Volume 13, Issue 5
November 1979, pages 457-579
pp 457-473 November 1979 Nuclear And Particle Physics
Effect of correlations on nuclear muon capture
The process μ^{−}+^{12}C→^{12}B+v_{μ} is studied using the modified Hartree Fock wavefunction obtained with the unitary-model-operator-approach starting from the realistic hardcore nucleon-nucleon interaction, with the aim of testing the wavefunctions and obtaining a numerical value for the induced pseudoscalar coupling constant (g_{P}). These observables, namely, the partial capture rate to the^{12}B(1^{+}; g.s), its recoil nuclear polarisation and the total capture rate, which exhaust the available experimental data in the above process have been calculated and compared with the other theoretical and experimental results.
As far as the partial capture rate is concerned the use of the unitary-model operator approach wave functions for^{12}C withb=2.09 fm and Cohen-Kurath wave function for^{12}B(1^{+}; g.s) reduces the pure shell model capture rate by about 30%. The effect of strong configuration mixing in the ground state of^{12}C in taken into account by introducing a scale factor ξ similar to the ‘amplitude reduction factor’ of Donnelly and Walecka. With this ξ the agreement with the experiment both for the partial capture rate and the beta decay ‘ft’ value is found to be satisfactory.
The^{12}B(1^{+}; g.s) recoil polarisation is found to be insensitive to the use of the unitary-model-operator-approach wave functions. When compared with the experimental data, we obtaing_{P}=(14.9±1.9)g_{A}.
The total capture rate is found to be sensitive to the use of the unitary-modeloperator-approach wave functions which contain the effect of nucleon-nucleon short range correlations and we obtain a satisfactory agreement with the experiment for^{16}O and^{12}C, thereby revealing the importance of the effect of such correlations in the total capture rate studies.
pp 475-493 November 1979 Nuclear And Particle Physics
Spectroscopy of light nuclei with skyrme-type interactions
Deformed Hartree-Fock calculations are performed for some light nuclei in a large configuration space consisting of first four major shells. The interaction employed is the modified Skyrme interaction in which the deformed density is replaced by the band averaged scalar density that makes the Hamiltonian rotationally invariant rendering the spectroscopic calculations feasible. It is shown that the introduction of density dependence spreads out the energy spectra and that the Skyrme variant SIV which has a weak density dependence gives best overall agreement for energy spectra and the available data for the electromagnetic properties of the nuclei studied. It is found that the maximum contribution to the energy of any state in the low lying spectrum comes from thes-state attractive ands-state repulsive parts of the Skyrme interaction. It is also shown that when two-body density dependent version of Skyrme interaction is used, the Koopmans theorem no longer holds.
pp 495-512 November 1979 Nuclear And Particle Physics
Asymmetry of mass and charge division in spontaneous fission
P P Chakraborty D N Sharma M R Iyer A K Ganguly
The order-disorder model has been used to explain asymmetry of mass and charge division and related phenomena in fission. According to this model the fission process involves two steps consisting of charge polarisation into two ‘impending fragment clusters’ with beta stable neutron numbers and subsequent distribution of the balance neutrons between the two. Mode of elemental division of the fissioning nuclei is attributed to the charge polarisation in the first step. Theory of reaction rate has been applied to the system.
The frequency term is obtained by applying the conditional stochastic process under charge polarisation constraint and the energy-dependent term is given by the condition of minimum in free energy of the system. Using this, the relative probability of polarisation into given charge pair is arrived at.
The model uses stable neutron numbers for the charges as the only input. No explicit assumption or quantification on the preference of formation of shell closure species in fission is necessary. The statistics developed on the principle of equala priori probability of all charge polarisation is used. The shell effects come into play only in deciding a stable neutron number for the charges. The total isotopic yield distribution for a number of fission reactions shows asymmetry in the actinide region which reduces with increasing mass/charge of the fissioning nuclide and bunching of the higherz peaks. Although the mass yields obtained therefrom for a number of fission reactions agree with experimental results, the peaks of the distributions are slightly shifted away from the symmetric point and the distributions are somewhat narrower. Charge distribution parameters obtained from these results are also presented.
pp 513-523 November 1979 Nuclear And Particle Physics
Mixing of meson isosinglets in SU(5) and an extension to SU(N)
The mixing angles of meson isosinglets belonging to the 24-dimensional and singlet representations of SU(5) are calculated under specific assumptions in the non-relativistic quark model. The procedure to extend the scheme to SU(N) has been outlined. The results have been compared with other earlier estimates.
pp 525-533 November 1979 Quantum Mechanics
Wave functions from an off-energy-shell generalisation of the Gordon’s method
An ansatz is introduced in the Gordon’s method for nonlocal separable potentials to construct expressions for off-shell wave functions associated with the physical, regular and standing wave boundary conditions. This method has certain calculational advantages and is particularly suitable for dealing with potentials of higher rank. Results obtained for the Mongan case IV potential agree with those derived by the complicated techniques.
pp 535-544 November 1979 Atomic And Molecular Physics
Symmetry-adapted many-body perturbation theory: use of the wave operator matrix elements
Debashis Mukherjee Dipan Bhattacharyya
In this paper we develop a simple method for adapting the closed-shell many-body perturbation theory to an arbitrary point group symmetry taking account of various classes of diagrams exactly to all orders. The method consists in deriving a linear operator equation for the closed-shell wave-operatorW which is then symmetry-adapted to the pertinent point groupG. It is shown that the system of equations thus derived enables one to include orbital-diagonalh-h, p-p andh-p ladders to all orders in a perturbative framework. The way to generalise the method through inclusion of a larger classes of diagrams to all orders is also indicated. Finally, the connection of the present mode of development with the non-perturbative coupled-cluster formalisms is briefly indicated.
pp 545-557 November 1979 Solids
Fluctuations and viscoelasticity
Viscoelasticity is exhibited by polymers, metals undergoing diffusion creep, etc. The strain is a linear functional of the stress, but there is no unique equilibrium relationship between them. Under a constant stress, the strain does not saturate to an equilibrium value. This divergence is the main difficulty facing a first-principles theory of viscoelasticity, in contrast to anelasticity which has already been understood as a relaxation process in terms of response theory, fluctuations and related concepts. We now present such a theory, based on the recognition that viscoelasticity occurs whenever the spontaneous fluctuations of the strainrate, butnot of the strain, form a stationary random process. We give fundamental formulas for the creep function and the complex compliance, in terms of the spontaneous fluctuations of the strain rate, that apply to both viscoelasticity and anelasticity. A detailed stochastic analysis of the basic viscoelastic network equation corroborates and complements these results. The unphysical instantaneous response of the network is eliminated, and the network parameters are related to internal fluctuations. A certain functional form of the creep function is derived that is common to several physical situations, a few of which are mentioned. Detailed applications will be taken up elsewhere.
pp 559-570 November 1979 Solids
Ionic compressibilities and ionic radii - systematic trends
Ionic radii and compressibilities have been calculated for a number of monovalent and divalent ions and radicals on the basis of the compressible ion theory. In this theory, the compression energy of an ion is given as a two-parameter function of its radius,A exp (−r/p), the radius and compressibility of the ion being monotonically decreasing functions of the compressing force acting on it. Choosing a standard force reflecting the average environment in the alkali halides, univalent radii and compressibilities have been calculated. This is the first theory to estimate ionic compressibilities. The values show systematic trends among groups of related ions. Anions are found to be significantly more compressible than cations (e.g., the compressibilities of Ca^{++}, K^{+}, Cl^{−} and S^{− −} are respectively 0.8530, 1.342, 2.952 and 5.150 × 10^{−12} cm^{2}/ dyne). Multivalent or ‘crystal’ radii and compressibilities have also been calculated by scaling the standard force by the square of the ionic charge. The calculated ionic radii are closer to experimental values than the classical empirical radii.
pp 571-579 November 1979 Solids
The problem of the relative stability of ionic structures is still unsolved current semi-empirical theories wrongly predict the caesium halides to have the NaCl structure. We point out here that these theories also predict some of the other alkali halides to occur in cubic ZnS structure. To understand these discrepancies, we study the effect of various interactions (such as second neighbour repulsion, van der Waals interaction and differences in ionic compressibilities) on the relative stability of simple structures. The results throw into question the radius ratio approach. It is suggested that one could allow for the presence of three-body interactions by relaxing the requirement that the repulsion interaction should be strictly proportional to the number of neighbours. Such an approach might explain the relative stability of simple ionic structures.
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