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In the case of LE-μSR, the muon stopping distribution might have a profound impact on the muon polarization function \(P(t)\). In case of transverse field μSR measurements it can be written as
+where \(n(z)\) is the normaized muon stopping distribution obtained from the Monte-Carlo code TRIM.SP. Normalized means
+\(\gamma_\mu = 2 \pi \times 135.54\) MHz/T is the gyromagnetic ratio of the muon and \(\varphi\) +is the initial phase of the muon spins with respect to the positron detector. Typically \(B(z)\) is the function which needs to be dealt with in a specific user function. A simple example would be the Meissner screening of a superconductor, for which
+with \(B_0\) being the applied magnetic field, and \(\lambda\) is the magnetic penetration depth.
+This means that one needs to deal with the \(n(z)\) objects in all these user functions. \(n(z)\) does not only depend on the depth, but also on the implantation energy \(E_{\rm impl}\). For a real experiment this means that one is calculating a collection (various energies) of muon stopping distribution profiles with TRIM.SP. In the language of TRIM.SP, these files are called rge-files.
+Since this is often needed in a detailed analysis of LE-μSR spectra, there is a special rge-file handler class implemented which deals with the loading, normalization and interpolation of these \(n(z, E_{\rm impl})\) objects. The essential user-interface of this class with the name PRgeHandler is given +here:
+class PRgeHandler : public TObject
+{
+ public:
+ PRgeHandler(std::string fln="");
+ virtual ~PRgeHandler() {}
+
+ virtual bool IsValid() { return fValid; }
+ virtual PRgeDataList GetRgeData() { return fData; }
+ virtual Double_t GetZmax(const Double_t energy);
+ virtual Double_t GetZmax(const Int_t idx);
+ virtual Double_t Get_n(const Double_t energy, const Double_t z);
+ virtual Double_t Get_n(const Int_t idx, const Double_t z);
+ virtual Int_t GetEnergyIndex(const Double_t energy);
+
+ private:
+ bool fValid{false};
+ PRgeDataList fData;
+
+ virtual bool ReadRgeFile(const std::string fln, PRgeData &data);
+};
+The rge-file objects are loaded internally (see below) and can easily be accessed via this interface. The \(n(z, E_{\rm impl})\) data can either be accessed via Get_n(const Double_t energy, const Double_t z), i.e. via the implantation energy (given in eV), or via Get_n(const Int_t idx, const Double_t z) with the index idx which is the energy index of the collection. Both this routines deliver \(n(z, E_{\rm impl})\) in normalized form. The on via the energy index is slightly more efficient. The routine GetEnergyIndex(const Double_t energy) allows the get the proper energy index of the collection.
+In order that class can find the rge-files at runtime, a xml-file is needed when calling the constructor. Very often, specific user-function need some additional input which is not delivered via the msr-files, but via a startup xml-file. In this case the rge-file will be just a part of the startup xml-file. For instance in the case of the Nonlocal Meissner screening user-function class, this looks like this
+<?xml version="1.0" encoding="UTF-8"?>
+<nonlocal xmlns="http://nemu.web.psi.ch/musrfit/nonlocal">
+ <comment>
+ Fourier and TrimSp information
+ </comment>
+ <nonlocal_par>
+ <fourier_points>262144</fourier_points>
+ </nonlocal_par>
+ <trim_sp>
+ <data_path>./profiles/</data_path>
+ <rge_fln_pre>Sn_E</rge_fln_pre>
+ <energy_list>
+ <energy>1000</energy>
+ <energy>2000</energy>
+ <energy>4000</energy>
+ <energy>6000</energy>
+ <energy>8000</energy>
+ <energy>10000</energy>
+ <energy>12000</energy>
+ <energy>14100</energy>
+ <energy>18000</energy>
+ <energy>22000</energy>
+ <energy>25000</energy>
+ <energy>27300</energy>
+ </energy_list>
+ </trim_sp>
+</nonlocal>
+The relevant portion for the rge-file handler class is starting with the xml tag <trim_sp> and contains four further tags:
+In the given example the files are searched for in the sub-directory call profiles of the current directory. The rge-files have file names like +Sn_E1000.rge, Sn_E2000.rge, etc.
+In the aforementioned Nonlocal Meissner screening class, in the constructor you will find the following invocation of the rge-handler object:
+PNL_PippardFitterGlobal::PNL_PippardFitterGlobal()
+{
+ ...
+
+ // load all the TRIM.SP rge-files
+ fRgeHandler = new PRgeHandler("./nonlocal_startup.xml");
+ if (!fRgeHandler->IsValid()) {
+ std::cout << std::endl << ">> PNL_PippardFitterGlobal::PNL_PippardFitterGlobal **PANIC ERROR**";
+ std::cout << std::endl << ">> rge data handler too unhappy. Will terminate unfriendly, sorry.";
+ std::cout << std::endl;
+ fValid = false;
+ }
+
+ ...
+}
+And in the operator() function call which calculates the muon spin polarization, it will look like this
+Double_t PNL_PippardFitter::operator()(Double_t t, const std::vector<Double_t> ¶m) const
+{
+ ...
+
+ // calculate field if parameter have changed
+ fPippardFitterGlobal->CalculateField(param);
+ Int_t energyIndex = fPippardFitterGlobal->GetEnergyIndex(param[0]);
+ if (energyIndex == -1) { // energy not found
+ std::cerr << std::endl << ">> PNL_PippardFitter::operator() energy " << param[0] << " not found. Will terminate." << std::endl;
+ assert(0);
+ }
+
+ ...
+
+ // calcualte polarization
+ Bool_t done = false;
+ Double_t pol = 0.0, dPol = 0.0;
+ Double_t z=0.0;
+ Int_t terminate = 0;
+ Double_t dz = 1.0;
+
+ do {
+ if (z < param[8]) { // z < dead-layer
+ dPol = fPippardFitterGlobal->GetMuonStoppingDensity(energyIndex, z) * cos(GAMMA_MU * param[6] * t + param[7] * DEGREE2RAD);
+ } else {
+ dPol = fPippardFitterGlobal->GetMuonStoppingDensity(energyIndex, z) * cos(GAMMA_MU * param[6] * fPippardFitterGlobal->GetMagneticField(z-param[8]) * t + param[7] * DEGREE2RAD);
+ }
+ z += dz;
+ pol += dPol;
+
+ // change in polarization is very small hence start termination counting
+ if (fabs(dPol) < 1.0e-9) {
+ terminate++;
+ } else {
+ terminate = 0;
+ }
+
+ if (terminate > 10) // polarization died out hence one can stop
+ done = true;
+ } while (!done);
+
+ return pol*dz;
+}
+A technical description of the musrfit framework can be found on its own docu.