# 3He Spin Filters

## 3He Spin Filter Calculations

Here is the list of functions used to calculate neutron spin filters characteristics that are provided by the "Neutron Scattering" XOP:

#### He3Efficiency(p, T, l, lbda, P3He)

The He3Efficiency function returns the polarisation efficiency of a 3He spin filter for a given neutron wavelength. The polarisation efficiency is defined by the equation below where p  is the 3He pressure in bar, l  is the effective length of the cell in cm, a.T is the volume of 1 mole of 3He at the given temperature T in Kelvin and P3He  is the 3He polarisation. lbda  is the neutron wavelength in Å and sigma_a  is the absorption cross section of 3He at 1 Å (about 2963 barn).

#### He3EfficiencySDev(p, T, l, lbda, P3He, pSDev, TSDev, lSDev, lbdaSDev, P3HeSDev)

The He3EfficiencySDev function returns the standard deviation of the polarisation efficiency of a 3He spin filter for a given neutron wavelength where p  is the 3He pressure in bar, l  is the effective length of the cell in cm, T is the temperature in Kelvin and P3He  is the 3He polarisation. lbda  is the neutron wavelength in Å and sigma_a  is the absorption cross section of 3He at 1 Å (about 2963 barn). The xSDEV terms are the standard deviations of these parameters.

#### He3Efficiency2(M10, M20, M1, M2)

The He3Efficiency2 function returns the polarisation efficiency of a 3He spin filter from monitor values. Two monitors are mounted before and after the spin filter cell, respectively M1 and M2. The polarisation efficiency is defined by the equation below where M10 and M20  are measured for the cell depolarised while M1 and M2 are measured when the gas is still polarised.

#### He3Efficiency2SDev(M10, M20, M1, M2)

The He3Efficiency2SDev function returns the standard deviation of the polarisation efficiency of a 3He spin filter from monitor values. The standard deviation of the polarisation efficiency is defined by the equation below where M10 and M20  are measured for the cell depolarised while M1 and M2 are measured when the gas is still polarised.

#### He3Transmission(p, T, l, lbda, P3He)

The He3Transmission function returns the unpolarised beam transmission of a 3He spin filter for a given neutron wavelength. The unpolarised beam transmission is defined by the equation below where p  is the 3He pressure in bar, l  is the effective length of the cell in cm, a.T is the volume of 1 mole of 3He at the given temperature T in Kelvin and P3He  is the 3He polarisation. lbda  is the neutron wavelength in Å and sigma_a  is the absorption cross section of 3He at 1 Å (about 2963 barn).

#### He3TransmissionSDev(p, T, l, lbda, P3He, pSDev, TSDev, lSDev, lbdaSDev, P3HeSDev)

The He3TransmissionSDev function returns the standard deviation of the unpolarised beam transmission of a 3He spin filter for a given neutron wavelength where p  is the 3He pressure in bar, l  is the effective length of the cell in cm, T is the temperature in Kelvin and P3He  is the 3He polarisation. lbda  is the neutron wavelength in Å and sigma_a  is the absorption cross section of 3He at 1 Å (about 2963 barn). The xSDEV terms are the standard deviations of these parameters.

#### He3Polarisation(p, T, l, lbda, Pin, Aout)

The He3Polarisation function returns the 3He polarisation of a 3He spin filter for a given neutron wavelength, incident polarisation, and measured final polarisation asymmetry Aout. If the incident beam is polarised or unpolarisaed, the polarisation of the gas is defined by the respective below expressions where p  is the 3He pressure in bar, l  is the effective length of the cell in cm, a.T is the volume of 1 mole of 3He at the given temperature T in Kelvin, lbda  is the neutron wavelength in Å, Pin  is the incident polarisation and Aout  is the final polarisation asymmetry after the cell.

#### He3PolarisationSDev(p, T, l, lbda, Pin, Pout, pSDev, TSDev, lSDev, lbdaSDev, PinSDev, PoutSDev)

The He3PolarisationSDev function returns the standard deviation of the 3He polarisation of a 3He spin filter for a given neutron wavelength, incident polarisation, and measured final polarisation asymmetry Aout where p  is the 3He pressure in bar, l  is the effective length of the cell in cm, T is the temperature in Kelvin, lbda  is the neutron wavelength in Å, Pin is the incident polarisation and Aout  is the final polarisation asymmetry after the cell. The xSDEV terms are the standard deviations of these parameters.