Extended theory of finite Fermi systems: collective vibrations in closed shell nuclei

We review an extension of Migdal's Theory of Finite Fermi Systems which has been developed and applied to collective vibrations in closed shell nuclei in the past ten years. This microscopic approach is based on a consistent use of the Green function method. Here one considers in a consistent way more complex 1p1h$\otimes$phonon configurations beyond the RPA correlations. Moreover, these configurations are not only included in the excited states but also explicitly in the ground states of nuclei. The method has been applied to the calculation of the strength distribution and transition densities of giant electric and magnetic resonances in stable and unstable magic nuclei. Using these microscopic transition densities, cross sections for inelastic electron and alpha scattering have been calculated and compared with the available experimental data. The method also allows one to extract in a consistent way the magnitude of the strength of the various multipoles in the energy regions in which several multipoles overlap. We compare the microscopic transition densities, the strength distributions and the various multipole strengths with their values extracted phenomenologically.

/pdf/extended-theory-of-finite-fermi-systems-collective-3uar3cldh3.pdf

Extended Theory of Finite Fermi Systems (Collective Vibrations in Closed Shell Nuclei)

We report measurements of cross sections and analyzing powers for reaction angles of ${\ensuremath{\theta}}_{\mathrm{lab}}={0.0}^{\ensuremath{\circ}}$--${10.0}^{\ensuremath{\circ}}$ and complete sets of polarization transfer observables and induced polarizations at ${\ensuremath{\theta}}_{\mathrm{lab}}={0.0}^{\ensuremath{\circ}}$--${7.0}^{\ensuremath{\circ}}$ for the ${}^{208}\mathrm{Pb}(\stackrel{P\vec}{p},\stackrel{P\vec}{n})$ reaction at a bombarding energy of ${T}_{p}=296$ MeV. A multipole decomposition technique was applied to the data to extract the Gamow-Teller (GT) and spin-dipole (SD) components from the continuum. The polarization observables were also used, for the first time, to separate the SD components into different spin-parity transfer ($\ensuremath{\Delta}{J}^{\ensuremath{\pi}}={0}^{\ensuremath{-}}$, ${1}^{\ensuremath{-}}$, and ${2}^{\ensuremath{-}}$) contributions. A significant strength with $\ensuremath{\Delta}{J}^{\ensuremath{\pi}}={1}^{+}$ is identified in the continuum beyond the GT giant resonance, which is due to configuration mixing effects and the isovector spin monopole (IVSM) contribution. The SD strength distributions were clearly dependent on $\ensuremath{\Delta}{J}^{\ensuremath{\pi}}$, which is reasonably reproduced by Hartree-Fock (HF) plus random phase approximation (RPA) calculations that include the Skyrme interaction with tensor components [Phys. Rev. C 83, 054316 (2011)].

Complete sets of polarization transfer observables for the 208 Pb ( p ⃗ , n ⃗ ) reaction at 296 MeV and Gamow-Teller and spin-dipole strengths for 208 Pb

The excitation and subsequent proton decay of the isovector spin-flip giant monopole resonance (IVSGMR) is studied via the $^{208}\mathrm{P}\mathrm{b}(^{3}\mathrm{H}\mathrm{e},t)$ reaction at 410 MeV. In the inclusive spectrum $(60\ifmmode\pm\else\textpm\fi{}5)%$ of the non-energy-weighted sum-rule strength for this $2\ensuremath{\hbar}\ensuremath{\omega}$ resonance was found in the region $29l{E}_{x}(^{208}\mathrm{B}\mathrm{i})l51\text{ }\mathrm{M}\mathrm{e}\mathrm{V}$. The central excitation energy and width of the IVSGMR are $37\ifmmode\pm\else\textpm\fi{}1\text{ }\mathrm{M}\mathrm{e}\mathrm{V}$ and $14\ifmmode\pm\else\textpm\fi{}3\text{ }\mathrm{M}\mathrm{e}\mathrm{V}$, respectively. It is found that the branching ratio for proton decay is $(52\ifmmode\pm\else\textpm\fi{}12)%$ and that the deep neutron-hole states in $^{207}\mathrm{P}\mathrm{b}$ are strongly fed.

Excitation and decay of the isovector giant monopole resonances via the Pb-208(He-3,tp) reaction at 410 MeV

High-resolution ($^{3}\mathrm{He}$,$t$) measurements on the double \ensuremath{\beta}-decay ($\ensuremath{\beta}\ensuremath{\beta}$) nucleus $^{48}\mathrm{Ca}$ have been performed at RCNP (Osaka, Japan) to determine Gamow-Teller (${\mathrm{GT}}^{\ensuremath{-}}$) transitions to the nucleus $^{48}\mathrm{Sc}$, which represents the intermediate nucleus in the second-order perturbative description of the $\ensuremath{\beta}\ensuremath{\beta}$ decay. At a bombarding energy of ${E}_{{}^{3}\mathrm{He}}=420$ MeV an excitation energy resolution of 40 keV was achieved. The measurements were performed at two angle positions of the Grand Raiden Spectrometer (GRS): ${0}^{\ifmmode^\circ\else\textdegree\fi{}}$ and $2.{5}^{\ifmmode^\circ\else\textdegree\fi{}}$. The results of both settings were combined to achieve angular distributions, by which the character of single transitions could be determined. To characterize the different multipoles, theoretical angular distributions for states with ${J}^{\ensuremath{\pi}}={1}^{+},{2}^{+},{2}^{\ensuremath{-}}$, and ${3}^{+}$ were calculated using the distorted-wave Born approximation (DWBA) Code DW81. The ${\mathrm{GT}}^{\ensuremath{-}}$ strength was extracted up to ${E}_{x}=7$ MeV and combined with corresponding ${\mathrm{GT}}^{+}$ strength deduced from the $^{48}\mathrm{Ti}$($d$,$^{2}\mathrm{He}$)$^{48}\mathrm{Sc}$ data to calculate the low-energy part of the $\ensuremath{\beta}\ensuremath{\beta}$-decay matrix element for the $^{48}\mathrm{Ca}$ $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay. We show that after applying trivial momentum corrections to the ($^{3}\mathrm{He}$,$t$) spectrum, the two reaction probes, ($p,n$) and ($^{3}\mathrm{He}$,$t$) reveal a spectral response to an impressively high degree of similarity in the region of low momentum transfer.

( He 3 , t ) reaction on the double β decay nucleus Ca 48 and the importance of nuclear matrix elements

Low-lying hexadecapole states in stable even-even neodymium isotopes have been investigated by means of inelastic electron scattering. Transition charge densities were extracted in a Fourier-Bessel analysis of the form factors. The analysis of the experimental results within the interacting sdg-boson model with only one g boson allowed the extraction of the radial shapes of the hexadecapole structure functions of three of the different boson-pair configurations (i.e., dd, sg, and dg) involved in the hexadecapole excitations.

/pdf/hexadecapole-interacting-boson-approximation-structure-8mey86gpg0.pdf

Hexadecapole interacting boson approximation structure functions in neodymium isotopes.

https://pure.uva.nl/ws/files/2941855/1121_11990y.pdf

Localized 1h-omega particle-hole strength in nuclei

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Hexadecapole interacting boson approximation structure functions in neodymium isotopes.

Localized 1h-omega particle-hole strength in nuclei