Relativistic two-phonon model for the low-energy nuclear response

The European Physical Journal A, 2004

We calculate, for the first time, the state-dependent pairing gap of a finite nucleus (120 Sn) diagonalizing the bare nucleon-nucleon potential (Argonne v14) in a Hartree-Fock basis (with effective k−mass m k ≈ 0.7 m), within the framework of the BCS approximation including scattering states up to 800 MeV above the Fermi energy to achieve convergence. The resulting gap accounts for about half of the experimental gap. We find that a consistent description of the low-energy nuclear spectrum requires, aside from the bare nucleon-nucleon interaction, not only the dressing of singleparticle motion through the coupling to the nuclear surface, to give the right density of levels close to the Fermi energy (and thus an effective mass m * ≈ m), but also the renormalization of collective vibrational modes through vertex and self-energy processes, processes which are also found to play an essential role in the pairing channel, leading to a long range, state dependent component of the pairing interaction. The combined effect of the bare nucleon-nucleon potential and of the induced pairing interaction arising from the exchange of low-lying surface vibrations between nucleons moving in time reversal states close to the Fermi energy accounts for the experimental gap.

Nuclear Physics, 1994

The fragmentation of two-phonon components in the structure of the low-lying states in 13sBa, 14'Ce, 142Nd and 144 Sm is investigated in the framework of the quasiparticle-phonon model. The level energies and the transitions relevant to the members of quadrupole-octupole and octupole-octupole two-phonon multiplets are calculated and compared to experiment in the case of '%4rn. For the other N = 82 nuclei considered in the paper, predictions are given. The two-phonon character of the first l-state is confirmed on the basis of calculations including a large one-, two-and three-phonon basis. A B(E1; 1; + g.s.) value of the order of 10M3 W.U. is obtained taking into account the influence of the giant dipole resonance. Several El, E2 and E3 transitions are calculated which give additional information on the properties of the two-phonon states in the N = 82 region.

Physical Review C, 2001

The quasiparticle representation of the phonon damping model ͑PDM͒ is developed to include the superfluid pairing correlations microscopically. The formalism is applied to calculate the photoabsorption and the electromagnetic ͑EM͒ differential cross sections of E1 excitations in neutron-rich oxygen and calcium isotopes. The calculated photoabsorption cross sections agree reasonably well with the available data for 16,18 O and 40,48 Ca. The fractions of energy-weighted sum of strength in the region of the pygmy dipole resonance ͑PDR͒ (E ␥ р15-16 MeV͒ and the PDR peaks in the EM cross sections for 20,22 O are also found in reasonable agreement with experimental systematics. The deviation from the prediction given by the cluster model's sum rule shows the importance of the effect of coupling to noncollective degrees of freedom in the damping of pygmy and giant dipole resonances.

Exotic Nuclei, 2015

The complex structure of low-lying as well as those of high-lying states is discussed within multiphonon approach. The approach is based on Quasiparticle-Phonon Model. This microscopic model goes beyond the quasiparticle random-phase approximation by treating a Hamiltonian of separable form in a microscopic multiphonon basis. It is therefore able to describe the anharmonic features of collective modes. In the case of low-lying part of excitations the model has close correspondence with the proton-neutron interacting boson model. Within the model highly-excited singleparticle states in nuclei are coupled with the excitations of a more complex character, first of all with collective phonon-like modes of the core. Although, on the level of one and two-phonon admixtures, the fully chaotic GOE regime is not reached, the eigenstates of the model carry significant degree of complexity that can be quantified with the aid of correlational invariant entropy.

Progress in Particle and Nuclear Physics, 2007

The covariant density functional theory is extended to include the dynamical effects going beyond the scope of the mean field theory. In analogy to the Fermi liquid theory of Landau and Migdal, the theory is based on quasi-particles, which are dressed with a cloud of low-lying collective excitations. These excitations are calculated in a consistent way within the framework of the Relativistic Random Phase Approximation (RRPA). This approach is applied to the study of single particle excitations in odd-mass nuclei, and to a quantitative description of the damping phenomenon in even-even spherical nuclei with closed shells. Since phonon coupling terms enrich the RRPA spectrum with a multitude of ph ⊗ phonon states, a noticeable fragmentation of giant resonance is obtained. The results are compared with experimental data and with results from the non-relativistic approach. We also investigate the influence of particle-vibrational coupling on the recently discovered soft dipole modes in nuclei with large neutron excess.

Nuclear Physics A, 1997

Excited states of the nuclei 122'126'13°Te were populated via the (y,,yt) reaction at endpoint energies of the bremsstrahlung between 4.5 and 5.5 MeV. Gamma rays were detected with a EUROBALL CLUSTER detector and a single HPGe detector. In all investigated nuclei two or three prominent dipole transitions were identified at E~, ~ 3 MeV. The corresponding low-lying J = l states are interpreted as two-phonon excitations. Quasiparticle-phonon-model calculations predict at about 3 MeV one l-state arising from the coupling of the first quadrupole and the first octupole phonon, and one 1 + state arising from the coupling of the first and the second quadrupole phonon, where the latter has isovector character. Such an excitation mode can be considered as an analogue of the scissors mode in vibrational nuclei. The calculated transition strengths are compatible with experimental ones within a factor of about 1.5. (~) 1997 Elsevier Science B.V.

Nuclear Physics A, 2004

The relativistic quasi-particle random phase approximation (RQRPA) is applied in the analysis of the evolution of isovector dipole response in nuclei with large neutron excess. In neutron-rich nuclei the dipole response is characterized by the fragmentation of the strength distribution and its spreading into the low-energy region.

Physical Review C, 2000

The damping of the giant dipole resonance ͑GDR͒ in neutron-rich nuclei 18,24 O, 60 Ca, and 150 Sn is calculated within the phonon damping model ͑PDM͒ and compared with those in ␤-stable isotopes. The Hartree-Fock single-particle energies obtained employing the SGII interaction are used in calculations. The PDM parameter for the ph-phonon interaction between the levels close to the Fermi surface in exotic nuclei has been chosen to simulate the strong coupling between the GDR phonon and dense incoherent ph configurations. The results of the calculations show the appearance of a low-lying structure ͑pigmy resonance͒ in all exotic nuclei under consideration. The calculations at nonzero temperature show that the GDR in hot medium and heavy neutron-rich nuclei exhibits a similar behavior as those of the hot GDR in stable nuclei. The pigmy resonance is smoothed out with increasing temperature.

Nuclear Physics A, 2005

A many-body Hamiltonian describing a system of Z protons and N neutrons moving in spherical shell model mean field and interacting among themselves through proton-proton and neutronneutron pairing and a dipole-dipole proton-neutron interaction of both particle-hole and particleparticle type, is treated within a fully renormalized (FR) pnQRPA approach. Two decoupling schemes are formulated. One of them decouples the equations of motion of particle total number conserving and non-conserving operators. One ends up with two very simple dispersion equations for phonon operators which are formally of Tamm-Dancoff types. For excitations in the (N-1,Z+1) system, Ikeda sum rule is fully satisfied provided the BCS equations are renormalized as well and therefore solved at a time with the FRpnQRPA equations. Next, one constructs two operators R † 1µ , R 1,−µ (−) 1−µ which commutes with the particle total number conserving operators, A † 1µ and A 1,−µ (−) 1−µ , and moreover could be renormalized so that they become bosons. Then, a phonon operator is built up as a linear combination of these four operators. The FRpnQRPA equations are written down for this complex phonon operator and the ISR is calculated analytically. This formalism allows for an unified description of the dipole excitations in four neighboring nuclei (N-1,Z+1),(N+1,Z-1),(N-1,Z-1),(N+1,Z+1). The phonon vacuum describes the (N,Z) system ground state.

Nuclear Physics A, 1993

Nuclear Resonance Fluorescence experiments have been performed on spherical nuclei around neutron number N=82. Detailed information on energies, cross sections and absolute transition strengths (i.e. lifetimes) of dipole excitations between 1 and 4 MeV have been obtained for the nuclei 141Pr, 142Nd and *43Nd. A very strongly excited l-state in 142Nd at 3.425MeV is assigned as a member of the two-phonon 2+ @ 3-multiplet. Calculations in the framework of the sdf-Interacting Boson Model for a similar state in the N=82 nucleus 144Sm confirm this assumption. In the neighbouring odd A nuclei 141Pr and 143Nd we found first evidence for the existence of two-phonon-particle-states which appear due to the coupling of the unpaired nucleon with the members of the 2+ @ 3-multiplet in the core nucleus.