[Paper Review] Interference pattern of the Coulomb and the strong Van der Waals forces in p-p scattering

Tetsuo Sawada|ArXiv.org|Jun 28, 2000

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper proposes measuring the angular distribution of low-energy proton-proton scattering (20–30 MeV lab energy) to detect a characteristic interference pattern between the repulsive Coulomb force and an attractive strong Van der Waals force. Using phase shift data and spectral analysis of the S-wave amplitude, the authors predict a 1% dip in the differential cross section at center-of-mass scattering angle θ_cm ≈ 14°, providing a direct experimental signature for long-range nuclear forces beyond standard short-range models.

ABSTRACT

In order to confirm the strong Van der Waals force in the nucleon-nucleon interaction, it is proposed to measure precisely the angular distribution of the cross section of the low energy ($T_{lab}=20 \sim 30MeV.$) proton-proton scattering. By using the spectrum of the long range interaction obtained from the analysis of the phase shift data of the S-wave of the p-p scattering, a characteristic interference pattern, which arises from the repulsive Coulomb and the attractive strong Van der Waals forces, is predicted. The pattern has a dip at $theta_{c.m.}=14^{\circ}$ with the depth around one per cent.

Motivation & Objective

• To provide a direct experimental test for the existence of long-range strong Van der Waals forces in nucleon-nucleon interactions.
• To identify a unique interference pattern in p-p scattering arising from the competition between repulsive Coulomb and attractive strong Van der Waals forces.
• To demonstrate that precise angular distribution measurements at low energy (20–30 MeV) can reveal the analytic structure of the scattering amplitude near t=0, signaling long-range forces.
• To establish that the observed dip at θ_cm ≈ 14° is a signature of the Van der Waals interaction, distinguishable from short-range forces.

Proposed method

• Analysis of S-wave phase shift data from p-p scattering to extract the spectrum of long-range interactions.
• Computation of the once-subtracted Kantor amplitude to isolate singularities at ν=0, removing unitarity and one-pion exchange cuts.
• Use of the spectral function of the long-range potential to model the t-channel singularity in the scattering amplitude A(s,t), with behavior ∝ t^γ near t=0.
• Derivation of the differential cross section Δσ/σ(θ) as a function of center-of-mass angle, incorporating interference between Coulomb and strong Van der Waals potentials.
• Numerical evaluation of coefficient functions g̃^s(θ) and g̃^t(θ) for singlet and triplet states to predict angular dependence.
• Comparison of theoretical predictions with experimental data by varying the off-forward region boundary θ₁ to test robustness of the dip feature.

Experimental results

Research questions

• RQ1 Can the interference pattern between the repulsive Coulomb force and the attractive strong Van der Waals force be experimentally observed in low-energy p-p scattering?
• RQ2 Does the presence of a long-range potential with V(r) ∝ -C/r⁶ lead to a distinctive singularity in the scattering amplitude A(s,t) at t=0?
• RQ3 Is the predicted dip in the differential cross section at θ_cm ≈ 14° robust under variations in the off-forward region boundary θ₁?
• RQ4 Can the spectral function of the long-range force be extracted from phase shift data to confirm its Van der Waals nature?
• RQ5 Does the observed angular distribution anomaly provide a more direct confirmation of long-range forces than conventional phase shift analysis?

Key findings

• A narrow dip of approximately 1% depth in the differential cross section Δσ/σ(θ) is predicted at center-of-mass scattering angle θ_cm ≈ 14° due to destructive interference between Coulomb and strong Van der Waals forces.
• The dip is robust across different off-forward region boundaries θ₁ = 30°, 45°, 60°, and 90°, indicating stability of the prediction.
• The predicted interference pattern arises from the t-channel singularity ∝ (-t)^{3/2} in the scattering amplitude, characteristic of a London-type Van der Waals potential with α = 6.
• The analysis of the once-subtracted S-wave amplitude reveals a cusp-like structure ∝ (c₀ - c₁√ν) at ν = 0, consistent with a long-range potential of the Van der Waals type.
• The parameters of the long-range force are extracted as γ = 1.95, C′ = 0.0161, and β = 0.144 from π-π scattering data, confirming a Casimir-Polder-type interaction.
• The prediction is most sensitive in low-energy p-p scattering (20–30 MeV), where the long-range force effect is enhanced and experimental precision is high.