One-pion Exchange Potential Research Articles

Ab initiostudy of the photoabsorption of4He

There are some discrepancies in the low energy data on the photoabsorption cross section of $^4$He. We calculate the cross section with realistic nuclear forces and explicitly correlated Gaussian functions. Final state interactions and two- and three-body decay channels are taken into account. The cross section is evaluated in two methods: With the complex scaling method the total absorption cross section is obtained up to the rest energy of a pion, and with the microscopic $R$-matrix method both cross sections $^4$He($\gamma, p$)$^3$H and $^4$He($\gamma, n$)$^3$He are calculated below 40\,MeV. Both methods give virtually the same result. The cross section rises sharply from the $^3$H+$p$ threshold, reaching a giant resonance peak at 26--27\,MeV. Our calculation reproduces almost all the data above 30\,MeV. We stress the importance of $^3$H+$p$ and $^3$He+$n$ cluster configurations on the cross section as well as the effect of the one-pion exchange potential on the photonuclear sum rule.

Deconstructing 1S0 nucleon-nucleon scattering

A distorted-wave method is used to analyse nucleon-nucleon scattering in the 1S0 channel. Effects of one-pion exchange are removed from the empirical phase shift to all orders by using a modified effective-range expansion. Two-pion exchange is then subtracted in the distorted-wave Born approximation, with matrix elements taken between scattering waves for the one-pion exchange potential. The residual short-range interaction shows a very rapid energy dependence for kinetic energies above about 100 MeV, suggesting that the breakdown scale of the corresponding effective theory is only 270MeV. This may signal the need to include the Delta resonance as an explicit degree of freedom in order to describe scattering at these energies. An alternative strategy of keeping the cutoff finite to reduce large, but finite, contributions from the long-range forces is also discussed.

Relativistic calculation of deuteron threshold electrodisintegration at backward angles

The threshold electrodisintegration of the deuteron at backward angles is studied in instant form Hamiltonian dynamics, including a relativistic one-pion-exchange potential (OPEP) with off-shell terms as predicted by pseudovector coupling of pions to nucleons. The bound and scattering states are obtained in the center-of-mass frame, and then boosted from it to the Breit frame, where the evaluation of the relevant matrix elements of the electromagnetic current operator is carried out. The latter includes, in addition to one-body, also two-body terms due to pion exchange, as obtained, consistently with the OPEP, in pseudovector pion-nucleon coupling theory. In order to estimate the magnitude of the relativistic effects we perform, for comparison, the calculation with a nonrelativistic phase-equivalent Hamiltonian and consistent one-body and two-body pion-exchange currents. Our results for the electrodisintegration cross section show that, in the calculations using one-body currents, relativistic corrections become significant (i.e., larger than 10%) only at high momentum transfer $Q$ (${Q}^{2}\ensuremath{\simeq}40$ fm${}^{\ensuremath{-}2}$ and beyond). However, the inclusion of two-body currents makes the relativistic predictions considerably smaller than the corresponding nonrelativistic results in the ${Q}^{2}$ region (18--40) fm${}^{\ensuremath{-}2}$. The calculations based on the relativistic model also confirm the inadequacy, already established in a nonrelativistic context, of the present electromagnetic current model to reproduce accurately the experimental data at intermediate values of momentum transfers.

Nucleon-nucleon cross sections via stochastic processes in phase space: One-dimensional scattering

One-dimensional nucleon-nucleon scattering is simulated by Monte Carlo techniques in the quasiclassical approximation of the Wigner representation. Nucleons are represented by minimum wave packets of approximate nucleon radii, their linear dispersion offset by intrinsic harmonic oscillation, inducing phase space spin in the nucleon Wigner function. A representative set of points evolve in four-dimensional phase space in deterministic classical and stochastic quantum momentum jumps. In the extended space, the inter-nucleon one-pion exchange potential is defined locally by the point coordinates. By the geometric analogy, cross sections are computed from collision distances considered as impact parameters. Results from the parameter free one-dimensional simulation show reasonable agreement with empirical data in the energy range 0.01 GeV to 5 GeV.

Evolution of nuclear shells with the Skyrme density dependent interaction

We present the evolution of the shell structure of nuclei in Hartree-Fock calculations using Skyrme's density-dependent effective nucleon-nucleon interaction. The role of the tensor part of the Skyrme interaction to the Hartree-Fock spin-orbit splitting in spherical spin unsaturated nuclei is reanalyzed. The contribution of a finite range tensor force to the spin-orbit splitting in closed shell nuclei is calculated. It is found that the exact matrix elements of a Gaussian and of a one-pion exchange tensor potential could be written as a product Skyrme's short range expression times a suppression factor which is almost constant for closed shell nuclei with mass number $A\ensuremath{\geqslant}48$. The suppression factor is $\ensuremath{\sim}0.15$ for the one-pion exchange potential.

Brueckner-AMD Method and Its Applications to Light Nuclei

We propose a new approach employing the Brueckner-AMD in which the G-matrix is calculated using the antisymmetrized molecular dynamics (AMD). Its applications to some light nuclei are demonstrated, and the high reliability of the description of the shell and cluster structures is discussed. In the conventional approach employing the G-matrix for the study of nuclear matter or the shell model, the constructed G-matrix is used to reproduce effective interactions. Therefore, the effective interactions are valid only in the model space. It is desirable for the model space to be as large as possible, but for practical reasons, a finite dimensional space is used. For this reason, the effective interaction is model dependent, 1) and one must accept the limits of its applicability. The conventional shell model calculations have failed in the description of nuclear cluster states, which are observed in the excited states around cluster thresholds. By contrast, the cluster model has been shown to provide a successful description of these states. Recent developments of the cluster model based on the antisymmetrized molecular dynamics (AMD) 2) have led to success in reproducing the various kinds of cluster structures of excited states, in addition to the shell model structure of the ground and low-lying states, without any assumption concerning cluster configurations. This result indicates that the functional space of AMD is very large; the wave functions of AMD can describe not only shell model configurations but also cluster configurations. However, to this time studies of AMD have been carried out without detailed investigations of the effective interactions. It is important to construct a framework of the G-matrix for AMD. In this letter, we propose a framework of the Brueckner-AMD to calculate the G-matrix for AMD. Since the pioneering cluster study of α + α, 3) there has been much interest in elucidating the role of the tensor force component resulting from the one-pion exchange potential (OPEP) in the α-cluster formation and the binding mechanism of the α-particle. 4) – 8) Study of the G-matrix has been carried out in association with the appearance of α-clustering and the cluster structures in the low-excitation [ (

Helium and deuterium abundances as a test for the time variation of the fine structure constant and the Higgs vacuum expectation value

We use the semi-analytic method of Esmailzadeh et al (1991 Astrophys. J. 378 504–18) to calculate the abundances of helium and deuterium produced during Big Bang nucleosynthesis assuming the fine structure constant and the Higgs vacuum expectation value may vary in time. We analyse the dependence on the fundamental constants of the nucleon mass, nuclear binding energies and cross sections involved in the calculation of the abundances. Unlike previous works, we do not assume the chiral limit of QCD. Rather, we take into account the quark masses and consider the one-pion exchange potential, within perturbation theory, for the proton–neutron scattering. However, we do not consider the time variation of the strong interactions scale but attribute the changes in the quark masses to the temporal variation of the Higgs vacuum expectation value. Using the observational data of the helium and deuterium, we put constraints on the variation of the fundamental constants between the time of nucleosynthesis and the present time.

Single-particle energies in neutron-rich nuclei by shell model sum rule

One of the most striking features in neutron-rich nuclei is the disappearance of magic number $N=8$ or 20, which indicates a change of single-particle energy spectra and the disappearance of a large energy gap at the magic number. A sum-rule method is formulated, based on the shell model, for the evaluation of single-particle energies. It is shown that the triplet-even central component of the $\mathit{NN}$ interaction plays a decisive role through the monopole interaction for a change of single-particle energy spectra, leading to a rapid decrease of the energy gap at $N=8$ and 20. The triplet-even attraction is due partly to the original central interaction and partly to the second-order tensor correlations of the one-pion exchange potential. A multipole expansion analysis of $\mathit{NN}$ interactions shows that the contribution to the single-particle energy from the monopole interactions between two orbits depends on the nodal quantum numbers of the orbits.

Power counting with one-pion exchange

Techniques developed for handing inverse-power-law potentials in atomic physics are applied to the tensor one-pion exchange potential to determine the regions in which it can be treated perturbatively. In S-, P- and D-waves the critical values of the relative momentum are less than or of the order of 400 MeV. The RG is then used to determine the power counting for short-range interaction in the presence of this potential. In the P-and D-waves, where there are no low-energy bound or virtual states, these interactions have half-integer RG eigenvalues and are substantially promoted relative to naive expectations. These results are independent of whether the tensor force is attractive or repulsive. In the 3S1 channel the leading term is relevant, but it is demoted by half an order compared to the counting for the effective-range expansion with only a short-range potential. The tensor force can be treated perturbatively in those F-waves and above that do not couple to P- or D-waves. The corresponding power counting is the usual one given by naive dimensional analysis.

Renormalization of one-pion exchange and power counting

The renormalization of the chiral nuclear interactions is studied. In leading order, the cutoff dependence is related to the singular tensor interaction of the one-pion exchange potential. In S waves and in higher partial waves where the tensor force is repulsive this cutoff dependence can be absorbed by counterterms expected at that order. In the other partial waves additional contact interactions are necessary. The implications of this finding for the effective field theory program in nuclear physics are discussed.

Nuclear effects on neutrino emissivities from nucleon-nucleon bremsstrahlung

The rates of neutrino pair emission by nucleon-nucleon (NN) bremsstrahlung are calculated with the inclusion of the full contribution from a nuclear one pion exchange potential (OPEP). We compute the contributions from the neutron-neutron (nn), proton-proton (pp), and neutron-proton (np) processes for physical conditions encountered in supernovae and neutron stars, both in the degenerate (D) and nondegenerate (ND) limits. We find a significant reduction of these rates, especially for the nn and pp processes, in comparison with the case when the whole nuclear contribution was replaced by constants, representing the high-momentum limits of the expressions of the nuclear potential. Furthermore, we also perform the calculations by including contributions due to the $\ensuremath{\rho}$ meson exchange between nucleons, in the OPEP. This may be relevant for processes produced in the inner core of neutron stars, where the density may exceed several times the standard nuclear density, and the short-range part of the NN interaction should be taken into account. These corrections lead to an additional suppression of the neutrino emission rates between (8 and 36)%, depending on the process [nn (pp) or np] and physical conditions (temperature and degeneracy of the nucleons).

Neutrino bremsstrahlung in neutron matter from effective nuclear interactions

We revisit the emissivity from neutrino pair bremsstrahlung in neutron–neutron scattering, nn→nnνν̄, which was calculated from the one-pion exchange potential including correlation effects by Friman and Maxwell. Starting from the free-space low-momentum nucleon–nucleon interaction Vlowk, we include tensor, spin-orbit and second-order medium-induced non-central contributions to the scattering amplitude in neutron matter. We find that the screening of the nucleon–nucleon interaction reduces the emissivity from neutrino bremsstrahlung for densities below nuclear matter density. We discuss the implications of medium modifications for the cooling of neutron stars via neutrino emission, taking into account recent results for the polarization effects on neutron superfluidity.

Two-pion exchange nucleon-nucleon potential:O(q4)relativistic chiral expansion

We present a relativistic procedure for the chiral expansion of the two-pion exchange component of the $NN$ potential, which emphasizes the role of intermediate $\pi N$ subamplitudes. The relationship between power counting in $\pi N$ and $NN$ processes is discussed and results are expressed directly in terms of observable subthreshold coefficients. Interactions are determined by one- and two-loop diagrams, involving pions, nucleons, and other degrees of freedom, frozen into empirical subthreshold coefficients. The full evaluation of these diagrams produces amplitudes containing many different loop integrals. Their simplification by means of relations among these integrals leads to a set of intermediate results. Subsequent truncation to $O(q^4)$ yields the relativistic potential, which depends on six loop integrals, representing bubble, triangle, crossed box, and box diagrams. The bubble and triangle integrals are the same as in $\pi N$ scattering and we have shown that they also determine the chiral structures of box and crossed box integrals. Relativistic threshold effects make our results to be not equivalent with those of the heavy baryon approach. Performing a formal expansion of our results in inverse powers of the nucleon mass, even in regions where this expansion is not valid, we recover most of the standard heavy baryon results. The main differences are due to the Goldberger-Treiman discrepancy and terms of $O(q^3)$, possibly associated with the iteration of the one-pion exchange potential.

Renormalizing the Lippmann-Schwinger equation for the one-pion exchange potential

We address the question whether the cut-off dependence, which has to be introduced in order to properly define the Lippmann-Schwinger equation for the one pion exchange potential plus local (delta-function) potentials, can be removed (up to inverse powers of it) by a suitable tuning of the various (bare) coupling constants. We prove that this is indeed so both for the spin singlet and for the spin triplet channels. However, the latter requires such a strong cut-off dependence of the coupling constant associated to the non-local term which breaks orbital angular momentum conservation, that the renormalized amplitude lacks from partial wave mixing. We argue that this is an indication that this term must be treated perturbatively.

Pion Cloud Effects on Δ-N Mass Splitting from Quark Models**The project supported by National Natural Science Foundation of China under Grant No. 10075056, Foundations of the Chinese Academy of Sciences (X-37), the Chinese Ministry of Education (B-22), Institute of Theoretical Physics and the Knowledge Innovation Project of the Chinese Academy of Sciences under Grant No. KJCX2-SW-N02

Pion cloud effects on Δ-N mass splitting are studied based on quark models. Pseudo-scalar pion-quark coupling is discussed in the relativistic and nonrelativistic frameworks. We separately calculate the pion cloud effects by the one-pion exchange potential and by another method which is consistent with the baryon chiral perturbation theory. Remarkable discrepancy in the mass splitting between the two methods is shown.

Effects of nonlocal one-pion-exchange potential in the deuteron

The off-shell aspects of the one-pion-exchange potential (OPEP) are discussed. Relativistic Hamiltonians containing relativistic kinetic energy, relativistic OPEP with various off-shell behaviors and Argonne $v_{18}$ short-range parameterization are used to study the deuteron properties. The OPEP off-shell behaviors depend on whether a pseudovector or pseudoscalar pion-nucleon coupling is used and are characterized by a parameter $\mu$. We study potentials having $\mu$=-1, 0 and +1 and we find that they are nearly unitarily equivalent. We also find that a nonrelativistic Hamiltonian containing local potentials and nonrelativistic kinetic energy provides a good approximation to a Hamiltonian containing a relativistic OPEP based on pseudovector pion-nucleon coupling and relativistic kinetic energy.

Quark Cluster Model of Baryon-Baryon Interaction

The quark cluster model of the baryon-baryon interaction is reviewed. The emphasis is on the foundation of the approach and the main features of the model. The origins of the short-range repulsion in the nuclear force and other baryonic interactions are discussed. The origin of the nuclear force is a central problem of nuclear physics. It has a long history since Yukawa 1) proposed the static one-pion exchange potential (OPEP) of the range of the pion Compton wave length. The discovery of the pion boosted both the experimental and theoretical investigation of the nuclear force. It was realized in the early stage that the short range part of the nuclear force requires further ingredients, including the two- and multi-pion exchange interactions. In order to study the shorter-range part, Taketani proposed to consider three regions of the nuclear force separately. 2) (I) The long-range part (R ≥ 2 fm) is described by OPEP. (II) The medium-range part (1 ≤ R ≤ 2 fm) is attributed to nonstatic part of the pion exchange, multipion exchanges and heavy meson exchanges. Finally, (III) the shortrange part (R ≤ 1 fm) is left for phenomenology as it is most “complicated”. The OPEP was firmly established since then and the region (II) was studied in various approaches that treat nonstatic contribution and heavy mesons. It is believed to give a strong attraction due mostly to exchange of two pions correlated in the S-wave, which is often represented by the exchange of a scalar sigma meson. It turned out that this strong attraction of the second region is crucial for the nuclear binding. The shortest range region (III) was found to have a strong repulsion as suggested from the medium-energy nucleon-nucleon ( NN ) scattering data. Thus the nuclear binding is on the balance between the attraction in the regions (I) and (II) and the repulsion in (III). Meanwhile, many phenomenological models have been constructed. Main source of information is the NN scattering observables as well as properties of the deuteron. The proposed models include the Hamada-Johnston potential, 3) the Reid soft core potential, 4) the Tamagaki potential, 5) all of which can explain the low energy observables fairly well. The real development in the study of region (II) was achieved in 1970’s resulting in two popular models of nuclear force, Bonn 6) and Paris 7) po

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.

Numerical toy-model calculation of the nucleon spin autocorrelation function in a supernova core

We develop a simple model for the evolution of a nucleon spin in a hot and dense nuclear medium. A given nucleon is limited to one-dimensional motion in a distribution of external, spin-dependent scattering potentials. We calculate the nucleon spin autocorrelation function numerically for a variety of potential densities and distributions which are meant to bracket realistic conditions in a supernova core. For all plausible configurations the width of the spin-density structure function is found to be less than the temperature. This is in contrast with a naive perturbative calculation based on the one-pion exchange potential which overestimates the width and thus suggests a large suppression of the neutrino opacities by nucleon spin fluctuations. Our results suggest that it may be justified to neglect the collisional broadening of the spin-density structure function for the purpose of estimating the neutrino opacities in the deep inner core of a supernova. On the other hand, we find no indication that processes such as axion or neutrino pair emission, which depend on nucleon spin fluctuations, are substantially suppressed beyond the multiple-scattering effect already discussed in the literature. Aside from these practical conclusions, our model reveals a number of interesting and unexpected insights. For example, the spin-relaxation rate saturates with increasing potential strength only if bound states are not allowed to form by including a repulsive core. There is no saturation with increasing density of scattering potentials until localized eigenstates of energy begin to form.

Supernova Neutrino Opacity from Nucleon‐Nucleon Bremsstrahlung and Related Processes

Elastic scattering on nucleons, \nu N -> N \nu, is the dominant supernova (SN) opacity source for \mu and \tau neutrinos. The dominant energy- and number-changing processes were thought to be \nu e^- -> e^- \nu and \nu\bar \nu e^+ e^- until Suzuki (1993) showed that the bremsstrahlung process \nu\bar \nu NN NN was actually more important. We find that for energy exchange, the related ``inelastic scattering process'' \nu NN NN \nu is even more effective by about a factor of 10. A simple estimate implies that the \nu_\mu and \nu_\tau spectra emitted during the Kelvin-Helmholtz cooling phase are much closer to that of \nu\bar_e than had been thought previously. To facilitate a numerical study of the spectra formation we derive a scattering kernel which governs both bremsstrahlung and inelastic scattering and give an analytic approximation formula. We consider only neutron-neutron interactions, we use a one-pion exchange potential in Born approximation, nonrelativistic neutrons, and the long-wavelength limit, simplifications which appear justified for the surface layers of a SN core. We include the pion mass in the potential and we allow for an arbitrary degree of neutron degeneracy. Our treatment does not include the neutron-proton process and does not include nucleon-nucleon correlations. Our perturbative approach applies only to the SN surface layers, i.e. to densities below about 10^{14} g cm^{-3}.