Particle-vibration Coupling Research Articles

Particle-vibration coupling in halo nuclei

In halo nuclei like 11 Li and 12 Be, polarization effects based on the particle-vibration coupling mechanism leads to a density dependent pairing interaction which provides most of the observed correlation energy which stabilizes the least two bound neutrons. The same mechanism is at the basis of the parity inversion phenomenon observed in 10 Li and 11 Be.

Deformations and electromagnetic moments in carbon and neon isotopes

Static and dynamic quadrupole moments of C and Ne isotopes are investigated by using the deformed Skyrme Hartree-Fock model and also shell model wave functions with isospin-dependent core polarization charges. We point out that the deformations of C and Ne isotopes have a strong isotope dependence as a manifestation of spontaneous symmetry breaking effect in nuclear physics. The effect of spontaneous symmetry breaking is a general phenomenon known in many fields of physics. It is shown at the same time that the quadrupole moments $Q$ and the magnetic moments $\ensuremath{\mu}$ of the odd C and odd Ne isotopes depend clearly on assigned configurations, and their experimental data will be useful to determine the deformations of the ground states of nuclei near the neutron drip line. Electric quadrupole $(E2)$ transitions in even C and Ne isotopes are also studied using the polarization charges obtained by the particle vibration coupling model with shell model wave functions. Although the observed isotope dependence of the $E2$ transition strength is reproduced properly in both C and Ne isotopes, the calculated strength overestimates an extremely small observed value in $^{16}\mathrm{C}$.

Mean field and beyond in nuclei far from stability lines

We calculate, for the first time, the state-dependent pairing gap of a finite nucleus (120Sn) diagonalizing the bare nucleon-nucleon potential (Argonne v14) in a Hartree-Fock basis. The resulting gap accounts for about half of the experimental gap. Going beyond the mean field in the particle-particle channel, 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. Examples for light, halo nuclei are also reported. The more studied effects of the particle-vibration coupling in the particle-hole channel are discussed for the low-lying quadrupole vibration in 120Sn and the giant dipole resonance in the unstable oxygen isotopes and 132Sn.

Gfactors of the9−and11−isomers inPb194andPb196: Configuration mixing and deformation

The $g$ factors of the ${9}^{\ensuremath{-}}$ and ${11}^{\ensuremath{-}}$ yrast states in $^{194}\mathrm{Pb}$ and $^{196}\mathrm{Pb}$ have been measured using the time-dependent perturbed angular distribution (TDPAD) technique. An analysis of the systematics of the properties of these states in the light Pb isotopes is presented. The results confirm the dominance of the $\ensuremath{\nu}(2{f}_{5∕2}^{\ensuremath{-}1}1{i}_{13∕2}^{\ensuremath{-}1})$ configuration in the ${9}^{\ensuremath{-}}$ isomer. The values for the ${11}^{\ensuremath{-}}$ isomers are consistent with the $\ensuremath{\pi}(3{s}_{1∕2}^{\ensuremath{-}2}1{h}_{9∕2}1{i}_{13∕2})$ configuration, but they are smaller than those in the Po isotones. The effects of core excitation and particle-vibration coupling are considered, but these do not lead to a detailed agreement between theory and experiment. A Nilsson approach, however, gives good agreement, providing support for a proposed oblate deformation.

Collective properties of low-lying octupole excitations in 20882Pb 126, 6020Ca 40 and 288O 20

The octupole strengths of three nuclei: β-stable nucleus 208 82Pb 126, neutron skin nucleus 60 20Ca 40 and neutron drip line nucleus 28 8O 20 are studied by using the self-consistent Hartree–Fock calculation with the random phase approximation. The collective properties of low-lying excitations are analyzed by particle–vibration coupling. The results show that there is the coexistence of the collective excitations and the decoupled strong continuum strength near the threshold in the lowest isoscalar states in 60 20Ca 40 and 28 8O 20. For these three nuclei, both the low-lying isoscalar states and giant isoscalar resonance carry isovector strength. The ratio B(IV)/ B(IS) is checked and it is found that, for 208 82Pb 126, the ratio is equal to (( N− Z)/ A) 2 in good accuracy, while for 60 20Ca 40 and 28 8O 20, the ratios are much larger than (( N− Z)/ A) 2. The study shows that the enhancement of the ratio is due to the excess neutrons that have small binding energies in 60 20Ca 40 and 28 8O 20.

Particle-core coupling in 141Nd

High-spin states in141Nd have been studied using in-beam γ-ray spectroscopic techniques via the130Te(16O, 5nγ)141Nd reaction. The level scheme of141Nd has been extended up to an excitation energy of 7614.5 keV including 12 new γ rays deexciting 15 new levels. According to particle-vibrator coupling and semi-empirical shell model calculations, the level structure of141Nd can be well interpreted by coupling an h11/2 neutron-hole to the respective excited states in142Nd core.

New Theoretical Results on the Proton Decay of Deformed and Near-Spherical Nuclei

We discuss new theoretical results on the decay of deformed and near-spherical nuclei. We interpret the latest experimental results on deformed odd-A proton emitters, including fine structure, and discuss the use of particle-vibration coupling to calculate the decay rates of near-spherical emitters.

Effects of collective modes on shell structure of 10Be and 24O core

We study the effects of collective modes on shell structure in nuclei near the neutron drip line close to 10Be and 24O. Energy shifts in single-particle energies are evaluated by a particle–vibration coupling model. In the case of the 10Be core, the coupling to 2 + states is found to reduce the shell gap between 2 s 1/2 and 1 p 1/2 states. In the case of the 24O core, the couplings to 3 − and 2 + states lead to a large energy gap between 2 s 1/2 and 1 d 3/2 states, in agreement with a recent experimental evidence of a new magic number at N=16 near the neutron drip line. In particular, the 3 − vibrations are found to play a crucial role to push down the energy of the 2 s 1/2 state.

Particle-vibration coupling in proton decay of near-spherical nuclei

A particle-vibration coupling model is applied to explain the spectroscopic factors and decay rates of odd-$A$ and odd-odd near-spherical proton emitters, as well as the branching ratio for the recently observed fine structure in the decay of ${}^{145}\mathrm{Tm}.$ In addition, a deformed solution for ${}^{145}\mathrm{Tm}$ with ${K=5/2}^{\ensuremath{-}}$ is presented. Using particle-vibration coupling, good agreement is achieved with observed spectroscopic factors for the near-spherical emitters, including ${d}_{3/2}$ cases. For the odd-odd emitters, the unpaired neutron is treated as a spectator. The single-particle potential used in this work has the same parameters as that used to successfully describe the decay rates of the deformed proton emitters ${}^{131}\mathrm{Eu}$ and ${}^{141}\mathrm{Ho}.$

A consistent approach in relativistic random phase approximation

The fine structure of the IsoVector Giant Dipole Resonance (IVGDR) in the doubly-magic nuclei 40,48Ca observed in inelastic proton scattering experiments under 0∘ is used to investigate the role of different mechanisms contributing to the IVGDR decay width. Characteristic energy scales are extracted from the fine structure by means of wavelet analysis. The experimental scales are compared to different theoretical approaches allowing for the inclusion of complex configurations beyond the mean-field level. Calculations are performed in the framework of RPA and beyond-RPA in a relativistic approach based on an effective meson-exchange interaction, with the UCOM effective interaction and, for the first time, with realistic two- plus three-nucleon interactions from chiral effective field theory employing the in-medium similarity renormalization group. All models highlight the role of Landau fragmentation for the damping of the IVGDR, while the differences in the coupling strength between one particle-one hole (1p-1h) and two particle-two hole (2p-2h) correlated (relativistic) and non-correlated (non-relativistic) configurations lead to very different pictures of the importance of the spreading width resulting in wavelet scales being a sensitive measure of their interplay. The relativistic approach with particle-vibration coupling, in particular, shows impressive agreement with the number and absolute values of the scales extracted from the experimental data.

Random phase approximation for odd nuclei and its application to the description of the electric dipole modes in17O

A consistent generalization of the random phase approximation (RPA) for odd nuclei is suggested. The derivation is based on the Green function method using the equation for the three-particle Green function. The model developed combines properties of both the standard RPA, and the particle-vibration coupling model. This gives a possibility to describe both the single-particle and collective parts of the excitation spectrum including giant resonances in the continuum and splitting of discrete collective states [particle (hole) $\ensuremath{\bigotimes}$ phonon multiplets] on a common basis. In the framework of this model, where the single-particle continuum is taken into account exactly, the $E1$ photoabsorption cross section and the isoscalar $E1$ resonance in ${}^{17}\mathrm{O}$ are calculated. The comparative RPA calculations of the same $E1$ modes in ${}^{16}\mathrm{O}$ nucleus are presented. The results obtained are compared with experiment for the $E1$ resonance in ${}^{16}\mathrm{O}$ and ${}^{17}\mathrm{O}.$ For the isoscalar $E1$ strength in ${}^{17}\mathrm{O}$ we obtained an additional and noticeable low-lying contribution below 12.5 MeV caused by the odd neutron only.

Single-neutron transfer from 11Be[formula omitted] via the (p, d) reaction with a radioactive beam

The 11Be(p,d)10Be reaction has been performed in inverse kinematics with a radioactive 11Be beam of E/A=35.3 MeV. Angular distributions for the 0+ ground state, the 2+, 3.37 MeV state and the multiplet of states around 6 MeV in 10Be were measured at angles up to 16°cm by detecting the 10Be in a dispersion-matched spectrometer and the coincident deuterons in a silicon array. Distorted wave and coupled-channels calculations have been performed to investigate the amount of 2+ core excitation in 11Begs. The use of “realistic” 11Be wave functions is emphasised and bound-state form factors have been obtained by solving the particle-vibration coupling equations. This calculation gives a dominant 2s component in the 11Begs wave function with a 16% [2+⊗1d] core excitation admixture. Cross sections calculated with these form factors are in good agreement with the present data. The Separation Energy prescription for the bound-state wave function also gives satisfactory fits to the data, but leads to a significantly larger [2+⊗1d] component in 11Begs.

Anharmonicity of giant resonances

Using the particle-vibration coupling for particles moving in the harmonic oscillator potential, the anharmonicity in two-phonon states of monopole, dipole, and quadrupole giant resonances of shape vibrations is studied. The anharmonic term in both the energy and strength of two-phonon giant resonances vanishes in the leading order of ${N}_{F}\ensuremath{\gg}1.$ Thus, instead of ${A}^{\ensuremath{-}1},$ the calculated energy shift becomes the order of ${A}^{\ensuremath{-}4/3},$ which is still the order of ${A}^{1/3}$ larger than that obtained from a macroscopic description of the vibrations.

Core excitation in [formula omitted]Be gs via the p( [formula omitted]Be, [formula omitted]Be)d reaction

The p( 11 Be, 10 Be)d reaction has been studied using a radioactive 11 Be beam of 35.3 MeV/nucleon. Differential cross sections have been compared with Distorted Wave Born Approximation calculations, using bound state form factors determined by solving the particle-vibration coupling equations. Calculated cross sections corresponding to a 16% core excitation admixture in the 11 Be gs wave function are in good agreement with the present data.

Mass and state dependence of the interaction function in the direct-semidirect capture model

In the original direct-semidirect (DSD) model for the radiative capture of nucleons in the region of the giant dipole resonance, the complex particle-vibration coupling function was introduced phenomenologically and the real and imaginary strengths V1 and W1 determined from the comparison of the calculated and rather scarce experimental results. One can, on the other hand, extract an analytical expression for this coupling from the recent formulation of the consistent DSD, in light of which we conclude that the strengths V1 and W1 are both spin and mass dependent. Such dependence has not been known before, while the real and the imaginary parts of the coupling function turn out to be indeed of the volume and the surface peaked shapes, respectively, as used in previous versions of the model. The mass dependence deduced is for the capture to the ground states V1 = 16.8A1/3 MeV for the real and W1 = 16.1A1/3 MeV for the imaginary part.

Nucleon-phonon coupling in hot, rapidly rotating nuclei (I)

The particle-vibration coupling formalism is generalized to deal with hot, strongly rotating nuclei. In this way the basis to carry out a microscopic description of the structure of compound nuclei has been developed, in particular the calculation of the effective mass of nucleons close to the Fermi energy. As a consequence, it will be possible to provide a realistic estimate of the nuclear level density as a function of rotational frequency and temperature, a quantity which is among the key ingredients needed in the study of the evolution of the cooling of the compound nucleus through nucleon and γ-decay.

Shears mechanism and particle-vibration coupling

The shears mechanism, underlying the rotational-like behavior observed in the $M1$ bands in neutron-deficient Pb isotopes, is interpreted as a consequence of a residual interaction between the proton and neutron blades. By deriving the angle \ensuremath{\theta} between the proton and neutron spin vectors ${j}_{\ensuremath{\pi}}$ and ${j}_{\ensuremath{\nu}}$ in the ${}^{198,199}\mathrm{Pb}$ bands, it is shown that the main ingredient of this effective force can be described by a ${P}_{2}(\ensuremath{\theta})$ term with a strength of 400--600 keV. Such an interaction can be mediated through the core by particle-vibration coupling, and qualitative agreement with experimental estimates may indicate the possible role of this coupling in the appearance of shears bands.

Octupole vibrational states in the lead region

Collective properties of206Pb,207Pb,208Pb and209Bi have been investigated with gamma-ray spectroscopy using electromagnetic excitation by208Pb projectiles. By measuring the absolute yields of the de-excitation γ-rays,B(E3) values for the 1-phonon octupole vibrational states were obtained. While the present data for208Pb and209Bi are consistent with earlier publications, much smaller values have been found for206Pb and207Pb. Only for the doubly magic nucleus208Pb one observes the largest octupole collectivity of 34Weisskopf units (W.u.), which is reduced to 60–70% by the particle-vibration coupling in nuclei which consist of the208Pb core plus (or minus) a few nucleons. As a consequence of the phonon vibration character of the 3- state, one expects a quadruplet of 2-phonon octupole states with spins and parities 0+, 2+, 4+ and 6+ at about twice the energy of the 1-phonon state, i.e. around 5.23 MeV. A first scattering experiment suggesting the observation of at least one member of the 2-phonon multiplet was performed via the reaction208Pb+208Pb at an incident energy well above the Coulomb barrier. In the present experiment the system208Pb+208Pb has been reinvestigated via Coulomb excitation at a safe bombarding energy of 5.0 MeV/u. The reduced cross-section for the excitation of the octupole states has been compensated by the higher full energy efficiency of five EUROBALL CLUSTER detectors. With the present experimental set-up transition probabilities down to 10-5 -10-6 can be measured.

Collective γ-vibrational bands in 165Ho and 167Er

The nuclear structures of 165Ho and 167Er have been investigated by means of Coulomb excitation. These nuclei excited at moderate spins exhibit γ-vibrational bands with K π = 11 2 −, 3 2 − in 165Ho and K π = 11 2 + in 167Er. The γ-vibrational bands in 165Ho are found to be isospectral; heaving very nearly identical in-band γ-ray energies. Gamma-ray branching ratios are analysed to extract information on collectivity and Coriolis mixing. Experimental results are compared with calculations performed with the Cranked Shell Moedl + RPA + particle-vibration coupling and by invoking the generalized intensity relations (GIR) in the unified model scheme. Although this model explains many features of the data, puzzling aspects such as identical transition energies for the bands in 165Ho remain unexplained. The role of the K quantum number in identical bands is discussed.

Structure of one neutron halo light nuclei11Be and19O

The low-lying excitation spectra of ${}^{11}$Be and ${}^{19}$O have been calculated on the basis of particle-vibration coupling model. Experimentally observed parity inversion of the ground state and first excited state of ${}^{11}$Be has been reproduced. A fairly good agreement with experiment is obtained regarding excitation energies and spectroscopic factors for both nuclei. Calculated neutron rms radii confirm the observed neutron halo for these nuclei.