A. I. Vdovin

Damping of high-lying single-particle modes in heavy nuclei

Abstract The recent experimental and theoretical results on the damping of high-lying single-particle modes in heavy nuclei are reviewed. In one-nucleon transfer reactions these states manifest themselves as broad “resonance”-like structures superimposed on a large continuum. The advantages and the limitations of the transfer reaction approach will be presented using the results from neutron and proton pick-up and stripping reactions. The problem raised by the subtraction of the underlying background, the assumptions made to describe the reaction process and the method used to extract the strength distributions are presented. The existing empirical systematics is summarized for nuclei ranging from 90Zr to 208Pb. The theoretical approaches used to explain the damping of the high-lying single-particle modes are based on the coupling between collective and single-particle degrees of freedom. In a first step the bare single-particle mode is spread over several doorway collective states due to the interaction with surface vibrations. In a second step the doorway states spread their strengths over many other degrees of freedom. These two steps of the damping mechanism are discussed in detail within the framework of the quasiparticle-phonon nuclear model. A large-scale comparison between the measured and calculated average energies, spreading widths and spectroscopic strengths of the high-lying single-particle (hole) states in heavy nuclei is presented. The systematic features of the damping (energy, angular momentum and isotopic dependence) are discussed. Recent advances of the experimental approaches, such as the γ-decay of the high-lying states or the use of heavy-ion transfer reactions at intermediate energies, are outlined. The detailed study of the damping mechanism of high-lying single-particle modes reveals new features and leads us to a new field in nuclear structure: “the spectroscopy of inner and outer subshells”.

Observation of a 1− two phonon 2+ ⊗ 3− excitation in 116Sn and 124Sn

Abstract In nuclear resonance fluorescence experiments with unpolarized and linearly polarized bremsstrahlung we have observed for the first time very strong electric dipole transitions at about 3.5 MeV in the spherical, semi magic 116 Sn and 124 Sn nuclei. These transitions can be attributed to possible two phonon 2 + ⊗ 3 − excitations. The measured transition strengths are compared to the results of a QRPA calculation.

Interplay between single-particle and collective degrees of freedom in the excitation of the low-lying states in 142Nd

Abstract The low-lying excited states in 142 Nd were investigated by inelastic electron scattering. The momentum transfer range covered was 0.5–2.8 fm −1 . Transition charge densities were extracted for natural-parity states from 0 + up to 9 − and up to an excitation energy of 3.5 MeV. For several new excited states spin and parity assignments have been suggested. The experimental transition charge densities have been interpreted with the aid of the quasiparticle-phonon model (QPM). The QPM is well-suited to investigate the contribution of collective and single-particle degrees of freedom to excited states in spherical nuclei. On the basis of the QPM calculations it is shown that in 142 Nd both degrees of freedom play an important role, as well as the interplay between them. Both the strength distribution and the structure of the transition charge densities of the low-lying excited states are well described by the calculations. The origin of the structure in the nuclear interior usually predicted by microscopic calculations but not observed experimentally is explained. An argument for the proton number dependence of the excitation energy of the 3 1 − state in the N = 82 isotones is given.

THE TFD TREATMENT OF THE QUASIPARTICLE-PHONON INTERACTION AT FINITE TEMPERATURE

The coupling of elementary excitation modes in hot nuclei is studied. For this aim the quasiparticle-phonon nuclear model (QPM) is extended to a finite temperature by using the formalism of the thermofield dynamics. First the energies and structures of one-phonon states are calculated in the thermal random phase approximation and then the thermal QPM Hamiltonian HQPM is expressed in terms of thermal quasiparticles and thermal RPA-phonons. The equation for the energies taking into account mixing of one-and two-thermal phonon states is derived. The expression of the coupling matrix element between thermal phonons is given.

ON THE TFD TREATMENT OF COLLECTIVE VIBRATIONS IN HOT NUCLEI

The approach in a theory of collective excitations in hot nuclei exploring the formalism of thermo field dynamics and the model Hamiltonian consisting of a mean field, the BCS paring interaction, and long-range particle–hole effective forces is reexamined. In contrast with earlier studies, it is found that a wave function of a thermal phonon is depended not only on the Fermi–Dirac thermal occupation numbers of the Bogoliubov quasiparticles consisting the phonon but also on the Bose thermal occupation numbers of the phonon. This strongly affects a thermal phonon coupling due to the renormalization of a phonon–phonon interaction and enlarging the number of thermal two-phonon configurations coupled with one-phonon ones. Moreover, it is shown that the formulation of the double tilde conjugation rule for fermions proposed by I. Ojima is more appropriate in the context of the present study than the original one by H. Umezawa and co-workers.

RENORMALIZED RPA AT FINITE TEMPERATURE

A method taking account of a deviation of state occupation numbers from the thermal RPA prescriptions is elaborated to study collective excitations in hot nuclei. This thermal renormalized random phase approximation (TRRPA) is from Ken-Ji Hara and D.J. Rowe. In developing the TRRPA, a formalism of the thermofield dynamics (TFD) is used. Some numerical results are given for the SU(2) model.

Thermal effects on neutrino-nucleus inelastic scattering in stellar environments

Thermal effects for inelastic neutrino-nucleus scattering off even-even nuclei in the iron region are studied. Allowed and first-forbidden contributions to the cross sections are calculated within the quasiparticle random-phase approximation, extended to finite temperatures within the Thermo-Field-Dynamics formalism. The GT0 strength distribution at finite temperatures is calculated for the sample nucleus 54Fe. The neutral-current neutrino-nucleus inelastic cross section is calculated for relevant temperatures during the supernova core collapse. The thermal population of the excited states significantly enhances the cross section at low neutrino energies. In agreement with studies using a large scale shell-model approach the enhancement is mainly due to neutrino up-scattering at finite temperatures.

Interplay between single-particle and collective degrees of freedom in the excitation of the low-lying quadrupole states in 142Nd

Abstract The low-lying quadrupole states in 142 Nd were investigated by inelastic electron scattering. The momentum transfer range covered was 0.5–2.8 fm − . The extracted transition charge densities indicate quite different characters for these states. On the basis of a quasiparticle-phonon nuclear model calculation this difference can be understood as arising from an interplay between collective and single-particle aspects.

Core polarization for M2 transitions in odd-A tin isotopes

Abstract The reduced M2 transition probabilities 11 2 − 1 → 7 2 + 1 in the odd- A isotopes 109–121 Sn are found to reveal a specific behaviour. B (M2) values are calculated in the framework of the quasiparticlephonon model. The coupling of a quasineutron with the 2 + , 3 − and 2 − one-phonon core excitation is taken into account. Inclusion of all one-phonon 2 − states up to 24 MeV in the wave functions of the excited states 11 2 − 1 and 7 2 + 1 reduces the theoretical B (M2) values by 3–4 times as compared to the single-particle values. The specific B (M2) dependence on the mass number appears to be due to the pairing effect.

High-lying single-proton states in spherical nuclei

Abstract The fragmentation of high-lying single-proton states in 145Eu and 209Bi is calculated within the quasiparticle-phonon nuclear model. The results of the calculation are compared with the data for the proton stripping reactions 144 Sm (α, t ) 145 Eu and 208 Pb (α, t ) 209 Bi .