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.     

Particle mixing and charge asymmetric nuclear forces

The charge asymmetric effect of ?ω and πη electromagnetic mixing on the ¹S₀ NN potential is reviewed. It is found that the ?ω contribution dominates and leads to an n-n potential which is more attractive than the p-p potential. The shift in the scattering lengths is then calculated to be |a_nn|?|a_pp| ≈ 0.9 fm and the shift in effective ranges is r_nn?r_pp ≈ ?0.02 fm.     

Investigation of the reaction 2H(n,np) at θn = 0°

The differential cross section of the ²H(n, np) reaction was measured at θ_n = 0°. Because of the applied special geometry the experimental data extend over a large fraction of the phase space, including several final state interaction regions as well as regions far from the dominance of quasi-two-body processes. The experiment was analysed with an exact three-body calculation using s-wave separable potentials (CEE). The analysis of the n-n and n-p final state interaction peaks gave a_nn = ?16.3 ± 1.6 fm for the n-n ¹S₀ scattering length and r_nn = 3.15 ± 0.7 fm for the effective range. Remarkable deviations from the calculated cross sections-were found in regions where no strong final state interaction was present.     

n-n Effective range from the photon spectrum of the reaction π−d→γnn

Notable improvements in the treatment of the reaction π^?d→γnn, extending the validity of the calculation to lower photon energies, permit a new analysis of a high statistics photon spectrum. A precise value of the effective range parameter γ_nn = 2.83 ± 0.11 fm has been obtained. The theoretical uncertainty is 0.11 fm. The value of the scattering length previously extracted from the same spectrum is confirmed, with a_nn = ? 18.6 ± 0.5 fm.     

Determination of low-energy parameters of neutron-neutron scattering from an analysis of the binding-energy difference between the 3H and 3He mirror nuclei

A relation between quantities that characterize the breaking of the charge symmetry of nuclear forces in systems of two and three nucleons is found on the basis of an analysis of the binding-energy difference between the ³H and ³He mirror nuclei. For the neutron-neutron scattering length and effective range, the values of a _nn = ?18.38(55) fm and r _nn = 2.84(4) fm, respectively, were obtained by using purely nuclear parameters of proton-proton scattering in the ¹ S ₀ state. The calculated values agree with present-day experimental results.     

A study of the n-n interaction from a complete experiment of the n + d break-up at 14.5 MeV

Results of the analysis of two complete experiments on ²H(n, nnp) at 14.5±0.1 MeV are given. In the first n-n final-state-interaction (f.s.i.) experiment (neutron lab angles θ₁ = θ₂ = +30°, n-n relative energy E_nn measured between 0 and ≈ 800 keV) about 4400 events were recorded. In the second n-p f.s.i. experiment (neutron lab angles θ₁ = +30°, θ₂ = −80°, and E_np ? 500 keV) about 2860 events were recorded. The analysis has been done by exact solutions of the Faddeev equations with separable potentials: the Amado model was extended using the Yamaguchi potential with charge-independent (a_nm = a_np) and with charge-dependent (a_nn = −16 fm, a_np = −23.7 fm) parameters. The results are: (a) the charge-independent (a_nn = −23.7 fm) model seems to give a better fit for the shape of the n-n f.s.i. peak, but (b) the two-nucleon separable potential calculations disagree by a factor ≈ 2 with the absolute cross sections measured for the f.s.i. peaks.     

Charge-symmetry breaking and n-n scattering lengths

Recent experimental and theoretical investigations of ρ-ω and η-π mixing have caused us to re-examine the effects of these mixings on the charge-symmetry breaking of nuclear forces. The charge asymmetry of the nucleon-nucleon force in the singlet S-state is used to predict the n-n scattering length in terms of the measured p-p one. The extra attraction of the n-n potential in the ¹S₀ state gives rise to a change of roughly −0.8 fm in the corresponding scattering length. The magnitude (and sign) of the charge asymmetry is approximately that required to understand the binding-energy differences of the mirror nuclei ³He-³H and ⁴¹Sc-⁴¹Ca.     

Low-energy parameters of neutron-neutron interaction in the effective-range approximation

The effect of the mass difference between the charged and neutral pions on the low-energy parameters of nucleon-nucleon interaction in the ¹ S ₀ state is studied in the effective-range approximation. On the basis of experimental values of the singlet parameters of neutron-proton scattering and the experimental value of the virtual-state energy for the neutron-neutron systemin the ¹ S ₀ state, the following values were obtained for the neutron-neutron scattering length and effective range: a _nn = ?16.59(117) fm and r _nn = 2.83(11) fm. The calculated values agree well with present-day experimental results.     

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.     

Neutron-neutron scattering length from the reaction γd → πnn employing chiral perturbation theory

We discuss the possibility to extract the neutron-neutron scattering length a_nn from experimental spectra on the reaction γd → π⁺ nn . The transition operator is calculated to high accuracy from chiral perturbation theory. We argue that for properly chosen kinematics, the theoretical uncertainty of the method can be as low as 0.1 fm.     

Determination of the 1S0 neutron-neutron scattering length in the nd breakup reaction at energies in the range En = 40?60 MeV

The first results are obtained in a kinematically complete experiment devoted to measuring the n + d → p + n + n reaction yield at energies in the range E _n = 40−60 MeV and various angles of divergence of two neutrons (Δθ = 4°, 6°, and 8°) in the geometry of neutron-neutron final-state interaction. The ¹ S ₀ neutron-neutron scattering length a _nn is determined by comparing the experimental energy dependence of the reaction yield with the results of a simulation in the Watson-Migdal approximation, which depend on a _nn . For E _n = 40 MeV and Δθ = 6° (the best statistics in the experiment), the value a _nn = −17.9 ± 1.0 fm was obtained. A further improvement of the experimental accuracy will make it possible to remove the existing disagreement of the results from different experiments.     

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.     

Interactions of slow neutrons with the chromium isotopes

Neutron transmission experiments and determinations of coherent scattering lengths were performed on natural chromium and enriched samples of⁵⁰Cr,⁵²Cr,⁵³Cr and⁵⁴Cr. By means of the Christiansen-filter-technique we obtained new values for the scattering lengths of the bound atoms:b(^natCr)=3.635±0.007 fm,b(⁵⁰Cr)=?4.50±0.05 fm,b(⁵²Cr)=4.914±0.015 fm,b(53Cr)=?4.20±0.03 fm, andb(⁵⁴Cr)=4.55±0.10 fm. The transmission experiments with neutrons of 510 ΜeV, 1.26 eV and 5.19 eV energy resulted in data for the absorption cross sectionσ _a (^natCr) =3.05±0.08 b and for the scattering cross section at “zero energy”:σ ₀ (^natCr)=3.381±0.010 b. Data for incoherent and spin-state scattering and for the potential-scattering radius of the nuclei could be deduced from these results.     

On the sign of the ρ-ω mixing charge asymmetric nn potential

The sign of the single-particle exchange nucleon force due to ρ°-ω mixing is shown on experimental and theoretical grounds to make the resulting charge asymmetric potential, V_nn ? V_pp in the ¹S₀ state, attractive. The sign agrees quite well with the binding energy difference in the A = 3 mirror nuclei and is not inconsistent with present knowledge of NN scattering lengths, predicting $\text{0 < ¦}\text{a}{}_{\mathrm{nn}}\text{¦ ? ¦a}{}_{\mathrm{<mtext>pp</mtext>}}\text{¦ ? 1}\text{fm}$.     

Further study of the reaction 2H(n,p2n) near 120 MeV

A kinematically complete experiment on the reaction ²H(n, p2n) is described, in which both outgoing neutrons were detected at a lab angle of 30° so as to enhance their final state interaction in a region far from interfering reaction mechanisms. The data were analysed in terms of the Watson-Migdal model to obtain two independent values for the neutron-neutron scattering length. We find a_nn to be ?13.3^+3.8_?3.1 fm (from a comparison with measurements of p-d breakup), and ? 17.5_?4.5^+4.0 fm (from the shape of the relative neutron energy spectrum), thus validating the Watson-Migdal model in this kinematic region.     

Neutron-neutron scattering length from the 2H(n,np)n reaction at bombarding energies up to 27 MeV

The n-n interaction has been investigated in a kinematically complete experiment with high statistical accuracy via the ²H(n, np)n reaction at bombarding energies up to 27 MeV, extending previous measurements to higher energies and to a different geometry. The analysis with exact three-body calculations yields ann = ?16.9 ± 0.6 fm.     

Universal correlations in pion-less EFT with the resonating group method: Three and four nucleons

The Effective Field Theory “without pions” at next-to-leading order is used to analyze universal bound-state and scattering properties of the 3- and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound-state properties of ³H and ⁴He , and for the singlet S -wave ³He -neutron scattering length a ₀(³He-n) . The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a ₀(³He-n) and the ³H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading order, between the ³H binding energy and the ³H charge radius, and the Tjon line. With the ³H binding energy as input, we get predictions of the effective field theory “without pions” at next-to-leading order for the root mean square charge radius of ³H of (1.6±0.2) fm, for the ⁴He binding energy of (28±2.5) MeV, and for Re{a ₀(³He-n)} of (7.5±0.6) fm. Including the Coulomb interaction, the splitting in binding energy between ³H and ³He is found to be (0.66±0.03) MeV. The discrepancy to data of (0.10±0.03) MeV is model independently attributed to higher-order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher-order effects, and carefully assess that numerical uncertainties are negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the ⁴He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.     

Electron scattering from 70Ge and 72Ge

Cross sections have been measured for the elastic and inelastic scattering of electrons from ⁷⁰Ge and ⁷²Ge for momentum transfers from 0.65 to 1.14 fm^?1. Values for the parameters of a Fermi type ground-state charge distribution were obtained from a phase shift analysis of the elastic cross sections. The rms charge radius corresponding to these parameters is 4.07±0.02 fm for ⁷⁰Ge and 4.05±0.03 fm for ⁷²Ge. Using DWBA analysis the reduced transition probabilities for the electroexcitation of the 2₁⁺ and 3₁^? states were found to be: B(E2, ω)↑ = 19.7±1.2, 26.8±2.0 W.u.; B(E3, ω)↑ = 36±5, 37±7 W.u. for ⁷⁰Ge and ⁷²Ge respectively. The J^π = 3^? assignments for the state at 2.562 MeV in ⁷⁰Ge and 2.515 MeV in ⁷²Ge are confirmed.