Single-particle Width Research Articles

EFECTO DE LA RENORMALIZACIÓN DEL FACTOR ESPECTROSCÓPICO EN EL DECAMIENTO DEL 212Po

In the present work, we use the complex-energy shell model formalism to describe the alpha decay of the 212Po nucleus. Single-particle bases constructed from Woods-Saxon potentials are used to build many-body basis. Spin-isospinGaussian effective interaction between all pairs of nucleons is considered. Four-body spectroscopic factor and single-particle width are calculated. The stability of the spectroscopic factor renormalization protocol is demonstrated, thus ensuring its physical significance, and its influence on the calculated alpha decay is presented. It is observed that the renormalization modifies the calculated half-life by∼40 %, which is a value three times larger than the experimental. Still, without appealing to any cluster structure from the beginning, i.e., all calculations were carried out using single nucleon degree of freedom.

Widths of P26(1+) and mass of P26(g.s.)

For the ${1}^{+}$ first-excited state of $^{26}\mathrm{P}$, the lifetime and the upper limit on the proton width have been combined with shell-model spectroscopic factors to place an upper limit on the proton single-particle (sp) width. With a potential model, this limit on sp width allows an upper limit on the ${1}^{+}$ resonance energy of ${E}_{\mathrm{r}}<124\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$. Combining with the known ${1}^{+}$ excitation energy provides a limit on the proton separation energy of $^{26}\mathrm{P}(\mathrm{g}.\mathrm{s}.)$ of ${S}_{\mathrm{p}}>40\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$, considerably better than a recent result of ${S}_{\mathrm{p}}>\ensuremath{-}135\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$ from a similar procedure that used $R$-matrix sp widths.

Identification of Dewetting Stages and Preparation of Single Chain Gold Nanoparticle Rings by Colloidal Lithography

Massively parallel nanoparticle assembly was carried out by means of colloidal lithographic experiments over a silicon substrate supported (sub)microparticle Langmuir-Blodgett monolayer, using high purity aqueous solution of PEGylated gold nanoparticles. The size of the polystyrene template particles in the monolayer was varied between 608 nm and 2.48 μm, while gold nanoparticles with diameters between 18 and 65 nm were used. Thanks to the PEGylation of the gold nanoparticles, they could be used as tracer objects to follow the drying process. In this way, different dewetting stages could be identified in the confined space between and underneath the template polystyrene spheres. Depending on the concentration of the nanoparticles, the presented approach allows the preparation of single-particle width necklace structures composed of gold particles. At the same time, the high purity of the substrate as well as of the evolved particle rings is preserved and unwanted particle deposition on the substrate surface is minimized.

Determination of theN=16Shell Closure at the Oxygen Drip Line

The neutron unbound ground state of (25)O (Z=8, N=17) was observed for the first time in a proton knockout reaction from a (26)F beam. A single resonance was found in the invariant mass spectrum corresponding to a neutron decay energy of 770_+20(-10) keV with a total width of 172(30) keV. The N=16 shell gap was established to be 4.86(13) MeV by the energy difference between the nu1s(1/2) and nu0d(3/2) orbitals. The neutron separation energies for (25)O agree with the calculations of the universal sd shell model interaction. This interaction incorrectly predicts an (26)O ground state that is bound to two-neutron decay by 1 MeV, leading to a discrepancy between the theoretical calculations and experiment as to the particle stability of (26)O. The observed decay width was found to be on the order of a factor of 2 larger than the calculated single-particle width using a Woods-Saxon potential.

Structure of polydisperse electrorheological fluids: Experiment and theory

Macroscopic properties of electrorheological (ER) fluids are often determined by the spatial arrangement of the suspended particles. We investigate the microstructure of polydisperse ER fluids at low concentrations in a DC electric field. Optical microscopy reveals that the particles with polydispersity in size or in both size and dielectric property are mixed in stable single particle width chains, showing different spatial arrangement. This qualitatively agrees with the theoretical results obtained from an energy approach based on the finite element analysis. Thus, it seems possible to achieve various microstructures and hence desired macroscopic properties of ER fluids, by choosing appropriate polydispersity.

Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes.

Using electrodynamics calculations, we have discovered one dimensional array structures built from spherical silver nanoparticles that produce remarkably narrow ( approximately meV or less) plasmon resonance spectra upon irradiation with light that is polarized perpendicular to the array axis. The narrow lines require a minimum particle radius of about 30 nm to achieve. Variations of the plasmon resonance wavelength, extinction efficiency and width with particle size, array structure, interparticle distance and polarization direction are examined, and conditions which lead to the smallest widths are demonstrated. A simple analytical expression valid for infinite lattices shows that the sharp resonance arises from cancellation between the single particle width and the imaginary part of the radiative dipolar interaction.

Many-body approach to proton emission and the role of spectroscopic factors

The process of proton emission from nuclei is studied by utilizing the two-potential approach of Gurvitz and Kalbermann in the context of the full many-body problem. A time-dependent approach is used for calculating the decay width. Starting from an initial many-body quasistationary state, we employ the Feshbach projection operator approach and reduce the formalism to an effective one-body problem. We show that the decay width can be expressed in terms of a one-body matrix element multiplied by a normalization factor. We demonstrate that the traditional interpretation of this normalization as the square root of a spectroscopic factor is only valid for one particular choice of projection operator. This causes no problem for the calculation of the decay width in a consistent microscopic approach, but it leads to ambiguities in the interpretation of experimental results. In particular, spectroscopic factors extracted from a comparison of the measured decay width with a calculated single-particle width may be affected.

Anisotropic Agglomeration of Surface-Modified Gold Nanoparticles in Solution and on Solid Surfaces

Anisotropic agglomeration of gold nanoparticles (diameter ca. 6 nm) was induced in aqueous media by modifying the particle surface with various organic thiols. The structural anisotropy of the agglomerates in solution depended on the type of the modifying reagents. Scanning tunneling microscopic images of the agglomerates transferred on gold (111) surfaces show that the agglomerates on the gold surface formed dot-interconnected lines with a single particle width. The length of the dot-interconnected lines was much longer on the surface than that in solution.

Static Yield Stress of Electrorheological Fluids

The electrorheological properties of suspensions consisting of inorganic shell/organic core composite particles dispersed in a silicone oil were studied by the use of a stress-controlled rheometer. On application of electric fields, the suspensions show a striking increase in steady-shear viscosity. Since the constant stress is generated within the limit of zero shear rate, the plateau in the flow curve corresponds to the Bingham yield stress. When the stress does not exceed the yield value, the suspensions are expected to behave as elastic solids. However, even at stresses less than the Bingham yield stress, the suspensions show viscoelastic relaxation or plastic response with an infinite relaxation time. The development of yield stress in steady shear (dynamic yield stress) can be derived from the single-chain model in which the particles all align into fully developed chains of single-particle width and equal spacing. However, the ideal model cannot explain the appearance of static yield stress as a critical point, below which no flow can be observed and above which the substance is a liquid with a plastic viscosity. The creep experiments indicate that the static yield stress may be controlled by the chain structure at strains of about 0.4. The transition of column structure from the body-centered tetragonal lattice to another metastable configuration is reasonably consistent with the experimental findings.

Creep behavior of electrorheological fluids

Composite particles consisting of a polymer core and an inorganic shell were formed by suspension polymerization. For suspensions in a silicone oil, the steady-shear viscosity and creep behavior were measured in electric fields up to 2.0 kV mm−1. Although the polymer core is not ER active, the suspensions of composite particles show a striking increase in the steady-shear viscosity and the flow curve changes from Newtonian to Bingham profiles. The ER effects can be attributed to the shell layers on the polymer surfaces. The creep curves at low stresses are composed of instantaneous elastic, retarded elastic, and viscous regions. With increasing stress the retarded elastic and viscous components decrease. At some critical stress the strain almost instantaneously increases and reaches the equilibrium without viscous flow. After the removal of the critical stress, the suspensions show no elastic recovery. Therefore the creep and recovery behavior is purely plastic and the critical stress corresponds to the static yield value. The application of stresses above the static yield value causes the suspensions to flow. The development of yield stress (plateau value) in steady shear can be derived from the ideal chain model in which the particles all align into chains of single particle width and equal spacing. However, the model cannot predict the instantaneous deformation without recovery below the yield stress. The thick column formed by several chains may be responsible for purely plastic responses.

Single-particle 2d5/2 strength in the 48Ca

The neutron total cross section of /sup 48/Ca+n has been measured up to 10 MeV and analyzed up to 4 MeV using the R-matrix formalism to obtain resonance parameters and potential scattering phase shifts. Very little s-wave neutron strength was observed, and the small cross section (0.5 +- 0.2 b) observed for low-energy neutrons (<150 keV) can be described by a real Woods-Saxon potential with V/sub 0/ = 47.3 +- 0.7 MeV, r/sub 0/ = 1.21 fm, and a = 0.66 fm. Three strong d/sub 5/2/ resonances amounting to 45% of the single-particle width were found in the 0.8- to 2.0-MeV energy region. These results compare well with cross-section predictions from two microscopic calculations. The p/sub 1/2/, p/sub 3/2/, and d/sub 3/2/ resonance strengths are very weak (much smaller than the d/sub 5/2/ strength).

Experimental evidence for dinuclear structure ofO16+C12resonances in the Coulomb barrier region

The total reaction cross section ${\ensuremath{\sigma}}_{R}$ for $^{16}\mathrm{O}$ + $^{12}\mathrm{C}$ has been determined between 8.5 and 14 MeV (c.m.) from elastic data using the optical theorem. It exhibits the well-known $^{16}\mathrm{O}$ + $^{12}\mathrm{C}$ resonances as pronounced structures. Elastic partial widths have been deduced from ${\ensuremath{\sigma}}_{R}$ for all resonances. Some of them represent a large fraction of the single particle width. This is a strong hint that the corresponding resonances have the structure of a dinuclear molecule.NUCLEAR REACTIONS $^{12}\mathrm{C}$($^{16}\mathrm{O}$,$^{16}\mathrm{O}$), $^{12}\mathrm{C}$($^{16}\mathrm{O}$,$^{12}\mathrm{C}$), $E=8.5\ensuremath{-}15$ MeV (c.m.), $\ensuremath{\Delta}E=85$ keV; measured $\ensuremath{\sigma}(\ensuremath{\theta}, E)$, deduced total reaction cross section and quasimolecular resonances and their elastic widths.

Spectral functions and hole nuclear states

An explicit expression for the spectral function of hole nuclear states is given in the framework of the coherent fluctuation model. It is shown that the spectral function and single-particle width, centroid energy, quasiparticle effective mass, etc., are functionals of the ground-state nucleon density distribution. Calculation of the spectral functions for58Ni,40Ca,28Si is carried out and the results are compared with the experimental data.

Single particle states in nuclei

We present a simple model for the single particle width, viewed as resulting from two-body collisions in a nuclear medium. Special emphasis is put on the features that are really needed in order to obtain the deviations of the mass operator from its Hartree-Fock values: the available phase space for particle-hole excitations, off-shell behaviour and consistent treatment of both real and imaginary parts. In several previous models or calculations, these features were not all present simultaneously. The single particle widths are also related to the width of collective excitations.

E1 isobaric analogue resonances of strongly deformed nuclei in (e, e′p) reactions

The cross sections of the (e, e′p) reaction on the deformed nuclei 159Tb, 165Ho, 169Tm, 175Lu and 181Ta have been measured in the vicinity of the ground isobaric analogue state. Resonances corresponding to the E1 isobaric analogue states are found and displacement energies are calculated from these resonances. These energies are smaller than those obtained from proton scattering, which shows their dependence on the reaction type. The radiative widths of the E1 transitions of the isobaric analogue resonances were obtained. The ratio of these to the single-particle width calculated with the Nilsson model is order of 0.1–1 for non-spin-flip transitions and more than 10 2 for spin-flip transitions. These results are similar to those of the spherical nuclei 139La, 141Pr, 207Pb and 209Bi.

Analysis of α-decay widths of light 4 n nuclei

Previous analyses of the α-widths of the ground state band of 20Ne are extended to most data for 20Ne, 16O, and 12C. The simple prescription that the spectroscopic factor is the ratio of the observed width to the single particle width calculated by a Woods-Saxon potential, is re-examined using R-matrix theory. Especially, the effects of antisymmetrization, the energy shift correction, and the energy dependence of the hard sphere scattering phase shift are taken into account. For narrow resonances the simple prescription gives good results, while for broad resonances the two latter effects are found important. We obtained a new formula for the spectroscopic factor which depends on the choice of the channel radius. The optimum value of the channel radius is also discussed. For levels whose nature is well known, we obtained generally good agreement with shell model predictions. For levels whose nature is not well known, the extracted spectroscopic factors are used to identify the band structure.

Extraction of spectroscop1c factors from isobaric analogue resonances with strong inelastic background

Abstract In cases for which the inelastic background is small, the proton partial width for populating an isobaric analogue state by scattering from a particular state of the target (channel) is proportional to the spectroscopic factor for stripping a neutron in the same state of the target to form the parent of the analogue state. The constant of proportionality is the single-particle width. In this paper it is shown that for cases for which the inelastic background is large, then the proton partial width for populating the analogue state is a linear combination of these spectroscopic factors for populating the analogue state through these strongly coupled channels. The matrix which couples the channels is obtained by solving a coupled-channels program for the proton wave function.

Isobaric Analog Resonances from Proton Scattering on the Barium Isotopes

With barium isotopes of mass 130, 132, 134, 136, and 138 as targets, proton elastic scattering excitation functions have been obtained at several angles. In the proton energy range 7.0-12.0 MeV, we observed several resonances which correspond to isobaric analogs of the low-lying states of the target-plus-neutron systems. The resonance data have been analyzed to extract proton elastic widths, total widths, and resonance energies. Spectroscopic factors have been extracted by comparing the measured proton elastic widths with the single-particle widths calculated on the basis of a shell-model description of the analog state. The spectroscopic factors so determined are compared with those from the $\mathrm{Ba}(d,p)$ reaction to the parent analog states. The variation of single-particle width with the parameters of the bound-state neutron well has been investigated. From the analog resonance energies and the $Q$ values for the parent states in $\mathrm{Ba}(d,p)$ reactions, the Coulomb shifts of the principal resonances have been found.

Isobaric analog resonances in the lead region

The isobaric analog states of the ground and low-lying levels of 205Pb, 207Pb and 208Pb were studied as compound-nucleus resonances in 205Bi, 207Bi and 208Bi by bombarding isotopically enriched targets of 204Pb, 206Pb and 207Pb with protons in the energy range of 11.00–16.00 MeV. The resonance parameters have been determined by fitting the elastic-scattering excitation functions with optical-model plus isolated-resonance expressions. The elastic-scattering partial widths of the 9 2 + analogs of the odd-lead isotopes and the elastic and inelastic partial decay widths of the analog of the ground state of 208Pb are compared with single-particle width estimates determined from a realistic, diffuse-edged potential model. The sensitivity of the single-particle width estimates to the well parameters is discussed. The off-resonance yields to the 5 2 − , 0.570 MeV state of 207Pb and the 2 +, 0.899 MeV state of 204Pb have been determined to be principally due to Coulomb excitation in the region of the ground state analogs of 205Pb and 208Pb. Destructive interference between the Coulomb excitation and resonance processes is observed in the large-angle yields to the latter two states. Striking elastic and inelastic-scattering systematics are seen in the formation and decay of the 9 2 + analogs of the odd-lead isotopes and in the decay of the related 5 − and 4 − analogs of 208Pb. Coulomb displacement energies and their isotope shifts deduced from the 9 2 + analogs are compared with the predictions of the uniform charge model as well as with a more detailed calculation using shell-model orbitals.

Coupled-Channels Calculation of the Elastic and Inelastic Scattering of Protons by Carbon-12

The elastic scattering of protons by ${\mathrm{C}}^{12}$ exhibits the following resonances with an appreciable fraction of the single-particle width: ${E}_{p}=0.461$ MeV (${s}_{\frac{1}{2}}$), 1.748 MeV (${d}_{\frac{5}{2}}$), and $\ensuremath{\approx}6.7$ MeV (${d}_{\frac{3}{2}}$). A narrow ${d}_{\frac{5}{2}}$ resonance is observed at 4.808 MeV and an anomaly in the ${d}_{\frac{3}{2}}$ phase shift at $\ensuremath{\approx}5.3$ MeV. It is demonstrated by means of a coupled-channel calculation that these last two features are due to the resonance in the inelastic channel (${\mathrm{C}}^{12*}+p$) corresponding to the 0.461-MeV $s$-wave resonance in the elastic channel. The experimental $s$- and $d$-wave phase shifts and damping parameters are accurately reproduced after adjustment of the depth of square-well potentials. The coupled-channel calculation also demonstrates that a resonance may be switched from one channel to another by changing the strength of the coupling.