Calculators – Fankang Li

Neutron Larmor Precession Calculator

With the unit on the left,

$\Phi=\frac{\gamma_n m \lambda}{h} B L \times 10^{-16}$

$V=\frac{h}{m\lambda} \times 10^{10}$

$f=\frac{\gamma_n B}{2\pi}\times 10^{-6}$

Please note:

With the unit on the left,

$\tiny T_{\pm}=T_{cell}\cdot e^{-(1\mp P_{He})\cdot O}$

$\tiny T=\frac{1}{2}(T_+ +T_-)=T_{cell}\cdot e^{-O}\cosh(O\cdot P_{He})$

$P=\frac{T_+-T_-}{T_++T_-}=\tanh(O\cdot P_{He})$

$\small Q_n=T\cdot P_n^2$

Reference:

With the unit on the left,

$\tau=\frac{\gamma_n m^2 \lambda^3}{2\pi h^2}BL \times 10^{-27}$

Please note:

With the unit on the left,

$\xi=\frac{\gamma_n m \lambda^2}{\pi h} BL \cot{\theta}\times 10^{-17}$

Please note:

γ_n: the gyromagnetic ratio

$-1.83247171(43)\times10^8 rad \cdot s^{-1}\cdot T^{-1}$

$-29.1646943(69)MHz/T$

m: the neutron mass

$1.67492735\times10^{-27}kg$

h: the Planck's constant

$6.62607\times10^{-34}m^2\cdot kg/s$

Pressure P_cell(bar):
Cell length L(cm):
Neutron wavelength λ(Å):
Empty cell transmission T_cell:
³He polarization P_He:

Neutron polarization P_n:
Unpolarized neutron transmission T:
Spin up state transmission T₊:
Spin down state transmission T_-:
Neutron flipping ratio:
Figure-of-merit Q_n: