Argonne V18 Research Articles

Nuclear matter equation of state and three-body forces

The energy per particle, symmetry energy, pressure, and free energy are calculated for symmetric nuclear matter using BHF approach with modern nucleon-nucleon CD-Bonn, Nijm1, Argonne v18, and Reid 93 potentials. To obtain saturation in nuclear matter we add three-body interaction terms which are equivalent to a density-dependent two-nucleon interaction a la Skyrme force. Good agreement is obtained in comparison with previous theoretical estimates and experimental data.

Contribution of Nuclear Field Theory medium effects to the pairing gap

We calculate the different contributions to the pairing gap for the case of the superfluid nucleus 120Sn, making use of the Dyson equation (also known as the Nambu-Gor'kov equation in the case of superfluid systems) to propagate leading medium polarization Nuclear Field Theory (NFT) processes to all orders. Starting from a mean field obtained with the SLy4 effective force (mk ≈ 0.7), we renormalize the single-particle states and the pairing gap obtained from 1S0 component of the Argonne v14 N – N interaction, through the interweaving of single-particle motion and collective vibrations of the system. The results provide a detailed description of the fragmentation of the quasiparticle strength and of the state-dependent pairing gap.

Nuclear symmetry energy and the role of the tensor force

Using the Hellmann--Feynman theorem we analyze the contribution of the different terms of the nucleon-nucleon interaction to the nuclear symmetry energy $E_{sym}$ and the slope parameter $L$. The analysis is performed within the microscopic Brueckner--Hartree--Fock approach using the Argonne V18 potential plus the Urbana IX three-body force. We find that the main contribution to $E_{sym}$ and $L$ is due to the tensor component of the nuclear force.

Benchmark calculation ofn-3H andp-3He scattering

The n-3H and p-3He elastic phase-shifts below the trinucleon disintegration thresholds are calculated by solving the 4-nucleon problem with three different realistic nucleon-nucleon interactions (the I-N3LO model by Entem and Machleidt, the Argonne v18 potential model, and a low-k model derived from the CD-Bonn potential). Three different methods -- Alt, Grassberger and Sandhas, Hyperspherical Harmonics, and Faddeev-Yakubovsky -- have been used and their respective results are compared. For both n-3H and p-3He we observe a rather good agreement between the three different theoretical methods. We also compare the theoretical predictions with the available experimental data, confirming the large underprediction of the p-3He analyzing power.

Momentum-space Argonne V18 interaction

This paper gives a momentum-space representation of the Argonne V18 potential as an expansion in products of spin-isospin operators with scalar coefficient functions of the momentum transfer. Two representations of the scalar coefficient functions for the strong part of the interaction are given. One is as an expansion in an orthonormal basis of rational functions and the other as an expansion in Chebyshev polynomials on different intervals. Both provide practical and efficient representations for computing the momentum-space potential that do not require integration or interpolation. Programs based on both expansions are available as supplementary material. Analytic expressions are given for the scalar coefficient functions of the Fourier transform of the electromagnetic part of the Argonne V18. A simple method for computing the partial-wave projections of these interactions from the operator expressions is also given.

Semi-microscopic model of pairing in nuclei

A semi-microscopic model for nucleon pairing in nuclei is presented starting from the ab intio BCS gap equation with Argonne v18 force and the self-consistent Energy Density Functional Method basis characterized with the bare nucleon mass. The BCS theory is formulated in terms of the model space S0 with the effective pairing interaction calculated from the first principles in the subsidiary space S0. This effective interaction is supplemented with a small phenomenological addendum containing one phenomenological parameter universal for all medium and heavy atomic nuclei. We consider the latter as a phenomenological way to take into account both the many-body corrections to the BCS theory and the effective mass effects. For protons, the Coulomb interaction is introduced directly. Calculations made for several isotopic and isotonic chains of semi-magic nuclei confirm the validity of the model. The role of the self-consistent basis is stressed.

A study of the ground-state energy of 4He with nucleon–nucleon potentials

Ground-state properties are evaluated for the finite nucleus 4He starting from realistic nucleon–nucleon interactions within the framework of the Green’s function approach. For the sake of comparison, the same calculations are performed using the Brueckner–Hartree–Fock approximation. For that purpose four high-quality modern nucleon–nucleon interactions represented in momentum space are employed: the Argonne V18, CD-Bonn, Bonn A and N 3LO potentials. In these potentials, the effects of charge dependence are taken into account. Additional binding energy is obtained from the inclusion of the hole–hole scattering term within the framework of the Green function approach. It has been shown that the Green function results agree well with the results obtained by accurate methods for few-nucleon systems such as the Faddeev–Yakubovsky calculation. In this study, a comparison of the calculated ground-state energies, obtained by using the Green function approach and different nucleon–nucleon potentials, with experimental values is carried out. The results show good agreement between the calculated values and the experimental ones.

Asymptotic normalization coefficients fromab initiocalculations

We present calculations of asymptotic normalization coefficients (ANCs) for one-nucleon removals from nuclear states of mass numbers 3 to 9. Our ANCs were computed from variational Monte Carlo solutions to the many-body Schroedinger equation with the combined Argonne v18 two-nucleon and Urbana IX three-nucleon potentials. Instead of computing explicit overlap integrals, we applied a Green's function method that is insensitive to the difficulties of constructing and Monte Carlo sampling the long-range tails of the variational wave functions. This method also allows computation of the ANC at the physical separation energy, even when it differs from the separation energy for the Hamiltonian. We compare our results, which for most nuclei are the first ab initio calculations of ANCs, with existing experimental and theoretical results and discuss further possible applications of the technique.

Parity nonconservation in deuteron photoreactions

We calculate the asymmetries in parity nonconserving deuteron photodisintegration due to circularly polarized photons gamma+d to n+p with the photon laboratory energy ranging from the threshold up to 10 MeV and the radiative capture of thermal polarized neutrons by protons n+p to gamma+d. We use the leading order electromagnetic Hamiltonian neglecting the smaller nuclear exchange currents. Comparative calculations are done by using the Reid93 and Argonne v18 potentials for the strong interaction and the DDH and FCDH "best" values for the weak couplings in a weak one-meson exchange potential. A weak NDelta transition potential is used to incorporate also the Delta(1232)-isobar excitation in the coupled-channels formalism.

Muon capture on deuteron andHe3

The muon capture reactions 2H(\mu^-,\nu_\mu)nn and 3He(\mu^-,\nu_\mu)3H are studied with conventional or chiral realistic potentials and consistent weak currents. The initial and final A=2 and 3 nuclear wave functions are obtained from the Argonne v18 or chiral N3LO two-nucleon potential, in combination with, respectively, the Urbana IX or chiral N2LO three-nucleon potential in the case of A=3. The weak current consists of polar- and axial-vector components. The former are related to the isovector piece of the electromagnetic current via the conserved-vector-current hypothesis. These and the axial currents are derived either in a meson-exchange or in a chiral effective field theory (chiEFT) framework. There is one parameter (either the N-to-\Delta axial coupling constant in the meson-exchange model, or the strength of a contact term in the chiEFT model) which is fixed by reproducing the Gamow-Teller matrix element in tritium beta-decay. The model dependence relative to the adopted interactions and currents (and cutoff sensitivity in the chiEFT currents) is weak, resulting in total rates of 392.0 +/- 2.3 Hz for A=2, and 1484 +/- 13 Hz for A=3, where the spread accounts for this model dependence.

Towards microscopic ab initio calculations of astrophysical [formula omitted]-factors

Low energy capture cross sections are calculated within a microscopic many-body approach using an effective Hamiltonian derived from the Argonne V18 potential. The dynamics is treated within Fermionic Molecular Dynamics (FMD) which uses a Gaussian wave-packet basis to represent the many-body states. A phase-shift equivalent effective interaction derived within the Unitary Correlation Operator Method (UCOM) that treats explicitly short-range central and tensor correlations is employed. As a first application the 3He(α,γ) 7Be reaction is presented. Within the FMD approach the microscopic many-body wave functions of the 3 / 2 − and 1 / 2 − bound states in 7Be as well as the many-body scattering states in the 1 / 2 + , 3 / 2 + and 5 / 2 + channels are calculated as eigenstates of the same microscopic effective Hamiltonian. Finally the S -factor is calculated from E 1 transition matrix elements between the many-body scattering and bound states. For 3He( α , γ ) 7Be the S -factor agrees very well, both in absolute normalization and energy dependence, with the recent experimental data from the Weizmann, LUNA, Seattle and ERNA experiments. For the 3H( α , γ ) 7Li reaction the calculated S -factor is about 15% above the data.

Muon capture on A = 2 and 3 nuclei

We present the results of a recent simultaneous study of the muon capture reactions 2H(μ-,vμ)nn and 3He(μ-,vμ)3H. The initial and final A=2 and 3 nuclear wave functions are obtained from the Argonne v18 or chiral N3LO twonucleon potential, in combination with, respectively, the Urbana IX or chiral N2LO three-nucleon potential in the case of A=3. The weak current consists of polar- and axial-vector components. The former are related to the isovector piece of the electromagnetic current via the conserved-vector-current hypothesis. These and the axial currents are derived either in a meson-exchange or in a chiral e_ective field theory (xEFT) framework. In the first case, the only parameter is in the axial-vector current and is fixed by reproducing the experimental Gamow-Teller matrix element in tritium _-decay (GTEXP). In the second case, the low-energy constants, two in the polar and one in the axial-vector current, are fixed, respectively, by reproducing the A=3 magnetic moments and GTEXP. The total rates are found to be 392.0±2.3s-1 for A=2, and 1484±13s-1 for A=3, where the spread accounts for the model dependence relative to the adopted interactions and currents and to cuto_ sensitivity in the xEFT currents. These values are compared with available experimental data and results of previous calculations.

Transverse electron scattering response function ofHe3withΔ-isobar degrees of freedom

A calculation of the $^3$He transverse $(e,e')$ inclusive response function, $R_T$, which includes $\Delta$ degrees of freedom is performed using the Lorentz integral transform method. The resulting coupled equations are treated in impulse approximation, where the $NNN$ and $NN\Delta$ channels are solved separately. As NN and NNN potentials we use the Argonne V18 and UrbanaIX models respectively. Electromagnetic currents include the $\Delta$-isobar currents, one-body N-currents with relativistic corrections and two-body currents consistent with the Argonne V18 potential. $R_T$ is calculated for the breakup threshold region at momentum transfers near 900 MeV/c. Our results are similar to those of Deltuva {\it et al.} in that large $\Delta$-isobar current contributions are found. However we find that these are largely canceled by the relativistic contribution from the one-body N-currents. Finally a comparison is made between theoretical results and experimental data.

Large-scale second random-phase approximation calculations with finite-range interactions

Second RPA (SRPA) calculations of nuclear response are performed and analyzed. Unlike in most other SRPA applications, the ground state, approximated by the Hartree-Fock (HF) ground state, and the residual couplings are described by the same Hamiltonian and no arbitrary truncations are imposed on the model space. Finite-range interactions are used and thus divergence problems are not present. We employ a realistic interaction, derived from the Argonne V18 potential using the unitary correlation operator method (UCOM), as well as the simple Brink-Boeker interaction. Representative results are discussed, mainly on giant resonances and low-lying collective states. The focus of the present work is not on the comparison with data, but rather on technical and physical aspects of the method. We present how the large-scale eigenvalue problem that SRPA entails can be treated, and demonstrate how the method operates in producing self-energy corrections and fragmentation. The so-called diagonal approximation is conditionally validated. Stability problems are traced back to missing ground-state correlations.

LOCV calculation of nuclear matter with relativistic Hamiltonian

The equation of state of symmetric nuclear matter is calculated using the relativistic Hamiltonian (HR) with potentials which have been fitted with the N -N scattering data using the relativistic two-body Hamiltonian ( \( \tilde{{v}}_{{14}}^{}\) and the non-relativistic two-body Hamiltonian, i.e. the Argonne V14 interaction. The boost interaction corrections as well as the relativistic one-body and two-body kinetic energy corrections in cluster expansion energy within the lowest-order-constrained variational method are calculated. It is shown that the relativistic corrections reduce the binding energy by 1.5MeV for \( \tilde{{v}}_{{14}}^{}\) and AV14 interactions. The symmetric nuclear-matter saturation energy is about -16.43 MeV at \( \rho\) = 0.253 (fm-3) with \( \tilde{{v}}_{{14}}^{}\) interaction plus relativistic corrections. Finally, various properties of the symmetric nuclear matter are given and a comparison is made with the other many-body calculations.

3He Transverse (e,e’) Response Function in the Quasielastic Region

The transverse electron scattering response function RT of 3 He is studied in the quasielastic peak region for momentum transfers between 500 and 700 MeV/c. The calculation is carried out in the active nucleon Breit frame. The response in the laboratory frame is then obtained via a transformation of RT from the active nucleon Breit frame to the laboratory frame. For the current operator one- and two-body parts are taken into account. The one-body current operator includes all leading order relativistic corrections. For the two-body part meson exchange currents consistent with the employed NN potential (Argonne V18) are taken. As three-nucleon force the Urbana IX model is used. In comparison with experiment one finds an excellent agreement of the peak positions. The peak height agrees well with experiment for the lowest considered momentum transfer (500 MeV/c), but tends to be too high for higher momentum transfer (10% at 700 MeV/c).

Neutron stars,β-stable ring-diagram equation of state, and Brown-Rho scaling

Neutron star properties, such as mass, radius, and moment of inertia, are calculated by solving the Tolman-Oppenheimer-Volkov (TOV) equations using the ring-diagram equation of state (EOS) obtained from realistic low-momentum $\mathit{NN}$ interactions ${V}_{\mathrm{low}--\mathrm{k}}$. Several $\mathit{NN}$ potentials (CDBonn, Nijmegen, Argonne V18, and BonnA) have been employed to calculate the ring-diagram EOS where the particle-particle hole-hole ring diagrams are summed to all orders. The proton fractions for different radial regions of a $\ensuremath{\beta}$-stable neutron star are determined from the chemical potential conditions ${\ensuremath{\mu}}_{n}\ensuremath{-}{\ensuremath{\mu}}_{p}={\ensuremath{\mu}}_{e}={\ensuremath{\mu}}_{\ensuremath{\mu}}$. The neutron star masses, radii, and moments of inertia given by the aforementioned potentials all tend to be too small compared with the accepted values. Our results are largely improved with the inclusion of a Skyrme-type three-body force based on Brown-Rho scalings where the in-medium meson masses, particularly those of $\ensuremath{\omega}$, $\ensuremath{\rho}$, and $\ensuremath{\sigma}$, are slightly decreased compared with their in-vacuum values. Representative results using such medium-corrected interactions are maximum neutron-star mass $M~1.8{M}_{\ensuremath{\bigodot}}$ with radius $R~9$ km and moment of inertia $~60{M}_{\ensuremath{\bigodot}} {\mathrm{km}}^{2}$, values given by the four $\mathit{NN}$ potentials being nearly the same. The effects of nuclei-crust EOSs on the properties of neutron stars are discussed.

Search for three-nucleon force effects on the longitudinal response function ofHe4

A detailed study of the $^{4}\mathrm{He}$ longitudinal response function ${R}_{L}(\ensuremath{\omega},q)$ is performed at different kinematics, with particular emphasis on the role of three-nucleon forces. The effects reported are the results of an $\mathrm{ab} \mathrm{initio}$ calculation where the full four-body continuum dynamics is considered via the Lorentz integral transform method. The contributions of the various multipoles to the longitudinal response function are analyzed, and integral properties of the response are discussed as well. The Argonne V18 nucleon-nucleon interaction and two three-nucleon force models (Urbana IX and Tucson-Melbourne\ensuremath{'}) are used. At lower momentum transfers ($q\ensuremath{\leqslant}200 \mathrm{MeV}/c$) three-nucleon forces play an important role. One even finds a dependence of ${R}_{L}$ on the three-nucleon force model itself, with differences of up to 10%. Thus a Rosenbluth separation of the inclusive electron scattering cross section of $^{4}\mathrm{He}$ at low momentum transfers would be of great value for differentiating among force models.

Density dependence of the nuclear symmetry energy: A microscopic perspective

We perform a systematic analysis of the density dependence of nuclear symmetry energy within the microscopic Brueckner-Hartree-Fock (BHF) approach using the realistic Argonne V18 nucleon-nucleon potential plus a phenomenological three-body force of Urbana type. Our results are compared thoroughly with those arising from several Skyrme and relativistic effective models. The values of the parameters characterizing the BHF equation of state of isospin asymmetric nuclear matter fall within the trends predicted by those models and are compatible with recent constraints coming from heavy ion collisions, giant monopole resonances, or isobaric analog states. In particular we find a value of the slope parameter $L=66.5$ MeV, compatible with recent experimental constraints from isospin diffusion, $L=88\ifmmode\pm\else\textpm\fi{}25$ MeV. The correlation between the neutron skin thickness of neutron-rich isotopes and the slope $L$ and curvature ${K}_{\mathrm{sym}}$ parameters of the symmetry energy is studied. Our BHF results are in very good agreement with the correlations already predicted by other authors using nonrelativistic and relativistic effective models. The correlations of these two parameters and the neutron skin thickness with the transition density from nonuniform to $\ensuremath{\beta}$-stable matter in neutron stars are also analyzed. Our results confirm that there is an inverse correlation between the neutron skin thickness and the transition density.

Investigation of the ExclusiveHe3(e,e′pn)H1Reaction

Cross sections for the 3He(e,e' pn)1H reaction were measured for the first time at energy transfers of 220 and 270 MeV for several momentum transfers ranging from 300 to 450 MeV/c. Cross sections are presented as a function of the momentum of the recoil proton and the momentum transfer. Continuum Faddeev calculations using the Argonne V18 and Bonn-B nucleon-nucleon potentials overestimate the measured cross sections by a factor 5 at low recoil proton momentum with the discrepancy becoming smaller at higher recoil proton momentum.