NN Potential Research Articles

Two-pion production processes, chiral symmetry and NN interaction in the medium

We study the two-pion propagator in the nuclear medium. This quantity appears in the ππ T-matrix and we show that it also enters the QCD scalar susceptibility. The medium effects on this propagator are due to the influence of the individual nucleon response to a scalar field through their pion clouds. This response is appreciably increased by the nuclear environment. It produces an important convergence effect between the scalar and pseudoscalar susceptibilities, reflecting the reshaping of the scalar strength observed in 2π production experiments. While a large modifications of the σ propagator follows, due to its coupling to two pion states, we show that the NN potential remains instead unaffected.

Low-energyNNscattering at next-to-next-to-next-to-next-to-leading order for partial waves withj≤5

The variable S-matrix approach offers a unique way to extract low-energy threshold parameters for a given NN potential. We extract those parameters for the np system from the NijmII and Reid93 potentials to all partial waves with total angular momentum $j\ensuremath{\le}5$, using the generalized effective-range expansion: $({{f}^{\mathit{sj}}}^{\ensuremath{-}1}){}_{l,{l}^{'}}{k}^{l}{k}^{{l}^{'}}=\ensuremath{-}({{a}^{\mathit{sj}}}^{\ensuremath{-}1}){}_{l,{l}^{'}}+\frac{1}{2}({r}^{\mathit{sj}}){}_{l,{l}^{'}}{k}^{2}+({{v}_{2}}^{\mathit{sj}}){}_{l,{l}^{'}}{k}^{4}+({{v}_{3}}^{\mathit{sj}}){}_{l,{l}^{'}}{k}^{6}+({{v}_{4}}^{\mathit{sj}}){}_{l,{l}^{'}}{k}^{8}+\dots{}\ensuremath{-}i{k}^{l+{l}^{'}+1},$ where ${f}^{\mathit{sj}}=({S}^{\mathit{sj}}\ensuremath{-}1)/(2ik)$ is the scattering amplitude and ${S}^{\mathit{sj}}$ is the unitary S matrix in coupled-channel space with total spin s and total angular momentum j. Our calculation includes all the relevant contributions of the full amplitude to $\mathcal{O}({k}^{8})$ in the c.m. momentum. We also discuss the validity of the generalized effective-range expansion in the region of analyticity $k\ensuremath{\le}{m}_{\ensuremath{\pi}}/2$ and its applicability as a stringent test for chiral effective theory.

Erratum: Magnetic moments of the21+states aroundSn132[Phys. Rev. C 71, 044317 (2005)

Our article neglected to cite the work of Coraggio et al. [1], where a low-momentum NN potential derived from the CD-Bonn NN potential was used to construct an effective interaction for a $^{132}\mathrm{Sn}$ core. This interaction was used to compare with the experimental energy level spectra of $^{132}\mathrm{Sb}$ and other nearby nuclei.

Spin-isospin stability of nuclear matter

We calculate the density-dependent spin-isospin asymmetry energy $J({k}_{f})$ of nuclear matter in the three-loop approximation of chiral perturbation theory. The interaction contributions to $J({k}_{f})$ originate from one-pion exchange, iterated one-pion exchange, and irreducible two-pion exchange with no, single, and double virtual \ensuremath{\Delta}-isobar excitation. We find that the approximation to $1\ensuremath{\pi}$-exchange and iterated $1\ensuremath{\pi}$-exchange terms (which leads already to a good nuclear matter equation of state by adjusting an emerging contact term) is spin-isospin stable, since $J({k}_{f0})\ensuremath{\simeq}24\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}>0$. The inclusion of the chiral $\ensuremath{\pi}N\ensuremath{\Delta}$ dynamics, necessary in order to guarantee the spin stability of nuclear matter, keeps this property intact. The corresponding spin-isospin asymmetry energy $J({k}_{f})$ stays positive even for extreme values of an undetermined short-distance parameter ${J}_{5}$ (whose possible range we estimate from realistic NN potentials). The largest positive contribution to $J({k}_{f})$ (a term linear in density) comes from a two-body contact term with its strength fitted to the empirical nuclear matter saturation point.

NN potentials from the J-matrix inverse scattering approach

A nucleon–nucleon interaction is constructed by means of the J-matrix version of inverse scattering theory as a set of small-rank matrices in the oscillator basis. Phase-equivalent transformations are used to fit the interaction to the properties of light nuclei. The resulting interaction, JISP6, accurately reproduces the NN scattering data, deuteron properties and spectroscopy of A ⩽ 6 nuclei within the no-core shell model.

Towards a consistent approach to nuclear structure: EFT of two- and many-body forces

We review the nuclear forces currently in use, i.e., the high-precision NN potentials of the 1990s and the nuclear two- and many-body forces based upon chiral effective field theory (EFT). We argue that the EFT approach is superior to any of the older schemes. Since accurate chiral forces are available now, the stage is set for microscopic nuclear structure to move into a new and exciting era.

Kirson-Babu-Brown core polarization diagrams and low-momentum shell model effective interactions

The Kirson-Babu-Brown (KBB) induced interaction approach is applied to the derivation of the sd-shell nucleon effective interactions. We start from a low-momentum NN interaction Vlow-k obtained by integrating out the high-momentum components of modern realistic NN potentials beyond a decimation momentum λ. Then a large class of core polarization diagrams are summed up to all orders by way of the KBB self-consistent equations. It is found that the solution of these equations is simplified by the use of Vlow-k, which is energy independent, and by treating them in terms of the Green's fuctions in the particle-particle and the particle-hole channels. The effective interactions calculated with the all-order KBB core polarizations and those with the polarization in second-order perturbation theory are found to be rather similar to each other, typical difference between them being less than 10%.

EIKONAL PHENOMENOLOGY FOR HEAVY-ION SCATTERING AT INTERMEDIATE ENERGIES

Working within the framework of the Coulomb modified Glauber model and the optical limit approximation, we propose a phenomenological method of analysis for heavy-ion elastic scattering data at intermediate energies. Instead of using the commonly employed Gaussian approximation for the input NN amplitude that is deficient in some respects at low intermediate energies, we evaluate it in terms of a three parameter phenomenological NN phase shift function. The application of the method to some 12 C -nucleus and 16 O -nucleus systems shows that a very good description of the elastic scattering data at several energies can be obtained in this way. In particular, the 12 C –12 C elastic scattering data at 200 MeV/nucleon is very well reproduced. We also calculate the effective NN potential using the phenomenological NN phase shift function by the method of inversion. The calculated potential shows the expected behavior and is found to vary smoothly with energy.

Longitudinal electron scattering response functions ofH3andHe3

Trinucleon longitudinal response functions R_L(q,omega) are calculated for q values up to 500 MeV/c. These are the first calculations beyond the threshold region in which both three-nucleon (3N) and Coulomb forces are fully included. We employ two realistic NN potentials (configuration space BonnA, AV18) and two 3N potentials (UrbanaIX, Tucson-Melbourne). Complete final state interactions are taken into account via the Lorentz integral transform technique. We study relativistic corrections arising from first order corrections to the nuclear charge operator. In addition the reference frame dependence due to our non-relativistic framework is investigated. For q less equal 350 MeV/c we find a 3N force effect between 5 and 15 %, while the dependence on other theoretical ingredients is small. At q greater equal 400 MeV/c relativistic corrections to the charge operator and effects of frame dependence, especially for large omega, become more important. In comparison with experimental data there is generally a rather good agreement. Exceptions are the responses at excitation energies close to threshold, where there exists a large discrepancy with experiment at higher q. Concerning the effect of 3N forces there are a few cases, in particular for the R_L of 3He, where one finds a much improved agreement with experiment if 3N forces are included.

A microscopic NN → NN ⋆(1440) potential

By means of a NN → NN *(1440) transition potential derived in a parameter-free way from a quark-model based NN potential, we determine simultaneously the π NN *(1440) and σ NN *(1440) coupling constants. We also present a study of the target Roper excitation diagram contributing to the p(d,d′) reaction.

Do we understand the $\eta N$ interaction from the near-threshold $\eta$ photoproduction on the deuteron?

The effects of final-state interaction in incoherent $\eta$ photoproduction on a deuteron are studied within a three-body approach including a realistic NN potential. The results are compared with available data, and differences with other theoretical predictions are analyzed. The role of the $\eta N$ interaction and the possibility of extracting the $\eta N$ scattering parameters from this reaction are discussed.

Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory

We present the first nucleon-nucleon potential at next-to-next-to-next-to-leading order (fourth order) of chiral perturbation theory. Charge-dependence is included up to next-to-leading order of the isospin-violation scheme. The accuracy for the reproduction of the NN data below 290 MeV lab. energy is comparable to the one of phenomenological high-precision potentials. Since NN potentials of order three and less are known to be deficient in quantitative terms, the present work shows that the fourth order is necessary and sufficient for a reliable NN potential derived from chiral effective Lagrangians. The new potential provides a promising starting point for exact few-body calculations and microscopic nuclear structure theory (including chiral many-body forces derived on the same footing).

Threshold electrodisintegration of3He

Cross sections were measured for the near-threshold electrodisintegration of ${}^{3}\mathrm{He}$ at momentum transfer values of $q=2.4,$ $4.4,$ and $4.7{\mathrm{fm}}^{\ensuremath{-}1}.$ From these and prior measurements the transverse and longitudinal response functions ${R}_{T}$ and ${R}_{L}$ were deduced. Comparisons are made against previously published and new nonrelativistic $A=3$ calculations using the best available nucleon-nucleon NN potentials. In general, for $ql2{\mathrm{fm}}^{\ensuremath{-}1}$ these calculations accurately predict the threshold electrodisintegration of ${}^{3}\mathrm{He}.$ Agreement at increasing q demands consideration of two-body terms, but discrepancies still appear at the highest momentum transfers probed, perhaps due to the neglect of relativistic dynamics, or to the underestimation of high-momentum wave-function components.

The reaction pd→(pp)n at high momentum transfer and short-range NN properties

A recent cross section measurement of the deuteron breakup reaction pd→(pp)(0°)+n(180°), in the GeV region in a kinematics similar to backward pd elastic scattering, strongly contradicts predictions of a pd→dp model based on the one-nucleon exchange, single pN scattering and Δ excitation mechanisms, and on the wave functions of the Reid soft core and Paris NN potentials. We show within the same model that for the CD Bonn NN potential there is qualitative agreement with the data. It is attributed to a reduction of the one-nucleon exchange at energies above 1 GeV and an increase of the Δ(1232)-isobar contribution, both related to the short-range properties of the wave functions generated by this potential.

Solar-neutrino reactions on deuteron in effective field theory

The cross sections for low-energy neutrino–deuteron reactions are calculated within heavy-baryon chiral perturbation theory employing a cut-off regularization scheme. The transition operators are derived up to next-to-next-to-next-to-leading order in the Weinberg counting rules, while the nuclear matrix elements are evaluated using the wave functions generated by a high-quality phenomenological NN potential. With the adoption of the axial-current-four-nucleon coupling constant fixed from the tritium beta decay data, our calculation is free from unknown low-energy constants. Our results exhibit a high degree of stability against different choices of the cutoff parameter, a feature which indicates that, apart from radiative corrections, the uncertainties in the calculated cross sections are less than 1%.

EIKONAL DESCRIPTION OF 12C–12C ELASTIC SCATTERING IN TERMS OF PHENOMENOLOGICAL EFFECTIVE NN POTENTIAL

A phenomenological method of analysis for heavy-ion elastic scattering data at intermediate energies is proposed within the framework of the optical limit approximation of the Glauber multiple scattering theory. The essential point of our method is to evaluate the NN scattering amplitude in terms of a phenomenological effective NN potential the parameters of which are varied to fit the experimental data. It is applied to analyze 12C–12C elastic scattering data in the energy range of 25–200 MeV/nucleon with a good degree of success.

Hypernuclear Auger effect within density dependent relativistic hadron field theory

The hypernuclear Auger effect, given by the de-excitation of a Lambda hypernucleus by means of the transition of a Lambda hyperon from an initial to a lower lying final single particle state in conjunction with neutron emission from the core nucleus is studied in relativistic DDRH field theory. Baryonic interactions are obtained from the Bonn NN potential by Dirac-Brueckner theory and theoretically derived scaling laws for the meson-hyperon vertices. The model is applied to the ^{209}_Lambda Pb hypernucleus. Lambda and nucleon bound states as well as scattering states are calculated self-consistently in mean-field approximation. The Auger spectra of the emitted neutrons are of complex structure due to a huge combinatorial number of possible hypernuclear transitions. The sensitivity of the neutron Auger spectra to changes in the Lambda sigma and Lambda omega vertices are investigated. The theoretical results show that experimental applications of the hypernuclear Auger effect will require special efforts, e.g. by tagging on the energy of the initially created hyperon.

Direct capture contribution to the [formula omitted]N reaction at astrophysical energies

The contribution of the direct mechanism to the 11 C( p,γ) 12 N capture reaction at astrophysically relevant energies is calculated using the overlap integral 〈 11 C| 12 N〉 and the p– 11 C local effective potential obtained within a microscopic approach. This approach is based on the solution of the inhomogeneous differential equation with the source term calculated within the translation-invariant 0 ℏω shell model. The calculations resulted in a zero-energy astrophysical S-factor S(0) equal to 0.149 keV b. This value was obtained with the two-body effective NN potential, which gives the asymptotic normalization coefficient (ANC) for mirror nucleus 12 B close to the available experimental value. A separate estimation of S(0) based on the ratio of mirror ANCs gave S(0)=0.111 +0.025 −0.020 keV b. This value is about three times larger than the one obtained from the Coulomb breakup of 12 N.

Compact and loosely bound structures in light nuclei

The role of various components in the wave function of loosely bound light nuclei is considered in terms of the cluster model by taking into account orbital polarization. We show that several structures corresponding to particular modes of nucleon motion can be concurrently important for such structures. Specific examples of simple and fairly flexible trial wave functions are given for the 8Be and 6He nuclei. Explicit expressions are derived for the microscopic wave functions of these nuclei and employed to calculate basic nuclear parameters for commonly used central exchange NN potentials.

Off-Shell behavior of the scattering amplitude and the structure of NN potentials

We perform calculations and comparative analysis of the off-shell scattering matrices and related pp → ppγ reaction observables for various types of NN potentials—with forbidden states and with short-range repulsion. The emphasis is on studying the effects of the shape and depth of the central part of forbidden-state potentials on the behavior of the above quantities and on establishing the role of meson-exchange components in the NN interaction. We show that, when using potentials that give a good description of phase shifts and the proper behavior of the scattering matrix for low momentum transfers, the reaction pp → ppγ does not allow the choice between the potentials to be made, at least up to a proton energy of 400 MeV in the laboratory frame.