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Register a new userNuclear excitations as coupled one and two random--phase--approximation modes
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We present an extension of the random--phase approximation (RPA) where the RPA phonons are used as building blocks to construct the excited states. In our model, that we call double RPA (DRPA), we include up to two RPA phonons. This is an approximate and simplified way, with respect to the full second random--phase approximation (SRPA), to extend the RPA by including two particle--two hole configurations. Some limitations of the standard SRPA model, related to the violation of the stability condition, are not encountered in the DRPA. We also verify in this work that the energy--weighted sum rules are satisfied. The DRPA is applied to low--energy modes and giant resonances in the nucleus $^{16}$O. We show that the model (i) produces a global downwards shift of the energies with respect to the RPA spectra; (ii) provides a shift that is however strongly reduced compared to that generated by the standard SRPA. This model represents an alternative way of correcting for the SRPA anomalous energy shift, compared to a recently developed extension of the SRPA, where a subtraction procedure is applied. The DRPA provides results in good agreeement with the experimental energies, with the exception of those low--lying states that have a dominant two particle--two hole nature. For describing such states, higher--order calculations are needed.
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The nuclear matrix element (NME) of the neutrinoless double-$beta$ ($0 ubetabeta$) decay is an essential input for determining the neutrino effective mass, if the half-life of this decay is measured. The reliable calculation of this NME has been a long-standing problem because of the diversity of the predicted values of the NME depending on the calculation method. In this paper, we focus on the shell model and the QRPA. The shell model have a rich amount of the many-particle many-hole correlations, and the QRPA can obtain the convergence of the result of calculation with respect to the extension of the single-particle space. It is difficult for the shell model to obtain the convergence of the $0 ubetabeta$ NME with respect to the valence single-particle space. The many-body correlations of the QRPA are insufficient depending on nuclei. We propose a new method to modify phenomenologically the results of the shell model and the QRPA compensating the insufficient point of each method by using the information of other method complementarily. Extrapolations of the components of the $0 ubetabeta$ NME of the shell model are made toward a very large valence single-particle space. We introduce a modification factor to the components of the $0 ubetabeta$ NME of the QRPA. Our modification method gives similar values of the $0 ubetabeta$ NME of the two methods for $^{48}$Ca. The NME of the two-neutrino double-$beta$ decay is also modified in a similar but simpler manner, and the consistency of the two methods is improved.
Using the Hartree-Fock plus random-phase-approximation (HF+RPA), we study the impurity effect of $Lambda$ hyperon on the collective vibrational excitations of double-$Lambda$ hypernuclei. To this end, we employ a Skyrme-type $Lambda N$ and $LambdaLambda$ interactions for the HF calculations, and the residual interactions for RPA derived with the same interactions. We find that inclusion of two $Lambda$ hyperons in $^{16}$O shifts the energy of the collective states towards higher energies. In particular, the energy of the giant monopole resonance of $^{,,18}_{LambdaLambda}$O, as well as that of $^{210}_{LambdaLambda}$Pb, becomes larger. This implies that the effective incompressibility modulus increases due to the impurity effect of $Lambda$ particle, if the $beta$-stability condition is not imposed.
We make use of a subtraction procedure, introduced to overcome double--counting problems in beyond--mean--field theories, in the second random--phase--approximation (SRPA) for the first time. This procedure guarantees the stability of SRPA (so that all excitation energies are real). We show that the method fits perfectly into nuclear density--functional theory. We illustrate applications to the monopole and quadrupole response and to low--lying $0^+$ and $2^+$ states in the nucleus $^{16}$O. We show that the subtraction procedure leads to: (i) results that are weakly cutoff dependent; (ii) a considerable reduction of the SRPA downwards shift with respect to the random--phase approximation (RPA) spectra (systematically found in all previous applications). This implementation of the SRPA model will allow a reliable analysis of the effects of 2 particle--2 hole configurations ($2p2h$) on the excitation spectra of medium--mass and heavy nuclei.
We develop a fully self-consistent subtracted second random-phase approximation for charge-exchange processes with Skyrme energy-density functionals. As a first application, we study Gamow-Teller excitations in the doubly-magic nucleus $^{48}$Ca, the lightest double-$beta$ emitter that could be used in an experiment, and in $^{78}$Ni, the single-beta-decay rate of which is known. The amount of Gamow-Teller strength below 20 or 30 MeV is considerably smaller than in other energy-density-functional calculations and agrees better with experiment in $^{48}$Ca, as does the beta-decay rate in $^{78}$Ni. These important results, obtained without textit{ad hoc} quenching factors, are due to the presence of two-particle -- two-hole configurations. Their density progressively increases with excitation energy, leading to a long high-energy tail in the spectrum, a fact that may have implications for the computation of nuclear matrix elements for neutrinoless double-$beta$ decay in the same framework.
In a recent article by C. Barbieri, E. Caurier, K. Langanke, and G. Martinez-Pinedo cite{Bar.08}, low-energy dipole excitations were studied in proton-rich $^{32,34}$Ar with random-phase approximation (RPA) and no-core shell model (NCSM) using correlated realistic nucleon-nucleon interactions obtained by the unitary correlation operator method (UCOM) cite{Fel.98}. The main objective of this Comment is to argue that the article cite{Bar.08} contains an inconsistency with respect to previous study of excitations in the same UCOM-RPA framework using identical correlated Argonne V18 interaction cite{Paa.06}, it does not provide any evidence that the low-lying state declared as pygmy dipole resonance in $^{32}$Ar indeed has the resonance-like structure, and that prior to studying exotic modes of excitation away from the valley of stability one should ensure that the model provides reliable description of available experimental data on nuclear ground state properties and excitations in nuclei. Although the authors aimed at testing the UCOM based theory at the proton drip line, available experimental data that are used as standard initial tests of theory frameworks at the proton drip line have not been considered in the UCOM case (e.g., binding energies, one-proton separation energies, two-proton separation energies).
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