The cranked harmonic oscillator in coordinate space

The spectroscopic factor is considered for two-nucleon transfer reactions involving the excitation of quadrupole one-phonon states. Special attention is payed to the number of particles conservation condition in the dynamically distorted average potential of the deforming nucleus. It is required that the mean square of the time-derivtive of the particle number operator is zero in the collective phonon state. The condition is satisfied by a specially chosen residual interaction terms.     

Phonon–particle coupling effects in the single-particle energies of semi-magic nuclei

A method is presented to evaluate the particle–phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei. In such nuclei, always there is a collective low-lying 2⁺ phonon, and a strong mixture of single-particle and particle–phonon states often occurs. As in magic nuclei the so-called g _L ² approximation, where g _L is the vertex of the L-phonon creation, can be used for finding the PC correction δΣ^PC(ε) to the initial mass operator Σ₀. In addition to the usual pole diagram, the phonon “tadpole” diagram is also taken into account. In semi-magic nuclei, the perturbation theory in δΣ^PC(ε) with respect to Σ₀ is often invalid for finding the PC-corrected single-particle energies. Instead, the Dyson equation with the mass operator Σ(ε) = Σ₀ + δΣ^PC(ε) is solved directly, without any use of the perturbation theory. Results for a chain of semi-magic Pb isotopes are presented.     

Proton-neutron interactions in nuclei withA∼90

An extension of the cluster-(quadrupole-octupole) phonon model is proposed for nuclei withA～90 to describe simultaneously positive- and negative-parity states, in which quadrupole as well as octupole vibrations of the⁸⁸Sr core are allowed. The cluster states include particle and particle-hole core excitations. The residual interaction is a delta-function force with spin-spin exchange plus a quadrupole-quadrupole force. The model is applied to⁸⁷Sr,⁸⁹Sr,⁸⁸Y, and⁹⁰Y nuclei. For each case, energy levels, spectroscopic factors, and electromagnetic properties are calculated and compared with experiment.     

Q-phonon scheme in the collective nuclear model

The Q-phonon scheme developed on the basis of the algebraic collective nuclear model is discussed. It is shown that, within this scheme, low-lying collective states of even-even nuclei can be described to a precision higher than 90% of the norm by using one or, at maximum, two components of the Q-phonon basis constructed by applying a fixed number of the quadrupole operators Q to the exact ground state of the system. Various applications of this approximate scheme are discussed. It is shown that, by using this scheme, the relations between several E2-transition probabilities or between the energies of the collective states can be derived. It is also shown that the Q-phonon scheme can be used to extract information about the equilibrium shapes of nuclei and their fluctuations from data on the E2-transition probabilities.     

Dipole excitations in 122Te, 126Te and 130Te

Excited states of the nuclei ¹²²Te, ¹²⁶Te and ¹³⁰Te were populated via the (γ, γ') 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 detector. In all nuclei several dipole transitions were identified at energies around 3 MeV. The lowest corresponding J = 1 states are interpreted as two-phonon excitations. Quasiparticle-phonon-model calculations predict one 1^? 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 isovector second quadrupole phonon at about 3 MeV. The calculated transition strengths are compatible with experimental ones.     

In-plane polarized collective modes in detwinned YBa2Cu3O6.95 observed by spectral ellipsometry

The in-plane dielectric response of detwinned YBa₂Cu₃O_6.95 has been studied by far-infared ellipsometry. A surprisingly large number of in-plane polarized modes are observed. Some of them correspond to pure phonon modes. Others possess a large electronic contribution which strongly increases in the superconducting state. The free carrier response and the collective modes exhibit a pronounced a–b anisotropy. We discuss our results in terms of a charge density wave state in the 1-D CuO chains and induced charge density fluctuations within the 2-D CuO₂ planes.     

Single-nucleon transfer reactions to 100Ru

Proton stripping and neutron pickup reactions have been studied to the levels of ¹⁰⁰Ru, a nucleus with collective properties that have been thoroughly studied. The neutron pickup results are consistent with a calculation for the neutron-hole structure of the J^π = 2⁺ phonon state. The proton stripping results show no resemblance to either the phonon structure calculation or to the prediction of a shell model with good seniority. Strong proton excitation of the known 8⁺ state at 3.06 MeV shows that this is not the four-boson state predicted by the ⊙IBA at that excitation.     

Halo and skin nuclei

The changes in nuclear structure far from the stability line are reviewed for light nuclei. The basic concepts of neutron and proton skins and neutron halos are presented with several experimental data. Signatures of new mode of collective excitation as consequences of such exotic structures are also shown. These changes of structure point to the need for the detailed study of single-particle orbitals for unstable nuclei. Such recent studies, in particular, the spectroscopic information of halo states, are reviewed. Changes of neutron orbital ordering away from the stability line are observed from such studies. Its most profound implication has emerged in the change of magic numbers. An over view of magic number variation is presented. To cite this article: I. Tanihata, R. Kanungo, C. R. Physique 4 (2003).     

Study of the Gamow-Teller resonance in 90Nb and 208Bi

An approach is proposed for studying the spreading properties of the Gamow-Teller resonance (GTR) in heavy nuclei including the coupling to 2p2h configurations and the ground-state correlations beyond RPA. The GTR is generated by a proton p-neutron h (πp-νh) phonon within the renormalized RPA. The second-order configuration mixing beyond RPA is realized by constructing two-phonon configurations, in which one of two intermediate phonon states is a πp-νh phonon. The numerical calculations are performed in the parent nuclei ⁹⁰Zr and ²⁰⁸Pb making use of M3Y nucleon-nucleon interaction and the single-particle wave functions obtained in the standard harmonic oscillator potential. The single-particle energies around the Fermi surface are substituted with the empirical values or those given by a Woods-Saxon potential. The results obtained provide a reasonable account for recent experimental findings on the GTR in these nuclei. The extension of the present approach to highly excited (hot) nuclei is also provided. The GTR is found to be stable against temperatures up to T = 6 MeV.     

On magnetic dipole form factors in deformed nuclei

Properties of magnetic dipole form factors for deformed nuclei are discussed in terms of the angular momentum projected Hartree-Fock-Bogoljubov approximation and the neutron-proton interacting boson model. It is pointed out that there exists a relation between the M1 form factor for the excitation of the orbital K^π=1⁺ band, the M1 form factor for the ground-state band, and the collective M1 form factor in odd-A nuclei.     

A semi-empirical correlation energy for nuclei

A semi-empirical interaction is used to calculate higher order corrections to the binding energies of even—even nuclei close to the line of stability. These corrections are taken to come from two phonon configurations and are treated as a perturbation with respect to the BCS nuclear ground state which is obtained from applying the energy density method to finite nuclei. The overall correspondence between theory and experiment for the 60 nuclei calculated between A =52 and A =234 is good, with excellent agreement for the non-deformed nuclei situated within the regions A = 72 to 144 and A = 200 to 212. The large correction enegies (several MeV per nucleus on the average) indicate that these correlations are of importance for explaining nuclear binding energies and that it is necessary to include them within energy functional itself. The fact that these correlations come almost exclusively from nucleons close to the fermi surface is also discussed.     

Extraction of spectroscopic factors using R-matrix theory

The relation of the dimensionless reduced width of a state to its spectroscopic strength is discussed and the spectroscopic factor is calculated as the ratio of the reduced width to that of an optical potential analyzed with the same channel radius and boundary condition number. From a model square well problem, the reduced width is shown to be sensitive to these parameters. Neutron scattering to the 5.08 MeV state of ¹⁷O is analyzed with R-matrix theory and the value obtained for its spectroscopic factor is 0.80. This value is shown to be moderately independent of the parameters of the optical potential, a fact which greatly simplifies analysis by eliminating the strong dependence upon the location of the pure single particle state.     

Semi-microscopic calculation of the level density in spherical nuclei

The level density at the neutron binding energy for 90 spherical nuclei in the interval 50 < A < 205 is calculated by a method of direct counting of the number of states taking into account collective vibrational excitations. The results of calculations are in satisfactory agreement with the experimental data. The difference in the level density of doubly even and odd-A nuclei is correctly described. The effect of nuclear vibrations on the level density is studied, and it is shown that the account of them leads to an increase in the density by a factor of 1.5–10 and to a decrease in the density fluctuations. It is also studied how the level density depends on excitation energy. With increasing excitation energy, our results come nearer the corresponding values obtained by the statistical model. It is found that the density fluctuations decrease with increasing excitation energy but remain still strong at the neutron binding energy for nuclei with A = 50–70 and for nuclei around closed shells. The density ρ(I^π) is studied as a function of spin and parity. It is shown that at the neutron binding energy the ratio $\text{ρ(I}{}^{\mathrm{+}}\text{)}\text{ρ(I}{}^{\mathrm{?}}\text{)}$ is different from unity for the majority of nuclei. This difference is especially striking for ⁵⁷Fe and ⁵⁸Fe nuclei.     

Nuclear level densities with collective rotations included

The level density is calculated from the single particle energies in a Woods-Saxon potential with pairing included in the BCS approximation. The collective rotations are included by addition of a rotational band on top of each of the intrinsic levels. The nuclei investigated have mass numbers in the region 100 ≦ A ≦ 253. At the ground state deformation and at the neutron separation energy for the nucleus in question we compare calculated and observed level densities. The dependence on the parameters in the model are investigated. Considering the uncertainties in these parameters the calculated results are believed accurate to within a factor of 3. The rotations contribute typically a factor of 40. They must be included for deformed and not for spherical nuclei. We underestimate systematically the level density by a factor of 4 with fluctuations around the average value by a factor of 3. The nuclei lighter than ¹³⁸Ba are an exception. We obtain around a factor 100 too few levels in the calculation.     

An effective dynamic interaction for the two-particle propagator

In nuclear structure calculations the collective excitations of the core introduce dynamic effects in the interaction between particles. Under the restriction of including forward-going contributions only, it is shown that the two-particle propagator which yields the spectra and two-particle transfer strengths of nuclei with two nucleons outside a closed shell, can be written in a Dyson-like equation in which a two-particle self-energy or dynamic effective interactionΔ is introduced. An expression forΔ is given in terms of the irreducible vertex part of the Bethe-Salpeter equation and partial summations forΔ using phonon exchange interactions to represent the core-polarization diagrams, are discussed. The single-particle propagators are also dressed with phonon-exchange contributions.     

A hamiltonian with broken supersymmetry for the xenon isotopes

A hamiltonian with broken $\text{u}\text{(}\text{6}\text{2}\text{j+1)}$ supersymmetry is proposed that can describe collective excitations in nuclei with high-spin, single-j orbitals. Its bosonic part is identical with IBA, while the fermionic degrees of freedom, are characterized by the seniority quantum number. The ground state as well as excited energies of eight xenon isotopes with both odd and even mass are fairly well described by the so(6) limit of this hamiltonian with only one set of parameters.     

Dynamical properties of nucleus boundaries in photoinduced structural change

Dynamics of the boundaries of photoinduced nuclei in electron–phonon systems is theoretically studied. By regarding the spatial distribution of the excited electronic state population as a geometric pattern, we applied the multifractal analysis to it and calculated the temporal behavior of the fractal dimension f(α)$f(\alpha )$ as a function of the Lipschitz–Hölder exponent α, which is an appropriate method for understanding the cooperative relaxation process of photoexcited states. We found that the incubation period observed in various types of photoinduced cooperative phenomena corresponds to the formation of embryonic nuclei which is driven by nonadiabatic/adiabatic transition between electronic states during the relaxation of the Franck–Condon state.