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.

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

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.

Electromagnetic transitions for A=3 nuclear systems

Recent advances in the study of pd radiative capture in a wide range of center-of-mass energy below and above deuteron breakup threshold are presented and discussed.Comment: Invited lead talk at the 19th European Conference on Few-Body Problems in Physics, Groningen, The Netherlands, 8/23 - 8/27 2004, 5 pages, 4 figure

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.

Electromagnetic structure of A=2 and 3 nuclei and the nuclear current operator

Different models for conserved two- and three-body electromagnetic currents are constructed from two- and three-nucleon interactions, using either meson-exchange mechanisms or minimal substitution in the momentum dependence of these interactions. The connection between these two different schemes is elucidated. A number of low-energy electronuclear observables, including (i) $np$ radiative capture at thermal neutron energies and deuteron photodisintegration at low energies, (ii) $nd$ and $pd$ radiative capture reactions, and (iii) isoscalar and isovector magnetic form factors of $^3$H and $^3$He, are calculated in order to make a comparative study of these models for the current operator. The realistic Argonne $v_{18}$ two-nucleon and Urbana IX or Tucson-Melbourne three-nucleon interactions are taken as a case study. For $A$=3 processes, the bound and continuum wave functions, both below and above deuteron breakup threshold, are obtained with the correlated hyperspherical-harmonics method. Three-body currents give small but significant contributions to some of the polarization observables in the $^2$H($p,\gamma$)$^3$He process and the $^2$H($n,\gamma$)$^3$H cross section at thermal neutron energies. It is shown that the use of a current which did not exactly satisfy current conservation with the two- and three-nucleon interactions in the Hamiltonian was responsible for some of the discrepancies reported in previous studies between the experimental and theoretical polarization observables in $pd$ radiative capture.Comment: 48 pages, 25 figures, 4 tables, revtex4. Submitted to Phys. Rev.

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

The muon-capture reactions 2H(\mu^-,\nu_\mu)nn and 3He(\mu^-,\nu_\mu)3H are studied with nuclear strong-interaction potentials and charge-changing weak currents, derived in chiral effective field theory. The low-energy constants (LEC's) 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 vector weak current is related to the isovector component of the electromagnetic current via the conserved-vector-current constraint, and the two LEC's entering the contact terms in the latter are constrained to reproduce the A=3 magnetic moments. The muon capture rates on deuteron and 3He are predicted to be 399(3) sec^{-1} and 1494 (21) sec^{-1}, respectively, where the spread accounts for the cutoff sensitivity as well as uncertainties in the LEC's and electroweak radiative corrections. By comparing the calculated and precisely measured rates on 3He, a value for the induced pseudoscalar form factor is obtained in good agreement with the chiral perturbation theory prediction.Comment: 4 pages, 2 figures, revisited version accepted for publication on Phys. Rev. Let

Electromagnetic structure of A=2 and 3 nuclei in chiral effective field theory

The objectives of the present work are twofold. The first is to address and resolve some of the differences present in independent, chiral-effective-field-theory (\chiEFT) derivations up to one loop, recently appeared in the literature, of the nuclear charge and current operators. The second objective is to provide a complete set of \chiEFT predictions for the structure functions and tensor polarization of the deuteron, for the charge and magnetic form factors of 3He and 3H, and for the charge and magnetic radii of these few-nucleon systems. The calculations use wave functions derived from high-order chiral two- and three-nucleon potentials and Monte Carlo methods to evaluate the relevant matrix elements. Predictions based on conventional potentials in combination with \chiEFT charge and current operators are also presented. There is excellent agreement between theory and experiment for all these observables for momentum transfers up to q< 2.0-2.5 (1/fm); for a subset of them, this agreement extends to momentum transfers as high as q~5-6 (1/fm). A complete analysis of the results is provided.Comment: 34 pages, Revte

Thermal neutron captures on dd and 3^3He

We report on a study of the $nd$ and n\,^3He 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\,^3He 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\,^3He cross sections obtained in the conventional framework for both potentials and currents.Comment: 4 pages, 4 eps figures; references added; corrections to text and abstract as suggested by referee adde

Tritium β\beta-decay in chiral effective field theory

We evaluate the Fermi and Gamow-Teller (GT) matrix elements in tritium $\beta$-decay by including in the charge-changing weak current the corrections up to one loop recently derived in nuclear chiral effective field theory ($\chi$ EFT). The trinucleon wave functions are obtained from hyperspherical-harmonics solutions of the Schrodinger equation with two- and three-nucleon potentials corresponding to either $\chi$ EFT (the N3LO/N2LO combination) or meson-exchange phenomenology (the AV18/UIX combination). We find that contributions due to loop corrections in the axial current are, in relative terms, as large as (and in some cases, dominate) those from one-pion exchange, which nominally occur at lower order in the power counting. We also provide values for the low-energy constants multiplying the contact axial current and three-nucleon potential, required to reproduce the experimental GT matrix element and trinucleon binding energies in the N3LO/N2LO and AV18/UIX calculations.Comment: 19 pages,6 figures, corrections to Text as suggested by Referee added; Erratum: 4 pages, 3 figures, corrections to Eq.(20), Tables I, II, III, Figures 4, 5, conclusions unchange