Added documentation relevant to beta-NMR asymmetry fits, fittype 5.

doc/html/_sources/user-manual.txt

@@ -855,7 +855,7 @@ Currently the supported GLOBAL block entries are:
 * ``rrf_freq`` for fittype 1, 3
 * ``rrf_packing`` for fittype 1, 3
 * ``rrf_phase`` for fittype 1, 3
-* ``packing`` for fittype 0, 2, 4
+* ``packing`` for fittype 0, 2, 4, 5
 
 For a detailed discussion of these entries see the section :ref:`RUN block <msr-run-block>`.
 
@@ -1049,6 +1049,8 @@ In order to describe the operations needed for fitting and plotting, quite some
     Asymmetry RRF Fit (only for online analysis)
   **4**
     MuMinus Fit. This is a single histogram fit especially for negative muon |mgr|\SR
+  **5**
+    beta-NMR Asymmetry Fit
   **8**
     Non-|mgr|\SR Fit   
 
@@ -1061,8 +1063,8 @@ In order to describe the operations needed for fitting and plotting, quite some
 .. index:: alpha-beta
 .. _msr-alpha-beta:
 
-**alpha, beta** (fit type 2, 3)
+**alpha, beta** (fit type 2, 3, 5)
-  These parameters are used to correct the asymmetry for different detector efficiencies, solid angles and initial asymmetries. They are defined as :math:`\alpha = N_{0,b}/N_{0,f}` and :math:`\beta = A_{0,b}/A_{0,f}`. If the parameters are not specified in the :ref:`RUN block <msr-run-block>`, for each one the value of 1 is assumed. Example for alpha with fit parameter number 1:
+  These parameters are used to correct the asymmetry for different detector efficiencies, solid angles and initial asymmetries. They are defined as :math:`\alpha = N_{0,b}/N_{0,f}` and :math:`\beta = A_{0,b}/A_{0,f}`. If the parameters are not specified in the :ref:`RUN block <msr-run-block>`, for each one the value of 1 is assumed (for fittype 5 alpha is estimated from the ration of sum of Bp+Bm and Fp+Fm). Example for alpha with fit parameter number 1:
 
   ::
 
@@ -1141,10 +1143,19 @@ In order to describe the operations needed for fitting and plotting, quite some
     forward   1-3
     backward  7-9
 
+**forward, backward** (fit type 5)   
+  Numbers of the histograms in the data file that should be taken to calculate the asymmetry. Two forward and backward histograms should be given indicationg positive and negative helicities. The asymmetry from opposite helicities will be subtracted. Examples: 
+  
+  ::
+  
+    # build forward/backward asymmetry with histogram 1 and 3 then subtract asymmetry built with histograms 2 and 4
+    forward  1 2
+    backward 3 4
+
 .. index:: backgr.fix
 .. _msr-backgr.fix:
 
-**backgr.fix** (fit types 0, 1, 2, 3)    
+**backgr.fix** (fit types 0, 1, 2, 3, 5)    
   A fixed constant background in counts per nanosecond or per bin (see :ref:`below <msr-commands-block>`) may be given at this point. 
   The background is specified for all histograms in the order :math:`B_f B_b [B_r B_l]`. If this keyword is present, *any* information on a ``background`` line is ignored. 
     
@@ -1162,7 +1173,7 @@ In order to describe the operations needed for fitting and plotting, quite some
 .. index:: background-asymmetry
 .. _msr-background-asymmetry:
 
-**background** (fit types 2, 3)     
+**background** (fit types 2, 3, 5)     
   The numbers of the first and the last channel of an interval from which the constant background should be calculated are specified here. 
   For all the histograms this is done together in the following order: :math:`k_{f,\rm first} k_{f,\rm last} k_{b,\rm first} k_{b, \rm last} [k_{r,\rm first} k_{r,\rm last} k_{l,\rm first} k_{l,\rm last}]`. 
   In case histograms are being grouped, the specified channels are interpreted with respect to the first histograms. Example:
@@ -1186,7 +1197,7 @@ In order to describe the operations needed for fitting and plotting, quite some
 .. index:: data-asymmetry
 .. _msr-data-asymmetry:
 
-**data** (fit type 2, 3) 
+**data** (fit type 2, 3, 5) 
   The numbers of the first and the last channel of an interval from which the data is taken are specified here. 
   Typically these channels are referred to as first good bin / last good bin (fgb/lgb). For all the histograms this is 
   done together in the following order: :math:`k_{f,\rm first} k_{f,\rm last} k_{b,\rm first} k_{b, \rm last} [k_{r,\rm first} k_{r,\rm last} k_{l,\rm first} k_{l,\rm last}]`. 
@@ -1210,8 +1221,8 @@ In order to describe the operations needed for fitting and plotting, quite some
 .. index:: t0-asymmetry
 .. _msr-t0-asymmetry:
 
-**t0** (fit type 2, 3)     
+**t0** (fit type 2, 3, 5)     
-  The numbers of time-zero channels of the histograms in the order :math:`t_{0,f} t_{0,b}`. Example:
+  The numbers of time-zero channels of the histograms in the order :math:`t_{0,f} t_{0,b}`. For fit type 5, the time-zero is the channel of the start of beam pulse. Example:
   
   ::
   
@@ -1229,7 +1240,7 @@ In order to describe the operations needed for fitting and plotting, quite some
 .. index:: addt0-asymmetry
 .. _msr-addt0-asymmetry:
 
-**addt0** (fit type 2, 3) 
+**addt0** (fit type 2, 3, 5) 
   The numbers of time-zero channels of the histograms in the order :math:`t_{0,f} t_{0,b} [t_{0,r} t_{0,l}]`. 
   If grouping of histograms is present (see :ref:`forward <msr-forward-backward>`) the same syntax as for :ref:`t0 <msr-t0-asymmetry>` applies. 
   If one addt0 is given, the total number of addt0's needs to be equal to the total number of :ref:`ADDRUN <msr-addrun>`\'s! 
@@ -1851,6 +1862,55 @@ where :math:`i` runs over the different lifetime channels of :math:`\mu^{-}`, an
    
 Since MuMinus is quite generic, the full functional depends has to be written in the :ref:`THEORY Block <msr-theory-block>`.
    
+.. index:: bnmr-asymmetry-fit
+.. _bnmr-asymmetry-fit:
+
+beta-NMR Asymmetry Fit (fit type 5)
++++++++++++++++++++++++++++++++++++
+
+For a beta-NMR asymmetry fit (fit type 5) four histograms are needed, two for positive and two for negative helicities. These are given by the :ref:`forward <msr-forward-backward>` and :ref:`backward <msr-forward-backward>` keywords 
+in the :ref:`RUN block <msr-run-block>`. Additionally, the parameters :ref:`alpha <msr-alpha-beta>` and :ref:`beta <msr-alpha-beta>` which relate the detector 
+efficiencies, solid angles and initial asymmetries of the two detectors can be supplied. The constant background for the two histograms is either given by 
+:ref:`background-determined intervals <msr-background-asymmetry>` or specified through :ref:`backgr.fix <msr-backgr.fix>` in the :ref:`RUN-block <msr-run-block>`. 
+
+The experimental asymmetry :math:`a(k)` then is calculated from the four histograms:
+
+.. math::
+
+   a(k)=\frac{\left[N_{\mathrm{fp}}(k)-B_{\mathrm{fp}}\right]-\left[N_{\mathrm{bp}}(k)-B_{\mathrm{bp}}\right]}{\left[N_{\mathrm{fp}}(k)-B_{\mathrm{fp}}\right]+\left[N_{\mathrm{bp}}(k)-B_{\mathrm{bp}}\right]}
+   - \frac{\left[N_{\mathrm{fm}}(k)-B_{\mathrm{fm}}\right]-\left[N_{\mathrm{bm}}(k)-B_{\mathrm{bm}}\right]}{\left[N_{\mathrm{fm}}(k)-B_{\mathrm{fm}}\right]+\left[N_{\mathrm{bm}}(k)-B_{\mathrm{bm}}\right]},
+   
+with
+
+   * :math:`N_{\mathrm{fp}}(k)`: counts in the **forward** histogram channel with positive helicity :math:`k`
+   * :math:`N_{\mathrm{bp}}(k)`: counts in the **backward** histogram channel with positive helicity :math:`k`
+   * :math:` B_{\mathrm{fp}}`: constant background in the **forward** histogram with positive helicity (RUN block: :ref:`backgr.fix <msr-backgr.fix>` or :ref:`background <msr-background-asymmetry>`) 
+   * :math:` B_{\mathrm{bp}}`: constant background in the **backward** histogram with positive helicity (RUN block: :ref:`backgr.fix <msr-backgr.fix>` or :ref:`background <msr-background-asymmetry>`) 
+   * :math:`N_{\mathrm{fm}}(k)`: counts in the **forward** histogram channel with negative helicity :math:`k`
+   * :math:`N_{\mathrm{bm}}(k)`: counts in the **backward** histogram channel with negative helicity :math:`k`
+   * :math:` B_{\mathrm{fm}}`: constant background in the **forward** histogram with negative helicity (RUN block: :ref:`backgr.fix <msr-backgr.fix>` or :ref:`background <msr-background-asymmetry>`) 
+   * :math:` B_{\mathrm{bm}}`: constant background in the **backward** histogram with negative helicity (RUN block: :ref:`backgr.fix <msr-backgr.fix>` or :ref:`background <msr-background-asymmetry>`) 
+   
+This theoretical asymmetry :math:`a(t)` is used to fit the function   
+
+.. math::
+
+   a(t)=\frac{(\alpha\beta +1)A(t)-(\alpha -1)}{(\alpha +1)-(\alpha\beta -1)A(t)} - \frac{(\alpha -1)-(\alpha\beta 1)A(t)}{(\alpha +1)+(\alpha\beta -1)Am(t)}, 
+    
+where
+
+   * :math:`\alpha`: accounts for the different detector efficiencies and solid angles (RUN block: :ref:`alpha <msr-alpha-beta>`).
+   * :math:`\beta`: accounts for the different detector asymmetries (RUN block: :ref:`beta <msr-alpha-beta>`).
+   * :math:`A(t)`: is the depolarization function as given in the :ref:`THEORY block <msr-theory-block>`.
+   
+For the graphical representation in plot type 5 the equation above is rearranged to get :math:`A(t)`:   
+
+.. math::
+
+    A(t)=\frac{(\alpha -1)+(\alpha +1)a(t)}{(\alpha\beta +1)+(\alpha\beta -1)a(t)}-\frac{(\alpha +1)a(t)-(\alpha -1)}{(\alpha\beta +1)+(1-\alpha\beta)a(t)}=\frac{\alpha\left[N_{\mathrm{fp}}(t)-B_{\mathrm{fp}}\right]-\left[N_{\mathrm{bp}}(t)-B_{\mathrm{bp}}\right]}{\alpha\beta\left[N_{\mathrm{fp}}(t)-B_{\mathrm{fp}}\right]+\left[N_{\mathrm{bp}}(t)-B_{\mathrm{bp}}\right]} -\frac{\alpha\left[N_{\mathrm{fm}}(t)-B_{\mathrm{fm}}\right]-\left[N_{\mathrm{bm}}(t)-B_{\mathrm{bm}}\right]}{\alpha\beta\left[N_{\mathrm{fm}}(t)-B_{\mathrm{fm}}\right]+\left[N_{\mathrm{bm}}(t)-B_{\mathrm{bm}}\right]}
+    
+and plotted together with the function given in the THEORY block.     
+
     
 .. index:: non-musr-fit
 .. _non-musr-fit: