Returns energy loss.
Can be called with any pdg, but only calculates energy loss for electrons and positrons (otherwise returns 0). Uses a gaussian approximation (Bethe-Heitler formula with Migdal corrections). For positrons the energy loss is weighed with a correction factor.
486 if (fabs(
fpdg)!=11)
return 0;
489 static const double C[101]={ 0.0,-0.960613E-01, 0.631029E-01,-0.142819E-01, 0.150437E-02,-0.733286E-04, 0.131404E-05, 0.859343E-01,-0.529023E-01, 0.131899E-01,-0.159201E-02, 0.926958E-04,-0.208439E-05,-0.684096E+01, 0.370364E+01,-0.786752E+00, 0.822670E-01,-0.424710E-02, 0.867980E-04,-0.200856E+01, 0.129573E+01,-0.306533E+00, 0.343682E-01,-0.185931E-02, 0.392432E-04, 0.127538E+01,-0.515705E+00, 0.820644E-01,-0.641997E-02, 0.245913E-03,-0.365789E-05, 0.115792E+00,-0.463143E-01, 0.725442E-02,-0.556266E-03, 0.208049E-04,-0.300895E-06,-0.271082E-01, 0.173949E-01,-0.452531E-02, 0.569405E-03,-0.344856E-04, 0.803964E-06, 0.419855E-02,-0.277188E-02, 0.737658E-03,-0.939463E-04, 0.569748E-05,-0.131737E-06,-0.318752E-03, 0.215144E-03,-0.579787E-04, 0.737972E-05,-0.441485E-06, 0.994726E-08, 0.938233E-05,-0.651642E-05, 0.177303E-05,-0.224680E-06, 0.132080E-07,-0.288593E-09,-0.245667E-03, 0.833406E-04,-0.129217E-04, 0.915099E-06,-0.247179E-07, 0.147696E-03,-0.498793E-04, 0.402375E-05, 0.989281E-07,-0.133378E-07,-0.737702E-02, 0.333057E-02,-0.553141E-03, 0.402464E-04,-0.107977E-05,-0.641533E-02, 0.290113E-02,-0.477641E-03, 0.342008E-04,-0.900582E-06, 0.574303E-05, 0.908521E-04,-0.256900E-04, 0.239921E-05,-0.741271E-07,-0.341260E-04, 0.971711E-05,-0.172031E-06,-0.119455E-06, 0.704166E-08, 0.341740E-05,-0.775867E-06,-0.653231E-07, 0.225605E-07,-0.114860E-08,-0.119391E-06, 0.194885E-07, 0.588959E-08,-0.127589E-08, 0.608247E-10};
490 static const double xi=2.51, beta=0.99, vl=0.00004;
492 #if defined(BETHE) // no MIGDAL corrections
493 static const double C[101]={ 0.0, 0.834459E-02, 0.443979E-02,-0.101420E-02, 0.963240E-04,-0.409769E-05, 0.642589E-07, 0.464473E-02,-0.290378E-02, 0.547457E-03,-0.426949E-04, 0.137760E-05,-0.131050E-07,-0.547866E-02, 0.156218E-02,-0.167352E-03, 0.101026E-04,-0.427518E-06, 0.949555E-08,-0.406862E-02, 0.208317E-02,-0.374766E-03, 0.317610E-04,-0.130533E-05, 0.211051E-07, 0.158941E-02,-0.385362E-03, 0.315564E-04,-0.734968E-06,-0.230387E-07, 0.971174E-09, 0.467219E-03,-0.154047E-03, 0.202400E-04,-0.132438E-05, 0.431474E-07,-0.559750E-09,-0.220958E-02, 0.100698E-02,-0.596464E-04,-0.124653E-04, 0.142999E-05,-0.394378E-07, 0.477447E-03,-0.184952E-03,-0.152614E-04, 0.848418E-05,-0.736136E-06, 0.190192E-07,-0.552930E-04, 0.209858E-04, 0.290001E-05,-0.133254E-05, 0.116971E-06,-0.309716E-08, 0.212117E-05,-0.103884E-05,-0.110912E-06, 0.655143E-07,-0.613013E-08, 0.169207E-09, 0.301125E-04,-0.461920E-04, 0.871485E-05,-0.622331E-06, 0.151800E-07,-0.478023E-04, 0.247530E-04,-0.381763E-05, 0.232819E-06,-0.494487E-08,-0.336230E-04, 0.223822E-04,-0.384583E-05, 0.252867E-06,-0.572599E-08, 0.105335E-04,-0.567074E-06,-0.216564E-06, 0.237268E-07,-0.658131E-09, 0.282025E-05,-0.671965E-06, 0.565858E-07,-0.193843E-08, 0.211839E-10, 0.157544E-04,-0.304104E-05,-0.624410E-06, 0.120124E-06,-0.457445E-08,-0.188222E-05,-0.407118E-06, 0.375106E-06,-0.466881E-07, 0.158312E-08, 0.945037E-07, 0.564718E-07,-0.319231E-07, 0.371926E-08,-0.123111E-09};
494 static const double xi=2.10,
fbeta=1.00, vl=0.001;
499 double THIGH=100., CHIGH=50.;
505 if(BCUT>=mom) BCUT=mom;
511 if(BCUT>=THIGH) kc=CHIGH;
523 double Y=log(kc/(E*vl));
529 for (
unsigned int I=1;
I<=2; ++
I) {
531 for (
unsigned int J=1; J<=6; ++J) {
539 for (
unsigned int I=3;
I<=6; ++
I) {
541 for (
unsigned int J=1; J<=6; ++J) {
543 if(Y<=0.) S=S+C[K]*XX*YY;
544 else S=S+C[K+24]*XX*YY;
553 for (
unsigned int I=1;
I<=2; ++
I) {
555 for (
unsigned int J=1; J<=5; ++J) {
563 for (
unsigned int I=3;
I<=5; ++
I) {
565 for (
unsigned int J=1; J<=5; ++J) {
567 if(Y<=0.) SS=SS+C[K]*XX*YY;
568 else SS=SS+C[K+15]*XX*YY;
582 double FAC=
fmatZ*(
fmatZ+xi)*E*E * pow((kc*CORR/T),beta) / (E+me);
583 if(FAC<=0.)
return 0.;
591 S=(1.-0.5*RAT+2.*RAT*RAT/9.);
593 S=S/(1.-0.5*RAT+2.*RAT*RAT/9.);
597 S=BCUT*(1.-0.5*RAT+2.*RAT*RAT/9.);
599 S=S/(kc*(1.-0.5*RAT+2.*RAT*RAT/9.));
601 dedxBrems=dedxBrems*
S;
608 if (dedxBrems<0.) dedxBrems = 0;
613 static const double AA=7522100., A1=0.415, A3=0.0021, A5=0.00054;
621 double W=A1*X+A3*pow(X,3.)+A5*pow(X,5.);
622 ETA=0.5+atan(W)/M_PI;
629 if(ETA<0.0001) factor=1.E-10;
630 else if (ETA>0.9999) factor=1.;
634 if(E0<1.E-8) factor=1.;
635 else factor = ETA * ( 1.-pow(1.-E0, 1./ETA) ) / E0;
639 double DE =
fstep * factor*dedxBrems;
640 double momLoss = sqrt(mom*mom+2.*sqrt(mom*mom+
fmass*
fmass)*DE+DE*DE) - mom;
see a below echo or echo I(indirect symbol).'echo" If the symbol is local (non-external)
see a below echo S(symbol in a section other than those above)
then echo echo For and will not be changed by echo further linking echo echo B echo The symbol is in the uninitialized data multiple common symbols may appear with the echo same name If the symbol is defined the common echo symbols are treated as undefined references For more echo details on common see the discussion of warn common echo in *Note Linker see the discussion of warn common echo in *Note Linker such as a global int variable echo as opposed to a large global array echo echo I echo The symbol is an indirect reference to another symbol This echo is a GNU extension to the a out object file format which is echo rarely used echo echo N echo The symbol is a debugging symbol echo echo R echo The symbol is in a read only data section echo echo S echo The symbol is in an uninitialized data section for small echo objects echo echo T echo The symbol is in the the normal defined echo symbol is used with no error When a weak undefined symbol echo is linked and the symbol is not the value of the echo weak symbol becomes zero with no error echo echo W echo The symbol is a weak symbol that has not been specifically echo tagged as a weak object symbol When a weak defined symbol echo is linked with a normal defined the normal defined echo symbol is used with no error When a weak undefined symbol echo is linked and the symbol is not the value of the echo weak symbol becomes zero with no error echo echo echo The symbol is a stabs symbol in an a out object file In echo this the next values printed are the stabs other echo the stabs desc and the stab type Stabs symbols are echo used to hold debugging information For more echo see *Note or object file format specific echo echo For Mac OS X
constexpr double kc
Speed of light in vacuum in LArSoft units [cm/ns].
![\[ \left(\begin{array}{c} x'\\ y'\\ z'\\ a_{x}'\\ a_{y}'\\ a_{z}'\\ \frac{q}{p}'\end{array}\right)=\left(\begin{array}{ccccccc} \cos\psi & \sin\psi & 0\\ -\cos\vartheta\sin\psi & \cos\vartheta\cos\psi & \sin\psi\\ \sin\vartheta\sin\psi & -\sin\vartheta\cos\psi & \cos\vartheta\\ & & & \cos\psi & \sin\psi & 0\\ & & & -\cos\vartheta\sin\psi & \cos\vartheta\cos\psi & \sin\psi\\ & & & \sin\vartheta\sin\psi & -\sin\vartheta\cos\psi & \cos\vartheta\\ & & & & & & 1\end{array}\right)\left(\begin{array}{c} x\\ y\\ z\\ a_{x}\\ a_{y}\\ a_{z}\\ \frac{q}{p}\end{array}\right)=R^{T}\left(\begin{array}{c} x\\ y\\ z\\ a_{x}\\ a_{y}\\ a_{z}\\ \frac{q}{p}\end{array}\right)\]](../../form_106.png)
![\[ \left(\begin{array}{c} x\\ y\\ z\\ a_{x}\\ a_{y}\\ a_{z}\\ \frac{q}{p}\end{array}\right)=\left(\begin{array}{ccccccc} \cos\psi & -\cos\vartheta\sin\psi & \sin\vartheta\sin\psi\\ \sin\psi & \cos\vartheta\cos\psi & -\sin\vartheta\cos\psi\\ 0 & \sin\psi & \cos\vartheta\\ & & & \cos\psi & -\cos\vartheta\sin\psi & \sin\vartheta\sin\psi\\ & & & \sin\psi & \cos\vartheta\cos\psi & -\sin\vartheta\cos\psi\\ & & & 0 & \sin\psi & \cos\vartheta\\ & & & & & & 1\end{array}\right)\left(\begin{array}{c} x'\\ y'\\ z'\\ a_{x}'\\ a_{y}'\\ a_{z}'\\ \frac{q}{p}'\end{array}\right)=R\left(\begin{array}{c} x'\\ y'\\ z'\\ a_{x}'\\ a_{y}'\\ a_{z}'\\ \frac{q}{p}'\end{array}\right) \]](../../form_107.png)
is the multiple scattering error-matrix in the 
coordinate system. 
are the multiple scattering angles. There is only an error in direction (which later leads to an error in position, when 
is propagated with 
). ![\[ M=\left(\begin{array}{cc} \sigma^{2} & 0\\ 0 & \sigma^{2}\end{array}\right)\]](../../form_114.png)
in the local cs' via jacobian J. The mean scattering angle is always 0, this means that 
![\[ J=\frac{\partial\left(x',y',z',a_{x}',a_{y}',a_{z}',\frac{q}{p}'\right)}{\partial\left(\theta_{1},\theta_{2}\right)}\]](../../form_117.png)
![\[ J=\left(\begin{array}{cc} 0 & 0\\ 0 & 0\\ 0 & 0\\ \cos\theta_{1} & 0\\ 0 & \cos\theta_{2}\\ -\frac{\cos\theta_{1}\sin\theta_{1}}{\sqrt{\cos^{2}\theta_{1}-\sin^{2}\theta_{2}}} & -\frac{\cos\theta_{2}\sin\theta_{2}}{\sqrt{\cos^{2}\theta_{1}-\sin^{2}\theta_{2}}}\\ 0 & 0\end{array}\right) \overset{\theta_{1/2}=0}{=} \left(\begin{array}{cc} 0 & 0\\ 0 & 0\\ 0 & 0\\ 1 & 0\\ 0 & 1\\ 0 & 0\\ 0 & 0\end{array}\right)\]](../../form_118.png)
![\[ \overline{M}=J\: M\: J^{T}=\left(\begin{array}{ccccccc} 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & \sigma^{2} & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & \sigma^{2} & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\end{array}\right)\]](../../form_119.png)
:![\[ N=R\overline{M}R^{T}=\sigma^{2}\left(\begin{array}{ccccccc} 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & \cos^{2}\psi+\cos^{2}\theta-\cos^{2}\theta\cos^{2}\psi & \cos\psi\sin\psi\sin^{2}\theta & -\cos\theta\sin\psi\sin\theta & 0\\ 0 & 0 & 0 & \cos\psi\sin\psi\sin^{2}\theta & \sin^{2}\psi+\cos^{2}\theta\cos^{2}\psi & \cos\theta\cos\psi\sin\theta & 0\\ 0 & 0 & 0 & -\cos\theta\sin\psi\sin\theta & \cos\theta\cos\psi\sin\theta & \sin^{2}\theta & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\end{array}\right)\]](../../form_121.png)
(at the final point, with direction #directionAfter). 
1.8.5