Proton magnetic shielding correction

$σ_{p}^{'}$ = 2.567 15(41) × 10⁻⁵

Value: 2.567 15 × 10⁻⁵
Standard uncertainty: 4.1 × 10⁻⁹
Relative uncertainty: 1.6 × 10⁻⁴ (160 parts per million)
Status: Measured
Symbol: $σ_{p}^{'}$
Source: CODATA 2022 via NIST · NIST entry

Use in a calculation

# proton magnetic shielding correction, CODATA 2022 (NIST)
proton_magnetic_shielding_correction = 2.56715e-5  # standard uncertainty 4.1e-9

# SciPy: scipy.constants.physical_constants['proton mag. shielding correction']

What it is

The fraction by which the electrons around a proton in a spherical sample of pure water at 25 °C reduce the magnetic field it feels. It links the bare proton's magnetic moment to the shielded value used in magnetic resonance.

How the value changed, 1998–2022

Each point is one CODATA adjustment, plotted as its difference from the 2022 value; the bars show one standard uncertainty (an arrowhead means the bar runs off the chart).

Relative uncertainty

CODATA	Value (uncertainty)	Relative uncertainty	Change from previous
2022	2.567 15(41) × 10⁻⁵	1.6 × 10⁻⁴	−1.6 σ of 2018
2018	2.5689(11) × 10⁻⁵	4.3 × 10⁻⁴	−0.2 σ of 2014
2014	25.691(11) × 10⁻⁶	4.3 × 10⁻⁴	−0.2 σ of 2010
2010	25.694(14) × 10⁻⁶	5.4 × 10⁻⁴	+0.0 σ of 2006
2006	25.694(14) × 10⁻⁶	5.4 × 10⁻⁴	+0.3 σ of 2002
2002	25.689(15) × 10⁻⁶	5.8 × 10⁻⁴	+0.1 σ of 1998
1998	25.687(15) × 10⁻⁶	5.8 × 10⁻⁴

“Change from previous” is the shift in the value divided by the standard uncertainty of the previous adjustment. Earlier values are converted into the current unit where NIST changed it (for example J s to J Hz⁻¹).