Nuclei Mode Research Articles

An exact microscopic multiphonon approach to collective modes in nuclei

We propose a method for solving the nuclear eigenvalue problem using a Hamiltonian of general form in a space spanned by multiphonon states built out of particle-hole TammDancoff phonons. The method consists in deriving for a given n-phonon subspace a set of equations of motion of simple structure, where all quantities are expressed in terms of energies and one-body density matrices determined in the (n − 1)-phonon subspace. Their solution, therefore, yields states built out of particle-hole operators applied on top of the (n−1)phonons basis states. Because of this peculiar structure, the states so generated form an overcomplete set. The redundancy, however, is removed completely and efficiently by a procedure based on the Choleski decomposition. The phonon composition of the basis states allows to remove naturally and maximally the spurious admixtures induced by the center of mass motion. The iteration of the equations from n = 0 up to an arbitrary number N of phonons generates an orthogonal basis spanning a space which is the direct sum of 0+1+..+N phonon subspaces. This basis decomposes the full Hamiltonian into N diagonal blocks plus off-diagonal terms coupling the n-phonons with the (n ± 1)and (n ± 2)-phonon subspaces. These off-diagonal terms are easily computed by recursive relations. The Hamiltonian can, therefore, be easily diagonalized by resorting to importance sampling techniques [1,2], which allow to truncate the multiphonon space while monitoring the accuracy of the solutions. The method can be easily upgraded so as to generate a particle-hole or quasiparticle RPA multiphonon basis. It is suitable for describing with high accuracy low-lying multiphonon spectra, whose experimental evidence is rapidly growing, as well as high-energy resonances like the recently discovered double dipole giant resonance. It can account with great accuracy for the anharmonicities associated to all collective modes. Last, but not least, it yields a highly correlated ground state which contains explicitly up to N particle N hole configurations and, therefore, applies to the cases where the quasiboson approximation breaks down. For illustrative purposes, we apply the method to 16O, whose low-lying states are dominated by complex configurations containing up to 4 particle 4 hole states. Such a calculation probes the extreme accuracy of the method, on the one hand, and, on the other hand, provides a complete and exhaustive information on the microscopic structure of low and high energy states in 16O.

The physical characteristics of sulfur aerosols

A review of the physical characteristics of sulfur-containing aerosols, with respect to size distribution of the physical distributions, sulfur distributions, distribution modal characteristics, nuclei formation rates, aerosol growth characteristics, and in situ measurement, has been made. Physical size distributions can be characterized well by a trimodal model consisting of three additive lognormal distributions. When atmospheric physical aerosol size distributions are characterized by the trimodal model, the following typical modal parameters are observed: 1. Nuclei mode – geometric mean size by volume, DGV n, from 0.015 to 0.04 μm. σ gn=1.6, nucler mode volumes from 0.0005 over the remote oceans to 9 μm 3 cm −3 on an urban freeway. 2. Accumulation mode – geometric mean size by volume, DGV a, from 0.15 to 0.5 μm, σ ga=1.6–2.2 and mode volume concentrations from 1 for very clean marine or continental backgrounds to as high as 300 μm 3 cm −3 under very polluted conditions in urban areas. 3. Coarse particle mode – geometric mean size by volume, DGV c, from 5 to 30 μm, σ gn=2–3, and mode volume concentrations from 2 to 1000 μm 3 cm −3. It has also been concluded that the fine particles ( D p <2 μm) are essentially independent in formation, transformation and removal from the coarse particles ( D p >2 μm). Modal characterization of impactor-measured sulfate size distributions from the literature shows that the sulfate is nearly all in the accumulation mode and has the same size distribution as the physical accumulation mode distribution. Average sulfate aerodynamic geometric mean dia. was found to be 0.48±0.1 μm (0.37±0.1 μm vol. dia.) and σ g=2.00±0.29. Concentrations range from a low of about 0.04 μg m −3 over the remote oceans to over 8 μg m −3 under polluted conditions over the continents. Review of the data on nucleation in smog chambers and in the atmosphere suggests that when SO 2, is present, SO 2-to-aerosol conversion dominates the Aitken nuclei count and, indirectly, through coagulation and condensation, the accumulation mode size and concentration. There are indications that nucleation is ubiquitous in the atmosphere, ranging from values as low as 2 cm −3 h −1 over the clean remote oceans to a high of 6×10 6 cm −3 h −1 in a power plant plume under sunny conditions. There is considerable theoretical and experimental evidence that even if most of the mass for the condensational growth of the accumulation mode comes from hydrocarbon conversion, sulfur conversion provides most of the nuclei.

NUCLEAR MATTER PROPERTIES FROM COLLECTIVE MODES IN NUCLEI

Bulk properties of nuclear matter associated with the equation of state, the nuclear matter incompressibility coefficient, Knm, in particular, are very important physical quantities required in the study of properties of nuclei, supernova collapse, neutron stars and heavy-ion collisions. Here we review the current status of Knm and the experimental and theoretical methods used to determine the value of Knm from the excitation cross-sections and the transition strength distributions of compression modes in nuclei, mainly the the isoscalar giant monopole resonance and the isoscalar giant dipole resonance.

Soft dipole mode in 17Ne and the astrophysical 2p capture on 15O

Abstract Using the two-proton-halo candidate 17 Ne as an example, we discuss the possibility of a soft-dipole mode in protonrich nuclei. The study is based on a three-body model considering 17 Ne as an 15 O core and two protons. Our calculation predicts a relatively narrow peak in the E1 strength function which exhausts a considerable part of the E1 cluster sum rule at energies only a few MeV above the 2 p threshold. We also calculate the 2 p capture cross section on 15 O at astrophysical conditions appropriate for explosive hydrogen burning in novae and X-ray bursts. Our calculation includes consistently resonant and non-resonant contributions to the astrophysical capture rate. We find that for a broad range of temperatures (including temperatures in excess of 10 9 K) the rate is dominated by non-resonant contributions.

Deducing the nuclear-matter incompressibility coefficient from data on isoscalar compression modes

Accurate assessment of the value of the incompressibility coefficient, K, of symmetric nuclear matter, which is directly related to the curvature of the equation of state (EOS), is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K as determined from experimental data on isoscalar giant monopole and dipole resonances (compression modes) in nuclei, by employing the microscopic theory based on the random-phase approximation (RPA).

06/02271 Optimal configuration of a two-heat-reservoir heat-engine with heat-leak and finite thermal-capacity: Chen, L. et al. et al. Applied Energy, 2006, 83, (2), 71–81.

The objective of this study was to evaluate the response of a suite of portable, real-time aerosol instruments to Diesel exhaust aerosol with and without a catalytic stripper (CS) to determine the change in response as a function of particle size and volatility. The response of the photoemission aerosol sensor (PAS) was strongly influenced by the physical and chemical nature of Diesel aerosol. The presence of a large, predominantly volatile nuclei mode, and/or the presence of volatile material on the surface of the solid carbonaceous agglomerates in the accumulation mode suppressed the PAS response. Removal of the volatile material by passage of the aerosol through the CS enhanced the response, and improved correlations between the PAS, the diffusion charger (DC) and the scanning mobility particle sizer (SMPS). Data on aerosol size distributions, number, volume, and surface area concentrations with and without the CS in the sample stream are reported.

Current status of equation of state of nuclear matter

The equation of state (EOS) of symmetric nuclear matter (SNM) is a very important ingredient in the study of various phenomena of interest in nuclear physics and astrophysics. Accurate assessment of the value of the SNM incompressibility coefficient, K, which is directly related to the curvature of the EOS, is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K as determined from experimental data on compression modes in nuclei using the mean-field-based random-phase approximation.

Observation of states beyond band termination in 156, 157, 158Er and strongly deformed structures in 173, 174, 175Hf

High-spin terminating bands in heavy nuclei were first identified in nuclei around 158Er90. While examples of terminating states have been identified in a number of erbium isotopes, almost nothing is known about the states lying beyond band termination. In the present work, the high-spin structure of 156, 157, 158Er has been studied using the Gammasphere spectrometer. The subject of triaxial superdeformation and ‘wobbling’ modes in Lu nuclei has rightly attracted a great deal of attention. Very recently four strongly or superdeformed (SD) sequences have been observed in 174Hf, and cranking calculations using the Ultimate Cranker code predict that such structures may have significant triaxial deformation. We have performed two experiments in an attempt to verify the possible triaxial nature of these bands. A lifetime measurement was performed to confirm the large (and similar) deformation of the bands. In addition, a high-statistics, thin-target experiment took place to search for linking transitions between the SD bands, possible wobbling modes, and new SD band structures.

The Dependency on the Dissipation Tensor of Multi-modal Nuclear Fission

In the study of the fission of actinide nuclei at low excitation energies including the spontaneous fission, it was found that the fragment mass distribution and the total kinetic energy (TKE) distribution consist of more than one component, in contrast to the simple single peak structure that is found in the fission at high excitation energies. 1– 6 This phenomenon is attributed to the existence of more than one fission path and is called the multi-modal fission. The mass and TKE distributions depend sensitively on the excitation energy and the position of the peaks of the mass distribution suggests the influence of the closed shell structure of the fragments. Therefore, it is supposed that the microscopic energy plays an important role for the manifestation of this phenomenon. It is a great challenge for us to understand this phenomenon in terms of nuclear many-body dynamics. Several authors studied the potential energy surface (PES) including the microscopic energy in a multi-dimensional parameter space that describes various nuclear shapes; one can deduce the possible fission paths by studying the location of the saddle points and the fission valleys in multi-dimensional parameter space. 7 With this method, they could explain the general trend of the position of the peaks of the mass distribution. The dynamical point of view is necessary to progress the study of the fission mode. We have applied the Langevin approach to the study of the fission modes in uranium nuclei and in fermium nuclei. 8–10 We studied the mass and TKE distributions and demonstrated that we can decompose the fission events into several components by tracing the Langevin trajectories. We also studied the isotope dependence and the excitation energy dependence of the fission mode. 8–10 In the previous studies, we adopted the wall-and-window type one-body friction as the dissipation mechanism of the nuclear fission dynamics. The validity of this dissipation mechanism has been demonstrated by one of the authors (T.W.) who studied the dissipation tensor dependence of the pre-scission neutron multiplicity and the mean TKE. 11–14 From the comparison of the results of the dynamical calculation with experimental data, they excluded the possibility of the two-body type dissipation to be the dominant mechanism by showing that it cannot reproduce the pre-scission neutron data and the TKE data simultaneously. On the other hand, they showed that the wall-and-window type one-body friction can reproduce both data reasonably well and concluded that it is a reasonable model for the dissipation mechanism of nuclear fission. There are other models that are of one-body nature, e.g. surface-plus-window formula, modified wall-and-window formula and chaos weighted wall formula. 15–17 Though there were no free parameters in the original derivation of the one-body friction, 18, 19 the strength has been modified frequently in order to reproduce some experimental data. For example, in the study of the light particle evaporation and the mass distribution, Schmitt et al. used the strength as a free parameter. 17 The modification itself should be acceptable when we take account of the simplicity of the model; it is a macroscopic model without any microscopic effect and it has no dependence on the temperature. However, when one modifies the strength of the nuclear dissipation just to reproduce only one physical quantity, it might be inappropriate to conclude that the deduced strength has definite physical meanings. It may reflect the other effects completely different from the dissipation, like the insufficiency of the model space. It is very important to compare many (at least more than one) physical quantities at the same time. Among the physical quantities that are measured in nuclear fission, the TKE and mass distributions are well investigated experimentally in many cases. In this study, we use these quantities to discuss the dissipation dependence of the fission modes. It is shown that the TKE distribution is, as was expected, directly connected to the strength of the dissipation and we can put some constraints on the strength of the dissipation. Furthermore, it is shown that the mass distribution changes rather drastically when one uses different models for the dissipation mechanism. These results demonstrate the importance and the usefulness of the dynamical approach to the study of the fission mode. Section 2 gives a concise description of our framework. Results are shown in Sec. 3 concerning the fission of 264 Fm nucleus at Ex = 20 MeV. Summary is given in Sec. 4. 2. Methods

Core excited Fano-resonances in exotic nuclei

Fano-resonances are investigated as a new continuum excitation mode in exotic nuclei. By theoretical model calculations we show that the coupling of a single particle elastic channel to closed core-excited channels leads to sharp resonances in the low-energy continuum. A signature for such bound states embedded in the continuum (BSEC) are characteristic interference effects leading to asymmetric line shapes. Following the quasiparticle-core coupling model we consider the coupling of 1-QP (one-quasiparticle) and 3-QP components and find a number of long-living resonance structures close to the particle threshold. Results for 15C are compared with experimental data, showing that the experimentally observed spectral distribution and the interference pattern are in qualitative agreement with a BSEC interpretation.

Relativistic transport approach to collective nuclear dynamics

The isoscalar giant monopole resonance (ISGMR) and isovector giant dipole resonance (IVGDR) in finite nuclei are studied within the framework of a relativistic transport approach. Small-amplitude oscillations are analyzed with the relativistic Vlasov equation, i.e., neglecting nucleon collision terms. The excitation energies of ISGMR and IVGDR are obtained for spherical nuclei with various sets of Lagrangian parameters. In the case of $^{208}\mathrm{Pb}$ we study in detail the dependence of the monopole response on the effective mass and symmetry energy at saturation ${a}_{4}$ given by the used covariant effective interaction. We show that a reduced ${m}^{*}$ and a larger ${a}_{4}$ can compensate for the effect on the ISGMR energy centroid of a much larger compressibility modulus ${K}_{\mathit{nm}}$. The role of the symmetry energy is confirmed by the observation of reduced corrections for the more symmetric $^{90}\mathrm{Zr}$. This result is important for overcoming the conflicting determination of nuclear compressibility between nonrelativistic and relativistic effective interactions. For symmetry-energy dynamical effects, we analyze the influence of the inclusion of an effective isovector-scalar channel, \ensuremath{\delta}-meson field, with constant- and density-dependent couplings. We show that the \ensuremath{\delta}-meson contribution, keeping fixed the equilibrium ${a}_{4}$ value, leads to a reduction in the centroid energy of the ISGMR and IVGDR for $^{208}\mathrm{Pb}$. The same mechanism can account for the apparent paradox of a decrease of the frequency of a IVGDR mode in heavy nuclei (of volume type) even in presence of a larger ${a}_{4}$. All that in fact reveals the sensitivity of the ISGMR and IVGDR collective motions for neutron-rich systems on the slope (or pressure) of the symmetry energy at saturation. Density-dependent vertices do not much affect our conclusions. Following as a guidance the dispersion relations in nuclear matter, we see two main reasons for that: The smoothness of the density dependences around saturation and the presence of compensation effects coming from rearrangement terms.

On-road evaluation of two Diesel exhaust aftertreatment devices

Two Diesel particulate matter emission control devices; the continuously regenerating trap ( CRT TM ) and the catalyzed continuously regenerating trap ( CCRT TM ) were evaluated using a mobile emissions laboratory. The source of emissions was the lab's engine that was fueled with 15 ppm sulfur fuel, and specially formulated, low sulfur (1300 ppm) lubrication oil. The objective was to characterize performance using real-time aerosol instrumentation, real-world dilution, and on-road driving conditions. The devices when combined with low S fuel and lube oil effectively removed Diesel particulate matter. The CRT produced large quantities of nuclei mode particles, the quantity of which increased as a function of exhaust temperature. The CCRT reduced the exhaust particle number concentration to levels not detectable above background storage sites, thus eliminating precursors that form nuclei mode particles. Use of low S fuel and lubrication oil prolongs the storage process. Over time it is expected that this material would be released.

Measurement of Electrical Charge on Diesel Particles

Nanoparticles (D p < 50 nm), which are formed as diesel engine exhaust cools and dilutes, constitute minority of total particle mass but majority of total particle number. There are several different theories to explain the nucleation of nanoparticles from diesel exhaust. The two main theories are homogeneous binary nucleation of sulfuric acid and water, and ion-induced nucleation. This study examined the ion-induced nucleation theory. In order to test the ionic nucleation theory, the charged fraction of the diesel particles were measured as a function of particle size using regular diesel fuel in this study. A very small amount of charge was found for the diesel nanoparticles in the nuclei mode, whereas there was a large charged fraction for the diesel particles in the accumulation mode. If ion-induced nucleation were the dominant mechanism for the nucleation of nanoparticles from diesel exhaust, one would expect a significant charge on the nuclei mode particles. The results from this study suggest that ion-induced binary nucleation is at least not a dominant mechanism for the nucleation of diesel exhaust when using regular diesel fuel. This study also examined the influence of metal additives on nucleation and particle charging. The metal additives examined are of the type used to enhance particle oxidation in diesel particulate filters. When used, the additives led to a large increase in the concentration of solid particles in the nuclei mode, and significantly raised the level of particle charge for particles of all sizes. When additives were used, some of the solid particles in the nuclei mode carried a charge. We believe that these metal related particles form early enough in the combustion process to be charged by ions present during and shortly after combustion.

INTRUDER LEVELS AND VIBRATIONAL MODES IN THE SD-PAIR SHELL MODEL

The influence of the intruder level on vibrational modes in atomic nuclei is examined within the framework of the nucleon-pair shell model truncated to a SD-subspace. The vibrational character of the spectra is found to depend upon the size of the active model space and not on the parity of the populated levels.

On-road and laboratory evaluation of combustion aerosols—Part1: Summary of diesel engine results

The objective was to characterize diesel exhaust aerosols on road and to duplicate the results in the laboratory without altering the physical characteristics of the nuclei mode. On-road emissions from four, heavy-duty diesel truck engines were measured. The same engines were reevaluated in the manufacturers’ laboratories. For highway cruise and acceleration conditions, all engines produced bimodal size distributions with the nuclei mode ranging in size from 6 to 11 nm and the accumulation mode from 52 to 62 nm. On-road size distribution measurements nearly always showed a nuclei mode while laboratory measurements showed a nuclei mode under many, but not all conditions. Laboratory studies showed that nuclei mode particles consisted mainly of heavy hydrocarbons. More than 97% of the volume of 12 and 30 nm particles disappeared on heating to 400 °C. The volatility resembled that of C24–C32 n-alkanes implying a significant contribution from lubricating oil.

Global modeling of aerosol dynamics: Model description, evaluation, and interactions between sulfate and nonsulfate aerosols

The IMPACT global chemistry and transport model has been updated to include an aerosol dynamics module. Here it is used to simulate the dynamics of sulfate aerosol and its interaction with nonsulfate aerosol components: carbonaceous aerosol (organic matter (OM) and black carbon (BC)), dust, and sea salt. The sulfate aerosol dynamics is based on the method of modes and moments. In the current implementation, two modes are used for sulfate aerosol (nuclei and accumulation mode), and two moments are predicted within each mode (sulfate aerosol number and mass concentration). The aging of carbonaceous aerosol and dust particles from hydrophobic to hydrophilic depends on the surface coating of sulfate which occurs as a result of the condensation of sulfuric acid gas H2SO4 (g) on their surface, and coagulation with pure sulfate aerosol. The model predicts high sulfate aerosol number concentrations in the nuclei mode (over 104 cm−3) in the tropical upper troposphere, while accumulation mode sulfate number concentrations are generally within 50–500 cm−3 in most parts of the free troposphere. The model predicted mass concentrations of sulfate, OM, BC, dust, and sea salt, H2SO4 (g) concentration, aerosol number, and size distributions are compared with measurement data. Our model predicts ∼80% of global sulfate existing as a pure sulfate aerosol (9.7% in nuclei and 69.8% in accumulation mode), with 14.3% on carbonaceous aerosol, 3.3% on dust, and 2.7% on sea salt. In the boundary layer, over 40% of sulfate is associated with nonsulfate aerosols in many regions of the world whereas less than 10% of sulfate is associated with nonsulfate aerosols in the upper troposphere. The model predicted mass fraction of sulfate in the sulfate‐carbonaceous aerosol mixture suggests that carbonaceous aerosol in most of the troposphere is internally mixed with sulfate and thus generally hygroscopic except near the source regions where the mass fraction is less than 5%. On the global mean, 54% and 93% of carbonaceous aerosol are coated with sulfate in the boundary layer and in the upper troposphere, respectively. Our result suggests that carbonaceous aerosols have a shorter lifetime (3∼4 days) than predicted (4∼8 days) using models that treat these aerosols as partly hydrophobic with an arbitrary e‐folding time from hydrophobic to hydrophilic.

Beyond band termination in 157Er and the search for wobbling excitations in strongly deformed 174Hf

High-spin terminating bands in heavy nuclei were first identified in nuclei around 158Er90. While examples of special terminating states have been identified in a number of erbium isotopes, almost nothing is known about the states lying beyond band termination. In the present work the high-spin structure of 157Er has been studied using the Gammasphere spectrometer.The subject of triaxial superdeformation and ‘wobbling’ modes in Lu nuclei has rightly attracted a great deal of attention. Very recently, four strongly or superdeformed (SD) sequences have been observed in 174Hf and ultimate cranker calculations predict such structures may have significant triaxial deformation. We have performed two experiments in an attempt to verify the possible triaxial nature of these bands. A lifetime measurement was performed to confirm the large (and similar) deformation of the bands. In addition, a high-statistics, thin-target experiment was run to search for linking transitions between the SD bands and possible wobbling modes.

Characterization of metal-bearing diesel nanoparticles using single-particle mass spectrometry

Acute and chronic health effects have been associated with diesel particulate matter (DPM). Since both ultrafine particles and metals have been implicated in this correlation, we are conducting investigations to characterize the metal content of diesel nanoparticles. For this study, DPM was generated by a 1.5 l engine and ferrocene was added to the fuel to raise the level of metal in the system. The exhaust particles were analyzed in real time using a recently developed single-particle mass spectrometer (SPMS) that has the capability of ablating each particle down to its elemental constituents, thereby yielding the relative mass of elements in each particle. Particle-size calibration of the instrument was achieved by correlating the SPMS signal intensity with measured DPM size. Using this approach, we present size- and composition-resolved elemental species distributions for both the nuclei mode and ultrafine portion of the accumulation mode of DPM. Results show that when the fuel is doped with ferrocene, iron-rich nanoparticles are formed and their number and size increase with level of doping. Larger iron-bearing particles are also formed, but it is observed that the metal to carbon ratios increase for smaller particle sizes. Hydrogen to carbon ratios were measured as a function of particle size, which allowed us to determine the relative amounts of organic carbon and elemental carbon in the particles and showed that the hydrogen to carbon ratios increase for smaller sized particles. The combined results are used to discuss the effects of metal doping level and engine load on particle nucleation and mechanisms of DPM formation.

A new dual-type DMA for measuring nanoparticles emitted from combustion engines

A new dual-type differential mobility analyzer (dual-type DMA) was developed in order to detect transient number concentrations of airborne nanoparticles with diameters centralized at around 10 nm (for nuclei mode particles) and 100 nm (for accumulation mode particles) in automobile exhaust gas. The apparatus divides the gas sample into two parts, and each part is sent through one of two coaxially nested sections for analysis. For the scanning mode measurement, the nanoparticles are charged by 241Am and their size distributions are determined by varying the applied voltage over 2 min. The transient mode measurement, on the other hand, fixes the voltages for the two sections at peaks near 10 and 100 nm in order to monitor the transient behavior of the exhaust nanoparticles. The measurement principles and design of the dual-type DMA are detailed and the results for time response experiments are presented using model nanoparticles charged by a corona charger. The transient concentrations of the nuclei mode and the accumulation mode particles from a diesel engine were shown to be detected by this method, when 241Am was used for charging the particles.

Effects of current engine strategies on the exhaust aerosol particle size distribution from a Heavy-Duty Diesel Engine

The influence of injection pressure (IP), start of injection (SOI) and exhaust gas recirculation (EGR) on the aerosol exhaust particle size distribution emitted by a state-of-the-art Heavy Duty Diesel engine was experimentally investigated. Increasing IP was found to reduce the accumulation mode particle number and favour the formation of nuclei mode particles. The application of EGR produced the suppression of the nucleation mode and an increase in the accumulation mode particle number. Advanced SOI reduced slightly the accumulation mode without variation of the count median diameter (CMD). The impact of the engine parameters on the size classes of the distributions and the sensitivity to progressive variations of the factors were examined. A correlation study showed that there is a relationship between the particle number and the CMD of the size distributions obtained at equal engine operating conditions, independently of the engine strategy applied.