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Physical Review C

Neutron-triton cross sections and scattering lengths obtained fromp −3 He scattering

Gerald M. Hale, D.C. Dodder, J. D. Seagrave, B.L. Berman, T. W. Phillips

Published Jul 1, 1990• 35 citations
Publisher

Abstract

An approximately Coulomb-corrected, charge-symmetric R-matrix prediction for n${\mathrm{\ensuremath{-}}}^{3}$H scattering from analyzing p${\mathrm{\ensuremath{-}}}^{3}$He data is described, which deviates at most by 2% from the n${\mathrm{\ensuremath{-}}}^{3}$H total cross section. The total cross section, together with a new measurement of the coherent scattering length now allows two possible sets of singlet and triplet scattering lengths ${\mathit{a}}_{\mathit{s}}$ and ${\mathit{a}}_{\mathit{t}}$. Our analysis agrees well with the new value of the coherent scattering length, and determines the set with ${\mathit{a}}_{\mathit{s}}$/${\mathit{a}}_{\mathit{t}}$>1 to be the correct one.

DOI
10.1103/physrevc.42.438

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Measuring the Spin-Dependent Scattering Length of $^{3}$He using Neutron Interferometry

M. G. Huber, F. E. Wietfeldt, M. Arif +5 more

Bulletin of the American Physical Society•Oct 12, 2007•0 citations
An approximately Coulomb-corrected, charge-symmetric R-matrix prediction for n\ensuremath−3{\mathrm{\ensuremath{-}}}^{3}\ensuremath−3H scattering from analyzing p\ensuremath−3{\mathrm{\ensuremath{-}}}^{3}\ensuremath−3He data is described, which deviates at most by 2% from the n\ensuremath−3{\mathrm{\ensuremath{-}}}^{3}\ensuremath−3H total cross section. The total cross section, together with a new measurement of the coherent scattering length now allows two possible sets of singlet and triplet scattering lengths as{\mathit{a}}_{\mathit{s}}as​ and at{\mathit{a}}_{\mathit{t}}at​. Our analysis agrees well with the new value of the coherent scattering length, and determines the set with as{\mathit{a}}_{\mathit{s}}as​/at{\mathit{a}}_{\mathit{t}}at​>1 to be the correct one.
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 elastic scattering of two hydrogen atoms interacting at very small energies is explored numerically using the most accurate potential-energy curves available for the X $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ and $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{+}$ states of H2{\mathrm{H}}_{2}H2​. The scattering lengths and low-temperature-averaged cross sections are determined and compared with previous calculations. The scattering lengths are 0.41a0{\mathit{a}}_{0}a0​ for the singlet case and 1.91a0{\mathit{a}}_{0}a0​ for the triplet. The predicted total triplet cross section at 2 K is 5.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ cm2{\mathrm{cm}}^{2}cm2 but it could be lower, at 4.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ cm2{\mathrm{cm}}^{2}cm2, with a different fit to the triplet potential between 12a0{\mathit{a}}_{0}a0​ and 15a0{\mathit{a}}_{0}a0​. A more accurate triplet-state potential is needed at these separations.
Review of Indirect Methods Used to Determine the 1S0^1S_01S0​ Neutron-Neutron Scattering Length
We have determined a value for the 1S0^1S_01S0​ neutron-neutron scattering length (anna_{nn}ann​) from high-precision measurements of time-of-flight spectra of neutrons from the 2H(π−,nγ)n^2H(π^-,n γ)n2H(π−,nγ)n capture reaction. The measurements were done at the Los Alamos Meson Physics Facility by the E1286 collaboration. The high spatial resolution of our gamma-ray detector enabled us to make a detailed assessment of the systematic uncertainties in our techniques. The value obtained in the present work is ann=−18a_{nn} = -18ann​=−18.63 $\pm $0.10 (statistical) ±\pm± 0.44 (systematic) ±\pm± 0.30 (theoretical) fm. This result is consistent with previous determinations of anna_{nn}ann​ from the π−dπ^-dπ−d capture reaction. We found that the analysis of the data with calculations that use a relativistic phase-space factor gives a more negative value for anna_{nn}ann​ by 0.33 fm over the analysis done using a nonrelativistic phase-space factor. Combining the present result with the previous ones from π−dπ^-dπ−d capture gives: ann=−18a_{nn} = - 18ann​=−18.63 ±\pm± 0.27 (expt) ±\pm± 0.30 fm (theory). For the first time the combined statistical and systematic experimental uncertainty in anna_{nn}ann​ is smaller than the theoretical uncertainty and comparable to the uncertainty in the proton-proton 1S0^1S_01S0​ scattering length (appa_{pp}app​). This average value of anna_{nn}ann​ when corrected for the magnetic-moment interaction of the two neutrons becomes -18.9 ±\pm± 0.4 fm which is 1.6 ±\pm± 0.5 fm different from the recommended value of appa_{pp}app​, thereby confirming charge symmetry breaking at the 1% confidence level.
The stochastic variational method is used in conjunction with stabilization ideas to compute the low-energy s-wave phase shifts and scattering lengths for Ps-Ps scattering. The scattering lengths obtained were 8.44a0{8.44a}_{0}8.44a0​ for the singlet-singlet and 3.00a0{3.00a}_{0}3.00a0​ for the triplet-triplet states (the spin state refers to the coupling of the two electrons and the coupling of the two positrons in the system). The positive scattering length in the triplet-triplet channel means a stable Bose-Einstein condensate of triplet Ps atoms is physically possible. The large value of the ${}^{3}{\mathrm{Ps}}^{3}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{Ps}}}^{1}{\mathrm{Ps}}^{1}\mathrm{Ps}$ cross section, $7.41\ensuremath{\pi}{a}_{0}^{2}$ suggests the use of spin-polarized positrons as advanced by Platzmann and Mills [Phys. Rev. B 49 454 (1994)].
The scattering of orthopositronium from He, Ne, Ar, Li+,{\mathrm{Li}}^{+},Li+, Na+,{\mathrm{Na}}^{+},Na+, and K+{\mathrm{K}}^{+}K+ is investigated with the fixed-core stochastic variational method. The scattering length for $\mathrm{Ps}\ensuremath{-}\mathrm{He}$ scattering was 1.57a0,{1.57a}_{0},1.57a0​, a value consistent with the threshold cross sections derived from three positron lifetime experiments. The scattering lengths for the $\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{N}\mathrm{e}$ and $\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{A}\mathrm{r}$ systems were 1.55a0{1.55a}_{0}1.55a0​ and 1.79a0,{1.79a}_{0},1.79a0​, respectively. That there was only a 15% variation among the scattering lengths is compatible with the experiment of Coleman et al. [J. Phys. B 27, 981 (1994)], who found the low-energy cross sections for He, Ne, and Ar to be about the same size. The scattering lengths for Ps scattering from Li+,{\mathrm{Li}}^{+},Li+, Na+,{\mathrm{Na}}^{+},Na+, and K+{\mathrm{K}}^{+}K+ were 12.9a0,{12.9a}_{0},12.9a0​, 28.5a0,{28.5a}_{0},28.5a0​, and $\ensuremath{-}{1.9a}_{0}.$ The relatively small magnitude of the ${\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{K}}^{+}$ scattering length strongly supports previous suggestions that the ${\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{K}}^{+}$ system does not support a bound state. The annihilation parameter 1Zeff{}^{1}{Z}_{\mathrm{eff}}1Zeff​ has also been computed as part of the analysis. The present values of 1Zeff{}^{1}{Z}_{\mathrm{eff}}1Zeff​ are about 2.5--3 times smaller than the accepted experimental values since short-range electron-positron correlations were not taken into consideration when the annihilation matrix element was evaluated.
Measuring the Spin-Dependent Scattering Length of 3^{3}3He using Neutron Interferometry