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Register a new userFine structure of the pygmy quadrupole resonance in $^{112,114}$Sn isotopes
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The electric quadrupole response in $^{112,114}$Sn isotopes is investigated by energy-density functional (EDF) and three-phonon quasiparticle-phonon model (QPM) theory with special emphasis on 2$^+$ excitations located above the first collective quadrupole state and below 5 MeV. Additional quadrupole strength clustering as a sequence of states similar to the recently observed pygmy quadrupole resonance in $^{124}$Sn is found. The spectral distributions and transition densities of these 2$^+$ states show special features being compatible with oscillations of a neutron skin against the isospin-symmetric nuclear core. Furthermore, two new ($p$, $p gamma$) Doppler-shift attenuation (DSA) coincidence experiments were performed at the SONIC@HORUS setup. Quadrupole states with excitation energies up to 4.2 MeV were populated in $^{112,114}$Sn. Lifetimes and branching ratios were measured allowing for the determination of the reduced quadrupole transition strengths to the ground state. A stringent comparison of the new data to EDF+QPM theory in $^{112}$Sn and $^{114}$Sn isotopes hints at the occurrence of a low-energy quadrupole mode of unique character which could be interpreted as pygmy quadrupole resonance.
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Starting from the quasiparticle random phase approximation based on the Skyrme interaction SLy5, we study the effects of phonon-phonon coupling~(PPC) on the low-energy electric dipole response in $^{40-58}$Ca. Using the same set of parameters we describe available experimental data for $^{40,44,48}$Ca and give prediction for $^{50-58}$Ca. The inclusion of the PPC results in the formation of low-energy $1^-$ states. There is an impact of the PPC effect on low-energy $E1$~strength of $^{40,44,48}$Ca. The PPC effect on the electric dipole polarizability is discussed. We predict a strong increase of the summed $E1$~strength below 10MeV, with increasing neutron number from $^{48}$Ca till $^{58}$Ca.
The fragmentation of the Isoscalar Giant Quadrupole Resonance (ISGQR) in 40Ca has been investigated in high energy-resolution experiments using proton inelastic scattering at E_p = 200 MeV. Fine structure is observed in the region of the ISGQR and its characteristic energy scales are extracted from the experimental data by means of a wavelet analysis. The experimental scales are well described by Random Phase Approximation (RPA) and second-RPA calculations with an effective interaction derived from a realistic nucleon-nucleon interaction by the Unitary Correlation Operator Method (UCOM). In these results characteristic scales are already present at the mean-field level pointing to their origination in Landau damping, in contrast to the findings in heavier nuclei and also to SRPA calculations for 40Ca based on phenomenological effective interactions, where fine structure is explained by the coupling to two-particle two-hole (2p-2h) states.
A method of calculating static moments of excited states and transitions between excited states is formulated for non-magic nuclei within the Green function formalism. For these characteristics, it leads to a noticeable difference from the standard QRPA approach. Quadrupole moments of the first 2+ states in Sn and Pb isotopes are calculated using the self-consistent TFFS based on the Energy Density Functional by Fayans et al. with the set of parameters DF3-a fixed previously. A reasonable agreement with available experimental data is obtained.
The isoscalar giant monopole resonance (ISGMR) in Cd, Sn and Pb isotopes has been studied within the self-consistent Skyrme Hartree-Fock+BCS and quasi-particle random phase approximation (QRPA). Three Skyrme parameter sets are used in the calculations, i.e., SLy5, SkM* and SkP, since they are characterized by different values of the compression modulus in symmetric nuclear matter, namely K=230, 217, and 202 MeV, respectively. We also investigate the effect of different types of pairing forces on the ISGMR in Cd, Sn and Pb isotopes. The calculated peak energies and the strength distributions of ISGMR are compared with available experimental data. We find that SkP fails completely to describe the ISGMR strength distribution for all isotopes due to its low value of the nuclear matter incompressibility, namely K=202 MeV. On the other hand, the SLy5 parameter set, supplemented by an appropriate pairing interaction, gives a reasonable description of the ISGMR in Cd and Pb isotopes. A better description of ISGMR in Sn isotopes is achieved by the SkM* interaction, that has a somewhat softer value of the nuclear incompressibility.
The electric dipole excitation of various nuclei is calculated with a Random Phase Approximation phenomenological approach. The evolution of the strength distribution in various groups of isotopes, oxygen, calcium, zirconium and tin, is studied. The neutron excess produces $E1$ strength in the low energy region. Indexes to measure the collectivity of the excitation are defined. We studied the behavior of proton and neutron transition densities to determine the isoscalar or isovector nature of the excitation. We observed that in medium-heavy nuclei the low-energy $E1$ excitation has characteristics rather different that those exhibited by the giant dipole resonance. This new type of excitation can be identified as pygmy dipole resonance.
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