Slow-neutron cross sections of hafnium

Abstract

The slow-neutron scattering and related cross sections of hafnium pertinent to neutron diffraction study are the major subject of this paper. Nearly two dozen publications have dealt with cross sections of hafnium, since, apart from control and poison applications in nuclear reactors, the proton-neutron number correlation in hafnium isotopes provides an attractive subject for nuclear energy level studies. However, inconsistencies between the observed cross sections and those computed from the Breit-~¥igner dispersion formula suggest further study on the topic (see Itkin, 1962, for reference summary).The cross sections of naturally occurring hafnium at 293 -+3 °K have been re-examined at 0.0717 -+0.0002 eV (4 = 1.068 _+ ().002 A) and some at 0.0460 eV (/t = 1.333 /~) using a newly constructed neutron diffractometer (Atoji, 1964). The standard deviations cited for our experimental values are obtained from not less than six independent observations. No suitable hafnium compound with reliable composition and structural parameters was available. Consequently, the absolute intensities of hafnium metal filings, with nickel powder as standard, were measured based on the method of substitution and that of mixtures. Lack of sufficient impurity analysis apparently interfered with some of the earlier cross section values. The hafnium metal used in the present work was 99-13 wt. % pure, and was subjected to three independent spectroscopic analyses, which revealed, as major impurities, zirconium 8000 ppm, zinc 440 ppm, titanium 150 ppm and boron 1 ppm. These impurity contributions * Based on work performed under the auspices of the United States Atomic Energy Commission.t In Itkin's report, the mean level spacing of l~THf should read 3.58 eV and the reduced neutron width at 1 eV of 177Hf and 179Hf should be corrected to 2.11 and 0.843 mV respectively. January 1964)were not entirely insignificant in the data processing. Transmission measurements with a double-pinhole 3 cm-path cell were made, to obtain the total cross section. The observed Debye temperatures, 420 _+ 9 °K for Ni and 240 _+ 6 °K for Hf, possess larger uncertainties than the calorimetric values, 440 °K for Ni (Rayne & Kemp, 1956) and 260 °K for Hf (Wolcott, 1957). Subsequently, the latter values were chosen and low-angle reflections were employed for the coherent intensity measurement.The coherent scattering cross section of hafnium (13.2 barns for nickel) was then found to be 7-59 +0.27 barns at 0.0717 and 0-0460 eV, being significantly different from the previous value of 9.73 barns at about 0.046 eV (Sidhu, Heaton & Zauberis, 1956). The sign of the amplitude, b--0-777_+0.014× 10 -12 cm, was reconfirmed to be positive from the HfC0.95 data. For hafnium metal, the cross section values at 0.0717 eV for the total of coherent scattering with the finite diffraction effect (Bacon, 1962, p. 42). Debye thermal elastic incoherent scattering, and the sum of all other scattering are, respectively, 75.3 _+ 0.2, 5-77, 1.61 and approximately 4.0 barns. The paramagnetic sc...

Coherent neutron scattering amplitudes of fissionable nuclei,233U,235U, and239Pu

“…(3) The individual real components, R' and b' are sensitive to the refinement in the resonance analysis, although our conclusion regarding the wavelength dependence of b' will not be affected. (4) The coherent amplitude of naturally occurring uranium, 0.845+0-015, a statistical average of the reported values (Atoji, 1961;Roof et al 1962), can also be assigned to depleted uranium. Finally, the determination of these small b' and b" by means of the coherent-intensity analysis using non-centrosymmetric single crystals would require exceedingly high-accuracy measurement.…”

“…where (gF °) is the weighted-average reduced neutron width and (D) is the mean level spacing. In addition to the positive integers, n, ml and m2, the summation terms include al =E}I)/(D) and a2 = IE)2)I/ (D ), where E} l) and E) 2) are the highest measured positive and negative resonance energies, respectively (cf Atoji, 1964). The summation in (2) is a generalized Riemann zeta function, numerical tables of which have been given by Atoji & Clark (1965).…”