[Paper Review] E12-14-009: Ratio of the electric form factor in the mirror nuclei 3He and 3H

L. S. Myers, D. W. Higinbotham+1 more|arXiv (Cornell University)|Aug 22, 2014

Superconducting Materials and Applications4 citations

TL;DR

This paper proposes a 1.5-day experiment at Jefferson Lab to measure the ratio of electric form factors (G_E) in the mirror nuclei $^3$He and $^3$H using elastic electron scattering at 1.1 GeV beam energy and low momentum transfer (Q² ≤ 0.1 GeV²). By exploiting the high-statistics data from a 1 kCi $^3$H target and minimizing contributions from magnetic and Coulomb effects, the study aims to improve the precision of the charge radius difference between $^3$He and $^3$H by more than a factor of three, achieving a projected uncertainty of ±0.03 fm.

ABSTRACT

E12-14-009: We propose to extract the ratio of the electric form factor (G_E) of 3He and 3H from the measured ratio of the elastic-scattering cross sections at E_beam = 1.1 GeV. Measurements at low Q^2 ( < 0.1 GeV^2) will allow accurate extraction of G_E with minimal contributions from the magnetic form factor (G_M) and Coulomb corrections. From this data we will extract the difference between the charge radii for 3He and 3H. This short experiment, 1.5 days, will utilize the left Hall A high resolution spectrometer and the one-time availability of a 1 kCi tritium target at Jefferson Lab which has been approved for the E12-10-103, E12-11-112 and E12-14-011 experiments.

Motivation & Objective

• To improve the precision of the difference in charge radii between the mirror nuclei $^3$He and $^3$H beyond the current uncertainty of ±0.10 fm.
• To extract the ratio of electric form factors (G_E) in $^3$He and $^3$H using elastic electron scattering at low Q² to minimize sensitivity to magnetic and Coulomb effects.
• To reduce model-dependent uncertainties in G_E by leveraging high-statistics data to distinguish between dipole and monopole functional forms of the form factor.
• To provide a critical experimental benchmark for chiral Effective Field Theory (χEFT) and Green’s function Monte Carlo (GFMC) calculations of nuclear charge radii.
• To support future muonic atom measurements by enabling precise normalization between hydrogen and helium isotope chains.

Proposed method

• Measure the ratio of elastic electron scattering cross sections for $^3$He and $^3$H at beam energy ~1.1 GeV and Q² = 0.05–0.09 GeV² using the left Hall A High Resolution Spectrometer (HRS).
• Utilize the one-time availability of a 1 kCi $^3$H target, shared with E12-10-103, E12-11-112, and E12-14-011, to enable high-statistics data collection.
• Perform measurements at two scattering angles (12.5° and 15.0°) to access the Q² range and ensure kinematic consistency.
• Apply a sieve and collimator system to study spectrometer optics and acceptance, minimizing systematic uncertainties from beam position and target thickness.
• Use the ratio of form factors relative to the minimum Q² point to cancel common systematic errors, particularly those from target thickness and beam calibration.
• Fit the data using dipole and monopole parametrizations of G_E to assess model dependence and constrain acceptable functional forms.

Experimental results

Research questions

• RQ1 What is the precise ratio of the electric form factors G_E for $^3$He and $^3$H at low Q²?
• RQ2 How can the uncertainty in the difference of charge radii between $^3$He and $^3$H be reduced below the current ±0.10 fm level?
• RQ3 To what extent do the data constrain the functional form of G_E, particularly distinguishing between dipole and monopole parametrizations?
• RQ4 How does the measured G_E ratio compare with predictions from χEFT and GFMC calculations?
• RQ5 Can the high-precision form factor ratio improve the normalization of atomic isotope shift measurements in hydrogen and helium isotopes?

Key findings

• The experiment is projected to reduce the uncertainty in the charge radius difference between $^3$He and $^3$H to ±0.03 fm, improving upon the current uncertainty of ±0.10 fm by more than a factor of three.
• A 2% measurement of the relative cross section is expected to yield this improved precision, leveraging high-statistics data to minimize statistical uncertainty.
• The ratio of form factors at low Q² is largely insensitive to magnetic form factor and Coulomb corrections, enabling a clean extraction of G_E.
• The data will strongly disfavor a monopole form for G_E, as the dipole fit matches the data trend while the monopole does not, reducing model dependence.
• The use of the form factor ratio relative to the minimum Q² point cancels dominant systematic uncertainties, such as those from target thickness and beam calibration.
• The results will provide a critical benchmark for ab initio calculations using chiral N-N potentials and χEFT, with implications for three-body force and isospin symmetry studies.