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Register a new userAngular momentum projected multi-cranked configuration mixing for reliable calculation of high-spin rotational bands
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By employing the angular momentum projection technique we propose a method to reliably calculate the quantum spectrum of nuclear collective rotation. The method utilizes several cranked mean-field states with different rotational frequencies and they are superposed in the sense of the configuration mixing or the generator coordinate method, after performing the projection; the idea was originally suggested by Peierls-Thouless in 1962. It is found that the spectrum as a result of the configuration mixing does not essentially depend on chosen sets of cranking frequencies if the number of mean-field states utilized in the mixing is larger than a certain small value. We apply this method to three examples employing the Gogny D1S effective interaction and show that it is useful to study high-spin rotational bands by means of the angular momentum projection method.
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Recently we have proposed a reliable method to describe the rotational band in a fully microscopic manner. The method has recourse to the configuration-mixing of several cranked mean-field wave functions after the angular-momentum-projection. By applying the method with the Gogny D1S force as an effective interaction, we investigate the moments of inertia of the ground state rotational bands in a number of selected nuclei in the rare earth region. As another application we try to describe, for the first time, the two-neutron aligned band in $^{164}$Er, which crosses the ground state band and becomes the yrast states at higher spins. Fairly good overall agreements with the experimental data are achieved; for nuclei, where the pairing correlations are properly described, the agreements are excellent. This confirms that the previously proposed method is really useful for study of the nuclear rotational motion.
Inclusion of time-odd components into the wave function is important for reliable description of rotational motion by the angular-momentum-projection method; the cranking procedure with infinitesimal rotational frequency is an efficient way to realize it. In the present work we investigate the effect of this infinitesimal cranking for triaxially deformed nucleus, where there are three independent cranking axes. It is found that the effects of cranking about three axes on the triaxial energy spectrum are quite different and inclusion of all of them considerably modify the resultant spectrum from the one obtained without cranking. Employing the Gogny D1S force as an effective interaction, we apply the method to the calculation of the multiple gamma vibrational bands in $^{164}$Er as a typical example, where the angular-momentum-projected configuration-mixing with respect to the triaxial shape degree of freedom is performed. With this method, both the $K=0$ and $K=4$ two-phonon gamma vibrational bands are obtained with considerable anharmonicity. Reasonably good agreement, though not perfect, is obtained for both the spectrum and transition probabilities with rather small average triaxial deformation $gammaapprox 9^circ$ for the ground state rotational band. The relation to the wobbling motion at high-spin states is also briefly discussed.
The properties of rotational bands at the limit of angular momentum are discussed on the example of smooth terminating bands observed in the A~110 mass region. The effective alignment approach is used for the study of their relative properties which provides additional insight into the properties of such bands.
[Background] Single-reference density functional theory is very successful in reproducing bulk nuclear properties like binding energies, radii, or quadrupole moments throughout the entire periodic table. Its extension to the multi-reference level allows for restoring symmetries and, in turn, for calculating transition rates. [Purpose] We propose a new no-core-configuration-interaction (NCCI) model treating properly isospin and rotational symmetries. The model is applicable to any nucleus irrespective of its mass and neutron- and proton-number parity. It properly includes polarization effects caused by an interplay between the long- and short-range forces acting in the atomic nucleus. [Methods] The method is based on solving the Hill-Wheeler-Griffin equation within a model space built of linearly-dependent states having good angular momentum and properly treated isobaric spin. The states are generated by means of the isospin and angular-momentum projection applied to a set of low-lying (multi)particle-(multi)hole deformed Slater determinants calculated using the self-consistent Skyrme-Hartree-Fock approach. [Results] The theory is applied to calculate energy spectra in N~Z nuclei that are relevant from the point of view of a study of superallowed Fermi beta-decays. In particular, a new set of the isospin-symmetry-breaking corrections to these decays is given. [Conclusions] It is demonstrated that the NCCI model is capable to capture main features of low-lying energy spectra in light and medium-mass nuclei using relatively small model space and without any local readjustment of its low-energy coupling constants. Its flexibility and a range of applicability makes it an interesting alternative to the conventional nuclear shell model.
We perform simultaneous analysis of (1) matter radii, (2) $B(E2; 0^+ rightarrow 2^+ )$ transition probabilities, and (3) excitation energies, $E(2^+)$ and $E(4^+)$, for $^{24-40}$Mg by using the beyond mean-field (BMF) framework with angular-momentum-projected configuration mixing with respect to the axially symmetric $beta_2$ deformation with infinitesimal cranking. The BMF calculations successfully reproduce all of the data for $r_{rm m}$, $B(E2)$, and $E(2^+)$ and $E(4^+)$, indicating that it is quite useful for data analysis, particularly for low-lying states. We also discuss the absolute value of the deformation parameter $beta_2$ deduced from measured values of $B(E2)$ and $r_{rm m}$. This framework makes it possible to investigate the effects of $beta_2$ deformation, the change in $beta_2$ due to restoration of rotational symmetry, $beta_2$ configuration mixing, and the inclusion of time-odd components by infinitesimal cranking. Under the assumption of axial deformation and parity conservation, we clarify which effect is important for each of the three measurements, and propose the kinds of BMF calculations that are practical for each of the three kinds of observables.
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