Volume 9, Issue 3
September 1977, pages 203-320
pp 203-221 September 1977 Atomic And Molecular Physics
Effect of collisions on spectral lines in gases
Collisions between an emitter and the surrounding buffer gas particles influence the emission lines. A collision may perturb the emitter in its excited and ground states, cause direct transitions between the levels, and at the same time, change the velocity of the emitter. In this paper, we present a model which deals for the first time with all these effects when they occursimultaneously in each collision. The model assumes the emitter to be subject to random collisions by the surrounding gas particles which are taken to constitute a heat bath in thermal equilibrium. The collisions are assumed to be binary, instantaneous, and to occur with a probabiity given by the Poisson distribution. These assumptions are shown to be equivalent to the widely used impact approximation in the collision broadening theory. We discuss several special cases of the general result for the line shape obtained in the paper.
pp 223-227 September 1977 Crystallography
The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 Å (TmSe), 155 ± 7°K, 0·244 ± 0·012 Å (SmS), 153 ± 14°K, 0·221 ± 0·020 Å (SmSe) and 151 ± 20°K, 0·204 ± 0·027 Å (SmTe).
pp 229-238 September 1977 General Relativity
Initial-value problems and singularities in general relativity
Linearized solution of Datta in a non-symmetric and isentropic motion of a perfect fluid is studied by dealing with a Cauchy problem in co-moving coordinates in the framework of general relativity. The problem of singularities is discussed from the standpoint of a local observer both for rotating and non-rotating fluids. It is shown that, whatever the distribution of matter, a singularity which occurred in the past in both the rotating and non-rotating parts of the universe must occur again later after some finite proper time, if the universe is closed. A modification is incorporated in Penrose’s theorem by explicitly exhibiting that the universe defined by Penrose can possess a Cauchy hypersurface.
pp 239-247 September 1977 Nuclear And Particle Physics
Renormalizable theories from nonrenormalizable interactions
By using Kikkawa’s method the equivalence of the nonrenormalizable pair interaction$$\bar \psi \psi \phi ^2 $$ to a renormalizable theory is proved. Equivalence relationships between a few other nonrenormalizable and renormalizable interactions are also indicated.
pp 249-256 September 1977 Nuclear And Particle Physics
Hadronic final states and sum rules in deep inelastic processes
In order to get maximum information on the hadronic final states and sum rules in deep inelastic processes, we use Regge phenomenology and quarks parton model. The unified picture for the production of hadrons of typei as a function of Bjorken and Feynman variables with only one adjustable parameter is formulated. The results of neutrino experiments and the production of charm particles are discussed in sum rules.
pp 257-262 September 1977 Nuclear And Particle Physics
The relevance of the recent experimental observation of possible bound and resonant states in$$N\bar N$$ scattering to the Goldberger-Treiman (GT) relation is examined. It is pointed out that anS-wave resonance in$$N\bar N$$ scattering goes a long way towards accounting for the corrections to the GT relations. Values of the mass and width of the resonance capable of giving a reasonable fit for the GT relation are presented.
pp 263-272 September 1977 Nuclear And Particle Physics
Two particle-one hole states in^{41}Ca and^{41}Sc
A prescription has been given to calculate the two particle-one hole states, to explain the occurrence of non-normal parity states in nuclei having doubly closed shell and one extra particle. This prescription has been applied to calculate the even-parity states in^{41}Ca and^{41}Sc nuclei. The transition probabilities for the electro-magnetic decays of these states have also been calculated.
pp 273-281 September 1977 Nuclear And Particle Physics
Effective two-body forces in light and medium mass nuclei
From the spectroscopic information provided by single particle stripping reactions, we have extracted average effective two-body interaction between nucleons in thep-, sd-, andfp- shells. Using the derived interaction parameters, we have calculated the energy centroids of the level spectra of residual nuclei obtained via single nucleon stripping reactions involving light and medium mass nuclei as targets.
pp 283-296 September 1977 Solids
CV Manjunath Kumari Santosh R Srinivasan
A study of the hyperfine interaction in the ESR of Cu-Cu pairs in single crystals of copper diethyldithiocarbamate as a function of temperature has shown distinct differences in the hyperfine structure in the two fine structure transitions at 20 K, the spectrum not having the same hyperfine intensity pattern in the low field fine structure transition in contrast to that of the high field transition. The details of the structure of both the fine structure transitions in the 20 K spectrum have now been explained by recognizing the fact that the mixing of the nuclear spin states caused by the anisotropic hyperfine interaction affects the electron spin states | + 1 > and | −> differently. This has incidentally led to a determination of the sign ofD confirming the earlier model. The anomalous hyperfine structure is found to become symmetric at 77 K and 300 K. It is proposed that the reason for this lies in the dynamics of spin-lattice interaction which limits the lifetime of the spin states in each of the electronic levels | − 1 >, | 0 > and | + 1 > The estimate of spin-lattice relaxation time agrees with those indicated from other studies. The model proposed here for the hyperfine interaction of pairs in the electronic triplet state is of general validity.
pp 297-302 September 1977 Solids
Experimental results on the nuclear spin-lattice and nuclear spin-spin relaxation times in the ferromagnetic EuB_{6} at temperatures below 4·2 K are presented using the external magnetic field,H_{ext}, in the range of 0 ⩽H_{ext} ⩽ 10 kG. Nuclear spin-spin relaxation time computed on the basis of the Suhl-Nakamura process turns out to be 3·2µs, which compares well with the experimental value 11·1µs obtained with the 10 kG magnetic field at 1·7 K. It is found that in the ferromagnetic EuB_{6},T_{1} is approximately 5 × 10^{3} times larger thanT_{2} at 1·7 K with the 10 kG magnetic field. Thus the effect ofT_{1} onT_{2} can be neglected. From the experimental value ofT_{2}, the value of the homogeneous line broadening is found to be 14 kHz. The corresponding value obtained from the cw method is 175 kHz. This evidently shows the presence of the inhomogeneous line broadening in the cw NMR.
pp 303-309 September 1977 Mathematical Physics
Perturbation theory for large coupling constants
The perturbation technique for large coupling constantsg^{2} is used for obtaining the solutions of Schrödinger equation for a double exponential potential. In particular the solution valid forg^{2}e^{-r/2} g^{2}e^{-r/2} ≫ 1, is obtained int erms of confluent hypergeometric functions. A noteworthy aspect of this application is that the procedure developed can also be used for solving certain singular potentials.
pp 311-320 September 1977 Quantum Mechanics
Study of theS-matrix near bound states in the continuum
The behaviour ofS-matrix for potentials generating bound states in continuum in the neighbourhood of the positive bound state energies is studied. It is shown that unlike the case of usual negative energy bound states, theS-matrix does not have a pole at the positive bound state energy but becomes unity at the energy corresponding to bound states in continuum. Calculations ofS-waveS-matrix for a local potential constructed by Stillinger and Herrick and a separable nonlocal potential constructed by the present authors verify these results. Our results indicate that the bound states embedded in continuum constructedvia the von Neumann and Wigner procedure cannot be interpreted as resonances with zero width.
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