Formation of covalent nuclear molecules in the 13C + 12C system

Angular distribution's of the elastic scattering of ¹³C on ¹²C and the inelastic scattering leading to the lowest-lying $\text{1}\text{2}{}^{\mathrm{+}}$ and $\text{5}\text{2}{}^{\mathrm{+}}$ states in ¹³C have been measured at energies close to the Coulomb barrier. Analyses carried out in the framework of a complete coupled-reaction-channel theory show that extremely polarized single-particle molecular orbits (hybridization) are formed during the scattering process which give rise to a multiple-step interaction of the valence nucleon, i.e. the formation of a covalent nuclear molecule.     

Three body resonances in a coupled channel ND approach

Assuming a three body channel to be dominated by the formation of bound states and resonances, the three body problem is reduced to an effective two body coupled channel problem in which pairs of particles, either bound states or resonances, scatter from the remaining third particle. We treat this effective two body problem by the partial wave matrix $\text{N}\text{D}$ method. We study in particular a coupled two channel problem, one channel consisting of one resonance plus one particle, the other of one bound state plus one particle. Our main purpose is to investigate in a full coupled channel situation the possible generation of three particle resonances. With single particle exchange forces forming the dynamical input to the $\text{N}\text{D}$ integral equations, enhancements are generated in a spinless model which correspond to three-particle resonances. The model is then applied, with spin included, to the $\text{p + p +}{}^{12}\text{C}$ system at low energy, in which ($\text{p +}{}^{12}\text{C}$) can form either the bound state ¹³N (G.S.) or the resonance ¹³N¹ (1.944 Mev); the two channels are then $\text{p +}{}^{13}\text{N(G.S.)}$ and $\text{p +}{}^{13}\text{N}{}^1$. The p-p interaction is neglected. It is found that the main effect in this case is the force arising from the coupling of the channels, which is sufficiently strong to generate a three particle level in the composite system ¹⁴O.     

Exact solution of the particle-rotor model,angular momentum spread and transition rates

The particle-plus-rotor model with valence particles in an $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ shell is solved exactly including single-particle splitting and pairing forces. Backbending and the spread of angular momentum of the valence shell is studied in detail for the two lowest bands and quadrupole transition rates are calculated.     

An equation of motion method for deriving microscopic effective interactions in a correlated model space

Starting from a diagrammatic analysis of the equation of motion method, we derive an effective interaction theory for a correlated model space where the basis vectors correspond physically to the addition of valence particles and/or holes to the true ground state of the core nucleus. The resulting effective interaction $\text{V}$ is valence linked and connected, energy independent, and contains folded diagrams. In addition, it gives directly model eigenvectors with amplitudes that correspond to spectroscopic factors. With terms having the same number of folds grouped together, the general structure of $\text{V}$ is very simple. This is very useful in the application of the present theory to actual microscopic nuclear structure calculations. The treatment of core projection insertions is discussed in some detail. A proof of the cancellation of the disconnected diagrams is given. When folded diagrams are summed up using a partial summation method, the present effective interaction theory is shown to be consistent with the usual Green function theory for many-body problems.     

Dressing up a Reissner naked singularity

Spontaneous pair creation in the field of a large Reissner singularity (a point-like charge e whose mass M is such that $\text{MG}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{< e}$) is here considered. Using as a guide the definition of the positive and negative energy states of a classical particle in this field, a particular basis of quantum states is chosen which contains resonance states — these are interpreted by invoking particle creation. Extremely energetic particles are shown to burst out to infinity whereas the antiparticles dress up and neutralize the singularity. This result is contrasted with the process of pair production by black holes and compared with the isotropization of the early universe by creation of matter.     

Electronic structure of the GeGaAs (111) and (111) heterojunctions

The electronic density of states for GeGaAs (111) and ($\text{1}$$\text{1}$$\text{1}$) heterojunctions has been calculated. No interface states in the fundamental gap are found. A sizeable density of interface states below the top of the valence band is found for GeGa bonds-(111) junctions-interface states in the ionic gap are reported. The effect of varying the amount of the valence band discontinuity across the interface is discussed.     

Quantum gravitational bubbles

Spacetime is expected to have a “foamlike” structure on scales of the Planck length or less with high curvatures and complicated topology. This foam can be thought of as being built out of three basic kinds of units or “gravitational bubbles”, CP², S² × S² and K3. We investigate the propagation of particles in simple models of the first two types of bubble. The non-trivial topologies of the bubbles introduce extra singularities into the Green functions. These make large contributions to the S-matrix for scalar particles but only small contributions for $\text{spin}\text{-}\text{1}\text{2}$ or 1 particles at energies small compared to the Planck length. These results suggest that there is no inconsistency between the spacetime foam picture and everyday observations from which spacetime appears nearly flat, because all the elementary particles we have observed have spin $\text{1}\text{2}$ or greater. They do, however, suggest that Higgs scalar fields, if they exist at all, are probably bound states of higher spin particles rather than being elementary fields. Further developments may enable one to calculate processes in which quantum coherence is lost and intrinsic entropy is produced.     

Scattering from nonoverlapping potentials. III. Pion elastic scattering on 4He in the 3,3 region

The $\text{π}{}^{\mathrm{?}}{}^4\text{He}$ elastic scattering in the 3,3 resonance region is discussed in the framework of the nonoverlapping potentials model. Single and double scattering terms are considered together with their modification by reflection terms, which allow the projectile to oscillate back and forth an arbitrary number of times within a pair of nucleons. Reflections and spin and isospin flips are found to constitute a determining factor in a qualitative reproduction of the correct shape of observed angular distributions, in particular for backward scattering angles. Reflections are probably unimportant in πd scattering.     

Coupled-reaction-channel approach for molecular orbital phenomena of valence nucleons in heavy-ion collisions: The 12c + 13c system

A complete coupled-reaction-channel method is applied to molecular orbital phenomena of the valence nucleon in the scattering of ¹²C on ¹³C, i.e. in elastic and inelastic transitions to the single-particle states of ¹³C¹(gr., $\text{1}\text{2}{}^{\mathrm{?}}$ ; 3.086 MeV, $\text{1}\text{2}{}^{\mathrm{+}}$ ; 3.854 MeV, $\text{5}\text{2}{}^{\mathrm{+}}$) with consi ¹²C core-exchange process. The system is analyzed with respect to the occurrence of higher-order transitions of the direct (inelastic) and transfer (core-exchange) processes of the valence nucleon in ¹³C. It is found in the states of positive total parity that the transfer and direct processes act additively and lead to extreme higher-order steps of the multi-interactions, if the ground state (1p_{$\text{1}\text{2}$}) and the excited states (2s_{$\text{1}\text{2}$} and 1d_{$\text{5}\text{2}$}) are taken into account. Transitions between the excited subchannels show strong-coupling effects, which are due to the reorientations of the d_{$\text{5}\text{2}$} orbitals. The reoriented system couples to the ground channel (l-parity mixing) so favourably that the multi-interaction series hardly converges. The consequence of these observations are discussed in terms of the formation of molecular nucleon orbitals based on the polarization and the hybridization of the original orbitals.     

Hole mobility in p-type HgTe

Experimental data concerning the electrical conduction and Hall coefficient in HgTe samples with acceptor states have been collected and analysed. In the analysis three ranges of acceptor concentration have been distinguished: a low concentration range up to about 5 × 10¹⁵ cm^?3 (pure samples), a high concentration range from 10¹⁶ to 10¹⁸ cm^?3 (p-like samples), and an extremely high concentration range above 10¹⁸ cm^?3 (p-type samples). In pure HgTe samples the holes are in the valence band, in p-like samples the “holes” are in the impurity band, and in p-type HgTe samples the holes are in a strong mixing impurity-valence band. The mobility of holes in the valence band is of the order of $\text{10}{}^5\text{cm}{}^2\text{Vs}$. The mobility of “holes” in the impurity band decreases with increasing impurity concentration from about $\text{5 × 10}{}^3\text{cm}{}^2\text{Vs}$ to $\text{125}\text{cm}{}^2\text{Vs}$. The mobility of holes in p-type HgTe samples is independent of the acceptor concentration and is equal to $\text{125}\text{cm}{}^2\text{Vs}$.     

On the left-hand cut in potential scattering

Partial wave $\text{N}\text{D}$ equations in potential scattering are solved for the exponential, Hulthén and Morse potentials. The driving terms are taken to be either the contributions of a finite number of Born terms or the total contributions of only the nearest singularities (first n poles). For repulsive potentials one observes ghosts, anomalous bound states or resonances if the order of approximation is small with respect to the potential strength. The origin and meaning of these unphysical phenomena are explained. For attractive potentials such anomalies occur only at very large potential strengths if at all. Input-equivalent Bargmann potentials are employed to determine the quality and nature of the approximate $\text{N}\text{D}$ solutions. Rough criteria for the validity of approximations within the $\text{N}\text{D}$ approach are formulated.     

The anisotropy of the hot-hole drift velocity in Ge

This paper presents a microscopical interpretation of the anisotropy of the hot-hole drift velocity in Ge at 77°K. The theory makes use of the Monte Carlo technique in solving the Boltzmann equation and is based on a single valence band model (the heavy mass one) warped and parabolic. The theoretical calculations carried out in a general form show that: (i) the anisotropy of the hot-hole drift velocity originates from the warping of the valence band structure; (ii) the strong interaction of holes with optical phonons via emission processes plays a fundamental role in the anisotropy supporting the reliability of the streaming motion model first suggested by Pinson and Bray.The comparison between theory and experiment at 77°K in Ge is satisfactory for the whole range of fields examined $\text{(50 ? E ? 10}{}^4\text{V}\text{cm}\text{)}$, confirming the basic validity of the present approach. The importance of optical and acoustic scattering mechanisms have been found comparable, the coupling strength ratio $\text{w}{}_{\mathrm{op}}\text{w}{}_{\mathrm{ac}}$ assuming the value 1.36.     

Structure of high-spin states in 143Pm

High-spin states of ¹⁴³Pm have been studied in the reactions ¹⁴¹Pr(α, 2n)¹⁴³Pm and ¹⁴³Nd(d, 2n)¹⁴³Pm by means of in-beam spectroscopy. The level scheme, spin and parity assignments are based on results obtained from singles γ-ray spectra, conversion electron spectra, prompt and delayed γ-γ coincidences, γ-ray angular distribution and linear polarization measurements. Positive- and negative-parity states with energies up to 4580 keV and spins up to $\text{25}\text{2}$ have been established including 22 new levels. For two nanosecond isomeric states the nuclear spin precession in an external magnetic field was observed providing the following g-factors:

$\text{g(}\text{11?}\text{2}\text{, 959.7 keV)=1.14(9), g(}\text{15+}\text{2}\text{, 1898.3 keV)=1.00(7).}$

The experimental results are well understood by calculations which have been performed in the framework of the shell model (for positive-parity states of 11 valence protons above a Z = 50, N = 82 core) and of the cluster-vibration model (for 3 holes in a Z = 64, N = 82 core). In the case of positive-parity states no evidence for particle-core coupling could be found, while the negative-parity states could qualitatively be understood within the particle-core coupling picture.     

Splitting the degeneracy of harmonically-bound identical spinless bosons: General derivation

The Gartenhaus-Schwartz model of N particles interacting via pairwise harmonic potentials $\text{V}{}_{\mathrm{ij}}\text{=}\text{1}\text{2}\text{kR}{}_{\mathrm{ij}}{}^2$ is extended by addition of an arbitrary pairwise interaction small enough to be treated by degenerate perturbation theory. The theory is worked out for a rarefied fluid of N spinless bosons, to give the splittings of the degeneracies of the U(3N?3) symmetry inherent in the Gartenhaus-Schwartz model. Following Moshinsky and Kramer the external field is formally introduced in order to reduce the zeroth-order problem to the 3N-dimensional harmonic oscillator. For systems with more particles than quanta, a recipe is given to construct states in which all the excitation is in internal degrees of freedom and none is in translation. Analytical solutions are obtained for states with no more than two quanta in excitation of relative motion of any one pair of particles.     

The (α, α), (α, α′) and (α, 3He) reactions on 12C at 139 MeV

The nucleus ¹²C was bombarded with 139 MeV α-particles to study the characteristics of the elastic, inelastic, and (α, ³He) reactions. An optical model analysis of the elastic data yielded a unique family of Woods-Saxon potential parameters with central real well depth V ≈ 108 MeV, and volume integral $\text{J}\text{4A}\text{≈ 353}\text{MeV}\text{·}\text{fm}{}^3$. By comparing the present results with those of other studies above 100 MeV, we find that the real part of the α-nucleus interaction decreases with increasing energy; the fractional decrease with energy is roughly one-half that observed for proton potentials. Using the optical potential parameters derived from the elastic scattering, first-order DWBA calculations with complex first-derivative form factors reproduced the inelastic scattering data to the 4.44 MeV (2⁺) and 9.64 MeV (3^?) states of ¹²C. For the 0⁺ state at 7.65 MeV it was necessary to employ a real, second-derivative form factor to fit the data. The deformation lengths β_lR_m and deformations β_l obtained in this and other experiments are summarized and compared. DWBA calculations using microscopic model form factors were also performed for the 2⁺ and 3^? states using the wave functions of Gillet and Vinh Mau. These reproduced the shapes and relative magnitudes of the differential cross sections. We also fit the shape of the 0⁺ differential cross section using a microscopic form factor which contains a node, which is similar to that occurring in the collective model second-derivative form factor. In the ($\text{α,}{}^3\text{He}$) reaction the differential cross sections to the ground state ($\text{1}\text{2}{}^{\mathrm{?}}$) and the 3.85 MeV ($\text{5}\text{2}{}^{\mathrm{+}}$) state in ¹³C could not be reproduced by zero-range local DWBA stripping calculations; it was necessary to employ finite-range and non-local corrections in the local-energy approximation. This DWBA analysis is notable in that unambiguous optical potentials were available for both entrance and exit channels. The ground state spectroscopic factor is in agreement with the prediction of Cohen and Kurath, while the relative spectroscopic factors agree fairly well with the rather few existing measurements of this kind.     

High-resolution measurements of analogue states in 55Co

Differential cross sections were measured at four angles for proton elastic and inelastic scattering on ⁵⁴Fe at energies from 3.25 to 4.0 MeV by means of a high-resolution beam. An overall resolution of 400 eV was realized using thin solid targets. Spins, parities and partial widths were extracted for all resonances observed: two p-wave, one f-wave and one g-wave analogue state, all of them being fragmented and identified in the elastic and inelastic data. Spectroscopic factors and Coulomb displacement energies were obtained for these analogue states. The γ-ray angular distributions and resonance strenghts were measured on the $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ resonances to determine rates of the IAR-AIAS M1 transition and the El transitions to the low-lying states including the g.s.     

The velocity distribution and the density near a particle of an equilibrium two component plasma

The electronic and ionic velocity distributions and densities of an equilibrium two component plasma at distances from a test particle (electron or ion) smaller than the interparticle distance, are derived using a technique developed recently by the author. In the case of particles repelled by the test particle the results agree with the results obtained by integrating the Gibbs distribution. In the case of particles attracted by the test particle however, the velocity distribution has the form of a translated maxwellian with an empty sphere in the middle and the asymptotic form of the density as r → 0 is given by n_a(r) ～r^{$\text{-1}\text{2}$}. By the latter formula the classical problem of stability of matter is locally resolved without using short distance repulsive potentials.