Binding Energies Of 3H Research Articles

Application of Semilocal Coordinate-Space Regularized Chiral Forces to Elastic Nd Scattering and Breakup

We solve three-nucleon (3N) Faddeev equations with nucleon–nucleon (NN) and three-nucleon forces (3NF) derived consistently in the framework of chiral perturbation theory, taking the semilocal coordinate-space regularized chiral N^4LO NN potential supplemented by the chiral N^2LO 3NF regularized in the same way. Based on these solutions the nucleon–deuteron (Nd) elastic scattering and deuteron breakup reactions are studied. We checked that the elastic Nd scattering cross section can be used as an alternative observable to the doublet neutron–deuteron (nd) scattering length to fix, together with the ^3H binding energy, the strengths of the contact terms of the N^2LO 3NF. We investigated the predicted 3NF effects in 3N continuum reactions putting an emphasis on the A_y puzzle in low energy nd elastic scattering and on cross sections in the symmetrical-space-star and quasi-free-scattering breakup configurations. We found that the N^2LO 3NF provides effects comparable to those of standard, (semi-)phenomenological 2pi -exchange Tucson-Melbourne 3NF.

Toward order-by-order calculations of the nuclear and neutron matter equations of state in chiral effective field theory

We calculate the nuclear and neutron matter equations of state from microscopic nuclear forces at different orders in chiral effective field theory and with varying momentum-space cutoff scales. We focus attention on how the order-by-order convergence depends on the choice of resolution scale and the implications for theoretical uncertainty estimates on the isospin asymmetry energy. Specifically we study the equations of state using consistent NLO and N2LO (next-to-next-to-leading order) chiral potentials where the low-energy constants cD and cE associated with contact vertices in the N2LO chiral three-nucleon force are fitted to reproduce the binding energies of 3H and 3He as well as the beta-decay lifetime of 3H. At these low orders in the chiral expansion there is little sign of convergence, while an exploratory study employing the N3LO two-nucleon force together with the N2LO three-nucleon force give first indications for (slow) convergence with low-cutoff potentials and poor convergence with higher-cutoff potentials. The consistent NLO and N2LO potentials described in the present work provide the basis for estimating theoretical uncertainties associated with the order-by-order convergence of nuclear many-body calculations in chiral effective field theory.

The proton–deuteron system in pionless EFT revisited

We provide a detailed discussion of the low-energy proton–deuteron system in pionless effective field theory, considering both the spin-quartet and doublet S-wave channels. Extending and amending our previous work on the subject, we calculate the 3He–3H binding energy difference both perturbatively (using properly normalized trinucleon wave functions) and non-perturbatively by resumming all Coulomb diagrams in the doublet channel. Our nonperturbative result agrees well with a calculation that involves the full off-shell Coulomb T-matrix. Carefully examining the cutoff-dependence in the doublet channel, we present numerical evidence for a new three-nucleon counterterm being necessary at next-to-leading order if Coulomb effects are included. Indeed, such a term has recently been identified analytically. We furthermore make a case for a simplified Coulomb power counting that is consistent throughout the bound-state and scattering regimes. Finally, using a ‘partially screened’ full off-shell Coulomb T-matrix, we investigate the importance of higher-order Coulomb corrections in low-energy quartet-channel scattering.

Dependence of dislocation damping on helium-3 concentration in helium-4 crystals

The mechanical properties of crystals are strongly affected by dislocation mobility. Impurities can bind to dislocations and interfere with their motion, causing changes in the crystal's shear modulus and mechanical dissipation. In 4He crystals, the only impurities are 3He atoms, and they can move through the crystal at arbitrarily low temperatures by quantum tunneling. When dislocations in 4He vibrate at speeds v < 45 μm/sec, bound 3He impurities move with the dislocations and exert a damping force B3v on them. In order to characterize 4He dislocation networks and determine the 3He binding energy, it is usually assumed that B3 is proportional to the concentration of 3He bound to the dislocations. In this preliminary report, we determine B3 in a crystal with 2.32 ppm 3He and compare with our previous measurements of B3 in natural purity 4He crystals to verify the assumption of proportionality.

Constraints on a possible dineutron state from pionless EFT

We investigate the sensitivity of the three-nucleon system to changes in the neutron–neutron scattering length to next-to-leading order in the pionless effective field theory, focusing on the triton–3He binding energy difference and neutron–deuteron elastic scattering. Due to the appearance of a proton–deuteron three-body counterterm at this order, the triton–3He binding energy difference remains consistent with the experimental value even for large positive neutron–neutron scattering lengths while the elastic neutron–deuteron scattering phase shifts are insensitive. We conclude that a bound dineutron cannot be excluded to next-to-leading order in pionless EFT.

Cross sections of fusion and transfer reactions in interactions between 3He and Pt and 197Au nuclei in the subbarrier energy region

The reactions of complete and incomplete fusion, along with nucleon transfer reactions in the range of 3He energies from 10 to 24.5 MeV, are investigated by irradiating gold and platinum targets with an accelerated 3He ion beam on the U-120M cyclotron at the Institute of Nuclear Physics, Czech Academy of Sciences, Řež. Activation is used to determine the yield of nuclides resulting from nuclear reactions. The γ-activity induced in the targets is measured using a with high-resolution HPGe detector. Despite the low binding energy of 3He and the reactions with positive Q values, the measured cross sections of fusion reactions exhibit no specific features, compared to reactions conducted using beams of other light stable particles. Transfer neutron reactions in the subbarrier energy region have relatively high cross sections. These cross sections continue to grow as the energy of 3He rises. When a neutron is captured by a nucleus of 3He, the cross sections of these reactions reach their maximum values in the Coulomb barrier region.

Cross sections for production of 43Sc, 44Sc, and 46Sc isotopes in the 45Sc + 3He reaction

Reactions 45Sc(3He, αn)43Sc, 45Sc(3He, α)44Sc, and 45Sc(3He, 2p)46Sc, resulting from the irradiation of scandium targets with a beam of 3He ions with energy from 5 to 24 MeV, are investigated in experiments on the U120M cyclotron of the Nuclear Physics Institute (Rez, Czech Republic). The activation technique is used to find the yield of the produced Sc isotopes. The induced γ activity in the targets is measured using a high-resolution HPGe detector. Despite the low binding energy of 3He and positive reaction Q values, which leads to formation of the 44Sc and 46Sc isotopes, the behavior of the excitation functions for the formation of these isotopes differs from the behavior of the excitation function for deuterons. Scandium-44 formation cross sections reach their maximum at the reaction Coulomb barrier. This is because not only 44Sc but also a stable 4He nucleus is formed in the reaction.

A Simple Approach to Study the Isospin Effect in Mass Splitting of Three-Nucleon Systems by Using Hyperspherical Functions

In this work, the binding energy and wavefunctions of three-nucleon systems are obtained by using hyperspherical harmonic approach. We have used a mathematical modification method to obtain the eigenvalues and eigenfunctions of Schrödinger equation for three-nucleon systems in calculation. Next, we have used a simple approach to obtain the difference between binding energy of 3H and 3He where gives us mass splitting of three-nucleon systems. We have compared our results with the other works and experimental values.

The Low-Energy p–d System in Pionless EFT

We summarize results presented at the 5th Asian Pacific Conference on Few Body Problems in Physics, which was held in Seoul in August 2011. We calculate low-energy quartet and doublet channel proton–deuteron scattering in the framework of pionless effective field theory. We obtain good agreement with the available phase shift analyses. Moreover, we calculate the Coulomb contribution to the 3He–3H binding energy difference in first order perturbation theory.

Triton Electric Form Factor at Low Energies

By using of the Effective Field Theory (EFT) expansion recently developed by the authors, the charge form factor of triton has been calculated up to next-to-next-to-leading order (N2LO). Three-nucleon forces (3NF) are required for renormalization of the three-nucleon system. 3NF effect is predicted for process and it is qualitatively supported by available experimental data. With the 3H binding energy and scattering length as input, we obtain predictions of the pionless EFT for the root-mean-square charge radius of 3H of (1.775 ± 0.023) fm up to N2LO. We show that, by including higher-order corrections, the calculated charge form factor and charge radius of 3H are in satisfactory agreement with the experimental data and modern nucleon-nucleon potential model calculations. Our result converges order by order in low-energy expansion and is also cutoff independent.

Universal correlations in pion-less EFT with the resonating group method: Three and four nucleons

The Effective Field Theory “without pions” at next-to-leading order is used to analyze universal bound-state and scattering properties of the 3- and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound-state properties of 3H and 4He , and for the singlet S -wave 3He -neutron scattering length a 0(3He-n) . The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a 0(3He-n) and the 3H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading order, between the 3H binding energy and the 3H charge radius, and the Tjon line. With the 3H binding energy as input, we get predictions of the effective field theory “without pions” at next-to-leading order for the root mean square charge radius of 3H of (1.6±0.2) fm, for the 4He binding energy of (28±2.5) MeV, and for Re{a 0(3He-n)} of (7.5±0.6) fm. Including the Coulomb interaction, the splitting in binding energy between 3H and 3He is found to be (0.66±0.03) MeV. The discrepancy to data of (0.10±0.03) MeV is model independently attributed to higher-order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher-order effects, and carefully assess that numerical uncertainties are negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the 4He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.

A realistic three-dimensional calculation of the 3H binding energy

Recently developed three-dimensional Faddeev integral equations for the three-nucleon bound state with two-nucleon interactions have been solved in momentum space for the Bonn-B potential.

Selected Topics in Correlated Hyperspherical Harmonics

Correlated hyperspherical-harmonic basis functions are used to expand the three- and four-nucleon wave functions. Bound and scattering states are considered. Results for the binding energies of 3H, 3He, and 4He calculated using modern two- and three-nucleon forces are given and discussed. For scattering states, results for N-d differential cross section and vector analyzing powers are shown. The importance of the Coulomb and magnetic moment effects are discussed.

Modern nuclear force predictions for the neutron-deuteron scattering lengths

The nd doublet and quartet scattering lengths have been calculated based on the modern NN and 3N interactions. We also studied the effect of the electromagnetic interactions in the form introduced in AV18. Switching them off for the various nuclear force models leads to shifts of up to +0.04 fm for doublet scattering length, which is significant for present day standards. The electromagnetic effects have also a noticeable effect on quartet scattering length, which otherwise is extremely stable under the exchange of the nuclear forces. For the current nuclear force models there is a strong scatter of the 3H binding energy and the doublet scattering length values around an averaged straight line (Phillips line). This allows to use doublet scattering length and the 3H binding energy as independent low energy observables.

Quantum Monte Carlo studies of relativistic effects in light nuclei

Relativistic Hamiltonians are defined as the sum of relativistic one-body kinetic energy, two- and three-body potentials and their boost corrections. In this work we use the variational Monte Carlo method to study two kinds of relativistic effects in the binding energy of 3H and 4He. The first is due to the nonlocalities in the relativistic kinetic energy and relativistic one-pion exchange potential (OPEP), and the second is from boost interaction. The OPEP contribution is reduced by about 15% by the relativistic nonlocality, which may also have significant effects on pion exchange currents. However, almost all of this reduction is canceled by changes in the kinetic energy and other interaction terms, and the total effect of the nonlocalities on the binding energy is very small. The boost interactions, on the other hand, give repulsive contributions of 0.4 (1.9) MeV in 3H (4He) and account for 37% of the phenomenological part of the three-nucleon interaction needed in the nonrelativistic Hamiltonians.

Dynamics of3He impurities in4He films

Using a microscopic variational theory we calculate the binding energy of3He impurities in films of4He absorbed to a graphite substrate. Without adjustable parameters, we obtain excellent agreement with the experimental binding energies for the ground state of the3He impurity.

Binding energy of 3He in thin 4He films

We report measurements of the magnetization of 0.1 monolayers of 3He in a thin 4He film as a function of temperature and from these we determine the binding energies of the 3He in the mixture film as a function of the 4He coverage. For 4He coverages between 0.21 and 0.53A˚ -2 the 3He binding energies obtained are in reasonable agreement with predictions of Pavloff and Treiner for the 4He coverage dependence of the binding energy.

Charge symmetry breaking in the A = 3 system and electromagnetic penguins (of the second kind)

We discuss difficulties with the traditional understanding of the origins of the non-coulombic portion of the 3H 3He binding energy difference (ΔBE) and analyze the contribution to ΔBE arising from certain mixed QED × QCD effects which are known to be important to the generation of isomultiplet splittings in the hadron spectrum. This contribution is shown, on general grounds, to be of O(100 keV) and, in the context of the quark cluster model, dominated by a single quark magnetic term, barring unnatural cancellations. More accurate data on Σ, Σ ∗ and Σ c isomultiplet splittings would help to pin down the model estimate more precisely. Despite the uncertainties, the A = 3 binding energy difference is noteworthy as an example of a nuclear observable for which quark level effects do not appear well represented by effective operators at the nucleon level.

Proton-induced break-up of 3He at 35MeV

The reactions 3He + p → d + p + p, and 3He + p → p + p + p + n have been studied at 35MeV. These reactions are dominated by quasi-two-body processes: pp and pd quasi-free scattering, pp final-state interactions, and neutron pick-up. We compare our data with phenomenological calculations which describe these processes and establish significant discrepancies. Our data are also compared with four-body calculations based on exact integral equations, which give a much better description and we show that if one would use potentials that yield the correct 3He binding energy and if one would take even approximately into account the Coulomb interaction a much better agreement would be achieved with all the data.

Reply to the ‘‘Comment on few-atom 3He–4He mixed molecules’’

The binding energy of 3He(4He)2 is recalculated with more correct ℏ2/M values. The Smith-Thakkar, HFDHE2, and mDD-2 potentials ensure its binding, while the Beck, Lennard-Jones, and ESMMSV potentials do not.