Approximate Angular Momentum Projection Research Articles

Angular momentum projection for a Nilsson mean-field plus pairing model

The angular momentum projection for the axially deformed Nilsson mean-field plus a modified standard pairing (MSP) or the nearest-level pairing (NLP) model is proposed. Both the exact projection, in which all intrinsic states are taken into consideration, and the approximate projection, in which only intrinsic states with K=0 are taken in the projection, are considered. The analysis shows that the approximate projection with only K=0 intrinsic states seems reasonable, of which the configuration subspace considered is greatly reduced. As simple examples for the model application, low-lying spectra and electromagnetic properties of 18O and 18Ne are described by using both the exact and approximate angular momentum projection of the MSP or the NLP, while those of 20Ne and 24Mg are described by using the approximate angular momentum projection of the MSP or NLP.

Microscopical Studies of the Energy Staggering in γ-Soft Nuclei**The project supported by National Natural Science Foundation of China

The energy staggering in γ-or quasi γ-band of γ-soft even-even nuclei is studied with the approximate angular moment um projection of the deformed Hartree–Fock (DHF) states. In the calculations of DHF states the modified surface δ-interaction matrix elements are used. It is found that in the K = 2 band produced by the angular momentum projection of DHF state the energy staggering appears only in certain conditions. Some points concerning with the angular momentum projection of K = 2 DHF states are discussed. The energy spectra of nuclei 74Se and 76Kr are calculated and compared with the experimental data, which show the staggering pattern of γ-soft rotor, the coincidence between them are fairly good.

Generator coordinate method for triaxial quadrupole collective dynamics in strontium isotopes

We discuss the algebraic structure of the generator coordinate method for triaxial quadrupole collective motion. The collective solutions are classified according to the representations of the permutation group of the intrinsic axes. Our method amounts to an approximate angular-momentum projection. We apply it to a study of the spherical-to-deformed-shape transition in light even strontium isotopes 78–88Sr. We find that triaxial configurations plays a significant role in explainingv the structure of the transitional isotopes 80–82Sr.

Low-lying nuclear deformed states and angular momentum projection

A fast computational method for approximate angular momentum projection is proposed for low-lying deformed nuclear states. The accuracy of the method is demonstrated by calculating the low-lying states of the ground-state band and the two 0 + excited bands in 168Er with good experimental comparison.

Electromagnetic properties of high spin states in158Dy and164Dy

We present calculations of electromagnetic properties of158Dy and164Dy based on the solution of the self-consistent cranking model and approximate angular momentum projection technique developed earlier. The calculated values compare fairly well with the existing experimental data.

Approximate angular momentum projection from an intrinsic random phase approximation Hartree-Fock state

An approximation procedure is described to calculate the projected energies from an intrinsicrpa hf wave function. The method of moments is used to find the relevant parameters. A model calculation is carried out for illustrative purposes.

Low-lying spectra of transitional odd-mass nuclei described in angular momentum projected one-quasiparticle states

A previously proposed model of a particle coupled to a soft rotor is extended in order that both of the unique parity and the normal parity orbits can be indiscriminately treated in the same framework. Numerical calculations are performed for the odd-mass La and Pd isotopes. The low-lying energy spectra and variation of the spectra with mass number are well reproduced.NUCLEAR STRUCTURE $^{127,129,131,133,135}\mathrm{La}$, $^{101,103,105,107,109}\mathrm{Pd}$; calculated levels, $J$, $\ensuremath{\pi}$. Approximate angular momentum projection out of one-quasiparticle states.

Approximate Angular Momentum Projection from Cranked Intrinsic States

High-spin spectra are determined by approximately projecting states of good angular momentum from cranked Hartree-Fock-Bogoliubov (CHFB) wave functions. For each J the projected energy is E/sub PROJ/ approx. = E/sub CHFB/ - (..delta..J)/sup 2//2 J/sub CHFB/, where the moment of inertia J and the fluctuation ..delta..J are spin dependent. For /sup 168,170/Yb and /sup 174/Hf the projected J is less than the CHFB value for all J. Consequently approximate projection increases all yrast excitation energies for these nuclei.

Triaxial description ofOs188andPt188

A scheme based on variation after approximate angular momentum projection from a triaxially symmetric intrinsic wave function has been developed and applied to the study of ground-state band and ..gamma.. band of /sup 188/Os and /sup 188/Pt nuclei. The intrinsic calculation has been performed in the framework of Hartree-BCS theory employing the pairing + QxQ interaction of Baranger and Kumar. The calculated level energies, B (E2) values and electromagnetic moments compare quite well with the available experimental values. The position of the K = 4/sup +/ band, many B (E2) values and electromagnetic moments have been predicted. This study predicts relatively more rigid triaxial shapes for these nuclei than have been usually believed.

On the validity of the cranked Hartree-Fock approximation

A consistency condition for the equivalence between the variational problem after an approximate angular momentum projection on a non-axial determinant and the cranked Hartree-Fock (HF) procedure is tested in some cases and found to be satisfied fairly well. However, the zero-point contribution to rotational energy which is generally neglected is found to vary significantly.

Centrifugal stretching in 158Er

A variational calculation after an approximate angular momentum projection for 158Er indicates that the anomalous behaviour of the energy spacings of high spin states may be due to centrifugal stretching — an increase in deformation accompanied by a decrease in pairing correlations.

Exact and approximate angular momentum projection for light nuclei (II)

Abstract The Peierls-Yoccoz angular momentum projection method is applied to axially symmetric Hartree-Fock wave functions for several sd-shell nuclei. Excitation energies, rms radii and B (E2; 2 + → 0 + ) values are calculated and compared with the results of two different approximation methods. This is also done for some 12 C wave functions considered earlier. A discussion of the accuracy of these approximations is given. An approximate formula for the B (E2; 2 + → 0 + ) value is presented, which gives much better agreement with the exact angular momentum projection results than the formula from the Bohr-Mottelson model.

Exact and approximate angular momentum projection for light nuclei

Angular momentum projection is carried out in an exact way on Slater determinant wave functions for the axially symmetric nuclei 8Be and 12C and the asymmetric 4p-4h state in 16O. In the latter case, it is shown that the projected energies and the B(E2, 2 + → 0 +) value for the K = 0 band in the 4p-4h state are consistent with the Brown and Green model. An approximate method for the calculation of the projected energies is given for the axially symmetric cases. Using this method, one obtains the binding energies of the projected states easily and with good accuracy. The excitation energies are less well reproduced.

Exact and approximate angular momentum projection for light nuclei

Exact and approximate angular momentum projection for light nuclei