Showing papers by "University of Madras published in 1975"

A quantum-mechanically solvable nonpolynomial Lagrangian with velocity-dependent interaction

Abstract: The quantum-mechanical problem of the nonlinear oscillator with the Lagrangian L= 1/2 [x2-k0x2)/(l-λx2)] is solved exactly and the energy levels and eigenfunctions are obtained completely. This model (whenk0=0) is the zero-space-dimensional isoscalar analogue of the nonlinearSU2⊗ SU2 chirally invariant Lagrangian in the Gasiorowicz-Geffen co-ordinates and may also be considered as a modified version of the anharmonic-oscillator and Lee-Zumino models. The bound-state energy levels are found to have a linear dependence on the coupling parameter, in sharp contrast to the case of the familiar oscillator With quartic anharmonicity where the energy, as a function of λ, has complicated singularities at λ = 0. We investigate how far certain standard approximation procedures reproduce the exact results. The Bohr-Sommerfeld quantization procedure is found to reproduce the form of the boundstate energy levels correctly. Interestingly a perturbation-theoretic treatment also reproduces the correct results at least up to the order (λ2) to which we have carried our calculations.

Rarita-Schwinger particles in homogeneous magnetic fields, and inconsistencies of spin-3/2 theories

Abstract: The Rarita-Schwinger equation for a spin-$\frac{3}{2}$ particle with minimal electromagnetic coupling is solved completely in the case when a constant homogeneous external magnetic field $\mathcal{H}$ is present. It is shown that the spectrum of energy eigenvalues includes complex values if $\mathcal{H}$ is such that $\ensuremath{\eta}\ensuremath{\equiv}(\frac{2e\mathcal{H}}{3{m}^{3}})g1$, and further that the norm of the Rarita-Schwinger wave function (i.e., the total "charge" integral defined from the Lagrangian) which is positive definite for $\ensuremath{\eta}l1$ becomes indefinite (even after taking account of the constraints) when $\ensuremath{\eta}$ exceeds unity. These results confirm that the difficulties in quantization first discovered by Johnson and Sudarshan are a reflection of the indefiniteness of the norm which appears already at the $c$-number level, and suggest that the nature of the energy spectrum (whether or not complex values are present) in the presence of very large magnetic fields would provide a quick means of predicting whether such difficulties would arise in quantization.

Positron annihilation in polycrystalline Al and Th-angular distribution

Abstract: A good geometry setup with well shielded collimators whose background is zero has been designed. The transmission and resolution of the setup are 0.16*10-3% and 0.8 mrad respectively. The angular correlations in aluminium and, for the first time, in thorium have been performed with shielded 75 mCi 58Co source. The density and momentum distributions are presented for Al and Th and their Fermi radii are 1.79+or-0.1 AA-1 for Al after subtracting the core contribution and 1.67+or-0.12 AA-1 for Th without subtracting the core contribution.

Causality of propagation of spin-3/2 fields coupled to spinor and scalar fields

Abstract: Recent investigations on the causality of propagation of spin-3/2 fields have revealed that the Bhabha--Gupta equation shares with the Fisk--Tait equation the advantage of being free from noncausality in the presence of minimal electromagnetic interaction, provided that the arbitrary parameters occurring in the theory are suitably restricted. Since the familiar Rarita--Schwinger theory is known to suffer from noncausality troubles, the above-mentioned result is of considerable importance. We extend it in this paper by showing that causality is preserved in the above theories even in the presence of a different type of interaction involving scalar and spinor fields. Thus the result obtained earlier with the electromagnetic interaction is not merely a fortuitous circumstance. (AIP)

Studies in molecular structure, symmetry and conformation XII: Crystal and molecular structure of D-alloisoleucine

Abstract: The crystal structure of D-alloisoleucine has been determined using three-dimensional photographic data. The crystals are monoclinic:P21,Z= 4,a= 9.76 °,b= 5.33 A,c=14.26 A and β = 98.6 °. The structure was solved by packing considerations on the basis of the structure of L-isoleucine and refined by full-matrix least-squares, including anisotropic thermal parameters for all nonhydrogen atoms, to anR-factor of 0.118 for 1057 observed reflections. The two molecules in the asymmetric unit have different conformations as in the case of L-isoleucine.

Evaluation of the density matrix for an ensemble of anharmonic oscillators by a path integral approach

Abstract: Considering the Feynman path integral representation for the configuration-space density matrix for an ensemble of anharmonic oscillators, we determine the ‘stationary paths’ near which the integrand remains stationary. By taking the path integral to be saturated by contributions from the neighborhood of the path which maximizes the integrand we evaluate the density matrix explicitly in analytic form. This seems to be the first such evaluation of a path integral for a system not describable by a quadratic Hamiltonian. We also comment briefly on the question of analyticity with respect to the perturbation parameter.

Effect of variations in peptide parameters and charges on the unperturbed dimensions of polypeptide chains

Abstract: The net charges on various atoms of poly (l-alanine), polyglycine, poly (N-methyl-l-alanine) and poly (N-methylglycine) were computed using the MOLCAO method of Del Re forσ charges and the Huckel MO method forπ charges. The characteristic ratiosC∞ were computed for all the above polypeptide chains, with different sets of parameters for the peptide unit. The calculated values ofC∞ are found to be very sensitive to the input peptide geometry. The calculated value of 2·2 forC∞ of poly (N-methylglycine) obtained with set-3 parameters (derived from a crystal structure containing prolyl residue) is closer to the experimental value of 1·8±0·2 than the value of 2·7 obtained with set 1 (Pauling-Corey parameters), suggesting that the peptide parameters of N-substituted aminoacids have close similarity to set 3 rather than to set 1. The calculated values ofC∞ of the polypeptide chains show no correlation with the number of allowed conformations, suggesting that the ratio ofC∞/Cf need not always provide information about the flexibility or freedom of rotation of chain units.

Studies in molecular structure, symmetry and conformation. IX. Crystal and molecular structure of the mixed crystal of L-threonine and L-allothreonine

Abstract: The mixed crystal ofL-threonine andL-allothreonine is orthorhombic, space groupP212121, witha = 13.60(1),b = 7.87(1),c = 5.16(1) A andZ = 4. The structure, which is closely isomorphous with that ofL-threonine, was solved from photographic data and refined to anR of 11.6%. The structure is spatially disordered, containing the molecules in bothL- andL-allo forms.

Crystal and molecular structure of 4-amino-4-carboxyl thiapyran hydrobromide

Abstract: 4-Amino-4-carboxylthiapyran hydrobromide crystallizes in the monoclinic space groupP21/m, witha= 9.72 A,b= 6.60 A andc=7.10 A,β = 94.8 ° andZ= 2. The structure was solved by the heavy atom method with 786 observed reflections and refined to anR of 0.076. There is an interesting weak interaction which the hetero sulfur atom of the thiapyran ring makes with a symmetry related amino nitrogen (N...S distance 3.34 A) which significantly affects the “puckered-chair” conformation of the thiapyran ring.

Crystal and molecular structure of 4-amino-4-carboxyl thiapyran

Abstract: 4-Amino-4-carboxylthiapyran crystallizes in space groupP21/c witha = 10.61,b = 6.55,c= 10.97 A, β =96.3 °, andZ = 4. The structure was solved by the heavy-atom method, with 897 observed reflections, and refined to anR of 0.093. The packing of the structure is found to be very similar to that in the structure of 1-aminocyclohexane carboxylic acid. The conformation of the thiapyran ring exists in the “puckered chair” form.

Studies in molecular structure, symmetry, and conformation X: Crystal and molecular structure of DL-allothreonine hydrobromide

Abstract: DL-allothreonine hydrobromide belongs to space groupP21/c with unit-cell dimensionsa = 8.91,b = 7.78,c = 18.91 A and β = 92.0 °. The structure was solved by the heavy-atom method and refined to anR-index of 10.7%. There are two molecules in the asymmetric part of the structure having different conformations.

Unstable Particles in a Self-Consistent Field Theory

Abstract: We indicate how unstable particles can be introduced into the self-consistent field theory formulation of Umezawa where the equal-time commutation relations for Heisenberg fields are derived and not assumed. The Lee model is used to illustrate the results.

Reinvestigation of the structure of 1-aminocyclohexane-1-carboxylic acid hydrochloride (C7H14ClNO2)

Abstract: The title compound, reported earlier by Chacko et al. (1971) in the noncentric space group P21, is refined in the centrosymmetric space group P21/m, with the same observed intensity data, to an R-index of 0.1 13. The structural features and esd's in parameters show marked improvement in the centrosymmetric space group. However, it is interesting to note that some of the atoms in the previous noncentric refinement show highly significant deviations from higher symmetry. The relevant crystal data are the same as reported earlier by Chacko et al. (1971), except that the structure is reanalyzed in the space group P21/m with Z = 2. During the structure investigation of the hydrobromide derivative of 4-amino-4-carboxylthiapyran (structurally very similar to the title compound except that the methylene group at the C(4) position of the cyclohexane is replaced by sulfur), it was found that the structure refined only in P21/m to

Equal-Time Commutation Relations for Heisenberg Fields in the Lee Model

Abstract: >~ 4 > has been successfully applied to problems in both high energy physics5> and the area of many-body problems, particularly in superconductivity 6> and ferromagnetism. 7> In this paper we apply this method to the solvable Dirac­ Lee model which, unlike the pair model considered in Ref. 3), has mass and coupling constant renormalizations. The equal-time commutation relations among Heisenberg fields are derived and not assumed. Further we show that the wave­ function renormalization constant is determined from microcausality. This result sheds light on the question why in Ref. 3) the existence of the~ bound state was found to be closely connected with microcausality. The self-consistent method exploits the duality between basic fields and observed particles concretely exhibited in the presence of interactions. The basic Heisenberg fields obey nonlinear field equations which reflect the laws of nature, while the physical particles are the ones that appear in observations. These physical fields obey free field equations and define the physical Fock space. The field equations for the Heisenberg fields are to be regarded as operator equations in this physical Fock space. The Heisenberg field is related to the physical field by means of a mapping known as the dynamical map.4> The set ?f physical fields is taken to form an irreducible operator ring. Therefore, any operator of the Fock space can be written as a sum of normal products of physical flelds. The ability of this method to predict new particles rests on this postulate. The asymptotic condition may tell us that the physical fields are not complete. The completion of this set of fields then requires the existence of other particles at the level of observation and should be incorporated. 8>·8> The success of this method therefore rests on the proper choice of the set of physical fields.

Residue-squaring iterative diagonalization method for perturbation problems

Abstract: We present a new method for the evaluation of the change in eigenvalues due to a perturbation of strength λ. It is a fast converging iterative method which, at thenth step, gives results accurate to order (2 n+1−1) in λ. Unlike the Rayleigh-Schrodinger perturbation theory in quantum mechanics, which becomes prohibitively cumbersome when carried to higher orders, the present method involves a routine which remains stralghtforward at all stages.

Peroxidase uptake through the tegument of the cestodeTaenia hydatigena

Abstract: Die Durchlassigkeit der Kutikula verschiedener Korperabschnitte vonTaenia hydatigena fur Eiweissmolekule wurde mittels Meerrettich-Peroxidase untersucht. Dabei wurde nachgewiesen, dass die Kutikula vonT. hydatigena nur im Bereich der reifen Proglottiden fur Peroxidase durchlassig ist. Dies lasst die Annahme zu, dass einzig in diesem Korperabschnitt vonT. hydatigena die Resorption von Eiweiss aus dem Darm des Wirtes erfolgt.

Dispersive Φ 4 wave propagation

Abstract: Whitham's theory (1965) of nonlinear water waves is applied to a nonlinear c-number field ( lambda phi 4 model) to investigate the propagation characteristics of the field in the plane-wave modes. A system of first-order partial differential equations is set up for the assumed slow variations of the wave parameters corresponding to each of the different types of Jacobian elliptic function wave modes. By the method of characteristics it is shown that the system is hyperbolic in two of the regimes, indicating that the disturbances in the wave parameters propagate with two different amplitude-dependent velocities.