Multistage radiation-stimulated changes in the microhardness of silicon single crystals exposed to low-intensity β irradiation

Radiation-stimulated and postradiation changes in the microhardness of silicon single crystals exposed to irradiation with a low-intensity flux of β particles (I = 9 × 10⁵ cm^?2 s^?1, W = 0.20 + 0.93 MeV) are studied. It is established that the inversion of the radiation-induced plastic effect occurs at a characteristic irradiation time τ_c = 75 min; i.e., irradiation of silicon single crystals for a time τ < τ_c leads to nonmonotonic reversible hardening, whereas nonmonotonic reversible softening is observed under irradiation for a time τ > τ_c. It is demonstrated that there exists a correlation between the nonmonotonic dependences of the microhardness and the concentration of electrically active defects at acceptor levels with energies E _c ? 0.11 eV, E _c ? 0.13 eV, and E _c ? 0.18 eV on the irradiation time.     

N.M.R. dipolar echoes in solids containing spin-1/2 pairs

The proton echo responses to resonant 90°-τ-β_90° (XY) and 90-τ-β_0° (XX) pulse sequences in powdered crystalline hydrates are reported. The echo produced by the XY sequence consists of two components: one is proportional to sin² β and the other to sin² β cos² β; the former component decays much faster than the latter on increasing the pulse spacing τ. In contrast, the XX sequence produces a single component echo of the form - sin² β cosβ. The maximum echo amplitudes for the sequences 90°-τ-90°_90° and 90°-τ-54°44′_0° exhibit a gaussian dependence on τ² over at least 95 per cent of their decays. The decay constant for the 90-τ-90°_90° echo corresponds to M ₂(inter) = 5/6 M ₂ ^vv(inter), where M ₂ ^vv(inter) is the interpair second moment calculated by the van Vleck procedure. These observations can be explained in terms of a simple model consisting of a planar arrangement of two spin-1/2 pairs provided the interpair dipolar hamiltonian is truncated so that [?^o _a(intra) + ?^{o, t} _d(inter), ?_z] = 0 and [?^o _a(intra), ?^{o, t} _d(inter)] = 0.

The model predicts the echo behaviour only if the spin-1 character of the eigenfunctions of ?^o _d(intra) + ?_z is preserved in the presence of the interpair interactions. It is shown that the XX echo and the sin² β cos² β components of the XY sequence originate solely in the interpair interactions and contain no contributions from the intrapair interactions. The decay of the maximum echo amplitude with increasing τ is caused by the incomplete refocusing of the interpair interactions by the XX and XY sequences; the correct decay is only determined provided the interpair dipolar hamiltonian is correctly truncated. The model also accounts for the proton echo behaviour in solid hydrogen reported by Metzger and Gaines.

Interestingly, the N.M.R. behaviour observed for these spin-1/2 pair systems is largely determined by the eigenfunctions of the spin Hamiltonian with M_z = 0.     

Calculation of the correlation time for motional narrowing of the 181Ta Mössbauer line due to hydrogen diffusion

The correlation time for motional narrowing of a Mössbauer resonance line (¹⁸¹Ta) by hydrogen diffusion has been calculated by applying the random walk theory. The correlation times τ_c are 12.546 541τ and 3.756 711τ for tetrahedral and octahedral occupancies, respectively, where τ is the mean residence time of a hydrogen atom.     

Photoinduced semiconductor-metal phase transition in a peierls system

The dynamical equation for the order parameter of the metal-semiconductor phase transition, as well as the kinetic equation for the density of nonequilibrium electron-hole pairs of a Peierls system in a light field, has been derived. An expression for the time τ of the nonthermal photoinduced semiconductor-metal phase transition has been obtained from these equations for the case of an ultrashort light pulse. It has been shown that, to initiate the phase transition, the energy density W of the light pulse must be higher than the critical value W _c. The W _c, τ, and optical absorption coefficient γ₀ that are calculated in the framework of the proposed model are in agreement with the experimental data (W _c ≈ 12 mJ/cm², τ ≈ 75 fs, and γ₀ ≈ 10⁵ cm^?1) on the irradiation of a vanadium dioxide film by a laser pulse with a duration of τ_p ≈ 15 fs, a photon energy of ?θ₀ = 1.6 eV, and an energy density of W = 50 mJ/cm².     

Conductivity of Wigner liquid

The conductivity of two-dimensional electron systems with low carrier concentration is considered on the basis of the previously suggested model (Fermi liquid with a soft mode) under the assumption that the equilibrium in each of the (fermion and boson) subsystems is established faster than the impurity relaxation and the relaxation between the subsystems (hydrodynamic approximation). The conductivity of the system depends on three characteristic times: τ₁(τ₂) is determined by the fermion (boson) impurity scattering and τ₁₂ is determined by the friction between the subsystems; the respective temperature dependences are obtained. The conductivity is related to the relaxation time τ in the usual way, and τ obeys the relationship τ^?1=τ ₁ ^?1 +(τ₂+τ₁₂)^?1. It follows from the results obtained that the resistivity of pure samples should increase with temperature and tend towards saturation.     

Theoretical methods for the calculation of Bragg curves and 3D distributions of proton beams

The well-known Bragg-Kleeman rule R _CSDA = A ⋅ E has become a pioneer work in radiation physics of charged particles and is still a useful tool to estimate the range R _CSDA of approximately monoenergetic protons with initial energy E ₀ in a homogeneous medium. The rule is based on the continuous-slowing-down-approximation (CSDA). It results from a generalized (nonrelativistic) Langevin equation and a modification of the phenomenological friction term. The complete integration of this equation provides information about the residual energy E(z) and dE(z)/dz at each position z(0 ≦ z ≦ R _CSDA). A relativistic extension of the generalized Langevin equation yields the formula R _CSDA = A ⋅ (E ₀ + E/2M ⋅ c ²)^p. The initial energy of therapeutic protons satisfies E ₀ ≪ 2M ⋅ c ²(M ⋅ c ² = 938.276 MeV), which enables us to consider the relativistic contributions as correction terms. Besides this phenomenological starting-point, a complete integration of the Bethe-Bloch equation (BBE) is developed, which also provides the determination of R _CSDA, E(z) and dE(z)/dz and uses only those parameters given by the BBE itself (i.e., without further empirical parameters like modification of friction). The results obtained in the context of the aforementioned methods are compared with Monte-Carlo calculations (GEANT4); this Monte-Carlo code is also used with regard to further topics such as lateral scatter, nuclear interactions, and buildup effects. In the framework of the CSDA, the energy transfer from protons to environmental atomic electrons does not account for local fluctuations. Based on statistical quantum mechanics, an analysis of the Gaussian convolution and the Landau-Vavilov distribution function is carried out to describe these fluctuations. The Landau tail is derived as Hermite polynomial corrections of a Gaussian convolution. It is experimentally confirmed that proton Bragg curves with E ₀ ≧ 120 MeV show a buildup, which increases with the proton energy. This buildup is explained by a theoretical analysis of impinging proton beamlets. In order to obtain a complete dose calculation model for proton treatment planning, some further aspects have to be accounted for: the decrease of the fluence of the primary protons due to nuclear interactions, the transport of released secondary protons, the dose contribution of heavy recoil nuclei, the inclusion of lateral scatter of the primary and secondary protons based on Molière’s multiple-scatter theory, and the scatter contributions of collimators. This study also presents some results which go beyond proton dose calculation models; namely, the application of the relativistic generalization of the Bragg-Kleeman rule to electrons and, in an appendix, a method to determine inelastic cross-sections of therapeutic protons in media of therapeutic interest.     

Drying of heterogels swollen in organic vapor

Fast transient fluorescence technique (FTRF), which uses a Strobe Master System (SMS), is used to study swelling and drying of disc shape heterogels. Disc shape heterogels are prepared by free radical copolymerization (FCC) of methyl (methacrylate) (MMA) and styrene (S) with ethylene glycol dimethacrylate (EGDM). Pyrene (P_y) is introduced as a fluorescence probe during polymerization and lifetimes, τ, of P_y are measured during the in-situ swelling process. Chloroform was used as an organic vapor agent to induce gel swelling. It is observed that τ values decrease as swelling proceeds. The Li-Tanaka equation is used to determine the time constant, τ_c, and cooperative diffusion coefficients, D _c, for the swelling processes. Lifetimes of pyrene increase during drying. An empirical equation is introduced to determine the desorption coefficient, D, for drying. Heterogels with high S content swell and dry much more slowly than heterogels with low S content.     

ESR-Linienbreite der Ionen der Eisengruppe in Lösungen

Electron spin resonance linewidths of ions belonging to the first transition group with quenched orbital angular momentum are calculated using a modified relaxationmatrix theory including third and fourth order perturbation terms. We base our calculation on a Hamiltonian, which depends on electron spin, nuclear spin, orbital angular momentum, rotation of the whole complex, and vibration of the ligands. Quadrupol effects, intermolecular electron-electron and electron-nucleus interactions are neglected. The results show that the well-known formula of the transverse relaxation time derived by using the spin-Hamiltonian is correct, if first the contribution of the rotational spin orbit process is taken in consideration and second the rotational correlation timeτ _c is replaced byτ _v =(1/τ _c +1/τ(0))^?1. 1/τ(0) describes the linewidth of the lowest energy value of the electrostatic energy of unpaired electrons in the ligand field. The linewidth arises from the normal modes of the complex; the calculation gives τ(0)=l0^?11...10^?12 sec.     

Relativistic geometrical optics

We investigate the gravitational and electromagnetic fields on the generalized Lagrange space endowed with the metricg _ij(x, y) = _ij(x) + {1 + 1/n ² (x, y)}y _iy_j. The generalized Lagrange spacesM ^m do not reduce to Lagrange spaces. Consequently, they cannot be studied by methods of symplectic geometry. The restriction of the spacesM ^m to a sectionS (M) leads to the Maxwell equations and Einstein equations for the electromagnetic and gravitational fields in dispersive media with the refractive indexn(x, V) endowed with the Synge metric. Whenn(x, V) = 1 we have the classical Einstein equations. If 1/n ²=1–1/c ² (c being the light velocity), we get results given previously by the authors. The present paper is a detailed version of a work in preparation.     

High-density percolation: Exact solution on a Bethe lattice

A new percolation problem is posed where the sites on a lattice are randomly occupied but where only those occupied sites with at least a given numberm of occupied neighbors are included in the clusters. This problem, which has applications in magnetic and other systems, is solved exactly on a Bethe lattice. The classical percolation critical exponents=gg=1 are found. The percolation thresholds vary between the ordinary percolation thresholdp _c (m=1)=l/(z – 1) andp _c(m=z) =[l/(z – 1)]¹/(z–1). The cluster size distribution asymptotically decays exponentially withn, for largen, p p _c .Supported in part by National Science Foundation grant DMR78-10813.     

N.M.R. solid echoes in systems of dipolar-coupled inequivalent spins-1 or dipolar-coupled inequivalent pairs of spins-1/2

Proton solid-echo transverse relaxation functions for many thermotropic and lyotropic mesophases, mapped by measurement of the echo amplitude S_yx (t′ = τ) as a function of τ using a P_y (90°)-τ-P_x (90°)-t′ sequence, yield gaussian behaviour of the form exp [-½M ^E ₂τ²] for decays up to 20–30 per cent of the value at τ = 0. M ^E ₂, the second moment for the dipolar interactions between the spin-½ pairs, is related to the van Vleck second moment M ^VV ₂ through a factor f. Whilst experiments suggested a value of 0·70–0·72 for f = M ^E ₂/M ^VV ₂, simple models that ignored the non-equivalence of the dipolar-coupled spin-pairs had predicted f = 0·65. In this paper we derive an exact analytic expression for the spin response of a model of two dipolar-coupled inequivalent spins-1 to the pulse sequence P_y (90°)-τ-P _α(β)-t′, and show that the present model, with the quenching of the spin-flip terms of the dipolar hamiltonian, resolves the afore-mentioned discrepancy. We also reconcile the differences between the experimental and the earlier predicted values of f for deuteron N.M.R. spin echoes in perdeuterated solids.     

NMR spin lattice relaxation in dilute CuFe alloys with impurity interactions

Previous measurements by Wilkening and Hesse have shown, that the excess relaxation rate ΔT^-1₁ of the matrix nuclei in $\text{CuF}$e dilute alloys can be explained in terms of the LD-model with rapid spin diffusion. Measurements reported in this paper confirm the existence of an electric quadrupole diffusion barrier. It could be shown that the influence of the quadrupole barrier is coupled to large clusters within the alloy. The electron spin lattice relaxation time τ₁ behaves temperature independent in the range 30 K ? T ? 300 K. This can be understood if an effective correlation time τ is introduced, which results from a distrubution of temperature dependent times τ^cl(T) belonging to clusters of different size.     

关于等离子体中的瞬变过程

利用Spitzer的广义欧姆定律分析等离子体中由垂直于磁场的压强梯度所引起的宏观瞬变性质。在垂直于磁场方向的初始流动速度为零的条件下,得出在恒稳磁场中的瞬时扩散系数(当ω_ceτ?1)为 D= (2km_ec²)/e² T/(B²τ)+(kc)/eT/Be^-m_e/(miτ)tsinω_cit,式中τ为电子离子的平均碰撞时间间隔。     

Solution of Ornstein-Zernike equation for wall-particle distribution function

The Ornstein-Zernike (OZ) equation is considered for the wall-particle distribution functiong ₀(x) in the case of a flat, impenetrable wall atx = 0 and a fluid of hard-core particles whose centers are constrained by the wall to occupy the semiinfinite spacex >/2, where is the particle diameter. A solution is given in terms of the wall-particle direct correlation function c₀(x) forx >/2, the bulk-fluid direct correlation function c_B (t), and p_B, the average bulk density. Explicit formulas for the contact surface density, total excess surface density, and the Laplace transform of the fluid density near the wall are given. For mean spherical type approximations, c₀ (x) forx >/2 and c_B (t) are both prescribed functions; for this case, a closed-form solution is obtained. An example is discussed and additional equations that enable one to go beyond the approximations considered above are introduced.Report #270, February 1976.The observation of this paper that the wall-particle problem can be treated using standard Wiener-Hopf techniques was independently made by Percus in his work, which came to our attention too late to be compared to, or incorporated into, our own results here.     

On the maximization of the central gravitational red-shift of a schwarzschild sphere with a given surface gravitational red-shift

Following Bondi static, spherically symmetric equilibrium configurations with a core and an envelope have been considered. It has been shown that for any configurations with nonnegative pressure and density and with a surface red-shiftz _s 4.77 arbitrarily large central red-shiftsz _c are possible in the limiting case of arbitrarily large radius. The effects of imposition of further constraints in the form of a real speed of sound not exceeding the speed of light are also examined. It is seen that for a given limiting sound-to-light-speed ratio . (i) There exists a limiting surface red-shiftz _s() 1.71. (ii) A configuration withz _s >z _s() is not possible, (iii) A configuration withz _s=z _s() has a unique and finitez _c=z _c(). (iv) Forz _s<z _s() arbitrarily large central red-shifts can be obtained for configurations with arbitrarily large radii.     

Critical thermodynamics of dysprosium ethyl sulphate,a pure dipolar Ising ferromagnet

Using a SQUID magnetometer the magnetization of the Ising ferromagnet dysprosium ethyl sulphate has been measured in the temperature range 0.015–3K and in external fields 0.004–30 Oe. The results atT0.4 K (precritical regime) confirm the pure dipolar nature of the magnetic interactions. Particular interest has been paid to the immediate neighbourhood of the critical pointT _c =118.17 mK andH=0 where the zero-field susceptibility(T) aboveT _c , the spontaneous magnetizationM _s (T), and the magnetization atT _c ,M _c (H), can be described by mean field laws modified by logarithmic singularities. The critical amplitudes, B, andD of, M _s andM _c , respectively, satisfy the relation (2/3B ²)^1/3=D. All these results agree with predictions of (i) the Larkin-Khmel'nitskii theory and (ii) exact solutions of the renormalization group equations for 3-dimensional dipolar Ising ferromagnets.A project of the Sonderforschungsbereich 65 Festkörperspektroskopie Darmstadt-Frankfurt, financed by special funds of the Deutsche Forschungsgemeinschaft     

Proton magnetic relaxation in ethylene oxide,tetrahydrofuran, and triethylene diamine as clathrate deuterates

Proton spin-lattice relaxation times (T ₁) have been measured for triethylene diamine, ethylene oxide, and tetrahydrofuran as clathrate deuterates. The results are interpreted in terms of anisotropic rotation of the guest molecules. Triethylene diamine is thought to be undergoing rotation about its C ₃ axis with a correlation time given by τ_c/s = 4·87 × 10^-14 exp (1680 K/T) at temperatures between 120 K and the decomposition point (308 K). Between 77 K and 120 K, T ₁ is dominated by conformational distortions of the guest molecule. Ethylene oxide and tetrahydrofuran rotate about at least two axes in the deuterate at rates sufficient to produce some motional narrowing. At high temperatures the relaxation is caused in both cases by rotation about an axis perpendicular to the C ₂ axis, and at lower temperatures by rotation about the C ₂ axis itself. The correlation times are for ethylene oxide τ_c/s = 6·76 × 10^-14 exp (450 K/T), T < 160 K; and for tetrahydrofuran τ_c/s = 4·79 × 10^-14 exp (470 K/T), T < 140 K.

The free induction decay shapes indicate that, in each case, low frequency motion is occurring about all axes throughout the temperature range studied (77 K to the decomposition temperature in each case). From the lack of an observable signal from the clathrate deuterates of hexamethylene tetramine and dioxan, it is deduced that there is no reorientational motion of these guests at frequencies greater than their rigid-lattice linewidths.     

Surface lifetime degradation in Si and Ge under low energy electron irradiation

The bombardment of n-type Ge and Si by 10–30 keV electron beams is shown to reduce the surface lifetime τ_P of minority carriers but not to affect mobility μ_P or diffusion constant D_P. For experiments, the electron beam in a scanning electron microscope is replaced a chopped light source to perform modified Haynes-Shockley experiment, and the measurements is used to calculate μ, D and τ. The reduction in τ is interpreted in terms of an increase in surface recombination velocity s. At a dose of approximately 10¹⁷ electrons cm^?2 for Ge and 10¹⁵ electrons cm^?2 for Si, a saturation value for s appears to be reached after which further bombardment has no effect. The values of τ obtained from both light and SEM Haynes-Shockley experiments performed in vacuum agree within approximately 5% both prior to and after bombardment. The initial values of lifetime can be restored by etching the samples.     

Scaling function for energy-density correlations: Dispersion theory andε-expansion forT>T c

A dispersion representation for the static energy-density correlation function ² (q) ²(–q) _c =C(q,T)=A+Bt ^–h(z ²), wherez=q , t=(T—T)_c/T _c and is the correlation length, is discussed.h(z ²) is calculated to order ² in the zero-field critical region (T>T _c) for the standard isotropicn-component ⁴Ginzburg-Landau-Wilson model. Utilizing a procedure similar to that introduced by Bray for the two-point correlation function, the-expansion results are used in conjunction with an approximant for the spectral functionF(z/2) Imh(—z ²) based on the asymptotically exact short-distance expansion resulth ^–1(z ²)z ^/v[D ₀+D ₁ z ^{–(1 —)/v} +D ₂ z ^–1/v ] to predict quantitatively the full momentum dependence ofC(q,T) forT>T _c. In contrast to the two-point correlation function,C(q,T) is found to be a monotonic function as the critical temperature is approached at fixedq (forT>T _c).     

Proton spin relaxation in hexagonal ice

Measurements of the rotating frame proton spin relaxation timeT _1p in hexagonal ice single crystals as a function of temperature ? for various rotating magnetic field strengths reveal the expectedT _1p minimum at the lowest practicable field values. This allows a very precise determination of the proton correlation (? molecular jump) time τ_c and the related activation energy ΔE by means of the theoretical reasoning of relaxation spectroscopy. We find the Arrhenius-law temperature dependenceτ _c=1.99×10^?17exp(0.603/8.61×10^?5 ?)sec, which is in good agreement with our earlier indirect derivation.