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With help of Green functions the transition rates for different types of two-photon absorption through diagram summations are calculated. The appearance of double-photon absorption characteristics in the photo-stimulated field emission is analyzed. It is shown that the two-step transitions can be discerned from the one-step excitations in this way. A convenient experimental technique is discussed.

We calculate the correction to the magnetic form factor of 3He and 3H arising from mesonic-exchange currents. We find contribution to the πN-resonance excitation diagram via SD matrix elements, to be considerable.

The coherent-potential approximation has been employed to discuss itinerant-electron magnetism of binary alloys by use of diagram techniques, which make clear the meanings of, and the differences between, the formulations by Hasegawa and Kanamori (HK), Levin etal. and Harris and Zuckermann. These diagram techniques make it easy to obtain the wave-vector and frequency-dependent susceptibility for the Wolff model at finite impurity concentrations. The results reduce to that of HK in the uniform and static limit. The formula enables us to discuss on the same footing both local exchange enhancement and paramagnons by changing the concentration of magnetic atoms. It is also shown that the charge transfer has some important consequences. By use of this susceptibility, the possibility of the spin-density-wave state has been discussed in similar ways as Penn's argument for pure systems. It is found that the occurrence of magnetic states is essentially related not to the total density of states but to the local density of states. In addition to the static properties, the diffusion constant of spin fluctuations is discussed in relation to the electronic specific heat.

The level scheme of 172Yb has been studied from the decay of 63.6 h 172Tm. Gamma-ray energy and intensity measurements were made using Ge(Li) spectrometers. Forty-eight γ-ray transitions, nine of them previously unreported, are observed. All of these have been incorporated into a 172Yb level scheme consisting of 16 excited states. The previously reported “1119 keV” γ-ray is shown to be a doublet, with one member de-exciting the I, Kπ = 2, 0+ state at 1117.8 keV and the other de-exciting the I, Kπ = 2, 1− octupole-vibrational state at 1198.5 keV. This observation, together with that of the additional γ-ray transitions, provides further information on the de-excitation of the 172Yb levels. Attention is focused on the properties of the excited Kπ = 0+ bands at 1042 and 1404 keV and the Kπ = 2+ bands at 1465 and 1608 keV. A phenomenological five-band mixing analysis of the γ-ray branching-ratio data, involving these four bands and the ground-state band, has been carried out. Results of this analysis are presented for two different assumptions concerning the signs of certain of the matrix elements coupling the excited bands. Additional measurements which could help in choosing between these two alternatives are indicated. Interesting similarities in some of the properties of the two excited 2+ bands are pointed out, and a qualitative explanation of them is given in terms of the Nilsson level diagram relevant to 172Yb.

The structure of integrated heads offers better possibilities of optimization than conventional heads. The length of the gap and the thickness of the pole tips can be optimized in order to obtain the best efficiency of the head during the writing process. This optimization relies on the magnetization distribution of a single transition. We will here study three transitions the separation of which is adjustable. The purpose of this paper is to show that the optimization of the write process is not always really convenient for high density recording. We use an iterative method the principle of which is identical to the one used for the calculation of a single transition. This method extended to three transitions reflects the magnetic history of the magnetization as faithfully as possible. During the computations, the magnetization varies on the major B-H loop or on the minor cycles taking into account the transition interactions and the demagnetizing fields. After the third position, the head is translated faraway. In order to understand better the method, a detailed diagram will be given. Results show us the density limitation of an integrated head with a given medium. In conclusion, this study shows that the pole tip thickness of integrated heads is an important parameter for magnetic peak-shift.

A mass spectrum of π o π o system in the final state of π − p → π o π o n reaction has been studied at the momenta 20 to 50 GeV/ c . The experiments were performed at the 70 GeV IHEP accelerator. In the mass distribution there has been selected a peak corresponding to f o meson production cross section decreases in the power form with the momentum. The differential cross section follows exponential dependence, exp ( bt ). The mass spectrum of unbounded π o π o system is satisfactorily described with multireggeon diagram of the ϱ and π exchange.

The enhancement factor κ in the electric dipole sum rule is calculated using the linked diagram perturbation theory for the effective operator and the Reid nucleon-nucleon potential. Results are in good agreement with the recent experimental values for 16 O and 40 Ca, namely κ is around 1.0. There is, however, a large discrepancy between theory and experiment for 4 He. The two-body correlations, especially those induced by the tensor force, are found to be extremely important for the enhancement factor.

We present here the analysis of an accelerator produced 10 + 13p shower event observed in nuclear emulsion. The DULLER-~ALKF.R method is applied to obtain the distribution of secondary shower particles, and the particles having the closest log,, tan Ot values are taken to form a cluster. This cluster formation is also confirmed by the target diagram method. If this cluster is conceived to be a high spin resonance and the secondary pions to be the decay products of this resonance, then the azimuthal integral distribution curve fits fairly well with our experimental data.

The ground state energy and the correlation energy of an electron gas are evaluated rigorously without using the smallr s expansion and the small momentum-transfer approximation in the ring diagram contribution and taking into consideration the first order and second order exchange graphs. The Fermi momentum is determined by solving the number density equation without using iteration and is compared with that obtained by iteration. The ground state energy is found to stay positive in contrast to the iterative solution which becomes negative beyond a certain value ofr s .

Two semiautomatic assignment programs have been developed as a part of an extensive computer-program system for the assignment and analysis of vibration-rotation spectra. One prints the Loomis-Wood diagram on which every observed line is marked with a digit indicating the line intensity. The second constructs a new diagram, which is based on the combination-difference method; the calculated wavenumbers are arranged in the order of their quantum numbers and the observed lines in vicinity of each calculated wavenumber are plotted as on the Loomis-Wood diagram. Using these diagrams, the assignment of the rotational structure may be made consistently and almost automatically. Applications to the assignments of spectra of OCS, CH3I, and C2H4 are shown as examples.

Under a hypothesis that the meson-baryon reaction amplitude corresponds to the urbaryon rearrangement diagram (URD), the X type (t-u dual) URD is related to the H type (s-t dual) one in the forward region by reversing the urbaryon line. It has been taken that the X type amplitude has the magnitude equal to the H type one and is real, and that the Z .type (s-u dual) amplitude is negligible; line reverse relation (LRR). There are, however, indications that the LRR is more or less broken. Two simple models resulting in the LR breaking under the URD hypothesis are investigated. (1) Zrr model. One· of the three Z type URD's, which is named Zrr, has a remarkable peculiarity that its t-channel quantum numbers are non-exotic irrespective of the exoticfour­ urbaryon configuration. If the Zrr amplitude survives up to high energies from this peculiarity, an apparent LR breaking results in KN-'nrY vs. rrN~KY processes. (2) Im X model. The imaginary part of the X amplitude, which may be compatible with the possible KN s-channel exotics such as Zo (P112) and Z 1 (P,;,), gives rise to an intrinsic LR breaking. A comparison between the two models and their consequences are examined. LR breakings in decuplet baryon production and of baryon exchange are also discussed.

Ab initio calculations have been carried out on some potential energy curves of the (XeH)+ molecule, with particular attention paid to the lowest states. The spin-orbit interaction has been taken into account using a semi-empirical method. These calculations suggest the use of a three-state basis when dealing with H+-Xe collisions at low energies. It is also found that the computer MO correlation diagram is in good agreement with that predicted by the 'promotion model' of Barat and Lichten (1972).

Results on the inclusive reaction π+ p→Δ++ X0 at 8, 16 and 23GeV/c are used for quantitative tests of the triple Regge formula. As predicted, the slopes ofthe missing mass (M) spectra at fixed t are independent of s. Furthermore the trajectory α(t) obtained from the s-iependence at fixed M appears consistent with that obtained from the M-dependence at fixed s. However, the pomeron intercept α (0) is found to depend on t, suggesting that no single triple Regge diagram dominates at the M and s values studied in this reaction. Provided such a t-dependence is allowed, a single term triple Regge formula gives a very satisfactory parametrisation of our data.

It is shown that, if one expresses the hadronic scattering amplitude as a sum of contributions from individual quark diagrams, each of these quark diagram contributions will obey a logarithmic scaling law in the high-energy fixed-angle limit. The ingredients of the proof are the linear motion of singularities in the complex angular-momentum plane and certain analyticity assumptions. The logarithmic scaling law emerges from the requirement of consistency of the behaviors of the individual quark diagram amplitude in the fixed-angle high-energy regime and in the Regge regime. Each quark diagram is found to have an intrinsic scale set by the slope of the «dominant» singularity in the complex angular-momentum plane of any one of its channels,i.e. the singularity whose trajectory lies highest for large negative values of that channel's Mandelstam variable. Complex angular-momentum plane singularities that are dominant in different channels of the same quark diagram must therefore have the same slope. As the Pomeranchuk singularity and Regge-Regge cuts are dominant in different channels of the same (twisted loop) quark diagram, it follows that they must have the same slope of ∼0.42 (GeV)−2. If one assumes a small number of quark diagrams to dominate the physical scattering amplitude at present energies and fixed angles, the differential cross-section is found also to obey a logarithmic scaling law which agrees with the wide-angle pp scattering data.

Re-investigation of the L-emission X-ray spectrum of tungsten has been undertaken using 40 cm and 20 cm radius curved mica crystal spectrographs of the transmission type. The study is restricted to the diagram lines only. A new line at lambda =1381.96 xu corresponding to the forbidden transition L2M2 has been reported for the first time. The existence of the lines corresponding to the transitions L3N3 and L2M3( beta 17) reported earlier by Kaufman only (1934) has been confirmed. The microphotometer records have been presented to establish the presence of the new line unambiguously. Wavelength data of different workers on the already reported lines of this spectrum have also been given for the sake of comparison.

A large class of ideal fluids satisfies the equation pv=gU, where U is the internal energy and g is a characteristic constant of the system. The 'ideal quantum gases' are here defined thermodynamically by this equation. These systems then include weakly interacting fermions or bosons either in the non-relativistic or in the extreme relativistic limit. The relationship between different ideal quantum gases can be shown in a diagram with horizontal coordinate g. It is desirable to represent the classical ideal gas, which is here defined thermodynamically by pv=NkT, 'orthogonally' by a horizontal line and this is achieved by the choice of the coordinate y=(1-1/ gamma ) (1+1/x), where gamma is Cp/Cv. The ideal classical gas has then states which lie on y=1. Such a diagram has the additional remarkable property that important simple systems have states represented by one single point. The theory of this diagram and the associated equations of state are analysed in detail.

The three-dimensional Ising model for the case S = ½ in an external magnetic field is considered by the diagram expansion of the Green temperature function. The state equation of the Ising model is proposed in the ladder approximation. The calculation of the state equation is given as magnetization curves for the temperature region T ⪆ Te and for magnetic fields H = 18 and 5 kOe. Also the Tyablikov equation is solved for the same temperatures and magnetic fields. The comparison shows a better agreement of the ladder approximation with the experimental data than the molecular field approximation or the Tyablikov equation. [Russian Text Ignored].

The diagrammatic methods of electron theory elaborated by Yonezawa for substitutional alloys have been applied to translationally disordered systems with short-range correlations (e.g., liquid metals). The counterparts of the well-known coherent potential approximation have been formulated by means of diagram renormalization both for free electron and tight-binding approximations. Results obtained for the nearly-free electron limit are equivalent to the Schwartz- Ehrenreich self-consistent approximation.

The differential cross section for the lepton trident production in the Coulomb field of nucleus is calculated using a standard technique of quantum electrodynamics. Eight diagrams are taken into account in calculation. Cross section formula in the text is expressed in the form which is most suitable for any type of numerical calculation. Since the formula is expressed in order to make the calculation of individual diagram possible, one can easily evaluate the contribution of certain diagram to cross section at a given experimental geometry. Propagator terms are expressed separately from the others making the modification of this part possible. Numerical calculation of the formula at a given experimental geometry shows a complete agreement with the one of the formula derived independently by Henry.

A procedure is given for including self-consistency and other insertion effects implicitly in the expansion for the effective interaction for open-shell nuclei. Harmonic oscillator states are used as a basis for the Bloch-Horowitz-Brandow diagram series and for the intermediate states of the reaction matrix. The procedure requires the use of a modified form of the reaction matrix and modified single-particle energies.

Mesonic second-class currents have been studied in semileptonic DELTA S == 0 transitions. The closed-loop diagram is finite for the i omega current, and its energy-dependent lepton part is dominant over the contributions from the two-body exchange diagram. The two-body exchange diagram has energy- dependent and energy-independent lepton parts, which are of comparable magnitude for the A = 12 triplet. A general form of the mesonic current has also been considered. A general theory of second-class effects, including both mesonic currents and the induced-tensor term for ft values and K/ BETA /sup +/ ratios, has been discussed. (auth)

The line shape theory of nuclear magnetic resonance is presented based on the linear response approximation, in which the retarded Green's function of magnetization vectors plays a central role. To estimate this the corresponding temperature Green's function, which is ordered with respect to the imaginary time, is first investigated with the diagram method, then the desired retarded one is obtained by analytical continuation. The results obtained are as follows: The main line is Lorentzian at the vicinity of the resonance frequency and is Gaussian at the wings. Satellite lines are also given with similar shapes and reasonable intensities.

The present work contains the analysis of various reactions proceeding at relatively small projectile energies (∼ 10 MeV) for which a mechanism described by the square diagram may be regarded as a dominant one. It is shown that such a mechanism may be realized both in reactions in which one or several nucleons are transferred and in reactions of nucleon or deutron inelastic scattering. Also, such an interesting property of the above diagrams is discussed as the extremely well pronounced forwardness of the angular distributions for the processes of inelastic scattering. Various variants of the theory are examined (DWBA, oscillator approximation, etc.). Formal properties of the square diagrams are also studied such as the dependence of differential cross section shape on the value of total orbital momentum transferred and the approximation on an energy surface for its calculation.

Dipole soundings are more sensitive to noise caused by lateral and superficial inhomogeneities than Schlumberger soundings. However, the former are preferable for deep explorations in view of the relatively short cables required. The simple solution of carrying out the field work by means of dipole spreads, and to transform the dipole resistivity diagrams into Schlumberger ones by means of proper formulae would be valid only for smooth and regular curves; but often, owing to the presence of lateral noises, the dipole data show a considerable scatter. For such cases a “continuous dipole sounding” method is proposed for which all successive dipoles are contiguous, so that all parts of the profiles are covered and interpolation is not necessary. Obviously the moving dipoles have lengths proportional to their distances, so that they appear equal in the usual bilogarithmic scale. It follows that only polar-dipole arrays may be used. The transition from a dipole to the corresponding Schlumberger apparent resistivity diagram requires an integration constant which is not unequivocally determined. Therefore, the solution is not unique, but all possible derived Schlumberger diagrams have a common part. Similarly, they have some common interpretative results, which may be referred to the original dipole diagram obtained in the field. A special measurement technique is required since the dipole-dipole voltages to be determined are noticeably smaller than the Schlumberger ones. This is true also because dipole soundings are used for great depths and for long distances between the two dipoles.

Employing a 40 cm curved mica crystal spectrograph of the transmission type, the beta -region of the L emission spectrum of holmium 67 has been investigated. Two new quadrupole lines at lambda =1601.2 and 1593.7 (xu) corresponding respectively to the transitions L3N2 and L3N3 have been reported for the first time. Wavelength data of different workers on the already reported lines in this region have been given for the sake of comparison.

To everyT-type diagram there corresponds a set ofr-type diagrams, which have support properties in momentum and configuration-space which are preserved under composition of diagrams, and which have the same combinatorial structure as the correspondingT-type diagram.

There exists a certain leakage flow in general after the turbine gate has closed in practical hydraulic plants. The leakage flow influences on the oscillatory pressure wave form of the pressure-time diagram after the closing motion of the gate has stopped. In this paper, assuming an ideal pressure change, it is indicated that the oscillatory pressure wave is damped rapidly by the existence of leakage flow. Moreover the relation with Gibson Method under these condition is checked.

A simple derivation of the three-body multiple-scattering expansions from the Faddeev equations is given for non-relativistic elastic, inelastic, rearrangement, and break-up processes. The Faddeev approach to the multiple scatterings is compared with the Watson multiple-scattering theory and is shown to be equivalent to a symmetric version of the Watson multiple-scattering theory, treating all three particles on the same footing. The significance of the Faddeev-Watson expansion is interpreted diagrammatically. The advantages of these expansions lie in the fact that there is no disconnected diagram, suggesting a better convergence behavior. The modifications required by the inclusion of an intrinsic three-body interaction are investigated.

Length-tension diagrams have been obtained from rat gastrocnemii stimulated under various stimulation-length sequences. The sequences were selected in an attempt to discover the origin of a secondary maximum on active and total length-tension curves, when these were derived by a commonly accepted technique. Two working hypotheses were advanced. The results indicate that several length-tension characteristics are dependent upon stimulation-length sequence, and that under the conditions examined the most important of these characteristics are extensibility and equilibrium length. As a consequence, neither working hypothesis appeared entirely satisfactory.

The electronic states of heavy atomic solids are sensitive to relativistic corrections. The effects of these corrections on the eigenvalues and eigenfunctions of a diatomic crystal are investigated, by seeking the solutions of the Dirac equation for a Kronig-Penney type of potential. The relativistic band structure diagram shows that, although the relativistic correction leaves the forbidden energy gap widths unchanged, it does cause a shrinking of the bands. The band shrinkage and constancy of the gap widths is accommodated by a downward shift of the band edges.

A Recent paper (Moppett1) described a successful biological adaptation of the X-ray spectrometer, the chorio-allantoic membrane of the chick forming a standard or test tissue. The X-ray action was found to be selective with respect to wave-length, according to the simplified diagram (Fig. 1A). In such a graph there are two variables, wave-length and degree of biological response. The wave-length is determined by successive angular settings of a (calcite) crystal, of which the reticular distance (d) is known to several significant figures, and if a constant slit width is used the resolution varies as 1/cos θ by differentiation of the diffraction formula λ=2d sin θ. The spectrum from 0·3 to 1 A. was covered in sixteen steps with slits arranged to give a total divergence 1/50 or a wave-length range 0·123 A. at 0·5 A., so that there was an overlap between successive settings. Degree of reaction may be estimated in terms of the character or size of the reaction or, more precisely, in terms of the threshold dos...

A modified “isobar approximation” is proposed, in which the “isobar” is described by means of a Regge pole. Rules are established to calculate Feynman diagrams containing Regge poles. Most properties of usual diagrams, in particular, the prescription for calculating imaginary parts remain valid for these generalized diagrams.

The nucleon form factors are calculated to lowest order in a new field theory on an 8-dimensional homogeneous space of the Poincare group. The simplest diagram does give both an electric and a magnetic form factor and a relation between them. It seems, however, difficult to reproduce the experimental data, ase.g., any anomalous magnetic moment does not appear in a natural way.

The eigenvalue problem of the finite linear chain with arbitrary asymmetric boundary conditions is solved strictly. The results are used in quantum theory of spin wave resonance (SWR) in thin asymmetric ferromagnetic films. A theory providing some new interpretations of experimentally known effects in SWR and predicting new as yet unobserved effects is proposed. The results are visualized in an especial surface pinning diagram which should prove highly useful for the comparison of experimental data with the theory.

Gribov has developed a calculus based on perturbation theory which permits a meaning to be attached to an arbitrary Reggeon diagram in two-body scattering. The rules thatGribov gives are for calculating thet-channel partial wave amplitudea(j,t). It is indicated howGribov’s discussion can be taken over to the case of production amplitude for the processA+B→1+2+3.

The results of the investigations by Stommel (1949) and Ichiye & Olson (1960), which gave values of the “neighbour-diffusivity” F(l) have, for this diagram, been converted to values of 1 2 d σ/ d t = 2K = F (1)/1.515 , according to Stommel (1949). Similar results published by Denner, Green & Snyder (1968) have not been included in Fig. 2; they apply to larger scales (2.7 to 12.4 km), but fit in well with the general trend of the values shown here.

The IBS spectrum accompanying a direct nuclear reaction is studied in a model using the non-relativistic Feynman-Shapiro diagram technique. The main attention is paid to the triangle diagrams. The threshold singularities and the magnitudes of angular momenta of particles interacting in vertices are investigated with regard to their influence on the shape of the IBS spectrum. The pole and the triangle diagram contributions to the total radiative amplitude are compared. The possibility of the experimental identification of the nuclear reaction mechanism is discussed.

About thirteen years ago, when officer of a vessel trading from London to Australia, and in the daily practice of verifying the error of the compass by azimuth's declination, the idea first occurred to me of projecting the sun's path on the plane of the horizon; and during the voyage I succeeded in solving the problem, and constructed a diagram which I used daily while at sea for several years, until I gave up long voyages, and had no further occasion to trouble about azimuths.

An analysis of the available paleomagnetic data has been completed to support and delineate the possible spasmodic drift of the southern continents. Correlation analysis of the drift rates of the Gondwanic continents show a high degree of similarity in their drift patterns. The possibility of momentum transfer and adjustment during drift is assessed with the application of Feynman's diagram and corresponding implications are also discussed.

Consequences of the octet dominance model based upon the tadpole diagram have been investigated. Especially the decays ω → 2π, K+ → 2π, and the mass difference between K 2 0 and K 1 0 have been computed.