Three-nucleon Force Effects Research Articles

PROTON-DEUTERON BREAK-UP MEASUREMENTS WITH BINA AT 135 MeV

High-precision measurements of the proton-deuteron elastic and break-up reaction have been performed in the past at KVI and elsewhere with the aim to study three-nucleon force (3NF) effects. In the present work, we explored 3NF effects in the break-up scattering process by performing a measurement of vector analyzing powers and differential cross sections using a 135 MeV polarized-proton beam impinging on a liquid-deuterium target. For this study, we used a new experimental setup, Big Instrument for Nuclear-polarization Analysis, BINA, which covers almost the entire kinematical phase space of the break-up reaction. The results are interpreted with the help of state-of-the-art Faddeev calculations.

Analysis of the Effects of Three-nucleon Forces in A = 3, 4 Systems

It is not possible to reproduce both the three- and four-nucleon binding energies using the available two-nucleon potentials. This is one manifestation of the need to include a three-nucleon force in the corresponding Hamiltonian. In this paper we will analyze the capability of a three-nucleon force model to describe not only the aforementioned binding energies but also some N − d low energy scattering observables.

A systematic study of 3NF effects in p + d break-up with BINA at 190 MeV

A systematic study of three-nucleon force (3NF) effects in break-up reactions has been carried out at KVI at several energies. In this article, the p + d → p + p + n reaction with a polarized-proton beam of 190 MeV will be discussed. The experiment was performed by exploiting a new detector called BINA. Some results for high-precision vector analyzing powers and differential cross sections are presented and compared with state-of-the-art Faddeev calculations with or without 3NF.

Study of three-body systems at KVI

In the past few years, a program has been set up at KVI to study the effects of three-nucleon forces in various reactions. Several observables in elastic and break-up channels in proton-deuteron scattering have been measured and compared with state-of-the-art Faddeev calculations using modern two-body forces and a number of three-body forces. For the elastic scattering process, the data-base is now large enough to perform a partial wave analysis to provide an unambiguous description of nuclear forces.

Elastic proton-deuteron scattering at intermediate energies

Observables in elastic proton-deuteron scattering are sensitive probes of the nucleon-nucleon interaction and three-nucleon force effects. The present experimental database for this reaction is large, but contains a large discrepancy between data sets for the differential cross section taken at 135 MeV/nucleon by two experimental research groups. This article reviews the background of this problem and presents new data taken at Kernfysisch Versneller Instituute (KVI). Differential cross sections and analyzing powers for the ${}^{2}\mathrm{H}(\stackrel{\ensuremath{\rightarrow}}{p},d)p$ and ${}^{1}\mathrm{H}(\stackrel{\ensuremath{\rightarrow}}{d},d)p$ reactions at 135 MeV/nucleon and 65 MeV/nucleon, respectively, have been measured. The differential cross-section data differ significantly from previous measurements and consistently follow the energy dependence as expected from an interpolation of published data taken over a large range at intermediate energies.

Nuclear Theory - Nuclear Power

Nuclear Theory - Nuclear PowerThe results from modern nuclear theory are accurate and reliable enough to be used for practical applications, in particular for scattering that involves few-nucleon systems of importance to nuclear power. Using well-established nucleon-nucleon (NN) interactions that fit well the NN scattering data, and the AGS form of the three-body theory, we have performed precise calculations of low-energy neutron-deuteron (n+d) scattering. We show that three-nucleon force effects that have impact on the low-energy vector analyzing powers have no practical effects on the angular distribution of then+dcross-section. There appear to be problems for this scattering in the evaluated nuclear data file (ENDF) libraries, at the incident neutron energies less than 3.2 MeV. Supporting experimental data in this energy region are rather old (>25 years), sparse and often inconsistent. Our three-body results at low energies, 50 keV to 10.0 MeV, are compared to the ENDF/B-VII.0 and JENDL (Japanese Evaluated Nuclear Data Library) -3.3 evaluated angular distributions. The impact of these results on the calculated reactivity for various critical systems involving heavy water is shown.

Spin-dependent three-nucleon force effects on nucleon-deuteron scattering

We construct a phenomenological three-nucleon force (3NF) model that gives a good description of polarization observables in elastic nucleon-deuteron ($N\text{\ensuremath{-}}d$) scattering at a low energy together with a realistic nucleon-nucleon force and a 3NF arising from the exchange of two pions. Parameters of the model, which consists of spin-independent, spin-orbit, and tensor components, are determined to reproduce the three-nucleon binding energy and polarization observables in $N\text{\ensuremath{-}}d$ scattering at 3 MeV. Predictions of the 3NF model on $N\text{\ensuremath{-}}d$ polarization observables at higher energies are examined, and the effects of each component on the observables are investigated.

Study of three-nucleon force effects in [formula omitted] break-up with BINA

Extensive studies of three-nucleon force (3NF) effects in elastic proton-deuteron scattering have been performed at KVI and elsewhere in the past. In the present work, we explored 3NF effects in the break-up scattering process by performing high precision measurement of vector analyzing powers and differential cross sections using a 190 MeV polarized-proton beam on a liquid deuterium target. The experiment was performed by exploiting a new detector called Big Instrument for Nuclear-polarization Analysis, BINA. Its unique design enables coverage of almost the complete reaction phase space. Preliminary differential cross sections and vector analyzing powers are presented and results are compared with state-of-the-art three-nucleon calculations.

Measurements of the [formula omitted] scattering at 250 MeV and three-nucleon forces

The differential cross sections and the vector analyzing powers for the nd elastic scattering at E n = 250 MeV have been measured for the study of the three-nucleon force (3NF) effects in the Coulomb-free system. To cover a wide angular region, the experiments were performed by using two different methods at the ( n , p ) facility and at the NTOF facility which constructed at the Research Center for Nuclear Physics (RCNP). The results were compared with theoretical predictions of the Faddeev calculations based on the modern nucleon-nucleon (NN) forces with the three-nucleon force (3NF). The inclusion of 3NFs leads to a good description of the cross section except for the backward angles. The results were also compared with the theoretical predictions with relativistic corrections. The direct data-to-data comparison of the cross sections of the nd and pd was performed.

Study of three-nucleon systems at KVI

In the past few years, a program has been setup at KVI in order to study the effects of three-nucleon forces in various reactions. Several observables in elastic and break-up channels in proton-deuteron scattering have been measured and compared with the state-of-the-art Faddeev calculations using modern two-body potentials and a number of three-body forces. Results show that, despite the successes of the calculations in predicting many observables, there are serious discrepancies calling for further investigation of the three-body forces.

Short-range three-nucleon forces effects on nucleon-deuteron scattering

Effects of three-nucleon forces arising from the exchange of a pion and a scalar-isoscalar object among three nucleons on nucleon-deuteron scattering observables are studied.

Three-nucleon force effects in cross section and spin observables of elastic deuteron-proton scattering at 90 MeV/nucleon

The cross section and several spin-dependent observables have been measured with high precision for the reaction H(d,p)d at 90 MeV/nucleon. Several calculations were performed based either purely on two-nucleon potentials or also including three-nucleon potentials (3NP). The cross sections are consistent with all calculations including 3NPs. However, no single calculation reproduces the analyzing powers and spin-transfer coefficients, although some spin observables are reproduced to various degrees by the different calculations. A good understanding of the spin structure of 3NP is still lacking.

Precision measurement of vector and tensor analyzing powers in elastic deuteron-proton scattering

High-precision vector and tensor analyzing powers of elastic deuteron-proton ( d + p) scattering have been measured at intermediate energies to investigate effects of three-nucleon forces. Angular distributions in the range of 70°-120° in the center-of mass frame for incident-deuteron energies E d lab = 130 and 180 MeV were obtained using the RIKEN facility. The beam polarization was unambiguously determined by measuring the ^12C (d, α)^10B(2+) reaction at 0°. Results of the measurements are compared with state-of-the-art three-nucleon calculations. The present modeling of nucleon-nucleon forces and its extension to the three-nucleon system is not sufficient to describe the high-precision data consistently and requires, therefore, further investigation.

The elastic pd scattering analyzing powers and spin correlation coefficients at Elab p = 135 and 200 MeV: Three-nucleon force and relativistic effects

The rich set of data for analyzing powers and spin correlation coefficients in pd elastic scattering at Elabp = 135 and 200 MeV taken at IUCF has been compared to theoretical predictions based on modern nuclear forces. To this aim the three-nucleon Faddeev equations have been solved with standard nucleon-nucleon potentials (AV18, CD Bonn, NijmI and II) alone or combined with the 2π-exchange Tucson-Melbourne three-nucleon force. For the AV18 potential also the Urbana IX three-nucleon interaction has been used. For some spin observables the addition of these three-nucleon forces improves the description of data whereas in other cases the description deteriorates. The relativistic effects for all studied spin observables have been investigated and found to be small. The conclusion is that significant parts of the three-nucleon force are missing.

New data for totalHe3(γ,p)D andHe3(γ,pp)n cross sections compared to current theory

A simultaneous measurement of the cross sections of the $^{3}\mathrm{He}$($\ensuremath{\gamma},p$)D and $^{3}\mathrm{He}$($\ensuremath{\gamma},\mathit{pp}$)n reactions has been performed for the first time using monoenergetic pulsed \ensuremath{\gamma}-rays at $\ensuremath{\langle}{E}_{\ensuremath{\gamma}}\ensuremath{\rangle}=$10.2 and 16.0 MeV. Charged fragments from the reactions were detected with an efficiency of 100% using a 4\ensuremath{\pi} time projection chamber containing $^{3}\mathrm{He}$ gas as an active target. The incident \ensuremath{\gamma}-ray flux was measured by a \ensuremath{\gamma}-ray detector. Both the track and energy loss signals of charged fragments were obtained in an off-line analysis and used to clearly identify the reaction channel. Thus, the ($\ensuremath{\gamma},p$) and ($\ensuremath{\gamma},\mathit{pp}$) cross sections have been determined with small uncertainty. A comparison of the new data to current theory based on the AV18+Urbana IX nuclear forces including \ensuremath{\pi}- and \ensuremath{\rho}-like meson exchange currents shows a severe discrepancy at 10.2 MeV, while at 16.0 MeV data and theory agree within about 12%. Three-nucleon force effects are small, but in general shift the theory in the correct direction.

Neutron-deuteron breakup experiment atEn=13MeV: Determination of the1S0neutron-neutron scattering lengthann

We report on results of a kinematically complete neutron-deuteron breakup experiment performed at Triangle Universities Nuclear Laboratory using an ${E}_{n}=13$ MeV incident neutron beam. The ${}^{1}{S}_{0}$ neutron-neutron scattering length ${a}_{\mathit{nn}}$ has been determined for four production angles of the neutron-neutron final-state interaction configuration. The absolute cross-section data were analyzed with rigorous three-nucleon calculations. Our average value of ${a}_{\mathit{nn}}=\ensuremath{-}18.7\ifmmode\pm\else\textpm\fi{}0.7$ fm is in excellent agreement with ${a}_{\mathit{nn}}=\ensuremath{-}18.6\ifmmode\pm\else\textpm\fi{}0.4$ fm obtained from capture experiments of negative pions on deuterons. We also performed a shape analysis of the final-state interaction cross-section enhancements by allowing the normalization of the data to float. From these relative data, we obtained an average value of ${a}_{\mathit{nn}}=\ensuremath{-}18.8\ifmmode\pm\else\textpm\fi{}0.5$ fm, in agreement with the result obtained from the absolute cross-section measurements. Our result deviates from the world average of ${a}_{\mathit{nn}}=\ensuremath{-}16.7\ifmmode\pm\else\textpm\fi{}0.5$ fm determined from previous kinematically complete neutron-deuteron breakup experiments, including the most recent one carried out at Bonn. However, this low value for ${a}_{\mathit{nn}}$ is at variance with theoretical expectation and other experimental information about the sign of charge-symmetry breaking of the nucleon-nucleon interaction. In agreement with theoretical predictions, no evidence was found of significant three-nucleon force effects on the neutron-neutron final-state interaction cross sections.

Systematic study of three-nucleon force effects in the cross section of the deuteron-proton breakup at 130 MeV

High precision cross-section data of the deuteron-proton breakup reaction at 130 MeV are presented for 72 kinematically complete configurations. The data cover a large region of the available phase space, divided into a systematic grid of kinematical variables. They are compared with theoretical predictions, in which the full dynamics of the three-nucleon (3N) system is obtained in three different ways: realistic nucleon-nucleon (NN) potentials are combined with model 3N forces (3NF's) or with an effective 3NF resulting from explicit treatment of the Delta-isobar excitation. Alternatively, the chiral perturbation theory approach is used at the next-to-next-to-leading order with all relevant NN and 3N contributions taken into account. The generated dynamics is then applied to calculate cross-section values by rigorous solution of the 3N Faddeev equations. The comparison of the calculated cross sections with the experimental data shows a clear prefernce for the predictions in which the 3NF's are included. The majority of the experimental data points is well reproduced by the theoretical predictions. The remaining discrepancies are investigated by inspecting cross sections integrated over certain kinematical variables. The procedure of global comparisons leads to establishing regularities in disagreements between the experimental data and the theoretically predicted values of the cross sections. They indicate deficiencies still present in the assumed models of the 3N system dynamics.

Systematic investigation of three-nucleon force effects in elastic scattering of polarized protons from deuterons at intermediate energies

The question, whether the high-quality nucleon-nucleon potentials can successfully describe the three-nucleon system, and to what extent three-nucleon forces (3NFs) play a role, has become very important in nuclear few-body physics. One kinematic region where effects because of 3NFs show up is in the minimum of the differential cross section of elastic nucleon-deuteron scattering. Another observable, which could give an indication about the contribution of the spin to 3NFs, is the vector analyzing power. To investigate the importance of 3NFs systematically over a broad range of intermediate energies, both observables of elastic proton-deuteron scattering have been measured at proton bombarding energies of 108, 120, 135, 150, 170, and 190 MeV, covering an angular range in the center-of-mass system between ${30}^{\ifmmode^\circ\else\textdegree\fi{}}$ and ${170}^{\ifmmode^\circ\else\textdegree\fi{}}$. The results show unambiguously the shortcomings of calculations employing only two-body forces and the necessity of the inclusion of 3NFs. They also show the limitations of the results of the present day models for few-nucleon systems at backward angles, especially at higher beam energies. New calculations based on chiral perturbation theory are also presented and compared with the data at the lowest energy.

The reactionH2(p,pp)nin three kinematical configurations atEp=16MeV

We measured the cross sections of the $^2$H(p,pp)n breakup reaction at E$_p$=16 MeV in three kinematical configurations: the np final-state interaction (FSI), the co-planar star (CST), and an intermediate-star (IST) geometry. The cross sections are compared with theoretical predictions based on the CD Bonn potential alone and combined with the updated 2$\pi$-exchange Tucson-Melbourne three-nucleon force (TM99'), calculated without inclusion of the Coulomb interaction. The resulting excellent agreement between data and pure CD Bonn predictions in the FSI testifies to the smallness of three-nucleon force (3NF) effects as well as the insignificance of the Coulomb force for this particular configuration and energy. The CST also agrees well whereas the IST results show small deviations between measurements and theory seen before in the pd breakup space-star geometries which point to possible Coulomb effects. An additional comparison with EFT predictions (without 3NF) up to order N$^3$LO shows excellent agreement in the FSI case and a rather similar agreement as for CD Bonn in the CST and IST situations.

Three-body electrodisintegration of the three-nucleon bound state withΔ-isobar excitation: Processes below pion-production threshold

Electron scattering from the three-nucleon bound state with two- and three-body disintegration is described. The description uses the purely nucleonic charge-dependent CD-Bonn potential and its coupled-channel extension CD-Bonn + $\Delta$. Exact solutions of three-particle equations are employed for the initial and final states of the reactions. The current has one-baryon and two-baryon contributions and couples nucleonic with $\Delta$-isobar channels. $\Delta$-isobar effects on the observables are isolated. The $\Delta$-isobar excitation yields an effective three-nucleon force and effective two- and three-nucleon currents beside other $\Delta$-isobar effects; they are mutually consistent.