到了带交叉的证据.     

高温空气中NO分子β(B2Πr-X2Πr)及γ(A2Σ+-X2Πr) 发光带系的Franck-Condon因子计算

在双原子分子核运动的波动方程中,计入分子的振转相互作用项,得出的波函数除与振动量子数有关外,还与转动量子数有关。本文用该波函数编程计算了高温空气中ＮＯ分子β（Ｂ２Πｒ－Ｘ２Πｒ）及γ（Ａ２Σ＋－Ｘ２Πｒ）带系的Ｆｒａｎｃｋ－Ｃｏｎｄｏｎ因子。计算中转动量子数的取值由Ｊ＝０取至Ｊ＝２００,结果适用于低温和高温条件。     

BS分子a带系A^2П→X^2∑＋及γ带系C^2П→X^2∑^＋法兰克—康登因子？…

在双原子分子核运动的薛定谔方程中，计入分子的振转相互作用项，在Ｍ势近似下得出的波函数除与振动量子数有关外，不写转动量子数有关。本和该波函数编程了ＢＳα带系Ａ＾２П→Ｘ＾２∑＾＋法兰克－康登因子。计算中转动量子数的取值由Ｊ＝０至Ｊ＝２００，其结果适用于低温、高温和强激波条件。     

BO分子α带系A~2Π-X~2Σ~ 及β带系B~2Σ~ -X~2Σ~ Franck-Condon因子的计算

在双原子分子核运动的波动方程中，计入分子的振转相互作用项，得出的波函数除与振动量子数有关外，还与转动量子数有关。用该波函数编程计算了ＢＯ分子α带系Ａ２Π－Ｘ２Σ＋及β带系Ｂ２Σ＋－Ｘ２Σ＋的Ｆｒａｎｃｋ－Ｃｏｎｄｏｎ因子。计算中转动量子数的取值由Ｊ＝０取至Ｊ＝２００，结果适用于低温、高温和强激波条件。     

BS分子α带系A~2Π→X~2Σ~+及γ带系C~2Π→X~2Σ~+法兰克-康登因子的计算

在双原子分子核运动的薛定谔方程中，计入分子的振转相互作用项，在Ｍｏｒｓｅ势近似下得出的波函数除与振动量子数有关外，还与转动量子数有关。本文用该波函数编程计算了ＢＳ分子α带系Ａ２Π→Ｘ２Σ＋及γ带系Ｃ２Π→Ｘ２Σ＋法兰克－康登（Ｆｒａｎｃｋ－Ｃｏｎｄｏｎ）因子（简称Ｆ－Ｃ因子）。计算中转动量子数的取值由Ｊ＝０至Ｊ＝２００，其结果适用于低温、高温和强激波条件。     

_(62)Sm~(152)核的g_R因子

考虑原子核理论中超导效应对g_R因子的影响,在给出偶核g_R因子在推转模型(crankingmodel)基础上的计算公式之后,利用Nilsson波函数计算了_(62)Sm~(152)核的g_R因子。计算结果与实验值符合很好,反映了原子核超导理论的正确性。     

Investigation of the cranking model wave function with respect to angular momentum

Projection of angular momentum on cranking model wave functions is performed for some simple cases. An extensive analysis has been possible since an algebraic projection technique is employed and a detailed numerical example is presented. The distribution of angular momentum as a function of rotational frequency and signature is analysed, and special attention is focused on the fact that the signature does not give any strict selection of angular momenta contained in the cranking wave function.     

Exact angular momentum projection of cranked Hartree-Fock-Bogoliubov wave functions

The angular momentum projection of triaxial cranking model wave functions of realistic heavy nuclei is carried out exactly. Technical details of the procedure are discussed. The method is used to test the validity of the Kamlah expansion and of the angular momentum constraint in the cranking model. It turns out that the expansion up to the second order is already a very good approximation to the exact projection.     

An approximate projection technique for the calculation of electromagnetic properties of deformed nuclei

A three-dimensional angular momentum projection is carried out for cranking model wave functions. The projected matrix elements of electromagnetic operators are evaluated using a method originally developed by Kamlah for the case of projected energy, which is valid for large deformations and weakly triaxial nuclei. The calculated spectroscopic quadrupole moments deviate substantially from the predictions of a rigid rotor model with axial symmetry. For E2 transitions the deviations are small. Projected values of the magnetic moments are almost identical with those of a semiclassical calculation. Cranking model wave functions are decomposed into its components having good angular momentum.     

Angular-momentum-projected cranked hfb approach to the study of nuclear rotations

Employing a pairing-plus-quadrupole interaction hamiltonian and projecting out good angular momentum states from the cranked Hartree-Fock-Bogoliubov (CHFB) intrinsic wave functions the yrast spectra of ¹⁵⁸Dy and ¹⁶⁸Yb are calculated up to moderately high spins (I_max = 16) as to include the backbending region. Then the variation of pairing correlation, g-factor and rotational alignment of neutron spin as a function of total angular momentum is studied. The effect of particle number projection on the spin-projected CHFB wave functions is also investigated and is found to be unimportant for the calculation of g-factors. On the other hand, corrections of the excitation energies for number fluctuations in the CHFB wave functions are essential. Furthermore, looking at the distribution of the total projection quantum number K in various cranking wave functions we are able to throw some light on the K ≠ 0 nature of the aligned s-band.A variation-after-spin projection calculation strictly for the axial shape, without cranking, is also carried out for both the nuclei considered here. In the low-spin region this numerically “cheaper” scheme produces energy spectra similar to that of the CHFB method, and may thus be used to readjust the interaction parameters.     

Problems of angular momentum projection in nuclear physics

In nuclear models approximate wave functions are often used which do no have sharp angular momentum as required of the exact wave functions. It seem obvious that model wave functions of this type should be improved by projection onto states of good angular momentum. It is not the purpose of this paper to discuss the technical difficulties of projection (which can be formidable for many particle systems), but rather to present in an elementary way certain fundamental ambiguities in the use of projection. An application to high spin states near the yrast line is suggested.     

Nuclear rotations and the double variational method

A self-consistent equation similar to the constrained variational equation is derived, which fully takes into account the effect of collective rotation on the internal dynamics of the nucleus. The derivation is based on the “double variation” method using a trial wave function with definite angular momentum. A geometry for the representation of the rotation group is introduced which makes it possible to obtain the linked cluster expansion in a compact form without symmetry assumptions about the intrinsic state. The relationship of the generator coordinate and cranking model formulations is discussed.     

Shell model theory of elastic scattering of nucleons by deformed nuclei

The escape width originating from a collective rotational state as a doorway state is calculated in the framework of the shell model theory of nuclear reactions. The rotational states are constructed by Yoccoz-Peierls angular momentum projection from deformed intrinsic states which are described by BCS wave functions. For some rare earth nuclei it is shown that there result escape widths of the order of magnitude of 20–100 keV.     

Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field

We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method. In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF) theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained. This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei ¹⁶O and ²⁰⁸Pb, the deformed nucleus ²⁰Ne. Good agreement is obtained.     

Symmetry restoration in Hartree-Fock-Bogoliubov based theories

We present a Pfaffian formula for projection and symmetry restoration for wave functions of the general Bogoliubov form, including quasiparticle excited states and linear combinations of them. This solves a long-standing problem in calculating states of good symmetry, arising from the sign ambiguity of the commonly used determinant formula. A simple example is given of projecting a good particle number and angular momentum from a Bogoliubov wave function in the Fock space of a single j-shell.