Theoretical Study of the d(d, p)^{3}H and d(d, n)^{3}He Processes at Low Energies

We present a theoretical study of the processes d(d,p)^{3}H and d(d,n)^{3}He at energies of interest for energy production and for big-bang nucleosynthesis. We accurately solve the four body scattering problem using the ab initio hyperspherical harmonics method, starting from nuclear Hamiltonians which include modern two- and three-nucleon interactions, derived in chiral effective field theory. We report results for the astrophysical S factor, the quintet suppression factor, and various single and double polarized observables. A first estimate of the theoretical uncertainty for all these quantities is provided by varying the cutoff parameter used to regularize the chiral interactions at high momentum.

Measurement of the Nucleon F_{2}^{n}/F_{2}^{p} Structure Function Ratio by the Jefferson Lab MARATHON Tritium/Helium-3 Deep Inelastic Scattering Experiment

The ratio of the nucleon F_{2} structure functions, F_{2}^{n}/F_{2}^{p}, is determined by the MARATHON experiment from measurements of deep inelastic scattering of electrons from ^{3}H and ^{3}He nuclei. The experiment was performed in the Hall A Facility of Jefferson Lab using two high-resolution spectrometers for electron detection, and a cryogenic target system which included a low-activity tritium cell. The data analysis used a novel technique exploiting the mirror symmetry of the two nuclei, which essentially eliminates many theoretical uncertainties in the extraction of the ratio. The results, which cover the Bjorken scaling variable range 0.19<x<0.83, represent a significant improvement compared to previous SLAC and Jefferson Lab measurements for the ratio. They are compared to recent theoretical calculations and empirical determinations of the F_{2}^{n}/F_{2}^{p} ratio.

The baryon density of the Universe from an improved rate of deuterium burning

Light elements were produced in the first few minutes of the Universe through a sequence of nuclear reactions known as Big Bang nucleosynthesis (BBN)^1,2. Among the light elements produced during BBN^1,2, deuterium is an excellent indicator of cosmological parameters because its abundance is highly sensitive to the primordial baryon density and also depends on the number of neutrino species permeating the early Universe. Although astronomical observations of primordial deuterium abundance have reached percent accuracy³, theoretical predictions^4-6 based on BBN are hampered by large uncertainties on the cross-section of the deuterium burning D(p,γ)³He reaction. Here we show that our improved cross-sections of this reaction lead to BBN estimates of the baryon density at the 1.6 percent level, in excellent agreement with a recent analysis of the cosmic microwave background⁷. Improved cross-section data were obtained by exploiting the negligible cosmic-ray background deep underground at the Laboratory for Underground Nuclear Astrophysics (LUNA) of the Laboratori Nazionali del Gran Sasso (Italy)^8,9. We bombarded a high-purity deuterium gas target¹⁰ with an intense proton beam from the LUNA 400-kilovolt accelerator¹¹ and detected the γ-rays from the nuclear reaction under study with a high-purity germanium detector. Our experimental results settle the most uncertain nuclear physics input to BBN calculations and substantially improve the reliability of using primordial abundances to probe the physics of the early Universe.

Nonresonant Density of States Enhancement at Low Energies for Three or Four Neutrons

The low energy systems of three or four neutrons are treated within the adiabatic hyperspherical framework, yielding an understanding of the low energy quantum states in terms of an adiabatic potential energy curve. The dominant low energy potential curve for each system, computed here using widely accepted nucleon-nucleon interactions with and without the inclusion of a three-nucleon force, shows no sign of a low energy resonance. However, both systems exhibit a low energy enhancement of the density of states, or of the Wigner-Smith time delay, which derives from long-range universal physics analogous to the Efimov effect. That enhancement could be relevant to understanding the low energy excess of correlated four-neutron ejection events observed experimentally in a nuclear reaction by Kisamori et al. [Phys. Rev. Lett. 116, 052501 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.052501].

Correlations imposed by the unitary limit between few-nucleon systems, nuclear matter, and neutron stars

The large values of the singlet and triplet two-nucleon scattering lengths locate the nuclear system close to the unitary limit. This particular position strongly constrains the low-energy observables in the three-nucleon system as depending on one parameter, the triton binding energy, and introduces correlations in the low-energy sector of light nuclei. Here we analyze the propagation of these correlations to infinite nuclear matter showing that its saturation properties, the equation of state of β-stable nuclear matter, and several properties of neutron stars, as their maximum mass, are well determined solely by a few number of low-energy quantities of the two- and three-nucleon systems. In this way we make a direct link between the universal behavior observed in the low-energy region of few-nucleon systems and fundamental properties of nuclear matter and neutron stars.

Erratum: Chiral Effective Field Theory Predictions for Muon Capture on Deuteron and ^{3}He [Phys. Rev. Lett. 108, 052502 (2012)]

This corrects the article DOI: 10.1103/PhysRevLett.108.052502.

Light-Nuclei Spectra from Chiral Dynamics

In recent years local chiral interactions have been derived and implemented in quantum Monte Carlo methods in order to test to what extent the chiral effective field theory framework impacts our knowledge of few- and many-body systems. In this Letter, we present Green's function Monte Carlo calculations of light nuclei based on the family of local two-body interactions presented by our group in a previous paper in conjunction with chiral three-body interactions fitted to bound- and scattering-state observables in the three-nucleon sector. These interactions include Δ intermediate states in their two-pion-exchange components. We obtain predictions for the energy levels and level ordering of nuclei in the mass range A=4-12, accurate to ≤2% of the binding energy, in very satisfactory agreement with experimental data.

Publisher's Note: JLab Measurements of the ^{3}He Form Factors at Large Momentum Transfers [Phys. Rev. Lett. 119, 162501 (2017)]

This corrects the article DOI: 10.1103/PhysRevLett.119.162501.

JLab Measurements of the ^{3}He Form Factors at Large Momentum Transfers

The charge and magnetic form factors, F_{C} and F_{M}, respectively, of ^{3}He are extracted in the kinematic range 25  fm^{-2}≤Q^{2}≤61  fm^{-2} from elastic electron scattering by detecting ^{3}He recoil nuclei and scattered electrons in coincidence with the two High Resolution Spectrometers of the Hall A Facility at Jefferson Lab. The measurements find evidence for the existence of a second diffraction minimum for the magnetic form factor at Q^{2}=49.3  fm^{-2} and for the charge form factor at Q^{2}=62.0  fm^{-2}. Both minima are predicted to exist in the Q^{2} range accessible by this Jefferson Lab experiment. The data are in qualitative agreement with theoretical calculations based on realistic interactions and accurate methods to solve the three-body nuclear problem.

Erratum: Implication of the Proton-Deuteron Radiative Capture for Big Bang Nucleosynthesis [Phys. Rev. Lett. 116, 102501 (2016)]

This corrects the article DOI: 10.1103/PhysRevLett.116.102501.

Implication of the Proton-Deuteron Radiative Capture for Big Bang Nucleosynthesis

The astrophysical S factor for the radiative capture d(p,γ)^{3}He in the energy range of interest for big bang nucleosynthesis (BBN) is calculated using an ab initio approach. The nuclear Hamiltonian retains both two- and three-nucleon interactions-the Argonne v_{18} and the Urbana IX, respectively. Both one- and many-body contributions to the nuclear current operator are included. The former retain for the first time, besides the 1/m leading order contribution (m is the nucleon mass), also the next-to-leading order term, proportional to 1/m^{3}. The many-body currents are constructed in order to satisfy the current conservation relation with the adopted Hamiltonian model. The hyperspherical harmonics technique is applied to solve the A=3 bound and scattering states. Particular attention is paid in this second case in order to obtain, in the energy range of BBN, an uncertainty on the astrophysical S factor of the order or below ∼1%. Then, in this energy range, the S factor is found to be ∼10% larger than the currently adopted values. Part of this increase (1%-3%) is due to the 1/m^{3} one-body operator, while the remaining is due to the new more accurate scattering wave functions. We have studied the implication of this new determination for the d(p,γ)^{3}He S factor on the deuterium primordial abundance. We find that the predicted theoretical value for ^{2}H/H is in excellent agreement with its experimental determination, using the most recent determination of the baryon density of the Planck experiment, and with a standard number of relativistic degrees of freedom N_{eff}=3.046 during primordial nucleosynthesis. This calls for a more accurate measurement of the astrophysical S factor in order to confirm the present predictions.

Measurement of double-polarization asymmetries in the quasielastic (3)He[→](e[→],e(')d) process

We present a precise measurement of double-polarization asymmetries in the ^{3}He[over →](e[over →],e^{'}d) reaction. This particular process is a uniquely sensitive probe of hadron dynamics in ^{3}He and the structure of the underlying electromagnetic currents. The measurements have been performed in and around quasielastic kinematics at Q^{2}=0.25(GeV/c)^{2} for missing momenta up to 270  MeV/c. The asymmetries are in fair agreement with the state-of-the-art calculations in terms of their functional dependencies on p_{m} and ω, but are systematically offset. Beyond the region of the quasielastic peak, the discrepancies become even more pronounced. Thus, our measurements have been able to reveal deficiencies in the most sophisticated calculations of the three-body nuclear system, and indicate that further refinement in the treatment of their two-and/or three-body dynamics is required.

JLab measurement of the 4He charge form factor at large momentum transfers

The charge form factor of 4He has been extracted in the range 29  fm(-2) ≤ Q2 ≤ 77  fm(-2) from elastic electron scattering, detecting 4He recoil nuclei and electrons in coincidence with the high resolution spectrometers of the Hall A Facility of Jefferson Lab. The measurements have uncovered a second diffraction minimum for the form factor, which was predicted in the Q2 range of this experiment. The data are in qualitative agreement with theoretical calculations based on realistic interactions and accurate methods to solve the few-body problem.

Effect of three-nucleon interactions in p-(3)He elastic scattering

We present a detailed study of the effect of different three-nucleon interactions in p-(3)He elastic scattering at low energies. In particular, two interactions have been considered: one derived from effective field theory at next-to-next-to-leading order and one derived from a more phenomenological point of view-the so-called Illinois model. The four-nucleon scattering observables are calculated by using the Kohn variational principle and the hyperspherical harmonics technique, and the results are compared with available experimental data. We have found that the inclusion of both interactions improves the agreement with the experimental data, in particular, for the proton vector analyzing power.

Chiral effective field theory predictions for muon capture on deuteron and {3}He

The muon-capture reactions {2}H(μ{-},ν{μ})nn and {3}He(μ{-},ν{μ}){3}H are studied with nuclear potentials and charge-changing weak currents, derived in chiral effective field theory. The low-energy constants (LECs) c{D} and c{E}, present in the three-nucleon potential and (c{D}) axial-vector current, are constrained to reproduce the A=3 binding energies and the triton Gamow-Teller matrix element. The muon-capture rates on deuteron and {3}He are predicted to be 399±3  sec{-1} and 1494±21  sec{-1}, respectively. The spread accounts for the cutoff sensitivity, as well as uncertainties in the LECs and electroweak radiative corrections. By comparing the calculated and precisely measured rates on {3}He, a value for the induced pseudoscalar form factor is obtained in good agreement with the chiral perturbation theory prediction.

Thermal neutron captures on d and 3He

We report on a study of the nd and n(3)He radiative captures at thermal neutron energies, using wave functions obtained from either chiral or conventional two- and three-nucleon realistic potentials with the hyperspherical-harmonics method, and electromagnetic currents derived in chiral effective field theory up to one loop. The predicted nd and n(3)He cross sections are in good agreement with data, but exhibit a significant dependence on the input Hamiltonian. A comparison is also made between these and new results for the nd and n(3)He cross sections obtained in the conventional framework for both potentials and currents.

Integral relations for three-body continuum states with the adiabatic expansion

The application of the hyperspherical adiabatic expansion to describe three-body scattering states suffers from the problem of very slow convergence. Contrary to what happens for bound states, a huge number of hyper-radial equations has to be solved, and even if done, the extraction of the scattering amplitude is problematic. In this Letter we show how to obtain accurate scattering phase shifts using the hyperspherical adiabatic expansion. To this aim two integral relations, derived from the Kohn variational principle, are used. The convergence of this procedure is as fast as for bound states.

Isospin mixing in the nucleon and 4He and the nucleon strange electric form factor

In order to isolate the contribution of the nucleon strange electric form factor to the parity-violating asymmetry measured in 4He(e-->],e')4He experiments, it is crucial to have a reliable estimate of the magnitude of isospin-symmetry-breaking (ISB) corrections in both the nucleon and 4He. We examine this issue in the present Letter. Isospin admixtures in the nucleon are determined in chiral perturbation theory, while those in 4He are derived from nuclear interactions, including explicit ISB terms. A careful analysis of the model dependence in the resulting predictions for the nucleon and nuclear ISB contributions to the asymmetry is carried out. We conclude that, at the low momentum transfers of interest in recent measurements reported by the HAPPEX Collaboration at Jefferson Lab, these contributions are of comparable magnitude to those associated with strangeness components in the nucleon electric form factor.

Polarization transfer in 4He(e-->,e'p-->)3H: is the ratio G E p/G M p ) modified in the nuclear medium?

Polarization observables in the (4)He(e-->,e'p-->)(3)H reaction are calculated using accurate three- and four-nucleon bound-state wave functions, a realistic model for the nuclear electromagnetic current operator, and a treatment of final-state interactions with an optical potential. In contrast to earlier studies, no significant discrepancies are found between theory and experiment both for the ratio of transverse to longitudinal polarization transfers and for the induced polarization, when free-nucleon electromagnetic form factors are used in the current operator. The present results challenge the current interpretation of the experimental data in terms of medium-modified form factors.

Precision measurement of the spin-dependent asymmetry in the threshold region of 3He(e, e')

We present the first precision measurement of the spin-dependent asymmetry in the threshold region of 3He(e,e') at Q2 values of 0.1 and 0.2 (GeV/c)2. The agreement between the data and nonrelativistic Faddeev calculations which include both final-state interactions and meson-exchange current effects is very good at Q2 = 0.1 (GeV/c)2, while a small discrepancy at Q2 = 0.2 (GeV/c)2 is observed.

The A(y) problem for p-3He elastic scattering

We present evidence that numerically accurate quantum calculations employing modern internucleon forces do not reproduce the proton analyzing power, A(y), for p- 3He elastic scattering at low energies. These calculations underpredict new measured analyzing powers by approximately 30% at E(c.m.) = 1.20 MeV and by 40% at E(c.m.) = 1.69 MeV, an effect analogous to a well-known problem in p-d and n-d scattering. The calculations are performed using the complex Kohn variational principle and the (correlated) hyperspherical harmonics technique with full treatment of the Coulomb force. The inclusion of the three-nucleon interaction does not improve the agreement with the experimental data.

Transverse asymmetry AT' from the quasielastic 3He(e,e') process and the neutron magnetic form factor

We have measured the transverse asymmetry A(T') in 3He(e,e(')) quasielastic scattering in Hall A at Jefferson Laboratory with high precision for Q2 values from 0.1 to 0.6 (GeV/c)(2). The neutron magnetic form factor G(n)(M) was extracted based on Faddeev calculations for Q2 = 0.1 and 0.2 (GeV/c)(2) with an experimental uncertainty of less than 2%.

Realistic calculation of the 3He + p (hep) astrophysical factor

The astrophysical factor for the proton weak capture on 3He is calculated with correlated hyperspherical harmonic wave functions corresponding to a realistic Hamiltonian consisting of the Argonne v(18) two-nucleon and Urbana-IX three-nucleon interactions. The nuclear weak current has vector and axial-vector components with one- and many-body terms. All possible transitions connecting any of the p 3He S- and P-wave channels to 4He are considered. The S factor at a p 3He center-of-mass energy of 10 keV is predicted to be 10. 1x10(-20) keV b, a factor of approximately 4.5 larger than the value adopted in the standard solar model. The P-wave transitions are found to contribute about 40% of the calculated S factor.