Theoretical Evaluation of Neutron-nucleus Scattering Parameters from Experimental Data in the 6 ≤ A ≤ 60 Mass Region

Abstract

Systematic calculations of the neutron-nucleus scattering parameters at several neutron energies Ei < 2 keV have been performed for 37 isotopes (6Li,... 59Co) in the mass region of 6 ≤ A ≤ 60, using the large compilation of experimental neutron-nucleus scattering data obtained in Garching. In the first stage of these calculations, the s-wave potential scattering radius R’, the scattering lengths bcoh, b±, and the bound state parameters (Eb, Γγ , gΓ0n) have been calculated for each isotope, employing the general least squares fit (GLSQF) for the experimental and the corresponding theoretical values of the total neutron-nucleus cross sections σexptot(Ei) at several energies Ei, absorption cross sections σabs(Eo) and of the coherent scattering lengths bcoh. The theoretical expressions for these parameters were deduced on the basis of the usual S-matrix formalism with no assumption about the particular shape of the optical model potential. In the second stage of our calculations, the spherical Fiedeldey- Frahn optical potential was employed for the pure theoretical description or the above mentioned neutron-nucleus scattering characteristics. The results obtained have been analyzed and compared with the values deduced from measurements.

New measurements of the coherent and incoherent neutron scattering lengths of13C

“…The zero spin of the isotope 12 C results in b incoh,12C = 0, whereas 13 C has I = 1/2 and leads to the following expressions: b coh,13C = b 13C = 3 be good agreement in the literature that the sign of 13 C's incoherent scattering length is negative, implying b +13C < b −13C . The currently accepted value of b incoh,13C = −0.52(9) fm fromGlättli et al (1979) is consistent with the theoretical result of −0.4 fm byNormand (1977) and has the same sign as the value of −0.26 fm deduced from the work ofAleksejevs et al (1998).On adopting this negative sign, the final value from our diffraction data becomesb incoh,13C = −0.42 ± 0.24 fm, and thus b +13C − b −13C = −0.97(55) fm from equation (3.11). Using our result for b coh,13C = 6.542(3) fm and equations (3.12) and (3.13), we can then derive spin-dependent scattering lengths of b +13C = 6.30(14) fm and b −13C = 7.27(42) fm, which are not very consistent with the values of b +13C = 5.6(5) fm and b −13C = 6.2(5) fm as tabulated by Rauch…”

“…The standard tabulated value of b incoh,13C = −0.52(9) fm results from a polarized neutron scattering experiment that measured the nuclear polarization of 13 C present in a sample of Ba 13 CO 3 powder (Glättli et al 1979). This standard value for b incoh,13C is marginally consistent with the theoretical value of −0.4 fm by Normand (1977), but the recent work of Aleksejevs et al (1998) suggests the smaller-magnitude value of −0.26 fm.…”

“…For I = 0, this leads to two spin-dependent scattering lengths b + (up) and b − (down). In our case of a non-polarized scattering system, the isotope's coherent and incoherent scattering lengths can be expressed as and Waschkowski (2002) and derived from the data-fitting calculations of Aleksejevs et al (1998). By contrast, the result of Glättli et al (1979) for b +13C − b −13C = −1.2(2) fm, when combined with our value for b coh,13C , leads to b +13C = 6.24(5) fm and b −13C = 7.44( 16) fm, which are consistent with our values for the spin-dependent scattering lengths, as expected.…”

Internal consistency of neutron coherent scattering length measurements from neutron interferometry and from neutron gravity reflectometry

“…Future analyses which make use of new data and also other high-precision neutron cross section measurements which extend over a broader range of neutron energies and momentum transfers can make use of this feature to help determine an internally-consistent set of values for b ne and b p and constrain α and λ. An example of a successful global analysis of this type was presented long ago [82] for a broad set of neutron optics and scattering data for n-A scattering for 6 < A < 60 using a S-matrix treatment of the potential and resonance scattering parameters, including a consistent treatment of effects from sub-threshold resonances.…”

The bound coherent neutron scattering lengths of the oxygen isotopes

“…The bound coherent b coh and incoherent b incoh neutron scattering lengths listed in today's standard tables (e.g. Rauch and Waschkowski 2003, Aleksejevs et al 1998, Sears 1992, Koester et al 1991, Mughabghab et al 1981 date largely from measurements performed decades ago and often have large experimental uncertainties or even recognizable systematic errors. These uncertainties are becoming a significant limitation to the attainable accuracy of neutron diffraction data, given the improvements offered by modern neutron diffraction instrumentation in terms of low systematic error and high counting statistics precision (e.g.…”