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Analysis of spin-dependent fission anisotropy
.4NNALS
OF PHYSICS:
Abstracts
18,
170 (1962)
of Papers
to Appear
in Future
Issues
=Lnalysis of Spin-Dependent Fission ilnisotropy. R. B. LEACHMAN and E. E. SANMANS. Los Alamos Scientific Laboratory, Los Alamos, New Mexico Several explanations of the anomalous increase of observed fission anisotropy with increasing target spin are examined. The Bohr theory that the fragment direction is along the K projection of the total angular momentum I is used in the classical limit. The sign and magnitude of the calculated effect of target spin are shown to vary with the form of the distribution in K, but the several different distributions used do not remove the anomaly. The calculated changes of moments of inertia, and thus of the width of the distribution in K, with the nuclear species undergoing fission also appear to be inadequate to explain t,he target spin effect. The effects of including in the method both nuclear deformation and an angular-momentum-dependent probability of the compound-nucleus transition to fission are calculated with the statistically-expected Gaussian distribution in K. The calculated effect of deformation is much less than the observed target spin effect. With the use of an adequate angularmomentum-dependent transition probability, agreement is reached between the calculated and observed anisotropy change with target spin. The magnitude of t,his required dependence represents an exponential decrease in the statistical level density with angular momentum that is an order of magnitude greater than expected from rigid moments of inertia. This result is qualitatively in agreement with other analyses of experimental data. Quantum Elecfrodynamics Without Potentials. STANLEY MANDELSTAM. Department of Mathematical Physics, University of Birmingham. Birmingham, England A scheme is proposed for quantizing electrodynamics in terms of the electromagnetic fields without the introduction of potentials. The equations are relativistically co-variant and do not require the introduction of unphysical states and an indefinite metric. Calculations carried out according to current quartization methods in the Coulomb or Lorentz gauges are justified in the new formalism. The theory exhibits an analogy between phases of operators and electromagnetic fields on the one hand, and co-ordinate systems and space curvature on the other. It is suggested that this analogy may be useful in quantizing the gravitational field. Quantization of the Gravitational Field. STANLEY MANDELSTAM. Department of Mathema&al Physics, University of Birmingham. Birmingham, England The scheme proposed in the preceding paper for the gauge-independent quantization of the electromagnetic field is here applied to the co-ordinate independent quantization of the gravitational field. Einstein’s theory is first re-formulated so as to avoid reference to a co-ordinate system. The quantization of the resulting theory is then carried through. No mention is made of unphysical variables such as the metric tensor except for the purpose of linking the present formalism with more conventional theories, the gravitational field is described by the Riemann tensor and its connection with space curvature is clear from the outset. First-order perturbation calculations are carried out and give results equivalent to those of “flat-space” theories. 170
OF PHYSICS:
Abstracts
18,
170 (1962)
of Papers
to Appear
in Future
Issues
=Lnalysis of Spin-Dependent Fission ilnisotropy. R. B. LEACHMAN and E. E. SANMANS. Los Alamos Scientific Laboratory, Los Alamos, New Mexico Several explanations of the anomalous increase of observed fission anisotropy with increasing target spin are examined. The Bohr theory that the fragment direction is along the K projection of the total angular momentum I is used in the classical limit. The sign and magnitude of the calculated effect of target spin are shown to vary with the form of the distribution in K, but the several different distributions used do not remove the anomaly. The calculated changes of moments of inertia, and thus of the width of the distribution in K, with the nuclear species undergoing fission also appear to be inadequate to explain t,he target spin effect. The effects of including in the method both nuclear deformation and an angular-momentum-dependent probability of the compound-nucleus transition to fission are calculated with the statistically-expected Gaussian distribution in K. The calculated effect of deformation is much less than the observed target spin effect. With the use of an adequate angularmomentum-dependent transition probability, agreement is reached between the calculated and observed anisotropy change with target spin. The magnitude of t,his required dependence represents an exponential decrease in the statistical level density with angular momentum that is an order of magnitude greater than expected from rigid moments of inertia. This result is qualitatively in agreement with other analyses of experimental data. Quantum Elecfrodynamics Without Potentials. STANLEY MANDELSTAM. Department of Mathematical Physics, University of Birmingham. Birmingham, England A scheme is proposed for quantizing electrodynamics in terms of the electromagnetic fields without the introduction of potentials. The equations are relativistically co-variant and do not require the introduction of unphysical states and an indefinite metric. Calculations carried out according to current quartization methods in the Coulomb or Lorentz gauges are justified in the new formalism. The theory exhibits an analogy between phases of operators and electromagnetic fields on the one hand, and co-ordinate systems and space curvature on the other. It is suggested that this analogy may be useful in quantizing the gravitational field. Quantization of the Gravitational Field. STANLEY MANDELSTAM. Department of Mathema&al Physics, University of Birmingham. Birmingham, England The scheme proposed in the preceding paper for the gauge-independent quantization of the electromagnetic field is here applied to the co-ordinate independent quantization of the gravitational field. Einstein’s theory is first re-formulated so as to avoid reference to a co-ordinate system. The quantization of the resulting theory is then carried through. No mention is made of unphysical variables such as the metric tensor except for the purpose of linking the present formalism with more conventional theories, the gravitational field is described by the Riemann tensor and its connection with space curvature is clear from the outset. First-order perturbation calculations are carried out and give results equivalent to those of “flat-space” theories. 170