Single-particle Unit Research Articles

Alpha decay measured in single-particle units as a manifestation of nuclear collectivity

A salient feature of quantum mechanics is the inherent property of collective quantum motion, when apparent independent quasiparticles move in highly correlated trajectories, resulting in strongly enhanced transition probabilities. To assess the extend of a collective quantity requires an appropriate definition of the uncorrelated average motion, often expressed by single particle units. A well known example in nuclear physics is the Weisskopf unit for electromagnetic transitions which reveals different aspects of collective motion. In this paper we define the corresponding single particle unit for alpha decay as induced by four uncorrelated/non-interacting protons and neutrons. Our definition facilitates an unified description of all alpha decay processes along the nuclear chart, revealing a simple mass dependence. The comparison of the uncorrelated decay rates with the experimentally observed ones, shows a significant enhancement of the decay rates pointing towards collective alpha like correlations in the nuclear ground state. As a limiting case, the formalism presented here is applied to proton decay revealing its single particle nature.

Constitutive model of metal matrix composites at high strain rates and its application

Particle reinforced metal matrix composites (PRMMCs) frequently undergo impact or shock loading during routine utilization. However, studies on the dynamic response of PRMMCs are currently insufficient compared with those on the quasistatic response. In this study, the multi-particle representative volume element (RVE) models were established to comprehensively investigate the influence of particle parameters (particle content and aspect ratio) on the dynamic behavior of PRMMCs, and a modified dynamic constitutive law was proposed to describe the dynamic mechanical behavior of PRMMCs more efficiently based on the concept of particle breakage probability. The verification results show that the dynamic stress–strain behaviors predicted by the RVE models agree better with the experimental data than those predicted by single-particle unit cell (RUC) models. Furthermore, the results predicted by the modified dynamic constitutive law agree well with the corresponding experimental data because the effect of particle breakage was included in the modified dynamic constitutive law. This paper provides the necessary guidance for the development and preparation of the particle reinforced metal matrix composites.

Super- and Subradiant Lattice Resonances in Bipartite Nanoparticle Arrays.

Lattice resonances, the collective modes supported by periodic arrays of metallic nanoparticles, give rise to very strong and spectrally narrow optical responses. Thanks to these properties, which emerge from the coherent multiple scattering enabled by the periodic ordering of the array, lattice resonances are used in a variety of applications such as nanoscale lasing and biosensing. Here, we investigate the lattice resonances supported by bipartite nanoparticle arrays. We find that, depending on the relative position of the two particles within the unit cell, these arrays can support lattice resonances with a super- or subradiant character. While the former result in large values of reflectance with broad lineshapes due to the increased radiative losses, the latter give rise to very small linewidths and maximum absorbance, consistent with a reduction of the radiative losses. Furthermore, by analyzing the response of arrays with finite dimensions, we demonstrate that the subradiant lattice resonances of bipartite arrays require a much smaller number of elements to reach a given quality factor than the lattice resonances of arrays with single-particle unit cells. The results of this work, in addition to advancing our knowledge of the optical response of periodic arrays of nanostructures, provide an efficient approach to obtain narrow lattice resonances that are robust to fabrication imperfections.

Application of different plasticity models to PC/ABS blends within micromechanical approaches

AbstractRubber‐toughened thermoplastic polymers such as PC/ABS blends exhibit a non‐monotonic dependence of fracture toughness on composition, e.g. [6]. The key parameters determining the mechanical response of PC/ABS are the PC vs. ABS ratio and the rubber content in ABS. In this contribution, two micromechanical modeling approaches (single particle unit cell models, random representative volume elements) are considered to investigate this behavior. Thereby, different visco‐plasticity models are utilized to capture the specific deformation behavior of each phase. Computational studies of both micromechanical modeling approaches are compared to each other as well as to experimental data.

Elastic Property Simulation of Nano-particle Reinforced Composites

A series of numerical micro-mechanical models for two kinds of particle (cylindrical and discal particle) reinforced composites are developed to investigate the effect of microstructural parameters on the elastic properties of composites. The effects of both the degree of particle clustering and particle’s shape on the elastic mechanical properties of composites are investigated. In addition, single particle unit cell approximation is good enough for the analysis of the effect of averaged parameters when only linear elastic response is considered without considering the particle clustering in particle-reinforced composites.

Numerical simulation of the influence of particle clustering on tensile behavior of particle-reinforced composites

The spatial distribution of reinforcement particles significantly influences the tensile behavior of particle-reinforced composites. In this study, the role of particle clustering on the macroscopic and microscopic behavior of these composites in the absence of damage was numerically investigated. An infinite material containing a periodic distribution of clustered, elastic, spherical particles was modeled using a unit cell approach. Three types of multi-particle unit cells were simulated with different arrangements of clustered particles as well as different cluster densities. The uniaxial stress–strain curves in tension were compared with the curves obtained from single-particle unit cell simulations. It was shown that clustering of particles increases the plastic strain accumulated in the matrix and slightly increases the work hardening rate. More importantly, it was observed that while the influence of the particle distribution on the overall behavior of the composite was not significant in uniaxial tension, the maximum principal stress inside the particles is acutely sensitive to the particle cluster morphology.

Multinucleon transfer studies in 12C+88Sr

Abstract vhoice Cross sections for multinucleon transfer reactions are measured at several angles in the reaction 88 Sr( 12 C,X) - X ranging from 9 Be to 14 C at an incident carbon-ion energy of 87.5 MeV. In case of single-nucleon transfer reactions, the measured angular distributions of cross sections in transition to the ground and low-lying states in the 87,89 Sr and 89 Y nuclei are described well in terms of finite-range DWBA calculations. The transfer probability obtained from the experiments to well-defined shell-model orbits forms the single-particle unit for evaluation of the mechanism in multinucleon transfer reactions. The analysis reveals a small enhancement of the transfer probability corresponding to a proton-pair stripping. The mechanism of one-step “direct” transfer of a cluster is predominant in deuteron and 3 He transfer reactions. However, the transfer of a neutron pair seems to proceed through a sequential transfer of two neutrons.

Comparison of magnetic dipole excitations in the f7/2 shell region with the new collective excitations in 156Gd.

It is noted that in a single j shell (f/sub 7/2/) calculation in the titanium isotopes one obtains M1 rates of about one single particle unit in strength to states at about 4 MeV excitation. This is systematically consistent with the recently discovered collective excitations in /sup 156/Gd, and neighboring nuclei. In the single j shell case, though, the spin and orbital contributions to the M1 matrix element are nearly the same.

Properties of 11.05 MeV state in 14N

The gamma decay of Ep = 3.77 MeV resonance in 13C(p,γ)14N has been measured. From the measured excitation functions, the natural width of the resonance was deduced to be 1.2 ± 0.4 keV. The resonance is found to strongly populate the 3.945 MeV level, in addition to the gs transition. Gamma angular distribution measurements determined the resonance spin as 3+. The reduced proton width is found to be 0.5% of the single particle unit. The transition strengths are measured to be B(E2) = 0.45 ± 0.07 and 3.0 ± 0.8 Wu for transitions to ground state and the level at 3.945 MeV, respectively.

Coulomb excitation of Yb nuclei

Multiple Coulomb excitation measurements have been performed with $^{16}\mathrm{O}$ projectiles on $^{168,170,172,174,176}\mathrm{Yb}$, Measured $\ensuremath{\gamma}$-ray yields were compared to the Winther-deBoer calculations in order to extract $B(E2)$ and $B(E3)$ values to vibrational and rotational states. The ${2}^{+}$ member of the $\ensuremath{\gamma}$-vibrational band was observed in all the nuclei, the ${4}^{+}$ member in three cases, and excited ${0}^{+}$ states in $^{168,170,172,174}\mathrm{Yb}$. The $B(E2;{0}^{+\ensuremath{'}}\ensuremath{\rightarrow}{2}^{+})$ values from ${0}^{+}$ states at 1228 keV in $^{170}\mathrm{Yb}$ and 1154 keV in $^{168}\mathrm{Yb}$ are in excess of one single-particle unit, the first such cases observed in Yb nuclei. $B(E3)$ values to octupole states were deduced for $^{172,174}\mathrm{Yb}$. Members of the ground state rotational band up to $I=8$ were excited in each nucleus. The measured yield of the ${8}^{+}$ state relative to that of the ${6}^{+}$ level is compared to calculations and discussed for the five nuclei studied.NUCLEAR REACTIONS $^{168,170,172,174,176}\mathrm{Yb}$($^{16}\mathrm{O}$, $^{16}\mathrm{O}^{\ensuremath{'}}\ensuremath{\gamma}$), $E=58\ensuremath{-}62$ MeV; measured $\ensuremath{\sigma}(E)$, ${I}_{\ensuremath{\gamma}}$. $^{168,170,172,174,176}\mathrm{Yb}$ deduced levels, $J$, $\ensuremath{\pi}$, $B(E2)$, $B(E3)$. Enriched targets; Ge(Li) detector.

The E5 Transition in 117Snm

In 117 Sn m an E 5 γ transition between the 314.2 keV (11/2 - ) and the ground (1/2 + ) states was observed by using a Compton suppression spectrometer. Its branching ratio was found to be (4.9±1.1)×10 -6 . A B ( E 5) value obtained here is (2.9±0.6)×10 4 e 2 fm 10 . An effective charge of the E 5 γ transition was deduced to be (0.23±0.03) e in Weisskopf estimate. This is of the same magnitude as those in 113 Cd m and 123 Te m . In the single particle unit the effective charge was obtained to be (0.089±0.010) e by using the 1 h 11/2 and 3 s 1/2 wave functions deduced from the Woods-Saxon potential. A core polarization charge due to the 5 - state at 2367 keV in 116 Sn was calculated to be 0.11 e , by taking into accounts of the effects due to the pairing.

α-Particle Decays of the 12.15-MeV State inNe20

The fractional branch for $\ensuremath{\alpha}$-particle decay of the 12.15-MeV ${6}^{+}$ state in $^{20}\mathrm{Ne}$ to the 6.13-MeV ${3}^{\ensuremath{-}}$ state in $^{16}\mathrm{O}$ has been measured by coincident detection of 6.13-MeV $\ensuremath{\gamma}$ rays and $\ensuremath{\alpha}$ particles from the reaction $^{12}\mathrm{C}(^{12}\mathrm{C},\ensuremath{\alpha})^{20}\mathrm{Ne}$. The measured width ratio, $\frac{{\ensuremath{\Gamma}}_{{\ensuremath{\alpha}}^{\ensuremath{'}}}}{\ensuremath{\Gamma}}=(6.0\ifmmode\pm\else\textpm\fi{}1.5)%$, together with the previously known quantity $\frac{{\ensuremath{\Gamma}}_{{\ensuremath{\alpha}}^{\ensuremath{'}}}{\ensuremath{\Gamma}}_{\ensuremath{\alpha}}}{\ensuremath{\Gamma}}=7.7\ifmmode\pm\else\textpm\fi{}3.8$ eV, implies a ground-state width of ${\ensuremath{\Gamma}}_{\ensuremath{\alpha}}=128\ifmmode\pm\else\textpm\fi{}72$ eV. The corresponding reduced width is about ${10}^{\ensuremath{-}3}$ of a single-particle unit: This value is consistent with the known small $\ensuremath{\alpha}$-particle reduced widths for the ${0}^{+}$, ${2}^{+}$, and ${4}^{+}$ states which have been suggested to be members of a rotational band built on an 8p-4h intrinsic state.

Gamma transition studies of 125Sb from the decay of 9.7 min l25mSn

Gamma transitions of 125Sb from the decay of 9.7 min 125mSn have been studied with Ge(Li) detectors and angular correlation measurements for five cascades have been performed by using a multicounter goniometer. The lifetime of the first excited state has been determined by the βγ delayed coincidence method as T 1 2 = 163 ± 10 ps. The internal conversion coefficient of the first to ground state transition has been found to be α k = 0.018 ± 0.005 by using a Si-Ge(Li) conversion coefficient spectrometer. The value of B(E2) obtained for the 332 keV transition is 0.02 e 2·. b 2, which is 1.1 times as large as the single-particle unit. The present experimental results are compared with the intermediate coupling model for 125Sb.

The l = 3 and 4 transitions in inelastic scattering of protons from 66Zn

Elastic and inelastic scatterings of protons from 66Zn have been studied at 55.01 MeV incident energy. Scattered protons have been analysed and detected by a broad-range magnetic spectrometer with a 200 proportional counter system. No strongly excited states have been observed in the excitation energy E x > 6 MeV. Angular distributions are analysed in terms of the DWBA method. In addition to the well-known first 2 + and 3 − states, six l = 3 transitions with reduced transition rates of 2 ∼ 1 in a single particle unit are observed for excitation energies in the 4.1–5.7 MeV region. Two l = 4 transitions are also observed for excitation energies of 3.08 and 4.70 MeV.

Evaluation of E0 pair transitions

Formulae, tables and graphs are presented for the extraction of the E0 matrix element from the electron pair transition rate taking into account the Coulomb field of the emitting nucleus. A single-particle unit suitable for measuring the strength of such transitions is defined and recommended.

RareE2Transition inC13

By means of a coincidence method it is shown that the $\frac{5}{2}+$ state of ${\mathrm{C}}^{13}$ at 3.86 Mev has an $E2$ branch of relative strength (9.3\ifmmode\pm\else\textpm\fi{}2.0)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ to the \textonehalf{}+ state at 3.09 Mev. From consideration of the likely strengths of the competing $E1$ transition to the $\frac{3}{2}\ensuremath{-}$ state at 3.68 Mev and the $M2$ transition to the ground state it is deduced that this branching ratio implies an $E2$ transition speed of the order of a single-particle (proton) unit. This in turn demands the substantial participation of at least one excited state of ${\mathrm{C}}^{12}$ in the parentage of at least one of the ${\mathrm{C}}^{13}$ states with respect to the $1d$ or $2s$ neutron. This eliminates in particular a $\mathrm{jj}$-coupling description of ${\mathrm{C}}^{13}$ in which the two states in question are $1{d}_{\frac{5}{2}}$ and $2{s}_{\frac{1}{2}}$ neutron states and more generally a weak-coupling model in which the ground state of ${\mathrm{C}}^{12}$ is the unique parent for the ${\mathrm{C}}^{13}$ states (with respect to $1d$ and $2s$ neutrons).