S. Rosati

A High-precision variational approach to three- and four-nucleon bound and zero-energy scattering states

The hyperspherical harmonic (HH) method has been widely applied in recent times to the study of the bound states, using the Rayleigh–Ritz variational principle, and of low-energy scattering processes, using the Kohn variational principle, of A = 3 and 4 nuclear systems. When the wavefunction of the system is expanded over a sufficiently large set of HH basis functions, containing or not correlation factors, quite accurate results can be obtained for the observables of interest. In this review, the main aspects of the method are discussed together with its application to the A = 3 and 4 nuclear bound and zero-energy scattering states. Results for a variety of nucleon–nucleon (NN) and three-nucleon (3N) local or non-local interactions are reported. In particular, NN and 3N interactions derived in the framework of the chiral effective field theory and NN potentials from which the high-momentum components have been removed, as recently presented in the literature, are considered for the first time within the context of the HH method. The purpose of this review is twofold. The first is to present a complete description of the HH method for bound and scattering states, also including detailed formulae for the computation of the matrix elements of the NN and 3N interactions. The second is to report accurate results for bound and zero-energy scattering states obtained with the most commonly used interaction models. These results can be useful for comparison with those obtained by other techniques and are a significant test for different future approaches to such problems.

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 {sup 3}H and {sup 3}He, are calculated to make a comparative study of these models for the current operator. The realistic Argonne v{sub 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 {sup 2}H(p,{gamma}){sup 3}He process and the {sup 2}H(n,{gamma}){sup 3}H cross section at thermal neutron energies. It is shown that the use of a current that did not exactly satisfy current conservation with the two- and three-nucleon interactions in the Hamiltonian was responsible for some of the discrepanciesmorexa0» reported in previous studies between the experimental and theoretical polarization observables in pd radiative capture.«xa0less

The Ay 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.

The A(y) problem for p - He-3 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.

Chiral effective field theory predictions for muon capture on deuteron and

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±3u2009u2009sec{-1} and 1494±21u2009u2009sec{-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.

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We present new accurate measurements of the differential cross section {sigma}({theta}) and the proton analyzing power A{sub y} for proton-{sup 3}He elastic scattering at various energies. A supersonic gas-jet target has been employed to obtain these low-energy cross-section measurements. The {sigma}({theta}) distributions have been measured at E{sub p}=0.99, 1.59, 2.24, 3.11, and 4.02 MeV. Full angular distributions of A{sub y} have been measured at E{sub p}=1.60, 2.25, 3.13, and 4.05 MeV. This set of high-precision data is compared to four-body variational calculations employing realistic nucleon-nucleon (NN) and three-nucleon (3N) interactions. For the unpolarized cross section, the agreement between the theoretical calculation and data is good when a 3N potential is used. The comparison between the calculated and measured proton analyzing powers reveals discrepancies of approximately 50% at the maximum of each distribution. This is analogous to the existing A{sub y} puzzle known for the past 20 years in nucleon-deuteron elastic scattering.

He

Abstract.The application of the hyperspherical harmonic approach to the case of non-local two-body potentials is described. Given the properties of the hyperspherical harmonic functions, there are no difficulties in considering the approach in both coordinate and momentum space. The binding energies and other ground-state properties of A = 3 and 4 nuclei are calculated using the CD Bonn 2000 and N3LO two-body potentials. The results are shown to be in excellent agreement with corresponding ones obtained by other accurate techniques.

Proton-He3elastic scattering at low energies

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.

Variational calculation on A=3 and 4 nuclei with non-local potentials

The Kohn variational principle and the hyperspherical harmonic technique are applied to study p− 3 He elastic scattering at low energies. Preliminary results obtained using several interaction models are reported. The calculations are compared to a recent phase shift analysis performed at the Triangle University Nuclear Laboratory and to the available experimental data. Using a three-nucleon interaction derived from chi- ral perturbation theory at N 2 LO, we have found a noticeable reduction of the discrepancy observed for the Ay observable.

Realistic Calculation of the hep Astrophysical Factor

The application of the hyperspherical harmonic approach to the case of the