Full Shell Research Articles

Signatures of Medium Effects on NN Interactions in Proton Scattering from Nuclei

Effective two nucleon (NN) interactions in the nuclear medium have been defined from an accurate mapping of NN g matrices obtained by solving the Brueckner–Bethe–Goldstone (BBG) equations for infinite nuclear matter. Those effective interactions have been used in fully microscopic calculations of proton-light nuclei (nonlocal) effective interactions from which predictions of the elastic scattering differential cross sections and analysing powers have been obtained. Results for incident proton energies of 65 and 200 MeV are considered in particular herein. The associated relative motion wave functions have been used as the distorted waves in distorted wave approximation (DWA) studies of select inelastic scattering events. The same effective interactions were used as the transition operators in those calculations. The relevant nuclear spectroscopy for the elastic and DWA (p, p′) calculations has been found from full (0 + 2)hϖ shell model evaluations of the nuclear structure; wave functions of which give good descriptions of form factors obtained from electron scattering.

Shell Model Monte Carlo Studies of gamma -Soft Nuclei.

We present Shell Model Monte Carlo calculations for nuclei within the full major shell 50-82 for both protons and neutrons. The interaction is determined solely by self-consistency and odd-even mass differences. The methods are illustrated for ${}^{124}$Sn, ${}^{128}$Te and ${}^{124}$Xe. We calculate shape distributions, moments of inertia and pairing correlations as functions of temperature and angular velocity. Our calculations are the first microscopic evidence of $\gamma$-softness of nuclei in this region.

Electron correlation, extended geminal models, and intermolecular interactions: Theory

Within this framework of extended geminal models, new and improved approximations are introduced for the calculation of electron triple pair correlation terms. There are three levels of increasing accuracy for these terms based on the coupled-cluster models: a model of single and double excitations, a model correct up to fourth order, and a model correct up to fifth order CCSD(TQ). A test calculation on the neon atom demonstrates that by adopting the CCSD(TQ) model for the triple pair correlation terms, the extended geminal model recovers 99.88% of the full CI valence shell correlation energy. To reduce the computational work involved in calculating double pair correlation terms and triple pair correlation terms, a modified set of natural orbital (NOs) is introduced. On the basis of these NOs a truncated virtual orbital space is defined. Test calculations on the neon atom, the helium dimer, and the helium trimer demonstrate that the dimension of this truncated space can be chosen to be considerably smaller than the dimension of the full virtual space at a small sacrifice in accuracy. The additive structure of the correlation terms implies that the models are appropriate for implementation on parallel processor computers. The extended geminal models have properties which make them ideally suited for describing intermolecular interactions: the models have a conceptual structure which facilitates interpretation, they can be applied for any intersystem distances, the models are size-extensive, they generate no basis set artifacts (basis set superposition errors), and the models are reliable and accurate.

The nuclear magnetic moment of by atomic beam laser spectroscopy

The magnetic dipole moment has been deduced for the nuclear ground state of the self-conjugate nucleus from the hyperfine splitting of the atomic ground state. The hyperfine structure of the 308.2 nm transition was measured by laser resonance fluorescence of an atomic beam. The tunable ultraviolet light was generated by frequency doubling using a lithium iodate crystal within the cavity of a dye laser. The result of fits well with the systematics of neighbouring -subshell nuclei and its small difference from the pure Schmidt value is satisfactorily described by a shell-model calculation in the full 2s1d shell.

Double-beta decay of 48Ca revisited

The 48Ca → 48Ti two neutrino double-beta decay rate is calculated exactly in the full fp shell with the hamiltonian describing well the spectroscopy of the A = 48 system. The resulting half-life is very near the experimental lower limit. In order to find out whether the shell model can at all accommodate longer 2 ν half-lives we modify the hamiltonian in several ways, keeping, however, the acceptable agreement with the main spectroscopic indicators intact. We conclude that, within such an approach, the longest possible half-life is about 10 20 yr, only a factor of three longer than the present limit. We stress that any possible modifications of the hamiltonian must be restricted by the comparison with available data on energy levels and transitions rates.

Gamow-Teller strength in 23Na(n,p) and a comparison to 23Na( micro-, nu ).

We report measurements of the $^{23}\mathrm{Na}$(n,p) differential cross section at an incident energy of 198 MeV and angles from 0\ifmmode^\circ\else\textdegree\fi{} to 24\ifmmode^\circ\else\textdegree\fi{} using the TRIUMF Charge Exchange Facility. From these data we determine Gamow-Teller (GT) transition probabilities to low lying 1/${2}^{+}$, 3/${2}^{+}$, and 5/${2}^{+}$ $^{23}\mathrm{Ne}$ states and the ${\mathrm{GT}}^{+}$ strength distribution up to 25 MeV excitation energy. The values of ${\mathrm{B}}_{\mathrm{GT}}^{+}$ to discrete states, and the ${\mathrm{GT}}^{+}$ strength below 10 MeV, are found to be in reasonable agreement with a full 1s-0d shell model calculation with a normalization factor of about 0.74. The ${\mathrm{GT}}^{+}$ strength above 10 MeV suggests the removal of strength from lower to higher excitation energies. We also compare the $^{23}\mathrm{Na}$(n,p) data with $^{23}\mathrm{Na}$(${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$,\ensuremath{\nu}) data and find agreement between the values of ${\mathrm{B}}_{\mathrm{GT}}^{+}$ to discrete levels extracted from the (n,p) and (${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$,\ensuremath{\nu}) reactions. The general consistency of the (n,p) and (${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$,\ensuremath{\nu}) data, and the full 1s-0d shell model calculation, give confidence in a recent extraction of the weak pseudoscalar coupling from ${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$ capture on $^{23}\mathrm{Na}$. Finally, using both ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}}$-decay and ${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$ capture data, we obtain unit cross sections from the $^{23}\mathrm{Na}$(n,p) measurement.

Development of Student Understanding: a case study of stability and lability in cognitive structure

Abstract This paper presents findings from a case study into the development of student understanding of a complex and abstract scientific concept: chemical bonding. The case study reveals significant progression in student understanding, but also highlights issues of how such progression should be addressed. Particular emphasis is given to the factors that were associated with ‘blocks’ to appropriate concept development. The learner discussed had her own ‘alternative conceptions’ of ionic charge and electrostatic attraction that, lacking the appropriate background knowledge, she used in order to make sense of chemistry. These alternative ideas blocked the development of an electrostatic framework for bonding to replace the ‘full outer shell heuristic’ used at the General Certificate of Secondary Education (GCSE) level, and had repercussions for the understanding of a range of related concepts. The importance of diagnosing learners’ alternative ideas is thus demonstrated, and some of the problems of carrying out such diagnoses are considered.

Breathing Vibrations of a Horizontal Circular Cylindrical Tank Shell, Partially Filled With Liquid

A theoretical approach to study breathing vibrations of cylindrical shells with horizontal axis, partially filled with liquid, is delineated and the results of some modal tests conducted on an industrially-manufactured tank are presented and discussed. The good agreement between theoretical and experimental results is preliminarily verified in the case of both an empty and completely full shell, in order to confirm that it is possible to apply the theoretical approach to real structures. The modal properties of a partially-filled shell as a function of liquid level are then experimentally studied, the mode shapes are compared using the Modal Assurance Criterium and a qualitative explanation of the dynamic behavior is proposed.

The vibrations of a conical shell filled with a variable volume of fluid

We consider the vibrations of a conical shell filled with a fluid. We obtain a system of differential equations that describes the interaction of a variable volume of fluid with the shell. We solve the problem of determining the natural frequencies for a completely full shell. We obtain a formula for computing the fundamental frequency as a function of the geometric parameters of the shell. One figure. Bibliography: 4 titles.

Sp(6)

The basis states generated in the sp(6)[contains]u(3) algebra of the fermion dynamical symmetry model (FDSM) are studied. The assumption made in the FDSM that the lowest-lying states of even nuclei are states with [ital u]=0 and the largest SU(3) quantum numbers is analyzed. A pairing plus quadrupole-quadrupole interaction is diagonalized for valence nucleons of the actinide region in (i) a complete basis for two protons and two neutrons, (ii) a truncated FDSM basis for 10 protons and 14 neutrons, and (iii) a strongly-coupled FDSM basis for 24 nucleons. The existence of a multiplicity of FDSM bases is taken into account. In all cases, the overlap between the truncated FDSM subspace and the full shell model space is very small for the [ital n]-identical-particle calculations. This implies that a complicated renormalization of shell model effective interactions is required before they can be used in the individual proton and and neutron spaces. However, with the proper forced choice of proton and neutron bases, a strong proton-neutron quadrupole-quadrupole interaction drives the states with the largest possible FDSM-SU(3) quantum numbers to lie lowest in energy. This leads to a rotational band structure in actinide nuclei with excited rotational bands ordered by the FDSM-SU(3) quantummore » numbers in the strong coupling limit.« less

Scaling behavior in photoelectron spectra of Ce- and Yb-based heavy fermions

The overall shape of photoelectron spectra of heavy fermion systems have been commonly analysed with the single impurity Anderson model (SIAM). We present here two studies providing direct evidences of the Kondo energy scale in the spectra. In the series CeSi x (1.6 ≤ × ≤ 2), the controlled and systematic variation of the Kondo temperature T K is reflected by the intensity evolution of the Kondo resonance around E F observed with photoemission and BIS. The typical transformation of the 4f character from itinerant to localised when temperature increases through T K is clearly observed for the nearly full 4f shell in YbAbCu 4. The spectral intensity close to E F displays the predicted temperature dependence of the Kondo resonance with its crystal field sidebands. This effect is markedly different from the conventional broadening mechanisms occurring in normal metals.

On a stress resultant geometrically exact shell model. Part VII: Shell intersections with [formula omitted]-DOF finite element formulations

If the mid-surface of a shell is smooth, the classical theory describes the orientation of the director field attached to the mid-surface by two independent (rotational) degrees of freedom. At a shell intersection, where this smoothness assumption no longer holds, it is shown that the director field in the full nonlinear continuum shell equations must be necessarily described by three degrees of freedom. This added degree of freedom, however, is totally unrelated to the so-called drill rotation, widely used as a means of tackling the shell intersection problem. A computational procedure involving a trivial modification of the global singularity-free update procedure described in Part III of this work is described, which completely resolves the shell intersection problem without introducing ‘drill springs’ or related ad-hoc devices. The proposed approach leaves unchanged standard finite element formulations in terms of 5 DOF/node, affects only the global update formulae and exhibits excellent performance, as illustrated by representative numerical simulations.

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.

Frequency-dependent conductivity, relaxation times, and the conductivity/viscosity coupling problem, in polymer-electrolyte solutions: LiClO 4 and NaCF 3SO 3 in PPO 4000

This contribution seeks to rationalize the striking differences between conductivity/mechanical responses in the salt-polymer and superionic glass extremes of the amorphous solid electrolyte field. The decoupling index, R τ, which is the ratio of structural to conductivity relaxation times and has values up to 10 14 for superionic glasses, was shown by Torell and Angell to have very small values, of order 10 −3, for salt/polymer solutions, but no clear interpretation could be provided. In the present work, we use ac conductivity and viscosity-derived mechanical relaxation times measured over wide composition ranges in systems of known ion-pair content to investigate the composition dependence of R τ, We observe systematic variations of R τ with salt concentration which go in the opposite direction from that expected from the composition dependence of ion pairing. In dilute polymer solutions, diffusing ion apparently “see” a microviscosity considerably greater than that detected by the light scattering-based longitudinal mechanical relaxation, which is, however, found to give correctly the conductivity relaxation time in aqueous systems. With increasing salt concentration the decoupling index is found to increase exponentially such that values of unity are predicted for salt contents greater than one mole per six polymer repeat units (M:O=1:6) where less than a full coordination shell of ether oxygens is available for the cation. Crude extrapolations suggest the possibility of a continuous progression from anion mobility-dominated supercoupled polymer-salt solution to cation mobility dominated, highly decoupled superionic glass, as the cation solvation sheaths are stripped away.

Study of the M1 isovector strength in 28Si

Inelastic electron scattering measurements up to 1.5 fm-1 of strong M1 transitions to the 10.900 MeV, 11.446 MeV and 12.330 MeV states in 28Si, which form the bulk of the 28Si M1 isovector giant resonance, have revealed striking differences in their transition form factors, and have allowed information on the configurations contributing to each transition to be deduced. Full 2s-1d shell model calculations have also shown large differences in the form factors of the lowest Jpi =1+, T=1 states, but do not agree, in detail, with the experimental data.

Magic numbers in molecular clusters: a probe for chemical reactivity

Abstract : When neutral van der Waals clusters, produced in a supersonic expansion, are ionized the resulting cluster ion distribution can exhibit dramatic intensity anomalies for very specific cluster sizes. These 'magic numbers' typically result from a particularly stable cluster ion geometry generated by the completion of a full solvent shell around a central ion core. In this paper we will review our current work which employs magic numbers as a probe, not only of cluster ion structure, but also of chemical reactivity within these species. That is, the appearance of certain magic numbers can be attributed to unique cluster reactions occurring between the ion and the solvating molecules within the cluster.

The effects of the spin-orbit and tensor interactions in nuclei

We devise a nucleon-nucleon interaction V c + xV so + yV t to study the effects of the spin-orbit and tensor interactions by varying x and y. For negative parity 1 p−1 h states in 16O, we find that in a TDA calculation, the weighted sum of the eigenenergies Σ J (2 J + 1) Σ i E i ( J, T) is zero for a pure two-body spin-orbit interaction or a pure tensor interaction. If a minor closed shell nucleus like 12C is taken as the core, the tensor interaction lowers the p 1 2 single-particle energy relative to p 3 2 . This is precisely opposite to what the two-body spin-orbit interaction does. For the 1 + states in 12C, a 1 p−1 h diagonalization leads to a near collapse with E ∗(T = 0) ∼ 0.9 MeV and E ∗(T = 1) ∼ 3.7 MeV as compared with experiment (12.7 MeV for T = 0 and 15.1 MeV for T = 1). Only a full scalar shell model calculation brings these states up to a respectable energy. We find that in a full shell model calculation, the excitation energies of these 1 + states are surprisingly insensitive to the spin-orbit interaction over a rather wide range of the parameter x and there does not appear to be any phase transition as we vary x. We reconsider the old problem of the effect of the spin-orbit and tensor interactions on the nearly vanishing Gamow-Teller matrix element 14C( J = 0, T = 1) → 14N( J = 1, T = 0). We calculate the single-particle energies with the same interaction that is used for the residual particle-particle or particle-hole matrix elements.

Excitation and amplification of cavity oscillations in spherically converging shells.

The stability of thin shells under arbitrary radial motions can be described by the evolution of two independent surface modes for the inside and outside shell boundaries. The evolution equations can be consistently decoupled for all mode numbers, and specific solutions for ballistic and accelerated shell motions are discussed. They show strong dependences on initial conditions and can explain significant amplification for low mode numbers by interference effects. The theory is applied to the excitation of cavity modes in accelerated high-aspect-ratio shells. By comparison with numerical solutions for the full shell equations, the validity of the analytic predictions is confirmed and the saturated oscillation amplitudes after acceleration can be estimated. The further amplification of these modes by convergence and deceleration effects is discussed and potential inertial confinement fusion applications are illustrated by a simple implosion model.

Production of the first mirror shell for ESA's XMM telescope by application of a dedicated large area replication technique

A large number of mirror shells are required for the European Space Agency's XMM telescope three mirror modules, each of which consists of 58 thin walled highly nested Wolter I mirrors. The specified performance of the XMM mirror modules requires new design concepts and application of new technologies for the production of the lightweight mirror shells. Under an ESA contract, Carl Zeiss is leading a European industrial/scientific consortium to develop technologies that allow production of real size XMM mirror shells by a dedicated metal/epoxy resin replication technique. In late 1988 the first full size XMM mirror shell was successfully replicated, having the following characteristics: total length 600 mm, maximum shell diameter 400 mm, carrier material/thickness graphite-epoxy/0.8 mm, replication layers gold/epoxy, and total replicated mirror surface 7500 cm2. The development, preparation, and mirror shell replication are described, and the first results of the performance of the mirror shell after measurements and x-ray testing are presented.

A comparison of an undecairon(III) complex with the ferritin iron core

The iron core of ferritin is comprised of up to 4,500 Fe(III) atoms as Fe 2O 3·nH 2O, which is maintained in solution by a surrounding, spherical coat of protein. Organisms as diverse as bacteria and man use the ferritin iron-protein complex as a reservoir of stored iron for other essential proteins. To extend studies of the steps in polynuclear iron core formation, a recently characterized undecairon(III) oxo-hydroxo aggregate [Fe 11 complex] (Gonin et al., J. Am. Chem. Soc. 109, 3337 [1987]) was examined by x-ray absorption spectroscopy as a model for an intermediate. The results, which are comparable to the previous x-ray diffraction studies, show near neighbors (Fe-O) at 1.90 Å that are distinct from those in ferritin and a longer distance of 2.02 Å. However, contributions from neighbors (Fe-C) known to exist at ca. 2.7 Å were obscured by a highly ordered Fe-Fe interaction and were not detectable in the Fe 11 complex in contrast to a previously characterized Fe(III) cluster bound to the protein coat. Of the two Fe-Fe interactions detectable in the Fe 11 complex, the shortest, at 3.0 Å is particularly interesting, occurring at the same distance as a full shell (CN = 6) in ferritin, but having fewer Fe neighbors (CN = 2–3) characteristic of an intermediate in core formation. The incomplete Fe-Fe shell is much more ordered than in ferritin, suggesting that the disorder in ferritin cores may be associated with the later steps of the core growth. Differences between the Fe 11 complex and the full core of ferritin indicate the possibility of intermediates in ferritin iron formation that might be like Fe 11.