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Register a new userNo-core configuration-interaction model for the isospin- and angular-momentum-projected states
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[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.
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The no-core configuration-interaction model based on the isospin- and angular-momentum projected density functional formalism is introduced. Two applications of the model are presented: (i) determination of spectra of 0+ states in 62Zn and (ii) determination of isospin-symmetry-breaking corrections to superallowed beta-decay between isobaric-analogue 0+ states in 38Ca and 38K. It is shown that, without readjusting a single parameter of the underlying Skyrme interaction, in all three nuclei, the model reproduces the 0+ spectra surprisingly well.
Background: The superallowed beta-decay rates provide stringent constraints on physics beyond the Standard Model of particle physics. To extract crucial information about the electroweak force, small isospin-breaking corrections to the Fermi matrix element of superallowed transitions must be applied. Purpose: We perform systematic calculations of isospin-breaking corrections to superallowed beta-decays and estimate theoretical uncertainties related to the basis truncation, time-odd polarization effects related to the intrinsic symmetry of the underlying Slater determinants, and to the functional parametrization. Methods: We use the self-consistent isospin- and angular-momentum-projected nuclear density functional theory employing two density functionals derived from the density independent Skyrme interaction. Pairing correlations are ignored. Our framework can simultaneously describe various effects that impact matrix elements of the Fermi decay: symmetry breaking, configuration mixing, and long-range Coulomb polarization. Results: The isospin-breaking corrections to the I=0+,T=1 --> I=0+,T=1 pure Fermi transitions are computed for nuclei from A=10 to A=98 and, for the first time, to the Fermi branch of the I,T=1/2 --> I,T=1/2 transitions in mirror nuclei from A=11 to A=49. We carefully analyze various model assumptions impacting theoretical uncertainties of our calculations and provide theoretical error bars on our predictions. Conclusions: The overall agreement with empirical isospin-breaking corrections is very satisfactory. Using computed isospin-breaking corrections we show that the unitarity of the CKM matrix is satisfied with a precision better than 0.1%.
The $A=4$ nuclei, i.e., $^4$H, $^4$He and $^4$Li, establish an interesting isospin $T=1$ isobaric system. $^4$H and $^4$Li are unbound broad resonances, whereas $^4$He is deeply bound in its ground state but unbound in all its excited states. The present situation is that experiments so far have not given consistent data on the resonances. Few-body calculations have well studied the scatterings of the $4N$ systems. In the present work, we provide many-body calculations of the broad resonance structures, in an textit{ab initio} framework with modern realistic interactions. It occurs that, indeed, $^4$H, $^4$Li and excited $^4$He are broad resonances, which is in accordance with experimental observations. The calculations also show that the first $1^-$ excited state almost degenerates with the $2^-$ ground state in the pair of mirror isobars of $^4$H and $^4$Li, which may suggest that the experimental data on energy and width are the mixture of the ground state and the first excited state. The $T = 1$ isospin triplet formed with an excited state of $^4$He and ground states of $^4$H and $^4$Li is studied, focusing on the effect of isospin symmetry breaking.
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.
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.
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