[Paper Review] Present status of the long range component of the nuclear force

Tetsuo Sawada|arXiv (Cornell University)|Apr 8, 2000

Quantum, superfluid, helium dynamics1 references3 citations

TL;DR

This paper investigates the existence of a long-range component in the nuclear force by analyzing the S-wave proton-proton scattering amplitude for an extra singularity at ν=0, corresponding to a long-range interaction. Using a regularized function derived from phase shift data, it finds a sharp cusp at ν=0 consistent with a square-root singularity, indicating an attractive long-range force resembling the London-type van der Waals interaction, with a threshold power γ ≈ 1.54, suggesting a super-strong underlying Coulombic interaction.

ABSTRACT

In order to settle the fundamental question whether the nuclear forces involve the long range components, the S-wave amplitude of the proton-proton scattering is analysed in search for the extra singularity at $ν=0$, which corresponds to the long range force. To facilitate the search, a function, which is free from the singularities in the neighborhood of $ν=0$ when all the interactions are short range, is constructed. The calculation of such a function from the phase shift data reveals a sharp cusp at $ν=0$ in contradiction to the meson theory of the nuclear force. The type of the extra singularity at $ν=0$ is close to what is expected in the case of the strong van der Waals interaction. Physical meanings of the long range force in the nuclear force are discussed. Low energy p-p experiments to confirm directly the strong long range interaction are also proposed, in which the characteristic interference patten of the Coulonb and the Van der Waals forces is predicted.

Motivation & Objective

• To determine whether the nuclear force includes a long-range component by probing for an extra singularity in the S-wave proton-proton scattering amplitude at ν=0.
• To isolate the long-range contribution from short-range interactions and electromagnetic effects using analytic structure analysis.
• To test whether the observed singularity matches the theoretical expectation for strong van der Waals interactions.
• To propose low-energy experiments to directly observe the interference pattern between Coulomb and long-range forces.

Proposed method

• Construct a regularized function K₀(ν) from the modified effective range function X₀(ν), removing known singularities from one-pion exchange and electromagnetic interactions.
• Apply a once-subtracted dispersion relation to K₀(ν) to form K̃₀^{once}(ν), enhancing sensitivity to singularities at ν=0.
• Use high-precision S-wave proton-proton phase shift data to fit the spectral function Aₜ(4m²,t) = πC't^γ exp(−βt), extracting parameters γ, β, and C′.
• Compare the observed singularity form to theoretical expectations for van der Waals forces, particularly the London type (γ=1.5) and Casimir-Polder type (γ=2.0).
• Estimate the strength of the underlying Coulombic force using inequalities on the C₆ coefficient of the van der Waals potential, constrained by hadron size and observed C₆.
• Propose low-energy pp scattering experiments at T_lab ≈ 25–40 MeV to detect the distinctive interference pattern between Coulomb and long-range forces.

Experimental results

Research questions

• RQ1 Does the S-wave proton-proton scattering amplitude exhibit an extra singularity at ν=0, indicating a long-range nuclear force?
• RQ2 Is the form of the singularity at ν=0 consistent with the square-root type expected for a strong van der Waals interaction?
• RQ3 What is the threshold power γ of the spectral function Aₜ(4m²,t) at t=0, and does it match predictions for known long-range forces?
• RQ4 Can the strength of the underlying Coulombic interaction be estimated from the observed long-range force parameters?
• RQ5 What is the optimal energy and angular range for experimentally detecting the interference between Coulomb and long-range forces?

Key findings

• The once-subtracted function K̃₀^{once}(ν) exhibits a sharp cusp at ν=0 with a square-root singularity form, consistent with the London-type van der Waals interaction.
• The threshold power γ of the spectral function is determined to be γ = 1.54 from a chi-square fit to multi-energy phase shift data, close to the theoretical value of 1.5 for the London-type force.
• The spectral function Aₜ(4m²,t) has a peak at √t = 4.9, corresponding to 660 MeV, indicating a dominant contribution near this momentum transfer.
• The peak of the once-subtracted amplitude spectrum Aₜ(4m²,t)/t is located at √t = 2.93, or 395 MeV, suggesting a dominant effective mass scale for the long-range interaction.
• The estimated strength of the underlying Coulombic force satisfies ∗e² > 3.3 for a hadron radius of 0.5 fm, and ∗e² > 14 for a radius of 0.25 fm, both exceeding typical values and consistent with a dyon model.
• The predicted interference pattern between Coulomb and long-range forces shows a dip of ~0.3% in the differential cross section at θ_c.m. ≈ 10°, most observable at T_lab ≈ 25–40 MeV.