Equilibrium Deformation Research Articles

Probing the shapes of hot nuclei with the GDR

A study of the angular distribution of the high energy γ rays emitted by the giant dipole resonance (GDR) in the compound nuclei 165–167Er, 175,176Hf and 109,110Sn at a variety of excitation energies (E∗ = 50–90 MeV) is presented. A comparison of the data with model predictions at the equilibrium deformation and in the adiabatic limit is discussed. In general, the adiabatic calculations give a fair account of the data exception made for Er at very low spin and Sn at very high spin.

Neutron emission as a clock and thermometer to probe the dynamics of fusion-fission and quasi-fission

A compilation of currently available data on pre-scission neutron multiplicities shows clearly that the excitation energy in the fission fragments hardly increases with bombarding energy. This can be explained if fission is always a slow process, whilst evaporation becomes more and more rapid. The neutron clock-thermometer is introduced as a tool to deduce the dynamical timescale for fusion-fission, giving (35±15)×10−21 s. Quasi-fission is faster than fusion-fission because the equilibrium deformation is never reached (the mononucleus is thought to be always very deformed) thus fragment temperatures are higher, and the strong variation of vpre with TKE shows that a significant number of neutrons are emitted while the fragments are accelerating after scission. This appears not to be the case for fusion-fission. The fall in vpre for asymmetric mass-splits suggests that the dynamical time scale is shorter: this will influence fission mass-distributions.

Transient phenomena in dispersive mixing

The deformation and breakup processes of single droplets in well-defined fields of flow have been extensively studied in the literature. In spite of the fact that in real mixers the conditions are far from equilibrium, most studies are confined to (Newtonian) systems undergoing almost stationary deformation. The transient character of the dispersive mixing process is much less documented. In a Plexiglas-walled Couette-apparatus, the time-dependent deformation of Newtonian droplets into extended threads has been studied When the shear rate is very slowly increased, allowing for almost equilibrium deformation, the results of the critical capillary number Ca crit as a function of viscosity ratio, as reported in the literature, are reproduced. However, in transient flows at capillary numbers Ca>> Ca crit, droplets are deformed into long slender bodies which continue to extend, until the shear has stopped. They then disintegrate into lines of droplets because of interfacial tension-driven disturbances. The time scale for deformation and breakup is important for a better understanding of the dispersive mixing process, e.g., during polymer blending in screw extruders.

Charge and mass characteristics of the fragments in the fission of uranium isotopes induced by 12C ions

238U, 235U and 233U were irradiated with 85, 90 and 100 MeV 12C ions to measure the fission-product nuclei radiochemically and elucidate the feature of the heavy-ion-induced fission of actinides in comparison with that of the light-ion-induced fission. Charge dispersion curves constructed with the observed isobaric triplets were concluded to have an equal width σ = 1.05 ± 0.10 irrespective of the target nuclides and incident energies within the error, which turned out to coincide with that of the energetic proton fission of 238U. The deduced charge distribution was then analyzed to suggest the fissioning nucleus that once reached the saddle follows essentially the identical fate as light-ion fission even if the behavior during the course from equilibrium deformation to the saddle might be different from each other. The width of the obtained mass-yield distribution was found to decrease as energy increases. This, with other observations, strongly suggests that the broad single-gaussian distribution generally accepted for heavy-ion fission should be replaced by a double-gaussian distribution: the separation of the centroids reduces as energy increases.

Thomas-Fermi approach to nuclear-mass formula

Abstract We summarize the main features of the first nuclear-mass table to be based entirely on microscopic interactions. A semi-classical approximation to the HF-BCS method is adopted, with full Strutinsky shell corrections included. The 9 parameters of the underlying Skyrme and δ-function pairing forces are fitted to all 1492 mass data for A ⩾ 36; the r.m.s. error of this fit is 0.730 MeV. Our tabulation covers the range 36 ⩽ A ⩽ 300, goes out to the neutron-drip line and extends beyond the proton-drip line. Equilibrium deformations of all nuclei are calculated, with axial symmetry assumed. We also calculated several fission barriers using the same force with no further adjustment of parameters; a satisfactory agreement with experiment is obtained.

A sensitive measure of surface stress in the resting neutrophil

The simplest parameterized model of the "passive" or "resting receptive" neutrophil views the cell as being composed of an outer cortex surrounding an essentially liquid-like highly viscous cytoplasm. This cortex has been measured to maintain a small persistent tension of approximately 0.035 dyn/cm (Evans and Yeung. 1989. Biophys. J. 56:151-160) and is responsible for recovering the spherical shape of the cell after large deformation. The origin of the cortical tension is at present unknown, but speculations are that it may be an active process related to the sensitivity of a given cell to external stimulation and the "passive-active" transition. In order to characterize further this feature of the neutrophil we have used a new micropipet manipulation method to give a sensitive measure of the surface stress as a function of the surface area dilation of the highly ruffled cellular membrane. In the experiment, a single cell is driven down a tapered pipet in a series equilibrium deformation positions. Each equilibrium position represents a balance between the stress in the membrane and the pressure drop across the cell. For most cells that seemed to be "passive," as judged by their spherical appearance and lack of pseudopod activity, area dilations of approximately 30% were accompanied by only a small increase in the membrane tension, indicative of a very small apparent elastic area expansion modulus (approximately 0.04 dyn/cm). Extrapolations back to zero area dilation gave a value for the tension in the resting membrane of 0.024 +/- 0.003 dyn/cm, in close agreement with earlier measures. A few cells showed virtually no change in cortical tension and fit the persistent cortical tension model of Evans and Yeung (1989. Biophys. J. 56:151-160). However, other cells that also appeared "passive," as judged by their spherical appearance, had membrane tensions that increased as the apparent surface area was increased. Thus, the postulated,persistent "cortical tension" does not appear to be a unique and constant parameter for all cells as the membrane area is dilated.This measurement of membrane tension could represent a sensitive indication of the first stages of cell activation and the"passive-active" transition.

Viscoplasticity characteristics of heat-resisting steels in a multiaxial stress state

Results are presented of the experimental examination of the viscoplastic properties of 15Kh2MFA, 15Kh2NMFA, and VK2 (KP-100) heat-resisting steels simulating radiation-embrittled 15Kh2NMFA steel, at different ratios of the main stresses in the temperature range 20–350°C, carried out using a specially prepared method. The experimental results are used to draw conclusions according to which the generalized quasistatic (equilibrium) deformation diagram, obtained at a strain rate tending to zero, is invariant to the type of stress state, and also that the toughness factors of the examined steels are invariant to the type of stress, state and cumulated plastic strain in the entire temperature range examined.

Symmetries of the nuclear average field hamiltonian and a search for possible exotic equilibrium deformations in superdeformed nuclei

Symmetry properties of the general average-field hamiltonian-matrix resulting from the geometrical symmetries of the hamiltonian itself are derived and discussed. The corresponding numerical algorithms are constructed. Total energy calculations for superdeformed nuclei are then extended to include the usually neglected deformation modes α λ = 3 μ ≠ 0 in the expansion of the nuclear surface expression R(ϑ, ϕ; {α}) = c ({α}) R 0 1+ ∑ λ ∑ μ=−λ λ α λμ ∗Y λμ(ϑφ) . The general trends in the shell-energy dependence on α λ = 3 μ and the implied instabilities in the superdeformed configurations of the rare earth nuclei are studied using the Strutinsky formula with the macroscopic part taken in the form of the folded-Yukawa plus exponential interaction. A possibility of new (double superdeformed minimum) structures coexisting in some nuclei and resulting from the proton shell effects is predicted and illustrated. No signficant neutron effects are found in the rare superdeformed nuclei considered.

Reflection-asymmetric shapes in odd- A actinide nuclei

Single-particle states in odd- A actinide nuclei with 86 ≤ Z ≤ 91 and 129 ≤ N ≤ 139 were calculated using the reflection-asymmetric mean field approach with an average Woods-Saxon potential and a monopole pairing residual interaction. Good agreement was found between experimental and calculated band heads. We find that strong polarization effects due to the odd nucleon explain systematic trends of known one-quasiparticle states. Configuration dependence of equilibrium deformations and coexistence of reflection-symmetric and reflection-asymmetric shapes are discussed.

High- j bands in 173Ir

High-spin states in rotational bands associated with the 11 2 −[505] , 1 2 −[541] and 1 2 +[660] Nilsson orbits have been observed in the previously unknown 173Ir nucleus using the 144Sm( 32S,p2n) reaction at 163 MeV. The B(M1; I → I − 1)/ B(E2; I → I −2) ratios have been extracted for the 11 2 −[505] band and compared with predictions of the semiempirical model by Dönau and Frauendorf. The quasineutron band crossing frequencies and alignment gains are discussed in terms of the CSM model. Calculations for equilibrium deformations suggest different deformations for the three bands observed.

Effect of the type of stress state on the micromechanisms of failure of maraging steels during equilibrium deformation

Fractographic and microstructural results are presented on the equilibrium failure of samples made of maraging steel, including those carrying stress concentrators of various form. It has been shown that it is possible to trace the actual micromechanism of failure of ductile materials during the growth and development of microcracks in terms of the stress state.

Nuclear equilibrium shapes nearA=100

Nuclear equilibrium shapes in the regionA=100 are studied in the context of the cranked shell model. Many nuclides with large equilibrium ground state deformations are found. Equilibrium deformations atI=20 are typically found to be substantially reduced.

Analysis of a theory of elasticity for masonry solids

A n analysis of a theory of plane elasticity for materials with negligible tensile strength is presented. We show that, when viewed in the context of finite elasticity, this theory furnishes equilibrium deformations that are unstable according to the energy criterion. The equations of equilibrium are shown to be hyperbolic in certain sectors of the principal strain plane. These conclusions contradict predictions based on the existing infinitesimal displacement theory.

Anomalous signature-dependence of rotational bands in odd-A nuclei explained in terms of gamma vibration.

The anomalous signature-dependence of proton ${\mathit{h}}_{11/2}$ rotational bands in $^{155,157}\mathrm{Ho}$, $^{159}\mathrm{Tm}$, $^{161,163,165}\mathrm{Lu}$ after the first band crossing is described in the framework of a model of particles plus symmetric rotor. We take into account rotor's degree of freedom that it undergoes \ensuremath{\gamma} vibration about an axially symmetric equilibrium deformation. By using a set of moments of inertia such that the largest one is around the shortest axis, the essential features of all the energy spectra are reproduced. We have calculated magnetic dipole and electric quadrupole transition strengths with the wave functions obtained, and have found that virtually every characteristic feature of the available experimental data is well reproduced.

Equilibrium deformations and excitation energies of single-quasiproton band heads of rare-earth nuclei

Noncollective single-proton states in odd-Z (Eu, Tb, Ho, Tm, Lu, Ta, Ir and Au) rare-earth nuclei have been calculated using the shell correction method with an average Woods-Saxon potential and a monopole pairing residual interaction. Calculated equilibrium deformations of the lowest single-proton states are presented, and calculated band head excitation energies are compared with experimental proton band heads for odd-Z rare-earth nuclei. Good agreement is found between the experimental and calculated band heads. We find that strong polarisation effects due to the odd proton explain many of the systematic trends of known band heads. Different deformation driving forces of the odd-proton orbitals can also partly explain deviations seen in high-spin data. Shape co-existence effects in Ir and Au isotopes are discussed. In addition, equilibrium deformations of even-even rare-earth nuclei are computed and compared with experimental values.

Equilibrium deformations and excitation energies of single-quasiproton band heads of rare-earth nuclei

Noncollective single-proton states in odd- Z (Eu, Tb, Ho, Tm, Lu, Ta, Ir and Au) rare-earth nuclei have been calculated using the shell correction method with an average Woods-Saxon potential and a monopole pairing residual interaction. Calculated equilibrium deformations of the lowest single-proton states are presented, and calculated band head excitation energies are compared with experimental proton band heads for odd- Z rare-earth nuclei. Good agreement is found between the experimental and calculated band heads. We find that strong polarisation effects due to the odd proton explain many of the systematic trends of known band heads. Different deformation driving forces of the odd-proton orbitals can also partly explain deviations seen in high-spin data. Shape co-existence effects in Ir and Au isotopes are discussed. In addition, equilibrium deformations of even-even rare-earth nuclei are computed and compared with experimental values.

Momentum distributions in axially symmetric deformed nuclei: The Nilsson model

We study velocity distributions in deformed nuclei within the Nilsson model. We analyse the condition of isotropy in momentum space as an equilibrium condition. We show results for Ne and Nd isotopes and discuss properties of overall and single-particle momentum distributions in these nuclei. We find that at the equilibrium deformation obtained with the Strutinsky method the overall momentum distribution is isotropic, or nearly isotropic, provided that ΔN ≠ 0 admixtures are taken into account in the diagonalization of the Nilsson hamiltonian. We also analyse the dependence on deformation of the single-particle and overall momentum distributions averaged over angle. We find that the dependence on the deformation of the mean field is much stronger for the single-particle momentum distributions than for the global momentum distributions. The latter are shown to be similar for spherical and deformed nuclei at equilibrium.

Indentation stiffness of young canine knee articular cartilage—Influence of strenuous joint loading

The indentation stiffness of knee articular cartilage subjected to strenuous physical training (SPT: treadmill running 20 km day −1 for 15 weeks, n = 6) of young Beagles was tested and compared to that obtained from age-matched (55 weeks, n = 9) controls. The mathematical solution for the shear modulus, as determined from indentation of an elastic layer bonded to a rigid half space, was extended to small Poisson's ratios and applied to the analysis of cartilage response after a step stress (0.39 MPa) application. In these measurements with an impervious, plane-ended indenter, the equilibrium deformation was systematically greater than values predicted from the instant response by the linear biphasic theory. Therefore, the accurate determination of Poisson's ratio from the creep curves was not possible. The mean shear modulus (calculated by using the deformation at 900 s after load application and assuming a constant Poisson's ratio of 0.40 for the matrix) of canine knee articular cartilage was 0.37 MPa. While the cartilage thickness was not affected by SPT, the cartilage of the lateral tibial plateau was stiffer (13.3%, p<0.05) than that in controls. However, in the femoral condyles, the stiffness was at the control level or even below. Our results on cartilage structure and properties suggest that SPT, in contrast to our previous findings with moderate training, does not necessarily improve the biological properties of articular cartilage in young animals.

Interplay between proton and neutron S-bands in the Xe-Ba-Ce-region

Two-quasiparticle bands of positive parity (S-bands) in even-even nuclei in the Xe-Ba-Ce region are systematically examined. The equilibrium deformations for the ground-state band as well as for proton and neutron ( h 11 2 ) 2 configurations are obtained from total routhian surface (TR-surfaces) calculations. By comparing systematic trends of calculated and experimental crossing frequencies, attempts are made to assign the various bands as having an ( h 11 2 ) 2 neutron or proton character, respectively.

Shape fluctuation as responsible for signature inversion.

The problem of signature inversion is studied by using a model of particles coupled to a rotor. We have assumed an axially symmetric equilibrium deformation and taken into account the \ensuremath{\gamma} vibration around it. The calculated signature dependence is found inverted in agreement with the experimental data if we adopt a set of moments of inertia which favor the rotation around the shortest axis, but not if we employ the set of the irrotational-flow model.