S-wave Potential Research Articles

Precision spectroscopy of pionic 1s states of Sn nuclei and evidence for partial restoration of chiral symmetry in the nuclear medium.

Deeply bound 1s states of pi(-) in (115,119,123)Sn were preferentially observed using the Sn(d,3He) pion-transfer reaction under the recoil-free condition. The 1s binding energies and widths were precisely determined and were used to deduce the isovector parameter of the s-wave pion-nucleus potential to be b1=-(0.115+/-0.007)m(-1)(pi). The observed enhancement of |b(1)| over the free piN value (b(free)1/b1=0.78+/-0.05) indicates a reduction of the chiral order parameter, f*pi(rho)2/f2pi approximately 0.64, at the normal nuclear density, rho=rho(0).

Contribution of vertically travelling planeS-waves to dynamic and static displacements near a finite fault

Representing seismic waves numerically by, for example, the discrete wavenumber method, we normally decompose waves into P-SV and SH components. This scheme, however, cannot treat the exactly vertically travelling S-waveelement (VTSE), which corresponds to k x = k y = 0, whereas VTSE exists except for a few cases of fault geometry. In order to deal with VTSE from a point source, a new S-wave potential must be introduced, so that its polarization is restricted on a horizontal plane. The polarization angle of VTSE is a function of the fault geometry represented by dip, rake and strike. In this study, we first point out that VTSE from a finite fault cannot be calculated even if we use the above new S-wave potential, because the terms originated from fault finiteness become zero if k x = k y = 0. In order to remedy this difficulty for a finite source, we define a new VTSE potential for a rectangular fault. The contribution of VTSE is large for displacements in a very low frequency range such as static displacement. The static displacement due to VTSE does not depend on a fault depth or station locations. When we take a small but finite value for k x and k y instead of zero, say δk = 10 - 5 , we can obtain practically accurate results even without the VTSE potential, including static displacements that have not been discussed in detail yet. Following the above scheme, accurate seismograms with both dynamic and static components can be simulated simultaneously for a fault of any configuration and station location.

Hadronic decays of η and η′ with coupled channels

The hadronic decays η→ πππ, η′→ πππ and η′→ ηππ are investigated within a U(3) chiral unitary approach. Final state interactions are included by deriving the effective s-wave potentials for meson–meson scattering from the chiral effective Lagrangian and iterating them in a Bethe–Salpeter equation. With only a small set of parameters we are able to explain both rates and spectral shapes of these decays.

η,η′photoproduction and electroproduction off nucleons

The photoproduction and electroproduction of the $\ensuremath{\eta},{\ensuremath{\eta}}^{\ensuremath{'}}$ mesons on nucleons are investigated within a relativistic chiral unitary approach based on coupled channels. The s-wave potentials for electroproduction and meson-baryon scattering are derived from a chiral effective Lagrangian, which includes ${\ensuremath{\eta}}^{\ensuremath{'}}$ as an explicit degree of freedom and incorporates important features of the underlying QCD Lagrangian such as the axial U(1) anomaly. The effective potentials are iterated in a Bethe-Salpeter equation and the cross sections for $\ensuremath{\eta},{\ensuremath{\eta}}^{\ensuremath{'}}$ photoproduction and electroproduction from nucleons are obtained. The results for the ${\ensuremath{\eta}}^{\ensuremath{'}}$ photoproduction cross section on protons reproduce the appearance of an ${S}_{11}$ resonance around 1.9 GeV observed at ELSA. The inclusion of electromagnetic form factors increases the predicted $\ensuremath{\eta}$ electroproduction cross sections on the proton, providing a qualitative explanation for the hard form factor of the photocoupling amplitude observed at CLAS.

Faddeev–Yakubovsky calculations for light ΛΛ hypernuclei

New Faddeev–Yakubovsky calculations are reported for 6 ΛΛ He and 10 ΛΛ Be in terms of clusters of α's and Λ's, using ΛΛ s-wave potentials motivated by several of the Nijmegen model interactions. The self consistency of the ΛΛ hypernuclear world data for these species is discussed. The newly reported 6 ΛΛ He event is found to be compatible with ΛΛ interaction strengths provided by the Nijmegen soft-core one-boson-exchange model NSC97. Faddeev calculations for 5 ΛΛ H and 5 ΛΛ He suggest that these ΛΛ hypernuclei are stable against emitting Λ's for any (essentially attractive) ΛΛ interaction, whereas calcualtions for 4 ΛΛ H do not allow a clear-cut conclusion whether or not it is particle stable.

Nonlocalities and Fermi motion corrections in K − atoms

We evaluate the p-wave K −N amplitudes from the chiral Lagrangians and from there construct the p-wave part of the K − nucleus optical potential plus a small s-wave part induced from the elementary p-wave amplitude and the nuclear Fermi motion. Simultaneously, the momentum and energy dependence of the s-wave optical potential, previously developed, are taken into account and shown to generate a small p-wave correction to the optical potential. All the corrections considered are small compared to the leading s-wave potential, and lead to changes in the shifts and widths which are smaller than the experimental errors. A thorough study of the threshold region and low densities is conducted, revealing mathematical problems for which a physical solution is given.

Systematic calculation of s-wave pion and kaon self-energies in asymmetric nuclear matter

We calculate the pion self-energies in asymmetric nuclear matter in the two-loop approximation of chiral perturbation theory. We find three types of corrections beyond the well-known linear density approximation. The resulting s-wave potential (or equivalent mass-shift) of a $\pi^-$ in the center of a heavy nucleus like Pb turns out to be $U_{\pi^-}=\Delta m_{\pi^-} \simeq 14$ MeV, about half of what is needed to form the deeply bound and narrow pionic atom-states recently observed at GSI. The potential for a $\pi^+$ under the same conditions is $U_{\pi^+}=\Delta m_{\pi^+} \simeq -1$ MeV. In the same way we calculate the mass-shifts of $K^+$-mesons in symmetric nuclear matter and neutron matter and find an increase of the $K^+$-mass by 9% and 5%, respectively. As a further application we give an analytical result for the third order term in the scattering length expansion of the in-medium self-energy of an interacting light-boson/heavy-fermion system.

𝒫𝒯-symmetrically regularized Eckart, Pöschl-Teller and Hulthén potentials

Version 1: The well known Eckart's singular s-wave potential is PT-symmetrically regularized and continued to the whole real line. The new model remains exactly solvable and its bound states remain proportional to Jacobi polynomials. Its real and discrete spectrum exhibits several unusual features. Version 2: Parity times time-reversal symmetry of complex Hamiltonians with real spectra is usually interpreted as a weaker mathematical substitute for Hermiticity. Perhaps an equally important role is played by the related strengthened analyticity assumptions. In a constructive illustration we complexify a few potentials solvable only in s-wave. Then we continue their domain from semi-axis to the whole axis and get the new exactly solvable models. Their energies come out real as expected. The new one-dimensional spectra themselves differ quite significantly from their s-wave predecessors.

Formulation of the linearized forward problems for multicomponent OBS data in a water/solid configuration using the reciprocity theorem

Summary As is the case with other geophysical data, the interpretation of multicomponent data from the new ocean bottom seismic (OBS) acquisition system requires a solution to the forward problem of predicting seismograms. Born approximation (a single-scattering approximation) is one of the classical tools used for solving forward problems. The adaptation of this solution to OBS data requires (1) the explicit introduction of the boundary conditions at a water/solid interface, (2) the use of the reciprocity theorem in a fluid/solid configuration and (3) the use of P- and S-wave potentials. We present a formulation of the linearized forward problem for predicting multicomponent OBS data using Born approximation and the reciprocity theorem. The results of our formulation are valid for pressure data (hydrophone data) as well as particle velocity data (geophone data). Specific cases where particle velocity data are cast into P- and S-wave potentials are also treated. For these scenarios, the background medium and the scatterer are considered arbitrarily anisotropic and heterogeneous.

Low-momentum effective theory for nucleons

Starting from a precise two-nucleon potential, we use the method of unitary transformations to construct an effective potential that involves only momenta less than a given maximal value. We describe this method for an S-wave potential of the Malfliet-Tjon type. It is demonstrated that the bound and scattering state spectrum calculated within the effective theory agrees exactly with the one based on the original potential. This might open an avenue for the construction of effective chiral few-nucleon forces and for a systematic treatment of relativistic effects in few-body systems.

Partial-Wave Analysis with the Optical Model for the Resolved and Unresolved Resonance Regions of 56Fe

An accurate database is used to study optical model fits to total neutron cross sections of 56Fe in the resolved and unresolved resonance regions. Averages over resolved resonances are calculated from resonance parameters in a Reich-Moore (reduced R matrix) approximation with Lorentzian weighting. Optical potential parameters are obtained for the s, p, and d waves that reproduce the smoothed cross sections in the resolved resonance region. The p-wave optical potential is found to differ from the s-wave potential. When the appropriate higher angular momentum contributions are added, the average total cross sections can be fitted quite well, from the resolved resonance region all the way up to 20 MeV.

Deeply bound pionic states and the effective pion mass in nuclear systems

We show that the s-wave pion-nuclear potential which reproduces the deeply bound pionic states in Pb, recently discovered at GSI, is remarkably close to the one constructed directly from low energy theorems based on chiral symmetry. Converting this information into an effective pion mass we find m π ∗ m π ⋍ 1.13 in the center of the Pb nucleus, and m π ∗ m π ⋍ 1.07 in symmetric nuclear matter.

Cross section, spin distribution and mean spin analysis of low-energy heavy-ion fusion by closed formulae

In this paper, we analyse the fusion cross sections , partial-wave fusion cross section and mean angular momenta of heavy-ion (HI) fusion reactions around the Coulomb barrier for a number of pairs of colliding nuclei. This is done by first formulating expressions for in closed forms. These expressions incorporate only the general characteristics, namely radius, height and curvature of the s-wave potential barrier. The formulation is based on our earlier effective fusion barrier (EFB) transmission model. The values of , and calculated around the Coulomb barrier using our expressions provide good fits to the corresponding experimental results in the cases of several HI systems, namely Zr, Mo and Er.

T-matrix formulation of impurity scattering in correlated systems.

Using a generalized T-matrix description which, in principle, exactly includes Coulomb correlations and potential scattering events, resonant and bound impurity states are discussed. Like in the non-interacting case, the effects of the scattering potential can be divided into different partial wave channels, exploiting the symmetry of the underlying lattice. Due to Coulomb correlations bare local (i.e.\ s-wave) potentials become dynamic and extended, being responsible also for p-, d-wave etc. scattering effects. Numerically exact results for both the two-dimensional t--J and Hubbard models are used to construct a simple (static) approximation to the effective impurity potential which is shown to reproduce the exact resonant scattering and bound states in the relevant symmetry channels.

Pocket and barrier resonances in potential scattering and their application to heavy-ion reactions

A comparative study of the properties of pocket and barrier resonances is carried out using finite-range potentials having a pocket and a barrier. Comparison is made between the s-wave potential barrier region resonances with an absorptive pocket, and the corresponding resonances of a potential barrier without an absorptive pocket. We numerically study the resonance states generated by the finite-range truncated parabolic barrier. In this case the location of resonances in the vicinity of the barrier are approximately equispaced, but deviation from this feature occurs for resonances farther away from the barrier top. Using these results as a basis we empirically analyse the resonances in the 16O+16O system within the broad framework of the barrier region resonance model.

S-wave pion optical potential from medium-modified ππ scattering amplitude

We show that a recent model of medium modifications of the ππ scattering amplitude leads to a new source of repulsion in the S-wave pion optical potential, which existing models are unable to explain. Our result indicates that pions do not condense through S-wave interactions.

Complex Kohn variational principle for the solution of Lippmann-Schwinger equations

A recently proposed version of the Kohn variational principle for the t matrix incorporating the correct boundary condition is applied for the first time to the study of nucleon-nucleon scattering. Analytic expressions can be obtained for all the integrals in the method for a wide class of potentials and for a suitable choice of trial functions. Closed-form analytic expressions for these integrals are given for Yakawa and exponential potentials. Calculations with two commonly used S-wave nucleon-nucleon potentials show that the method may converge faster than other solution schemes not only for the phase-shifts but also for the off-shell t matrix elements if the freedom in the choice of the trial function is exploited.

Finite-difference simulation of P--SV-wave propagation: a displacement-potential approach

SUMMARY A new finite-difference formulation is presented for the simulation of P-SV-wave propagation in heterogeneous, isotropic media. In this approach, the wave equations are separated as two sets of equations: one for the displacement fields and the other for potential fields. These two sets of equations involve only first-order spatial derivatives. In terms of potentials, the P-SV-wavefield can be split into P- and S-wave potential fields, which may open an opportunity of simulating P- and S-wave propagation in different ways. By assuming constant density and shear modulus, both P- and S-wave potentials can be expressed in the form of scalar wave equations. Thus, the Lindman 'free space' boundary condition (Lindman 1975) for scalar waves can be used. An improvement can be made by adding a dissipation zone to absorbing boundaries. For a 2-D model, four equations are used, which is one less than Virieux's (1986) velocity-stress approach. Therefore, the new algorithm is more efficient and requires less computer memory. The calculation is naturally performed in a staggered-grid manner which gives an excellent result for both internal discontinuities and model edges.

On relativistic corrections to the S-wave pion-nucleus potential

We analyze possible relativistic corrections to the pion-nucleus optical potential. We find that all relativistic effects which have been under discussion recently are already contained in the standard impulse-approximation result for the optical potential. In particular we show that the corrections due to an in-medium effective mass of the nucleon as recently proposed by Birbrair et al. are simply a result of an inconsistent use of free and in-medium spinors for the nucleons. We observe that in the relativistic framework there are cancellations of very large pieces. Hence usual approximations which are legitimate in most occasions spoil these cancellations here and introduce spurious terms of considerable size.

On the imaginary part of the S-wave pion-nucleus optical potential

The contribution of pion absorption to the imaginary part of the S-wave pion-nucleus optical potential is calculated with Slater determinantal antisymmetrized nuclear wave functions, taking fully into account the spin and isospin degrees of freedom. The potential obtained has an explicit dependence on the proton and neutron nuclear densities whose coefficients are directly related to the two-nucleon absorption coupling constants. The values of these coefficients extracted from mesic atoms data are in good agreement with those deduced from exclusive pion absorption experiments in 3He, but larger than the predictions of the pion rescattering model.