Measurement of the coherent neutron scattering length of 3He by neutron interferometry

A precise determination of the coherent scattering length of ³He with a neutron interferometer yields a value a_c = 4.29 ± 0.04 fm. A comparison with varoous theoretical perdictions is made and its relation to the few-body problem is discussed. A combination with other experimental results yield as most probable values for the free singlet- and triplet scattering length a_s = 8.0 ± fm and a_t = 3.05 ± 0.07 fm, respectively.     

Fredholm approximants for potential scattering

An approximate method based on Fredholm approximants is used to solve Lippmann-Schwinger equation fors-andp-wave Yukawa ands-wave exponential potential scattering problems. The method is then applied to a problem ofπ-π scattering i nvolving the use of a well known equivalent potential. The equation for partial wave amplitudes is solved to generate the first threeπ-π resonances,ρ, f ₀, andg, in a self-consistent manner.     

Neutron-interferometric measurement of the coherent scattering length of the isotopes of silver

Employing a new measuring scheme with the D 18 Neutron Interferometer at the ILL, Grenoble, the thermal neutron coherent scattering lengthb _c for bound atoms of natural Ag,¹⁰⁷Ag and¹⁰⁹Ag have been measured at the wavelengthλ=1.8742 Å. The results, corrected for composition and density of the actual samples, are nat Ag:b _c =5.922 (7) fm¹⁰⁷Ag:¹⁰⁷ b _c =7.555 (11) fm¹⁰⁹Ag:¹⁰⁹ b _c =4.165 (11) fm The result is in agreement with an earlier value obtained with the interferometer for nat Ag (5.932 (6)) using a different measuring scheme and a totally different sample. For nat Ag and¹⁰⁷Ag the values determined interferometrically are ?0.05 and ?0.08 fm smaller, repectively, than those measured with the Christiansen filter method.     

A precise measurement of the spin-dependent neutron scattering length of 3He

The poor knowledge of the spin-dependent neutron scattering length of ³He has until now handicapped nuclear four body theory and the interpretation of excitations in the quantum liquid. We have measured, for the first time directly, the real part of the bound incoherent neutron scattering length, b_i′ of ³He. A neutron spin echo spectrometer was used to detect pseudomagnetic precession of polarised neutrons passing through polarised ³He gas. Any absolute calibrations of sample and beam parameters were avoided using simple transmission measurements with non-polarised neutrons. The only a priory information required was the spin-dependent neutron absorption cross section of ³He. The result is b_i′ = -2.365(20) fm, which reduces the prior uncertainty by a factor 30. The corresponding new value of the bound incoherent scattering cross section is σ_i = 1.532(12) barn. Including the known value of the coherent neutron scattering length, we obtain new values for the real parts of the free triplet and singlet neutron scattering lengths, a_-′ = 7.370(58) fm and a₊′ = 3.278(53) fm.     

Precision measurement of the coherent neutron scattering length of 3He through neutron interferometry

Improved knowledge of the real part of the neutron scattering length of ³He is important for further development of nuclear few-body theory, as well as for a thorough understanding of neutron scattering off quantum liquids. The real part of the bound incoherent neutron scattering length b_i' has recently been measured directly with an experimental uncertainty of better than 1% by means of spin echo spectrometry. The uncertainty of the more fundamental bound multiplet scattering lengths b_±' is thus limited by today's 1.2% uncertainty of the spin-independent coherent part b_c'. Employing the skew-symmetric perfect crystal Si-interferometer at the S18 experimental site at ILL, Grenoble, we have re-measured the real part of the bound coherent neutron scattering length b_c' of ³He. Our result b_c' = 6.010(21)fm exhibits a significant deviation compared to the latest accepted value b_c' = 5.74(7)fm (H. Kaiser, H. Rauch, G. Badurek, W. Bauspiess, U. Bonse, Z. Phys. A 291, 231 (1979)). Including the known value of the incoherent neutron scattering length, we obtain new values for the real parts of the free singlet and triplet scattering lengths, a_-' = 7.573(30)fm and a₊' = 3.480(18)fm. Our result contravenes by more than 7 standard deviations the measurement of the same physical quantity that has recently been performed by a group at NIST in a very similar experiment (P.R. Huffman, D.L. Jacobson, K. Schoen, M. Arif, T.C. Black, W.M. Snow, S.A. Werner, Phys. Rev. C 70, 014004 (2004)) which yielded b_c' = 5.853(7)fm.     

Neutron scattering lengths of molten metals determined by gravity refractometry

Very accurate values of the coherent neutron scattering lengths of the heavy elements Bi and Pb are important quantities for the investigation of the electric interactions of neutrons with atoms. We performed, therefore, a series of experiments to determine accurate scattering lengths by means of neutron gravity refractometry on liquid mirrors of molten metals. The possible perturbations of the necessary reflection measurements have been discussed in details. After taking into account the uncertainties and corrections associated with observable pertubations we obtained the following values for bound atoms:b(Bi)=8.532±0.002 fm,b(Pb)=9.405±0.003 fm,b(Tl)=8.776±0.005 fm,b(Sn)=6.225±0.002 fm andb(Ga)=7.288±0.002 fm. These data are corrected for the local field effect occuring in the reflection on liquids. The recently reported results for the neutron's electric polarizability and the neutron-electron scattering length are supported by the Bi- and Pb-scattering length of this work.     

Neutron interferometric measurement of the coherent scattering length of cobalt

A precise determination of the coherent scattering length of Co with a neutron interferometer yields a valueb _Co =2.53(5) fm. It agrees well with the value 2.5(1) fm measured by Moon from diffraction work, but there is a disagreement with a value proposed by Koester et al. based on the Christiansen filter method.     

Refractive scattering and the nuclear rainbow in the interaction of12, 13C with12C at 20MeV/N

The elastic and inelastic scattering and the neutron transfer have been measured for the systems¹²C +¹²C and¹³C +¹²C at 20MeV/N up to θ_cm= 60° with theQ3D -spectrometer. The angular distributions of the elastic scattering show an enhanced cross section at angles larger than 40°. It can be identified as refractive scattering with the clear signature of a nuclear rainbow.L-cut-off calculations show that these contributions come fromL-values which are significantly lower than the grazingL-value. The deflection function has a broad minimum in thisL-range which is typical for rainbow scattering. TheS-matrix is decomposed by a phenomenological parametrization into a refractive and a diffractive part. The interference of these amplitudes plays an important role in the rainbow enhancement. The spatial localization of the refractive scattering is deduced from the turning points of the corresponding trajectories; a localization between 2.5 fm and 4 fm is found. Semi-classical calculations with complex trajectories in the single-turning-point approximation show good agreement with the quantummechanical calculations. Refractive contributions are not observed in the inelastic scattering. This can be explained by reducing the strength of the conventional collective form factor in the internal region. In contrast to this the enhancement at large angles is seen in the one-neutron transfer channels where the refractive scattering is dominant. This is the first observation of such contributions to heavy-ion transfer reactions.     

The n-n S-wave scattering length from the neutron spectra of the reaction π− +d → 2n+γ

We present a measurement of the neutron-neutron S-wave scattering length, a_nn, from an analysis of the neutron energy and angular spectra for the reaction d(π^?, γ)2n. This reaction provides the unique advantage that while all three final-state particles are experimentally detectable, only the neutrons are strongly interacting. The data are analyzed using the treatment of this reaction given by Bander, taking the effects of experimental resolution into account with Monte Carlo techniques. Two independent analyses of 4200 events yield a_nn = ?16.7 ±1.3 fm assuming r_nn = 2.65 fm. This value is in good agreement with calculations of a_nn which assume charge symmetry of the nuclear components of p-p and n-n interactions.     

The neutron zero-energy total cross section and scattering lengths for tritium

New results for the neutron total cross section for tritium extrapolate to 1.70 ± 0.03 b at zero energy. With a theoretical constraint A₁/A₀=0.92 ± 0.04, the scattering lengths A₁=3.60 ± 0.10, A₀ = 3.91 ± 0.12, and A_c=3.68 ± 0.05 fm can be inferred independently of, but consistently with, the previous experimental value for the coherent length A_c=3.82 ± 0.24 fm.     

Neutron-neutron effective range from quasifree scattering 2H(n,nn)p at 25 MeV

A neutron coincidence spectrum from the deuteron breakup ²H(n, nn)p was measured at the kinematical condition of quasifree neutron-neutron scattering with 25 MeV neutrons in the entrance channel. The efficiencies of both scintillation detectors were calibrated in the same experimental arrangement as the breakup measurement was performed. The neutron flux was monitored by a proton recoil telescope. Absorption, double scattering and geometric conditions have been simulated by the Monte Carlo technique. From a fit based on the Ebenhöh-Bruinsma-Stuivenberg code with the neutron-neutron scattering length a_nn = ?16.6 fm for the effective range, the value r_{nn = 2.69 ± 0.27 fm} was determined.     

Determination of the neutron scattering length of208Pb by the neutron interferometry method

The coherent scattering length of²⁰⁸Pb was measured by means of the neutron interferometry method and the value ofb _c =9.494(29) fm was obtained.     

On low energy pion-pion scattering

Pion-pions andp-wave amplitudes are investigated by means of dispersion relations for the inverse partial wave amplitudes. Possible low energy zeros of thes-waves are taken into account and their positions as well as other parameters are determined by the imposition of the Balachandran-Nuyts crossing constraints and Martin's conditions and by postulating the existence of the ? meson. Very narrow bands of solutions are obtained, where theI=J=0 phase shifts reach 90° and thes-wave scattering lengthsa ₀ vary between 0.13 and 0.23m _π ^-1 and the ratiosa ₀/a ₂ between —1.8 and —3.5. It is shown that inelasticity or the passage through 180° of δ ₀ ⁰ near 1 GeV do not change much the predictions in the low energy region.     

Experimentelle Untersuchungen der Reaktionenp (d,pp) n undd (d,dp) n mit 51,5 MeV Deuteronen

The external beam of 51.5 MeV deuterons from the Karlsruhe isochronous cyclotron was used to investigate the three particle reactionsp(d,pp)n andd(d, dp)n. A kinematically complete experiment was performed by detecting the two emitted protons respectively the proton and the deuteron in coincidence. The data for the reactionp (d, pp) n exhibit a pronounced final state interaction between the outgoing neutron and one proton. This final state interaction is mainly due to then— p singlet interaction and the extractedn— p scattering length is ¦a_s¦=(19±2.5) fm. In the investigation of the reactiond(d, dp)n the angles were chosen as to observe quasielastic deuteron-proton-scattering predominantly. The data was analysed in terms of the Chew Low Spectator model and we obtained by “on-energy-shell” extrapolation for thed?p cross section the value (7±2.5) [mb/sr]. This value has to be compared with the cross section for freed?p scattering which was independently measured and the value obtained for the corresponding angle is (16±1) [mb/sr].     

New methods for interferometric neutron scattering lengths measurements

A skew symmetric neutron interferometer has been used for tests of a nondispersive and phase contrast variation measuring technique of scattering lengths and for the measurement of anomalous scattering lengths of strongly absorbing substances. The following bound coherent scattering lengths have been obtained: b_c(Pt)=9.60 ± 0.01 fm, b_c(Te) =5.6 ± 0.1 fm and as real parts of anomalous scattering lengths at λ=l.86Å: b_c(Sm) =0.7 ± 0.2 fm, b_c(Eu)=5.3 ± 0.3fm, b_c(Gd)=5.1 ±0.4 fm, b_c(Dy)=16.9 ± 0.3 fm.     

The scattering of slow neutrons by phosphorus and nitrogen

The coherent scattering lengthsb and the free cross sections for the scattering of slow neutrons by P and N were measured on powdered samples. From the results we derived data for the incoherent cross sections and for the spin state scattering lengths. We found for phosphorus:b=5.13±0.01 fm, σ_free=3.134±0.010b and σ_inc=0.006±0.016b, and for nitrogen:b=9.36±0.02 fm, σ_free=10.03 ±0.08 b and σ_inc=0.4±0.1 b. Derived values for resonance parameters of N are given.     

The scattering of slow neutrons by cobalt

Different techniques have been used to determine with slow neutrons the coherent scattering amplitude b_c and the total scattering cross-section σ_sc of Co. We found values for the bound atom b_c=2.78+0.04 fm and for the free nucleus σ_sc=5.95+0.05 barns.From these quantities, the spin state scattering amplitudes b₊ and b_? corresponding to the compound nucleus states of spin I+1/2 or I?1/2 have been determined as b₊=?2.78±0.04 fm and b_?=+9.91±0.06 fm. These results are not in agreement with previous data, but they are found to be consistent with data obtained from resonance parameters.     

Determination of isotope shift crossed-second-order-effects and hyperfine-structure parameters in the Eu I configuration 4f 7 6s7s

In the Eu I configuration 4f ⁷(⁸ S)6s7s the isotope shift (IS) and hyperfine-structure (hfs) of the levelse ⁸ S _7/2 andf ⁸ S _7/2 were determined from the transitions 684.5 nm, 733.7 nm and 821.0 nm to 4f ⁷6s6p. Together with experimental results of our previous measurements a theoretical analysis of the IS and hfs for the complete configuration 4f ⁷ 6s7s can now be carried out. From the IS of the four 6s7s-levels we evaluated the two crossed-second-order-parametersg ₃(4f,6s)= ?l.l(l)mK andg ₃(4f, 7s)= ?0.1(l)mK. The ratiog ₃/G ₃ is determined for various Eu configurations and found to be equal to 5.6(3)·10^?6 in complete agreement with a theoretical value following from Hartree-Fock calculations. The single electron hfs splitting constantsa ¹⁰(4f)= ?1.9 (3) mK,a ¹⁰(6s)=396(3)mK, anda ¹⁰(7s)=65(3)mK are also determined and compared with those of other Eu configurations.