The hep reaction and the solar neutrino problem

The results of a new calculation of the astrophysical S-factor for the proton weak capture on 3He are here reviewed. The methods used to obtain very accurate initial and final state wave functions and to construct the nuclear weak current operator are described. Finally the implications of these results for the Super-Kamiokande solar neutrino data are discussed.Comment: 10 pages, 1 figure, XVII European Few-Body plenary talk, Evora, September 200

Muon capture on deuteron and the neutron-neutron scattering length

We study the capture rate in the doublet hyperfine initial state for the muon capture reaction $\mu^- + \,^2{\rm H} \rightarrow \nu_\mu + n + n$ ($\Gamma^D$) and the total capture rate for the reaction $\mu^- + \,^3{\rm He} \rightarrow \nu_\mu + \,^3{\rm H}$ ($\Gamma_0$). We investigate whether $\Gamma^D$ and $\Gamma_0$ could be sensitive to the $nn$ $S$-wave scattering length ($a_{nn}$). To this aim, we consider nuclear potentials and weak currents derived within $\chi$EFT. We employ the N3LO chiral potential with cutoff $\Lambda$=500 MeV, but the low-energy constant (LEC) determining $a_{nn}$ is varied so as to obtain $a_{nn}$=-18.95 (the present empirical value), -16.0, -22.0, and +18.22 fm. The last value leads to a $nn$ bound state with a binding energy of 139 keV. The LECs $c_D$ and $c_E$, present in the three-nucleon potential and axial-vector current, are fitted to reproduce the $A=3$ binding energies and the triton Gamow-Teller matrix element. The capture rate $\Gamma^D$ is found to be 399(3) s$^{-1}$ for $a_{nn}$=-18.95 and -16.0 fm; and 400(3) s$^{-1}$ for $a_{nn}$=-22.0 fm. For $a_{nn}$=+18.22 fm, we obtain 275(3) s$^{-1}$ (135(3) s$^{-1}$), when the final $nn$ system is unbound (bound). The rate $\Gamma_0$ is found to be 1494(15), 1491(16), 1488(18), and 1475(16) s$^{-1}$ for $a_{nn}$=-18.95, -16.0, -22.0, and +18.22 fm, respectively. The theoretical uncertainties are due to the fitting procedure and radiative corrections. Our results seem to exclude the possibility of constraining a negative $a_{nn}$ with an uncertainty of less than $\sim \pm$ 3 fm through an accurate determination of the muon capture rates, but the uncertainty on the present empirical value will not complicate the interpretation of the (forth-coming) experimental results for $\Gamma^D$. Finally, a comparison with the already available experimental data discourages the possibility of a bound $nn$ state.Comment: 5 pages, 2 figures; revisited version accepted for publication on Phys. Rev.

Muon capture on light nuclei

This work investigates the muon capture reactions 2H(\mu^-,\nu_\mu)nn and 3He(\mu^-,\nu_\mu)3H and the contribution to their total capture rates arising from the axial two-body currents obtained imposing the partially-conserved-axial-current (PCAC) hypothesis. The initial and final A=2 and 3 nuclear wave functions are obtained from the Argonne v_{18} two-nucleon potential, in combination with the Urbana IX three-nucleon potential in the case of A=3. The weak current consists of vector and axial components derived in chiral effective field theory. The low-energy constant entering the vector (axial) component is determined by reproducting the isovector combination of the trinucleon magnetic moment (Gamow-Teller matrix element of tritium beta-decay). The total capture rates are 393.1(8) s^{-1} for A=2 and 1488(9) s^{-1} for A=3, where the uncertainties arise from the adopted fitting procedure.Comment: 6 pages, submitted to Few-Body Sys

Electroweak structure of light nuclei within chiral effective field theory

We review the results of the most recent calculations for the electromagnetic structure of light nuclei, the weak muon capture on deuteron and 3He and the weak proton-proton capture reaction at energies of astrophysical interest, performed within the chiral effective field theory framework.Comment: 6 pages, 3 figures, submitted to Few-Body System

The proton-proton weak capture in chiral effective field theory

The astrophysical S-factor for proton-proton weak capture is calculated in chiral effective field theory over the center-of-mass relative-energy range 0--100 keV. The chiral two-nucleon potential derived up to next-to-next-to-next-to leading order is augmented by the full electromagnetic interaction including, beyond Coulomb, two-photon and vacuum-polarization corrections. The low-energy constants (LEC's) entering the weak current operators are fixed so as to reproduce the A=3 binding energies and magnetic moments, and the Gamow-Teller matrix element in tritium beta decay. Contributions from S and P partial waves in the incoming two-proton channel are retained. The S-factor at zero energy is found to be S(0)=(4.030 +/- 0.006) x 10^{-23} MeV fm^2, with a P-wave contribution of 0.020 x 10^{-23} MeV fm^2. The theoretical uncertainty is due to the fitting procedure of the LEC's and to the cutoff dependence.Comment: 4 pages, 3 figures; revisited version accepted for publication on Phys. Rev. Lett. A misprint in Table II has been correcte

Effect of three-nucleon interaction in p-3He elastic scattering

We present a detailed study of the effect of different three-nucleon interaction models in p-3He elastic scattering at low energies. In particular, two models 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 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 either one of the other force model improves the agreement with the experimental data, in particular for the proton vector analyzing power.Comment: 4 pages, 3 figure

Electromagnetic Structure of the Trinucleons

The electromagnetic form factors of the trinucleons 3H and 3He are calculated with wave functions obtained with the Argonne AV18 two-nucleon and Urbana IX three-nucleon interactions. Full account is taken of the two-body currents required by current conservation with the AV18 interaction as well as those associated with N-Delta transition currents and the currents of Delta resonance components in the wave functions. Explicit three-nucleon current operators associated with the two-pion exchange three-nucleon interaction arising from irreducible S-wave pion-nucleon scattering is constructed and shown to have very little effect on the calculated magnetic form factors. The calculated magnetic form factor of 3H, and charge form factors of both 3H and 3He are in satisfactory agreement with the experimental data. However, the position of the zero in the magnetic form factor of 3He is slightly underpredicted.Comment: 27 pages RevTex file, 19 PostScript figures, submitted to Phys. Rev.

Effect of three nucleon forces in p-3He scattering

The effect of the inclusion of different models of three nucleon (3N) forces in p-3He elastic scattering at low energies is studied. Two models 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 using the Kohn variational principle and the hyperspherical harmonic technique and the results are compared with available experimental data. We have found that with the inclusion of both 3N force models the agreement with the experimental data is improved, in particular for the proton vector analyzing power A_y.Comment: 8 pages, 4 figures, talk presented at the 20th International IUPAP Conference on Few-Body Problems in Physics, 20 - 25 August, 2012, Fukuoka, Japa

Electrodisintegration of 3^3He below and above deuteron breakup threshold

Recent advances in the study of electrodisintegration of 3He are presented and discussed. The pair-correlated hyperspherical harmonics method is used to calculate the initial and final state wave functions, with a realistic Hamiltonian consisting of the Argonne v18 two-nucleon and Urbana IX three-nucleon interactions. The model for the nuclear current and charge operators retains one- and many-body contributions. Particular attention is made in the construction of the two-body current operators arising from the momentum-dependent part of the two-nucleon interaction. Three-body current operators are also included so that the full current operator is strictly conserved. The present model for the nuclear current operator is tested comparing theoretical predictions and experimental data of pd radiative capture cross section and spin observables.Comment: 5 pages, 5 figures, submitted to Eur. Phys. J.