# Changeset 4f5afc9 in sasmodels

Ignore:
Timestamp:
Nov 15, 2017 6:12:11 PM (6 years ago)
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
ac60a39
Parents:
1e867a4
Message:

 r2c108a3 Models which define a scattering length density parameter can be evaluated as magnetic models. In general, the scattering length density (SLD = $\beta$) in each region where the SLD is uniform, is a combination of the nuclear and magnetic SLDs and, for polarised neutrons, also depends on the spin states of the neutrons. as magnetic models. In general, the scattering length density (SLD = $\beta$) in each region where the SLD is uniform, is a combination of the nuclear and magnetic SLDs and, for polarised neutrons, also depends on the spin states of the neutrons. For magnetic scattering, only the magnetization component $\mathbf{M_\perp}$ perpendicular to the scattering vector $\mathbf{Q}$ contributes to the magnetic scattering length. .. figure:: is the Pauli spin. Assuming that incident neutrons are polarized parallel (+) and anti-parallel (-) to the $x'$ axis, the possible spin states after the sample are then Assuming that incident neutrons are polarized parallel $(+)$ and anti-parallel $(-)$ to the $x'$ axis, the possible spin states after the sample are then: Non spin-flip (+ +) and (- -) * Non spin-flip $(+ +)$ and $(- -)$ Spin-flip    (+ -) and (- +) * Spin-flip $(+ -)$ and $(- +)$ Each measurement is an incoherent mixture of these spin states based on the fraction of $+$ neutrons before ($u_i$) and after ($u_f$) the sample, with weighting: .. math:: -- &= ((1-u_i)(1-u_f))^{1/4} \\ -+ &= ((1-u_i)(u_f))^{1/4} \\ +- &= ((u_i)(1-u_f))^{1/4} \\ ++ &= ((u_i)(u_f))^{1/4} Ideally the experiment would measure the pure spin states independently and perform a simultaneous analysis of the four states, tying all the model parameters together except $u_i$ and $u_f$. .. figure:: ===========   ================================================================ M0_sld        = $D_M M_0$ Up_theta      = $\theta_\mathrm{up}$ M_theta       = $\theta_M$ M_phi         = $\phi_M$ Up_frac_i     = (spin up)/(spin up + spin down) neutrons *before* the sample Up_frac_f     = (spin up)/(spin up + spin down) neutrons *after* the sample M0:sld      $D_M M_0$ mtheta:sld   $\theta_M$ mphi:sld     $\phi_M$ up:angle     $\theta_\mathrm{up}$ up:frac_i    $u_i$ = (spin up)/(spin up + spin down) *before* the sample up:frac_f    $u_f$ = (spin up)/(spin up + spin down) *after* the sample ===========   ================================================================ .. note:: The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range 0 to 1. The values of the 'up:frac_i' and 'up:frac_f' must be in the range 0 to 1. *Document History* | 2015-05-02 Steve King | 2017-05-08 Paul Kienzle | 2017-11-15 Paul Kienzle