We present a complete matrix formulation of the theory of small oscillations. Simple analytic solutions involving matrix functions are found which clearly exhibit the transients, the damping factors, the Breit-Wigner form for resonances, etc.

A generalization of Guderley's result for compression in a coalesced sequence of n strong shocks is presented. It is also shown that in coalesced sequences comprising a large number of weak shocks and a small number of strong shocks the last component determines the parameters of the self-similar motion.

An approximate analytical solution is obtained for the problem of spherical implosion of coalesced weak shocks in an ideal gas. Since the motion is assumed to be self-similar, our expressions are approximations to the exact solution which is valid close to the center of the sphere only. This has been achieved by replacing, in different time regimes, a nonlinear function of the reduced sound velocity and the reduced gas velocity appearing in the self-similar differential equation for these variables, by suitable functions of the reduced gas velocity alone. By considering a fully ionized D-T plasma to be an ideal gas of specific-heat ratio $\ensuremath{\gamma}=\frac{5}{3}$, it is shown explicitly that coalesced weak spherical shocks are much more efficient than a single strong spherical shock, in generating fusion energy.

We calculate the yield ofψ (3105) particles in N-N collisions in a model which associates the production of heavy particles with largeP T phenomenon. Our results show thatψ (3105) has a fairly strong coupling to other hadrons. We propose a criterion in the search for charmed particles and a parametrization for the expected yields of such particles.

Abstract The production of particle with large transverse momenta PT and other unexpected features observed with CERN ISR are explained on the basis of a model which traces their origin to a small class of events, called central collisions, involving “core-core” interactions. In each central collision, two massive fire balls, moving slowly in the C.M. system, are produced and they decay according to Fermi's statistical theory. The model makes specific predictions like a correlations between large PT, high multiplicities and production of antiprotons.

We consider a model where an incident particle (photon or pion) diffractively dissociates into resonating systems or perhaps kinematic enhancements (ρ0, A1, etc.) in the nucleus. This system then propagates through the nucleus being absorbed via the optical potential but also makes transitions to other channels. We have shown that the transparency of the nuclear matter to the diffractively dissociated system increases in the presence of interchannel couplings provided the interchannel potentials are purely imaginary.

Recently, in order to explain the experimentally observed (1) increase in the transparency of the nuclear matter to the propagation of a diffractively dissociated hadronic system D, VAN Hov~ has proposed a continuum model (~.s). In the latter i t is assumed that the system D consists of an infinite number of mutual ly interacting systems [~> having different masses but the same quantum numbers as D. This model predicts not only the increase in transparency but also a new phenomenon, namely that the mass distribution of [~}'s should exhibit diffractionlike interference patterns. However, the theoretical foundation for this prediction is rather restricted. For example, it is claimed that a) only a continuum model can predict such an effect, whereas a discrete model with a finite number of ]~}'s cannot, b) the DD interaction potential must have a smoothness property (2). I n this paper we show that the restriction a) is not necessary and indicate how b) can be relaxed to some extent. We also identify the dynamical causes underlying the increased transparency and the predicted diffraction patterns. Consider a high-energy collision between a hadron h and a nucleus. After the collision, h gets dissociated into a system D which we assume to consist of n states [~> having different masses but the same quantum numbers as D. For concreteness, we assume h to be a pion. Then, at high energies, the multiehanncl eikonal equations of propagation of = and D can be writ ten in matrix form as

Explicit relationships are established between the finite-transform sum rules derived previously and the finite-energy sum rule. The sine sum rule is applied to the pion-nucleon charge-exchange scattering in the forward direction. The assumption that the ρ trajectory alone dominates the charge-exchange amplitude leads to conflicts with analyticity even at 6 GeV. In the limit of the zero-mass pion the Born term in the sum rule is shown to be cancelled for all values of the continuous moment by a secondary trajectory with the intercept α′=−1 and the reduced residue γ′=−πf2, wheref2 is the pion-nucleon coupling constant. This secondary trajectory removes the conflict with analyticity at 6 GeV. Such a cancellation is a common feature of at least five sum rules. The local and global dualities are found to be violated whether or not the systematic errors are used and whether or not the Born term is subtracted out by means of the secondary trajectory. However, the usual low-mass resonances with well-determined quantum numbers satisfy the dualities better than the higher-mass resonances with mass >2.62 GeV. The CERN-Serpukhov data are amenable to the Reggepole description and are consistent with the Pomeranchuk theorem due to their large errors.

The experimental angular distribution of particles in p-p scattering seems to depend essentially on a single variablep t =q sinθ instead of depending separately on the momentumq and the angle of scatteringθ. For small values ofp t , the angular distribution can be represented as a Gaussian inp t as exp [−ap t 2 ] and for large values ofp t , as an exponential inp t as exp [−bp t ]. Using this empirical information we construct a scattering amplitude which has the Mandelstam singularity structure and which leads at the same time to the empirically observed transverse momentum dependence for small and largep t . The relevant spectral functions are calculated and the scattering amplitude expressed as the usual integrals over the spectral functions. We show that for spinless identical particles, the ratio of the real part to the imaginary part of the scattering amplitude in the forward direction goes to zero at high energies and that this ratio in nonforward directions is smaller than that in the forward direction. From the scattering amplitude suggested in this paper, we derive an optical potential which would give approximately the observed p-p scattering.