The Time Decay Constants in Neutron Thermalization

Corngold, Noel; Paul, M.; Wollman, W.

doi:10.13182/nse63-a26259

Cited by 67 publications

(8 citation statements)

References 2 publications

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“…∞) =0 are used. The eigenvalue spectrum for wave propagation can be derived by solving the integral equation (2). This spectrum is constituted of a continuous spectrum produced by the different spatial distributions of neutrons for different energies or for different directions of velocities, and of a point spectrum representing a common distribution combining both energy and angle in the solution of Eq.…”

Section: N Eigenv Alue Spectrum Inmentioning

confidence: 99%

“…(b) The angular distribution of /(z, μ， ψ obtained from Eq. (2) will no longer be analytic because of the singularity that wi1l have appeared at a specifìed energy E ' and/or a specifìed direction (μ ',<jJ'). In the frequency region ω>ω; ， where ω; has a value such that k ,p touches the edge of μ ， the point eigenvalue attaining k" w i1l disappear in most cases.…”

Section: ðIsappearance Of Point Eigenvalues and The Limiting Frequmentioning

confidence: 99%

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Theoretical Approach to Pseudo-Mode Neutron Waves in a Moderator

Utsuro

1969

J. Nucl. Sci. Technol.

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An analysis is presented on neutron wave propagation in moderators in the frequency region above the limiting frequency for discrete eigenvalues, and the distribution of the modulated neutrons in the medium is described by integrals over the continua.When a discrete eigenvalue reaches the edge of a continuum, a singularity appears in the angular distribution of the waves and causes the discrete mode waves to disappear. Further pursuit of the root of the dispersion law making use of the analytic continuation in the angular integral locates the root on a branch of the complex eigenvalue planes that adjoins the principal branch. This root on the adjacent branch can in certain cases bring about a sharp resonance_ i.e. a " pseudo-discrete wave eigenvalue" in the continuum. The conditions for the effectiye excitation of this kind of pseudo-mode wave were examined, which revealed that for this it is essential that the neutrons causing the limiting frequency have a weak coupling and that their injection be light. It was also demonstrated that the distance from source affects the pseudodiscrete eigenvalue.An application of this analysis to the case of graphite is also presented.

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Section: N Eigenv Alue Spectrum Inmentioning

confidence: 99%

Section: ðIsappearance Of Point Eigenvalues and The Limiting Frequmentioning

confidence: 99%

Theoretical Approach to Pseudo-Mode Neutron Waves in a Moderator

Utsuro

1969

J. Nucl. Sci. Technol.

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“…An important consideration in thermalization problems is the nature of the eigenvalue spectrum of the collision operator in the Boltzmann equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12). Much of the work in this area has been with a hard sphere cross section and we adopt this model in the present paper.…”

Section: Introductionmentioning

confidence: 99%

The role of pseudo-eigenvalues of the Boltzmann collision operator in thermalization problems

Blackmore¹,

Shizgal²

1983

Can. J. Phys.

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The calculation of the eigenvalues of the hard sphere Boltzmann collision operator using discrete matrix methods yields discrete eigenvalues. a large fraction of which are unconverged and lie in the continuum spectrum of the operator. The role of these pseudo-eigenvalues is examined. The results strongly suggest that for practical calculations the rigorous treatment of the continuum is not necessary provided that a moderately large number of pseudo-eigenvalues are included.Le calcul des valeurs propres de I'opCrateur de collision de sphkres dures de Boltzmann par des mCthodes de matrices discretes donne des valeurs propres discrttes dont une fraction considtrable sont sans convergence et situkes dans le spectre continu de I'opCrateur. On examine le rBle de ces pseudo-valeurs propres. Les rtsultats suggkrent fortement que le traitement rigoureux du spectre continu n'est pas ntcessaire pour les calculs pratiques, condition d'inclurc un nombrc modbrtment grand de pseudo-valeurs propres.[Traduit par le journal]Can.

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“…According to Corngold and others (11)(12)(13)(14) the discrete eigenvalues of the decay constant, are limited by…”

Section: Limiting Value Of the Decay Constantmentioning

confidence: 99%

“…**^« As Corngold and Michael (14) ;n = 1,2 (2.15) where M stands for the number of the discrete eigenvalues and the integral gives the contribution of the continuum.…”

Section: 12)mentioning

confidence: 99%

Neutron thermalization in water using spherical geometry

Nassar

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The Time Decay Constants in Neutron Thermalization

Cited by 67 publications

References 2 publications

Theoretical Approach to Pseudo-Mode Neutron Waves in a Moderator

Theoretical Approach to Pseudo-Mode Neutron Waves in a Moderator

The role of pseudo-eigenvalues of the Boltzmann collision operator in thermalization problems

Neutron thermalization in water using spherical geometry

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