N. G. Sjöstrand

Spectrum of one-speed Neutron transport operator with reflective boundary conditions in slab geometry

Abstract The time eigenvalue spectrum of the one-speed neutron transport equation has been investigated in the case of an infinite slab with reflective boundary conditions and isotropic scattering. The region Re ( ) v Σ t , too, is mainly contained in the resolvent set of the operator, the continuous spectrum consisting of only a set of discrete lines. Further it is shown that a finite number of real decay constants also exist in this region. We also give an upper limit for the magnitude of these eigenvalues. The analysis is supported by numerical calculations.

Non-monotonic variation of the criticality factor with the degree of anisotropy in one-speed neutron transport

Abstract The criticality factor c has been calculated for one—speed neutrons in spheres, infinite slabs and cylinders. The scattering is assumed to be a combination of linearly an isotropic scattering and strongly forward (Inonu) scattering. The earlier observed non—monotonic variation of the criticality factor with the degree of forward scattering has been shown to exist in this case, too, for slabs and cylinders. However, for such systems below a certain size the variation is monotonic. To facilitate these studies a simple criterion has been derived.

Thermal neutron induced charged particle reactions on58,59,61Ni

The thermal neutron induced charged particle spectroscopy on58, 59, 61Ni (target nuclei) was done at the 87 m thermal neutron curved guide of the Grenoble high flux reactor. In the59Nu(n, α)56Fe reaction two lines showed up corresponding toα-particle transitions to the ground and first excited states in56Fe with σα0=13.1±1.1 b and σα1 =0.188±0.01 b. A value of σγα≦13 mb was obtained for the two-step59Ni(n, γα)56Fe reaction. The technique to unfold theγα-spectrum and to get information on the primary low energyγ-rays is given and the present and our previous data on the143Nd(n, γα)140Ce reaction are analysed. For the59Ni(n, p)59Co reactionp0=1.34±0.18b,σp1<0.30 b were determined. The cross-sections for the58Ni(n,α)55Fe and61Ni(n,α)58Fe reactions were σα0≦30 Μb and σα0≦30 Μb respectively; these andσp1upper limit value are about 20–1500 times lower than the existing data. The other results are compared with the existing data and the differences are explained. The experimental data are compared with the values obtained from the statistical model.

Time eigenvalues for one–speed neutrons in reflected spheres

Abstract The spectrum of time eigenvalues has been studied for one-speed neutrons in isotropically scattering spheres with a reflexion coefficient R in the interval −1 ≤ R ≤ 1. It is proved that a continuous spectrum exists in the Hilbert space. This continuum disappears if we suitably enlarge the function space. It is also proved that for R ≤ 0 there are only discrete eigenvalues on the real axis. However, for R > 0 there is a continuum of eigenvalues beyond the Corngold limit. An expression is given for the lower boundary of the continuum, and it is supported through numerical calculations.

Comments on “Dispersion Law in Anisotropic Scattering Media, by T. Hino & Y. Ozawa”: Eigenvalues in Time-Dependent Monoenergetic Neutron Systems with Anisotropic Scattering

In a note to this journal Hino & Ozawa(1) have discussed the dispersion law in linearly anisotropically scattering media with application to the time-dependent problem. Already Davison(2) derived the corresponding eigenvalue equation for a stationary, critical system, and the problem has also been treated by Mika(3) and Meister(4). Thielheim & Claussenc(5) have given curves of the eigenvalues for various degrees of anisotropy. All these results for critical, stationary systems can easily be applied to time-dependent moderator systems through the wellknown close correspondence between such systems(6). Moreover, the eigenvalues for the time-dependent problem have been discussed by Meister(4) and by Kugeerc(7), who sketched the general behaviour of the eigenvalue curves. It is the purpose of this note to give a more complete picture of the eigenvalues in the time-dependent case.

DIFFUSION OF PARTICLES IN THE PRESENCE OF STRONG FORWARD–BACKWARD ANISOTROPIC SCATTERING

ABSTRACT We consider one-speed transport problems with forward–backward-isotropic scattering in an infinite medium and study its relationship with the diffusion equation. Both time dependent and time independent transport equations are considered. We also obtain the Greens function for this scattering model.

Criticality eigenvalues of the one-speed transport equation with strong forward—backward scattering -relationship with rod model

Abstract The one—speed neutron transport equation with strong forward and backward scattering (characterized by α and β) has been solved analytically for an infinite slab with a finite order Sn method. It is shown that the solution changes smoothly as c(α + β) passes unity. For a fixed criticality factor, c, a finite thickness is obtained both for α + β = 1/c and = 1. When the number of directions goes to infinity, the critical slab thickness vanishes at c(α + β) = 1. The total flux is then asymptotically given by a cosine function going to zero at the boundary. This is in contrast to the integral equation, which gives a different flux distribution. The results are supported by numerical calculations using the S4, S16 and S96 approximations.

One-speed neutron transport in spheres with totally absorbing cores

Stationary and time-dependent transport of neutrons of one speed has been studied in spheres with totally absorbing cores. For stationary, critical reactors the number of secondaries per collision has been calculated numerically for various inner and outer radii. In the time-dependent case, the decay constant has been calculated for spherical shells of different inner radii and thicknesses. For a fixed ratio between shell thickness and inner radius, the curve of the decay constant versus shell thickness crosses the Corngold limit in the same way as the curve for a homogeneous sphere. When the ratio goes to zero the curve approaches that for an infinite slab. The behaviour is discussed in view of a new result from collision theory, viz. that the following condition must be fulfilled for a body at the point where the decay constant curve crosses the Corngold limit: the average exit distance of the neutrons is equal to the mean free path for scattering.