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.     

On the Present Status of the Problem of Charge Dependence and Charge Asymmetry of the Nucleon-Nucleon Force

The charge dependence of the nucleon-nucleon force can be derived from the low-energy scattering parameters. The p-p and n-p parameters were measured in direct scattering experiments. The n-n parameters a_nn = (-16.70 ± 0.38) fm and r_nn = (2.78 ± 0.13) fm have been determined from few particle reactions. The difference of the scattering lengths (a_nn - a_nn) ≈ 7 fm demonstrates the violation of the charge independence. Information on the charge symmetry is still doubtful due to the inaccuracy of the charge correction for the p-p parameters. Whereas the n-n and the charge corrected p-p parameters known at present yield a weaker n-n force than the p-p force, the opposite result follows from the binding energy difference for ³He and ³H and the meson theory of the nuclear forces.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Feasibility Study of D(3H,3He)nn Experiment Searching for nn Ground State

Possibility of existence of nn ground state was discussed in 2011 by H. Witala and W. Glöckle based on anomalous enhancement of nn QFS (Quasi-Free Scattering) cross section in nd breakup at E _n = 26 MeV reported in 2002. To search for the nn ground state, we have made a feasibility study of D(³H,³He)nn and D(n, p)nn experiments. ³H and n secondary beams are produced respectively by D(d,³H)p and D(d, n)³He reactions at forward angle, and are injected on a CD₂ foil target. If an nn ground state exists, a single peak is observed in the ³He and p energy spectra. We conclude that these experiments are feasible.     

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.     

Solving the differential Yakubovsky equations for p 3He scattering by the cluster-reduction method

The cluster-reduction method has been used to solve numerically the differential equations for the s-wave Yakubovsky components in the nppp system. Proton scattering on a ³He nucleus has been considered for energies below the three-body threshold in the singlet and triplet spin states of the system. Nucleon-nucleon interaction has been simulated by the MT I–III potential, and the Coulomb interaction between the protons has been taken into account. Effective equations that describe the relative motion of clusters have been derived. The low-energy behavior of phase shifts has been analyzed. The values of ¹ A=8.2 fm and ³ A=7.7 fm have been obtained for, respectively, the singlet and triplet scattering lengths. The calculated phase shifts agree well with experimental data.     

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.     

Elastic scattering of 32S on 24Mg, 27Al and 40Ca and the effect of nuclear forces on the grazing collision

Elastic scattering of ³²S ions on ²⁴Mg, ²⁷Al and ⁴⁰Ca has been measured at energies between 67 MeV and 120 MeV. Angular distributions were analyzed with the optical model with Woods-Saxon potentials. Strong absorption radii are extracted with and without consideration of the nuclear interaction at the surface. The nuclear potential decreases the otherwise anomalously large strong absorption radii which can then be described by a radius parameter of r₀ = 1.41 fm.     

On the unitary pole expansion of the potentials I and III of Malfliet and Tjon

The unitary pole expansion for the local soft-core potentials I and III of Malfliet and Tjon is obtained, and the Faddeev-Lovelace equations are solved for the separable potentials. The energyE _T of the triton and the doublet scattering length² a have been obtained. The results are ?8.59 MeV ≦E_T≦ ?8.57 MeV and 0.89 fm≦² a≦0.91 fm. For the quartet scattering length a value₄ a = 6.39 fm has been found.