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Register a new userSubtraction method in the second random--phase approximation: first applications with a Skyrme energy functional
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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.
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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.
[Background] Giant resonance (GR) is a typical collective mode of vibration. The deformation splitting of the isovector (IV) giant dipole resonance is well established. However, the splitting of GRs with other multipolarities is not well understood. [Purpose] I explore the IV monopole and quadrupole excitations and attempt to obtain the generic features of IV giant resonances in deformed nuclei by investigating the neutral and charge-exchange channels simultaneously. [Method] I employ a nuclear energy-density functional (EDF) method: the Skyrme-Kohn-Sham-Bogoliubov and the quasiparticle random-phase approximation are used to describe the ground state and the transition to excited states. [Results] I find the concentration of the monopole strengths in the energy region of the isobaric analog or Gamow-Teller resonance irrespective of nuclear deformation, and the appearance of a high-energy giant resonance composed of the particle-hole configurations of $2hbar omega_0$ excitation. Splitting of the distribution of the strength occurs in the giant monopole and quadrupole resonances due to deformation. The lower $K$ states of quadrupole resonances appear lower in energy and possess the enhanced strengths in the prolate configuration, and vice versa in the oblate configuration, while the energy ordering depending on $K$ is not clear for the $J=1$ and $J=2$ spin-quadrupole resonances. [Conclusions] The deformation splitting occurs generously in the giant monopole and quadrupole resonances. The $K$-dependence of the quadrupole transition strengths is largely understood by the anisotropy of density distribution.
The isovector dipole E1 strength in Mo isotopes with A=92,94,96,98,100 is analyzed within the self-consistent separable random-phase approximation (SRPA) model with Skyrme forces SkT6, SkM*, SLy6, and SkI3. The special attention is paid to the low-energy region near the particle thresholds (4-12 MeV), which is important for understanding of astrophysical processes. We show that, due to a compensation effect, the influence of nuclear deformation on E1 strength below 10-12 MeV is quite modest. At the same time, in agreement with previous predictions, the deformation increases the strength at higher energy. At 4-8 MeV the strength is mainly determined by the tail of E1 giant resonance. The four Skyrme forces differ in description of the whole giant resonance but give rather similar results below 12 MeV.
Although many random-phase approximation (RPA) calculations of the Gamow-Teller (GT) response exist, this is not the case for calculations going beyond the mean-field approximation. We apply a consistent model that includes the coupling of the GT resonance to low-lying vibrations, to nuclei of the $fp$ shell. Among other motivations, our goal is to see if the particle-vibration coupling can redistribute the low-lying GT$^+$ strength that is relevant for electron-capture processes in core-collapse supernova. We conclude that the lowering and fragmentation of that strength are consistent with the experimental findings and validate our model. However, the particle-vibration coupling cannot account for the quenching of the total value of the low-lying strength.
We analyze the isoscalar response related to breathing modes with particular attention being paid to low-lying excitations in neutron--rich nuclei. We use the subtracted second random--phase approximation (SSRPA) to describe microscopically the response. By increasing the neutron excess, we study the evolution of the response in Ca isotopes going from $^{40}$Ca to $^{48}$Ca and to $^{60}$Ca as well as in $N=20$ isotones going from $^{40}$Ca to $^{36}$S and to $^{34}$Si. Finally, the case of $^{68}$Ni is investigated. We predict soft monopole modes in neutron--rich nuclei which are driven by neutron excitations. At variance with dipole pygmy modes, these neutron excitations are not only strongly dominant at the surface of the nucleus but over its entire volume. The effect of the mixing with two particle-two hole configurations induced by the SSRPA model is analyzed. The properties of such soft neutron modes are investigated in terms of their excitation energies, transition densities and wave--function components. Their collectivity is also discussed as a function of the isospin asymmetry and of the mass of the nucleus. The link between such low--energy compression modes and a compressibility modulus introduced for neutron--rich infinite matter is finally studied.
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