Pairing Vibrations Research Articles

Correlation energy contribution to nuclear masses

During the last few years, much effort has been made to develop a microscopic description of the nuclear masses based on mean field theory. The accuracy achieved, when phenomenological parameters are added to take specific effects into account (Wigner term, cut-off in pairing space, etc.), leads to a rms of 0.6–0.7 MeV [S. Goriely, F. Tondeur, J.M. Pearson, Atom Data Nucl. Data Tables 77 (2001) 311] (see also [M. Bender, P.H. Heenen, P.G. Reinhard, Rev. Modern Phys. 75 (2003) 121]). We present evidence that further progress can be made by taking into account medium polarization effects associated with surface and pairing vibrations [S. Baroni, M. Armati, F. Barranco, R.A. Broglia, G. Colò, G. Gori, E. Vigezzi, J. Phys. G: Nucl. Part. Phys. 30 (2004) 1353; S. Baroni, F. Barranco, P.F. Bortignon, R.A. Broglia, G. Colò, E. Vigezzi, Phys. Rev. C 74 (2006) 024305] (see also [M. Bender, G.F. Bertsch, P.-H. Heenen, Phys. Rev. C 73 (2006) 034322]).

Medium polarization isotopic effects on nuclear binding energies

There exist several effective interactions whose parameters are fitted to force mean field predictions to reproduce experimental findings of finite nuclei and calculated properties of infinite nuclear matter. Exploiting this tecnique one can give a good description of nuclear binding energies. We present evidence that further progress can be made by taking into account medium polarization effects associated with surface and pairing vibrations.

Experimental study on active vibration control of a gearbox system

An active internal gearbox structure is developed and evaluated experimentally to suppress gear pair vibration due to transmission error excitation. The approach is based on an active shaft transverse vibration control concept that was theoretically analyzed in an earlier study and determined to be one of the most feasible methods. The system comprises of a piezoelectric stack actuator for applying control forces to the shaft via a rolling element-bearing, and a highly efficient, enhanced delayed-x LMS control algorithm to generate the appropriate control signals. To avoid the aliasing effects of higher frequency signals and reduce the phase delay of conventional filters, a multi-rate minimum-phase low-pass digital filter is also integrated into the controller. The experimental results yield 8–13 dB attenuation in the gearbox housing vibration levels and correspondingly 5–8 dB reduction in measured gear whine noise levels at the first and second operating gear mesh frequencies.

Correlation energy contribution to nuclear masses**Communicated by Professor A Covello.

The ground-state correlation energies associated with collective surface and pairing vibrations are calculated for Pb and Ca isotopes. It is shown that this contribution, when added to those predicted by one of the most accurate modern nuclear mass formulae (HFBCS MSk7 mass formula), reduces the associated rms error by an important factor, making mean-field theory, once its time dependence is taken into account, a quantitative predictive tool for nuclear masses.

Search for pairing-vibration states of even Ca isotopes in 40Ca + 208Pb transfer reactions

Multi-nucleon transfer reactions in $^{40}$Ca+$^{208}$Pb have been studied at several bombarding energies close to the Coulomb barrier. Light reaction products have been identified in mass and charge with a time-of-flight spectrometer. The energy spectra of the inclusive two neutron pick-up channel show a population in a narrow region of excitation energies which corresponds to the predicted energy of pairing vibration states in $^{42}$Ca.

Study of giant pairing vibrations with neutron-rich nuclei

We investigate the possible signature of the presence of giant pairing states at excitation energy of about 10 MeV via two-particle transfer reactions induced by neutron-rich weakly-bound projectiles. Performing particle-particle RPA calculations on $^{208}$Pb and BCS+RPA calculations on $^{116}$Sn, we obtain the pairing strength distribution for two particles addition and removal modes. Estimates of two-particle transfer cross sections can be obtained in the framework of the 'macroscopic model'. The weak-binding nature of the projectile kinematically favours transitions to high-lying states. In the case of $(~^6He, \~^4He)$ reaction we predict a population of the Giant Pairing Vibration with cross sections of the order of a millibarn, dominating over the mismatched transition to the ground state.

Comparative analysis of actuator concepts for active gear pair vibration control

Four actuation concepts for the active suppression of gearbox housing mesh frequency vibrations due to transmission error excitation from the gear pair system are modelled and compared by computing the required actuation forces and amplifier power spectra. The proposed designs studied consist of (1) active inertial actuators positioned tangentially on the gear body to produce a pair of reactive force and moment, (2) semi-active gear–shaft torsional coupling to provide tuned vibration isolation and suppression, (3) active bearing vibration control to reduce vibration transmissibility, and (4) active shaft transverse vibration control to suppress/tune gearbox casing or shaft response. Numerical simulations that incorporate a transmission error term as the primary excitation are performed using a finite element model of the geared rotor system (dynamic plant) constructed from beam and lumped mass/stiffness elements. Several key comparison criteria including the required actuation effort, control robustness and implementation cost are examined, and the advantages and disadvantages of each concept are discussed. Based on the simulated data, the active shaft transverse vibration control scheme is identified as the most suitable approach for this application.

Low-energy monopole modes of a trapped atomic Fermi gas.

We consider the low energy collective monopole modes of a trapped weakly interacting atomic Fermi gas in the collisionless regime. The spectrum is calculated for varying coupling strength and chemical potential. Using an effective Hamiltonian, we derive analytical results that agree well with numerical calculations in various regimes. The onset of superfluidity is shown to lead to effects such as the vanishing of the energy required to create a Cooper molecule at a critical coupling strength and to the emergence of pair vibration excitations. Our analysis suggests ways to experimentally detect the presence of the superfluid phase in trapped atomic Fermi gases.

Enhanced excitation of giant pairing vibrations in heavy-ion reactions induced by weakly bound projectiles

The use of radioactive ion beams is shown to offer the possibility to study collective pairing states at high excitation energy, which are not usually accessible with stable projectiles because of large energy mismatch. In the case of two-neutron stripping reactions induced by 6He, we predict a population of the giant pairing vibration in 208Pb or 116Sn with cross-sections of the order of a millibarn, dominating over the mismatched transition to the ground state.

Coherent and chaotic properties of nuclear pairing

The properties of the pairing interaction in the shell model framework are considered with the aid of an exact numerical solution utilizing the quasispin symmetry. We emphasize the features which are out of reach for the usual approximate techniques based on the BCS approach supplemented by the random phase approximation treatment of pair vibrations, especially in the region of weak pairing where the BCS plus random-phase-approximation theory fails. Chaotic aspects of the mixing generated by the pairing interaction are studied. The level repulsion and large information entropy of the eigenstates coexist with the absence of thermalization of single-particle motion. The full spectrum of pair vibration on average displays a spin dependence similar to that for a rigid rotor.

Towards a Better Understanding of Nuclear Pairing and Its Interplay with Other Residual Interactions

Experimental evidence indicates that pairing interaction often plays a major role in determining physics of nuclear many-body systems. The goal of this work is to discuss properties of pairing in a mesoscopic nuclear environment, study the interplay of pairing and other residual interactions and develop new practical approaches. We use Sn isotopes as a testing arena. We utilize the exact solution of pairing problem based on quasispin formalism. 1), 2) This treatment of pairing (EP algorithm) is free of well-known BCS shortcomings and enables one to address fluctuating pair vibrations and chaotic effects of other residual interactions which significantly change the usual macroscopic BCS picture, 3) furthermore it provides a basis, with classification by seniority quantum numbers, that can be used for perturbatively accounting for other interactions. We demonstrate in a simple model that although in general twobody interactions do not preserve seniority, kinematics still often favors seniority conservation. The lowest seniority subspace can serve as a good starting truncation. Interactions of a non-pairing nature have only diagonal monopole contributions in this subspace. We show that this technique of exact pairing plus monopole 2) can be successful in the analysis of ground state properties of nuclei, furthermore being a well formulated variational method and part of a more general seniority truncation technique it is perfect for adjusting shell model parameters. Pairing and approximate treatment of other residual interactions can be combined through the Hartree-Fock (HF) and exact pairing (EP) technique. In Fig. 1 one-neutron separation energies are calculated for the Sn isotopes, including those beyond 132Sn. These energies were obtained from the fully self-consistent spherically symmetric solution of HF equations, using the SKX interaction, 4) with the EP solution based on renormalized G-matrix interactions from Ref. 5). The HF+EP approach can be considered as a variant of the density functional method. In this method we make an initial guess for the spherical HF potential from which the single particle energies are determined. In the valence subspace the pairing problem is solved using a fixed set of two-body matrix elements. This determines the particle distribution and pairing correlation energy. With new occupation numbers a new HF potential can be calculated. This procedure is repeated iteratively until convergence. The total energy is the sum of the Skyrme HF energy and the pairing correlation energy. Figure 1 shows an example of such calculations and exhibits an

Holmium polysulfides: crystal growth, structure and properties

Crystals of holmium polysulfides, up to 3×2×1.5 mm in size, were grown by spontaneous crystallization from melted KI. A diversity in morphology was observed from thin transparent plates to polyhedrons with mirror-like surfaces. For crystals of different forms, the composition was determined, and density as well as refractory index was measured. Several phases crystallized, two of which were characterized using single-crystal X-ray diffraction as HoS 1.885(5) (I), tetragonal, P4/ nmm, a=3.820(1), c=7.840(3) Å, V=114.40(6) Å 3, Z=2, d cal=6.542 g/cm 3 and HoS 1.863(8) (II), monoclinic P2 1/ m, a=10.961(2), b=11.465(2), c=10.984(2) Å, β=91.27(3)°, V=1380.0(4) Å 3, Z=24, d cal=6.486 g/cm 3. Raman spectra reveals the characteristic band, corresponding to S −–S − pair vibrations in the polyanionic layer. Crystals are transparent in the 0.65–25 μm spectral range, the bands with a fine structure in the transparency region being related to Ho 3+. The shortwave absorption edge is described by an exponential law (Urbach’s rule) due to tails of state density for conduction and valence bands.

GCM analysis of the collective properties of lead isotopes with exact projection on particle numbers

We present a microscopic analysis of the collective behaviour of the lead isotopes in the vicinity of Pb208. In this study, we rely on a coherent approach based on the Generator Coordinate Method including exact projection on N and Z numbers within a collective space generated by means of the constrained Hartree-Fock BCS method. With the same Hamiltonian used in HF+BCS calculations, we have performed a comprehensive study including monopole, quadrupole and octupole excitations as well as pairing vibrations. We find that, for the considered nuclei, the collective modes which modify the most the conclusions drawn from the mean-field theory are the octupole and pairing vibrations.

Collective T=0 pairing in N= Z nuclei? Pairing vibrations around 56Ni revisited

We present a new analysis of the pairing vibrations around 56Ni, with emphasis on odd-odd nuclei. This analysis of the experimental excitation energies is based on the subtraction of average properties that include the full symmetry energy together with the volume, surface, and Coulomb terms. The results clearly indicate a collective behavior of the isovector pairing vibrations and do not support any appreciable collectivity in the isoscalar channel.

Collective quadrupole excitations in transitional nuclei

The generalized Bohr Hamiltonian was used to describe the low-lying collective excitations in even-even isotopes of Ru, Pd, Te, Ba and Nd. The Strutinsky collective potential and cranking inertial functions were obtained using the Nilsson potential. The effect of coupling with the pairing vibrations is taken into account approximately when determining the inertial functions. The calculation does not contain any free parameters.

Integral Representation of the Random-Phase Approximation Correlation Energy

Using the spectral function F'(z)/F(z) the RPA correlation energy and other properties of a finite system can be written as a contour integral in a compact way. This yields a transparent expression and reduces drastically the numerical efforts for obtaining reliable values. The method applied to pairing vibrations in rotating nuclei as an illustrative example.

The low-lying quadrupole collective excitations of Ru and Pd isotopes

Quadrupole excitations of even-even Ru and Pd isotopes are described within a microscopic approach based on the general collective Bohr model which includes the effect of coupling with the pairing vibrations. The excitation energies and E2 transition probabilities observed in 104–114Ru and 106–110Pd are reproduced in the frame of the calculation containing no free parameters. Particularly interesting are 104Ru and 106–110Pd where good agreement to very rich information based on Coulomb excitation experiments is achieved.

Collective quadrupole excitations in the 50 < Z, N < 82 nuclei with the general Bohr Hamiltonian

The general Bohr Hamiltonian is applied to a description of low-lying collective excitations in even-even isotopes of Te, Xe, Ba, Ce, Nd and Sm. The collective potential and inertial functions are determined by means of the Strutinsky method and the cranking model, respectively. A shell-dependent parametrization of the Nilsson potential is used. An approximate particle-number projection is performed in the treatment of pairing correlations. The effect of coupling with the pairing vibrations is taken into account approximately when determining the inertial functions. The calculation does not contain any free parameter.

Fusion and peripheral processes in the16,18O+58,60,64Nisystems

Fusion cross section measurements for the ${}^{16,18}\mathrm{O}{+}^{58,60,64}\mathrm{Ni}$ systems, in the energy range $38&lt;~{E}_{\mathrm{lab}}&lt;~64$ MeV are presented. The standard radius deviations obtained from the data analysis, considering the zero-point motion of the nuclear surface, are compared to those associated to quadrupole and pairing vibration modes. Using the optical model analysis of the elastic data, the connection between the threshold anomaly and the subbarrier fusion enhancement is investigated.

Microscopic Description of Alpha Decay to Intruder 0(+)2 States in Pb, Po, Hg, and Pt Isotopes.

A microscopic description of the $\ensuremath{\alpha}$ decay to intruder ${0}_{2}^{+}$ states of Pb isotopes in terms of proton-neutron pairing vibrations is performed. The calculated hindrance factors with respect to $\ensuremath{\alpha}$ transitions into the ground state are in good agreement with the available experimental data. Predictions for further measurements are given. Hindrance factors corresponding to the decay towards Po, Hg, and Pt isotopes are calculated within a simple model. The calculated quantities agree well with the experimental data, indicating that $\ensuremath{\alpha}$ decay is a powerful tool to precisely determine the transition from spherical to deformed shapes in the region around $Z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}82$.