Pair Shell Model Research Articles

Even-even Nd isotopes in an SD -pair shell model

Nucleon pair shell model truncated to $SD$ collective pair subspace (SDPSM) was applied to study the properties of the low-lying states of the even-even $^{144--156}\mathrm{Nd}$ isotopes. It is found that, within the $M$ scheme, the systems with the number ${N}_{\ensuremath{\nu}}=7$ of neutron pairs (or the number ${N}_{\ensuremath{\pi}}=7$ of proton pairs) can be studied in the SDPSM for the first time. The results show that the properties of the low-lying states of the even-even Nd isotopes can be reproduced approximately, and the even-even $^{144--156}\mathrm{Nd}$ isotopes may be a good candidate for the first-order shape phase transition.

Nucleon pair shell model in M scheme

The nucleon pair shell model (NPSM) is casted into the so-called M-scheme for the cases with isospin symmetry and without isospin symmetry. The odd system and even system are treated on the same foot. The uncoupled commutators for nucleon-pairs, which are suitable for M-scheme, are given. Explicit formula of matrix elements in M-scheme for overlap, one-body operators, two-body operators are obtained. It is found that the $cpu$ time used in calculating the matrix elements in M-scheme is much shorter than that in the J-scheme of NPSM.

Spherical to deformed shape transitions in the nucleon pair shell model

A study of the shape transition from spherical to axially deformed nuclei in the even Ce isotopes using the nucleon-pair approximation of the shell model is reported. As long as the structure of the dominant collective pairs is defined in a framework appropriate to deformed nuclei, the model is able to produce a shape transition. The resulting transition is too rapid, however, with nuclei that should be transitional being fairly well deformed. The possibility of using several pairs with each angular momentum to improve the description of the transitional region is discussed as is the possibility of using a larger single-particle space to better describe the moments of inertia in the deformed regime.

Quantum phase transitional patterns in theSD-pair shell model

Patterns of shape-phase transition in the proton-neutron coupled systems are studied within the $\mathit{SD}$-pair shell model. The results show that some transitional patterns in the $\mathit{SD}$-pair shell model are similar to the U(5)-SU(3) and U(5)-SO(6) transitions with signatures of the critical point symmetry of the interacting boson model.

SD-PAIR SHELL MODEL FOR EVEN-EVEN SYSTEMS

A nucleon-pair shell model was proposed in 1993 by J. Q. Chen. Due to the success of the interacting boson model, the full shell model space in the nucleon-pair shell model was truncated to SD-pair subspace, called SD -pair shell model. Within this model, the experimental spectra in medium-weight and heavy nuclei, limiting cases in the interacting boson model, phase transitions, etc. can be reproduced approximately.

SD-pair shell model study forXe126andBa128

The $\mathit{SD}$-pair shell model is employed to study $^{126}\mathrm{Xe}$ and $^{128}\mathrm{Ba}$. The results show that the spectra and electromagnetic transition strengths can be nicely described in terms of a three-parameter Hamiltonian. In our previous paper, we got a conclusion that the $\mathit{SD}$-pair approximation improves with the number of $\mathit{SD}$ pairs $N$. This work shows that this conclusion can be extrapolated to the case with $N=5$.

Nucleon pair approximation of the nuclear collective motion

The nucleon pair shell model calculation is performed in terms of the SD collective pairs which are obtained in a suitable way to obtain the maximum collectivity. The method is applied to even-even Sn, Te, Xe, Ba, and Ce isotopes near the $A=130$ region employing the (monopole and quadrupole) pairing plus quadrupole-quadrupole-type interaction with a very few parameters. The structure of energy levels for the quasi-\ensuremath{\gamma} band as well as the ground band is well reproduced in each nucleus. Other properties such as $E2$ transition rates and binding energies also agree with experimental data very well. The overall fit with the experimental data is superior to the previous calculations.

Validity of theSD-pair truncation of the shell model

The validity of the SD-pair truncation of the shell model is tested in a single j shell and in many j shells within the framework of the nucleon pair shell model. It is found that the SD-pair truncation is a good approximation of the shell model in the single-j case when the Hamiltonian consists of (monopole and quadrupole) pairing plus quadrupole-quadrupole-type interaction. The SD-pair truncation deteriorates if the quadrupole-quadrupole interaction is artificially large compared with the monopole pairing interaction. For multi-j shells, schematic calculations in the degenerate sd, pf, and sdg shells are performed for the extreme case of a pure quadrupole-quadrupole interaction. There is a large difference between the binding energies in the SD-pair-truncated subspace and those calculated in the full shell model space as in the case of a single-j shell. However, it is found that the basic properties of the band structure remain intact, and that the difference in energy levels, i.e., moments of inertia, can be easily absorbed by adjusting interaction strengths without changing the transition rates.

Comparison of a combined quantum mechanics/interatomic potential function approach with its periodic quantum-mechanical limit: Proton siting and ammonia adsorption in zeolite chabazite

Comparison is made between a combined quantum mechanics/interatomic potential function approach (QM-Pot) and its fully quantum-mechanical limit, ab initio calculation applying periodic boundary conditions. The Hartree–Fock (HF) method is combined with ab initio-parametrized ion pair shell model potential functions. The CRYSTAL code is employed for the periodic Hartree–Fock calculations. The same double-/valence triple-zeta polarization basis sets are used in both the approaches. The proton siting and ammonia adsorption in a high-silica acidic zeolite catalyst, H-chabazite (Si/Al=11, space group P1, unit cell H–AlO2[SiO2]11) are examined. The combined QM-Pot relative stabilities and reaction energies deviate from the periodic full QM results by 4–9 kJ/mol only, which demonstrates the power of our combined approach. This conclusion is also supported by comparison of the electrostatic potential inside the zeolite pore, calculated from the periodic wave function and by the QM-Pot approach. Framework oxygen O1 is found to be the preferred proton site and on interaction with NH3 the proton is predicted to move to NH3 yielding NH4+. The NH4+ surface species is coordinated to two framework oxygen atoms. It is by 30–35 kJ/mol more stable than the neutral adsorption complex of NH3. Evidence is produced that the failure of previous periodic HF calculations to predict a stable NH4+ ion is due to the limitations of the minimum basis set used.

Comparing the Acidities of Microporous Aluminosilicate and Silico-Aluminophosphate Catalysts: A Combined Quantum Mechanics-Interatomic Potential Function Study

DFT-B3LYP calculations are performed on 4-ring models of aluminophosphates (AlPOs) and silico-aluminophosphates (SAPOs). The results are used to fit the parameters of ion pair shell model potential functions. The potentials obtained are tested in lattice energy minimizations for berlinite and the microporous materials AlPO-18, AlPO-40, AlPO-52, and VPI-5. Not only does the potential reproduce the observed structures (average error of the cell constants 1.3%), it also predicts vibrational frequencies over the whole frequency range equally well (maximum deviation 50 cm-1). The potential is used to predict the structures and properties of Bronsted acid sites in an aluminosilicate and a SAPO with the chabazite framework structure (HSSZ-13 and HSAPO-34). A new combined quantum mechanics-intermolecular potential function approach (QM-Pot) is used at the DFT level. Comparison is made with full periodic DFT calculations using plane wave basis sets. The deprotonation energies corrected for systematic errors of the methods used are 1 231-1 235 and 1 261-1 280 kJ/mol for HSSZ-13 and HSAPO-34, respectively. The same acid site has a lower acidity in a SAPO than in an aluminosilicate zeolite of the same structure.

EM Transition Sum Rules Within the Framework of sdg Proton-Neutron Interacting Boson Model, Nuclear Pair Shell Model and Fermion Dynamical Symmetry Model**The project supported by Development Project Foundation of China, National Natural Science Foundation of China, Doctoral Education Fund of National Education Committee, Fundamental Research Fund of Southeast University

By the techniques of the Wick theorem for coupled clusters, the no-energy-weighted electromagnetic sum-rule calculations are presented in the sdg neutron–proton interacting boson model, the nuclear pair shell model and the fermion-dynamical symmetry model.

Combiningab initio techniques with analytical potential functions for structure predictions of large systems: Method and application to crystalline silica polymorphs

A computational scheme is presented which combines quantum mechanical ab initio techniques with methods using analytical potential functions. The scheme is designed for use in structure optimizations and is also applicable to molecular dynamics simulations. The implementation covers both molecular and periodic systems. The problem of the link atoms is solved by a subtraction scheme which is easily implemented for any combination of methods. As a first application dense and microporous silica polymorphs are studied. The Hartree-Fock method is combined with both a force field and an ion pair shell model potential. Comparison is made with lattice energy minimizations which use the force field or the shell model potential alone as well as with free cluster optimizations and optimizations in which the outer part of the cluster is kept fixed. © 1997 by John Wiley & Sons, Inc.

Pair shell model description of collective motions

The shell model in the pair basis has been reviewed with a case study of four particles in a spherical single- j shell. By analyzing the wave functions according to their pair components, the novel concept of the optimum pairs was developed which led to the proposal of a generalized pair mean-field method to solve the many-body problem. The salient feature of the method is its ability to handle within the framework of the spherical shell model a rotational system where the usual strong configuration mixing complexity is so simplified that it is now possible to obtain analytically the band head energies and the moments of inertia. We have also examined the effects of pair truncation on rotation and found the slow convergence of adding higher spin pairs. Finally, we found that when the SDI and Q · Q interactions are of equal strengths, the optimum pair approximation is still valid.