Separation of spurious c.m. effects within the shell nucleon configuration framework in α-transfer structure studies

An exact method for the separation of the residual c.m. spurious contamination within the shell nucleon configuration framework has been derived from cluster model formulations. Expressions for the spurious weight α-spectroscopic amplitude and other factors relevant to α-transfer reactions have been obtained. Available methods to calculate α spectroscopic amplitude are extended to include excited shell nucleon configurations. Within the bounds of practically (i.e. within a few ?ω above the lowest configurations), the number of configurations in the extended treatment is relatively small, and therefore easily manageable. The calculations proposed are applicable to wave functions decomposed in terms of shell configuration states in the jj as well as the LS scheme.     

A coordinate-space study of kowalski's three-term separable approximation for the fully off-shell two-nucleon T-matrix

Using elementary coordinate-space methods, we show that a three-term separable approximate fully off-shell T-matrix proposed by Kowalski can be reduced to a simpler expression. This T-matrix incorporates off-shell unitarity exactly, is exact half off the energy shell, and is free from the spurious poles that arise in the Noyes approximation. However, numerical tests employing the wave-function model of Picker, Redish, and Stephenson show that for realistic ¹S_o interactions, the Noyes approximation is more accurate than Kowalski's approximation except near the spurious pole at 250 MeV. We give a plausible explanation of this result.     

双阱-集团壳模型中的质心运动伪态

本文指出了用微观双阱-集团壳模型来研究裂变和重离子反应过程中存在着质心运动伪态问题,推出了分解质心运动伪态波函数的一般表达式,并以Be⁸(α-α)为例,说明了伪态的存在,定量地计算了伪态成分以及它对能量矩阵元的修正。通过Be⁸核的分析,我们得到的结论是:虽然伪态成分仅占百分之几,但对于微观裂变位垒修正是很明显的,它甚至要超过库仑能对位垒的修正,因此在精确的定量计算中质心运动伪态是必须要考虑的。尤其是在核粒子数增多以及包含高激发态时,质心运动伪态更需仔细考虑。     

On the systematic energy difference between states of positive and negative parity

Comparison of the nuclear spectra in the mass region A = 10–40 shows a systematic difference between states of positive and negative parity. This systematic difference can be explained quantitatively with methods derived from statistical spectroscopy. The influence of spurious states is corrected for.     

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.     

Excited states of donor bound excitons and bound multiexciton complexes in silicon

The high resolution photoluminescence spectra reported here show new lines giving the first evidence of excited states of excitons bound to P donors in Si. These excited states are of crucial importance for a recently proposed theory of the bound multiexciton complexes which is based on a shell model. In addition several other new lines associated with the decay of the bound multiexciton complexes, which were predicted by the shell model theory, have been observed and their behaviour is found to be in argeement with the theory.     

A translationally invariant shell-model treatment of (0+1) ħω states in a=4–16 nuclei (I)

Shell-model calculations on positive- and negative-parity states have been performed for thep-shell nuclei. The model space includes all 0?ω and 1?ω harmonic-oscillator basis states without the use of a core. The matrix elements of the mass-independent two-body interaction and the harmonic-oscillator size parameter are determined empirically from a fit to experimental energy levels. The interaction is required to satisfy translational invariance. The single-particle energies are compatible with this requirement. The spurious states are isolated exactly from the nonspurious states.     

Excited baryons in the bag

We calculate the negative parityN ^* andΔ ^* states in the chiral bag model. After projecting out spurious center of mass states we reproduce the known masses reasonably well. Both the colour gluon exchange diagrams and the quark-quark spindependent forces due to the presence of Goldstone pions give important contributions to the ordering of the states. Previous calculations are examined and we conclude that the chiral bag models can sucessfully account for the negative parity states as well as the baryon ground states.     

Properties of isovector 1+ states in A=28 nuclei and nuclear muon capture

A method is proposed for taking into account, in a calculation of partial rates of muon capture by nuclei, experimental information about strength functions for Gamow-Teller and isovector M1 transitions. The method, which amounts to choosing an orthogonal transformation that acts in the subspace of wave functions for excited states, requires neither modifying transition operators nor introducing effective charges. The matrix of the above transformation is constructed as a product of the matrices of reflection in a plane. All calculations are performed on the basis of the multiparticle shell model. Numerical results are obtained for isovector states in A=28 nuclei. Strength functions for Gamow-Teller and isovector M1 transitions in ²⁸Si are considered, and the lifetimes of 1⁺ states in ²⁸Al and the branching fractions for gamma decays of this state are calculated. Owing to taking into account experimental information about the properties of isovector states, the branching fractions for the γ decays of the 1⁺ state at 2.201 MeV in ²⁸Al are successfully described for the first time. The above transformation of the wave functions changes substantially the distribution of partial rates of allowed muon capture by a ²⁸Si nucleus among the 1⁺ states of the final nucleus ²⁸Al in relation to the results of the calculations with the eigenfunctions of the Hamiltonian of the multiparticle shell model. The muon-capture rates calculated with the transformed functions agree well with experimental data.     

Algebraic properties of an integrable t-J model with impurities

We investigate the algebraic structure of a recently proposed integrable t-J model with impurities. Three forms of the Bethe ansatz equations are presented corresponding to the three choices for the grading. We prove that the Bethe ansatz states are highest weight vectors of the underlying gl(2′1) supersymmetry algebra. By acting with the gl(2′1) generators we construct a complete set of states for the model.     

Rotational properties of shell-model states infp-shell nuclei

The relation between the microscopic shell model and the collective rotor model is investigated. As the first step an extensive shell-model calculation is performed on about twentyfp-shell nuclei with massA=52–60. It turns out that, with the model space and the effective interaction chosen, the shell model is well able to reproduce the experimental data in this mass region. As the second step the shell-model wavefunctions are used to calculate energies, electromagnetic moments and transition rates of states with spin up toJ=16. As the third step the observables calculated with the shell model are used to investigate whether these microscopic results can be reproduced by a simple rotational model. About twenty pure axially symmetric rotor bands, generated by the shell model, could be localized. Their properties are presented and discussed.     

Seniority-three yrast states in theN=82 nucleus147Tb

Firm spin-parity assignments for the high-spin states up to 3.5 MeV in the one-proton nucleus¹⁴⁷Tb were obtained from¹⁴⁴Sm(⁶Li, 3n) in-beamγ-ray and conversion electron measurements. The energies of these two-particle one-hole excitations were calculated from the shell model with empirical nucleon-nucleon interaction energies. The calculated energy splittings agree well with experiment, whereas the theoretical excitation energies disagree by ?1 MeV if recently measured ground state masses are used.     

Lattice gases and exactly solvable models

We detail the construction of a family of lattice gas automata based on a model of 't Hooft, proceeding by use of symmetry principles to define first the kinematics of the model and then the dynamics. A spurious conserved quantity appears; we use it to effect a radical transformation of the model into one whose spacetime configurations are equivalent to the two-dimensional states of an exactly solvable statistical mechanics model, the symmetric eight-vertex model with parameters restricted to a disorder variety. We comment on the implications of this identification for the original lattice gas.     

Resonance scattering with modified continuum states: (II). Application of the unified model with one particle in the continuum to the 12C + n system

Starting from the conventional shell model, different methods for the treatment of the continuum are given. Using the modified continuum states of part I together with the reaction operator formalism, the present approach unifies the numerical features of the R-matrix theory and the physical picture of the shell model. As it treats the bound states and the scattering states in the same basis we calculated both for the ¹²C + n system as a test case. It is found that the results resemble the experimental data quite well, including for the first time the negative-parity resonances.     

Calculation of the yield of Xe<Superscript><Emphasis Type="Italic">i</Emphasis>+</Superscript> photoions upon the decay of <Emphasis Type="Italic">M</Emphasis><Subscript>45</Subscript> vacancies through intermediate states in coincidence with energy-selected Auger electrons

A theoretical model is proposed for calculating the yield of photoions detected in coincidence with energy-selected Auger electrons. This model provides a correct explanation for experimental data on the yield of photoions upon ionization of the M₄₅ shell of xenon atoms. In the framework of the proposed model, the intermediate-coupling approximation is used to calculate both the structure of the terms of the N^?2 two-hole states generated through the M₄₅NN Auger decays and the probabilities of branching due to decays of these states into three-hole states upon the Auger, Coster—Kronig, and super-Coster—Kronig transitions. The probabilities of branching for subsequent branches of the cascade decay are calculated in the configuration-average approximation. The results of these calculations are in good agreement with the experimental data.     

Coupling of two quasiparticles to coherent cores in the Pt isotopes

A model for coupling the motion of particles to that of a quadrupole-collective core is proposed. The quadrupole vibrations and rotations of the core are described by angular momentum projected coherent states. The spherical shell model particles interact among themselves by pairing and surface delta interactions. The particles are coupled to the core through a multipole-multipole interaction. The method is applied to several even mass isotopes of Pt. The agreement with experimental data of the excitation energies, gyromagnetic factors andE2 probabilities is very good.     

Revised model for 5d electrons in the heavy rare earth metals

A revised version of a recently published model for 5d electrons in the ferromagnetic state of the heavy rare earth metals is described. The model involves the broadening of local 5d states into overlapping bands with individual widthsW. In the new approach it is assumed that the local 5d wave functions lie at some point between those for atomic 4f _n 5d 6s ² configurations and those calculated for such configurations subject to the restriction that the 4f shell is kept with its moment rigidly fixed in some given direction. The admixture of non-aligned 4f states as in the atom lowers the local energy, but it also lowers the 5d bandwidth due to misfit of the 4f states which occur with and without the presence of a 5d electron. This second effect raises the energy of the low lying states in the band. The best local states are determined by minimising the total electronic energy of the system, using approximations which are most suitable for 4f shells with large excitation energies. Bandwidths are found by fitting the observed saturation magnetic moments in Gd and Tm, and satisfyW?1 eV.