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Physical Review A

Precision measurement of the bound-coherent-neutron scattering length of U235

M. Arif, Helmut Kaiser, S. Werner, Jeffrey O. Willis

Published Apr 1, 1987• 9 citations
Publisher

Abstract

With use of the neutron interferometric technique, the real parts of the bound-coherent scattering length, b, of $^{235}\mathrm{U}$ have been precisely measured for five different incident neutron energies in the range of 30 to 92 meV. The value of b at each incident neutron energy was obtained from the average of two independent measurements using two samples of different thicknesses. The results are b=10.47\ifmmode\pm\else\textpm\fi{}0.04 fm (E=30.34 meV), b=10.47\ifmmode\pm\else\textpm\fi{}0.03 fm (E=41.02 meV), b=10.51\ifmmode\pm\else\textpm\fi{}0.03 fm (E=51.43 meV), b=10.39\ifmmode\pm\else\textpm\fi{}0.03 fm (E=74.90 meV), b=10.41\ifmmode\pm\else\textpm\fi{}0.03 fm (E=91.39 meV). The uncertainty in these results is about an order of magnitude smaller than the present literature value. The small energy dependence of the observed scattering lengths has been used to establish the parameters of the negative energy resonance level (-1.4 eV) using the Breit-Wigner formalism.

DOI
10.1103/physreva.35.2810

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With use of the neutron interferometric technique, the real parts of the bound-coherent scattering length, b, of 235U^{235}\mathrm{U}235U have been precisely measured for five different incident neutron energies in the range of 30 to 92 meV. The value of b at each incident neutron energy was obtained from the average of two independent measurements using two samples of different thicknesses. The results are b=10.47\ifmmode\pm\else\textpm\fi{}0.04 fm (E=30.34 meV), b=10.47\ifmmode\pm\else\textpm\fi{}0.03 fm (E=41.02 meV), b=10.51\ifmmode\pm\else\textpm\fi{}0.03 fm (E=51.43 meV), b=10.39\ifmmode\pm\else\textpm\fi{}0.03 fm (E=74.90 meV), b=10.41\ifmmode\pm\else\textpm\fi{}0.03 fm (E=91.39 meV). The uncertainty in these results is about an order of magnitude smaller than the present literature value. The small energy dependence of the observed scattering lengths has been used to establish the parameters of the negative energy resonance level (-1.4 eV) using the Breit-Wigner formalism.
Review of Indirect Methods Used to Determine the 1S0^1S_01S0​ Neutron-Neutron Scattering Length
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We have extended an earlier phase-shift analysis of $p{\ensuremath{-}}^{3}\mathrm{He}$ scattering data by including additional low-energy measurements in the dataset. The $p{\ensuremath{-}}^{3}\mathrm{He}$ zero-energy scattering lengths obtained from this analysis depend sensitively on a group of cross section and analyzing power measurements at proton energies below 1 MeV. When this group of measurements is included in the dataset, two possible phase-shift solutions are found. The first solution yields a singlet scattering length of as=15.1fm{a}_{s}=15.1\mathrm{fm}as​=15.1fm and a triplet scattering length of at=7.9fm,{a}_{t}=7.9\mathrm{fm},at​=7.9fm, while the second solution yields values of as=7.2fm{a}_{s}=7.2\mathrm{fm}as​=7.2fm and at=10.4fm.{a}_{t}=10.4\mathrm{fm}.at​=10.4fm. Without this group of measurements, the best-fit scattering lengths are as=10.3fm{a}_{s}=10.3\mathrm{fm}as​=10.3fm and at=8.2fm.{a}_{t}=8.2\mathrm{fm}.at​=8.2fm. We believe that the scattering lengths are currently not well determined experimentally and that additional low-energy $p{\ensuremath{-}}^{3}\mathrm{He}$ data are needed in order to clarify the situation.
The conventional theory of neutron beams interacting with many-body systems treats the beam as a classical system, i.e. with its dynamical variables appearing in the quantum dynamics of the scattering process not as operators but only as c-numbers. Moreover, neutrons are described with plane waves, i.e. the concept of neutron's (finite) coherence length is here irrelevant. The same holds for electron, atom or X-ray scattering. This simplification results in the full decoupling of the probe particle's dynamics from the quantum dynamics of the scatterer---a well-known fact also reflected in the standard formalism of time-correlation functions (see textbooks). Making contact with modern quantum theoretical approaches (e.g., quantum entanglement, 'which-path detection' versus interference, von Neumann measurement, Week Values, etc.) new observable effects may be exposed and/or predicted, for instance, a momentum-transfer deficit and an intensity deficit in neutron scattering from protons of hydrogen-containing samples. 7
In continuation of previous work explicitly demonstrating the basic quantum-mechanical principles of the static and the time-dependent superposition of spinors, a new double-resonance coil experiment is described, where a spin-flip process associated with an exchange of energy quanta happens in both beams of a perfect-crystal neutron interferometer. It is shown that under the given circumstances of neutron self-interference coherence is preserved in spite of the energy transfer to every neutron, which may stimulate renewed epistemological discussions about the interpretation of quantum mechanics. Furthermore quantum beating on a macroscopic time scale has been observed by introducing an exceedingly small energy difference of 8.6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}17}$ eV between the two interfering beams. According to the statistical accuracy of the data thereby an energy sensitivity of 2.7\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}19}$ eV has been achieved.
The perfect crystal neutron interferometer has been used continuously for test measurements on quantum mechanics. Polarized neutrons were used to perform the quantum mechanical spin-superposition experiment on a macroscopic scale. This experiment was continued with two resonance coils in the beams, in which the coherence persisted, even if an energy exchange occurred with certainty between the neutron and the resonator system. A quantum beat effect was observed when slightly different resonance frequencies were applied to both beams. In this case, an extremely high energy sensitivity of 2.7×10 −19 eV was achieved. Neutron spectroscopy is thus able to cover time domains from microscopic to macroscopic scales. All the results obtained until now are in agreement with the formalism of quantum mechanics and stimulate discussion about the interpretation of this basic theory L'interferometre a neutrons a cristal parfait a servi sans discontinuer a faire des mesures tests en mecanique quantique. Des neutrons polarises ont ete utilises pour effectuer une experience de superposition de spins quantiques a l'echelle macroscopique. Cette experience fut reprise, en interposant deux solenoides resonnants dans les faisceaux et la coherence montree persister meme si un echange d'energie s'effectuait de maniere certaine entre le neutron et le systeme resonnant. Un effet de battement quantique a ete observe quand des frequences de resonance legerement differentes sont appliquees aux deux faisceaux. Dans ce cas une sensibilite en energie extremement grande (2,7×10 −19 et) a ete atteinte. La spectroscopie de neutrons peut donc couvrir des domaines temporels allant de l'echelle microscopique a l'echelle macroscopique. Tous les resultats obtenus jusqu'a present sont en accord avec le formalisme de la mecanique quantique et suscite des discussions sur l'interpretation de cette theorie fondamentale
In the standard Breit-Wigner approach to scattering the phase shift is to have a form tan⁡δBW=Γ1/(E1−E)\tanδ_{\rm BW} =Γ_1/(E_1-E)tanδBW​=Γ1​/(E1​−E) at a real energy resonance. This leads to complex energy poles in the scattering amplitude at EBW=E1−iΓ1E_{\rm BW}=E_1-iΓ_1EBW​=E1​−iΓ1​, poles that are identified with unstable physical particles. By solving the square well scattering problem we identify some challenges to this approach. We find that setting tan⁡δBW=Γ1/(E1−E)\tanδ_{\rm BW} =Γ_1/(E_1-E)tanδBW​=Γ1​/(E1​−E) is not always a good description of the real energy scattering amplitude, that Γ1Γ_1Γ1​ can be negative, that EBWE_{\rm BW}EBW​ is not in fact an energy eigenvalue (and thus not a physical particle), and that states that decay in energy possess spatial wave functions that unacceptably grow exponentially. All of this is resolved by noting that because of its antilinear PTPTPT symmetry solutions to the square well Schrödinger equation appear in complex conjugate energy pairs E∓=E2∓iΓ2E_{\mp}=E_2\mp i Γ_2E∓​=E2​∓iΓ2​ with E−≠EBWE_- \neq E_{\rm BW}E−​=EBW​, doing so in a way that gives a time independent probability amplitude that neither grows nor decays in time or space, and leads to just one now observable physical resonance not two.