External module function dm1 - used by mcdisp

In order to visualized magnetic moment fluctuations and to calculate neutron intensities in dipole approximation the external single ion module has to provide the transition matrix elements of the magnetic moment operator in units of $\mu_B$ by the vector $m1$, which is given by: ${\rm m1}^s_{\alpha}=\sqrt{(p_--p_+)}\langle -\vert\hat m^s_{\alpha}-\langle\hat m^s_{\alpha}\rangle_{\mathbf H,T}\vert+\rangle$.

The format to be used is:

extern "C" int dm1(int & tn,double & T,Vector & Hxc,Vector & Hext,double * g_J,Vector & MODPAR,
char ** sipffilename,ComplexVector & m1,float & maxE, ComplexMatrix & est)

The meaning of the symbols is as follows:

on input
   |tn|            transition-number  
   sign(tn)        >0 standard, <0 routine should do some printout to stdout for user information
   MODPAR          Vector with Parameters  read in single ion property file
   sipffilename    file name of the single ion parameter file
   g_J             Lande factor
   T               Temperature[K]
   Hxc             vector of exchange field [meV] (can be n-dimensional, for a set of n operators)
   Hext            external magnetic field [T]
   est             eigenstate matrix (initialized by estates)
                   it should/may also contain population numbers of the states
				   (imaginary part of row 0)
                   and eigenvalues (real part of row 0) with values set by the most recent call
				   for this ion (use of this matrix is optional)
   u1(1)           ninit + i pinit (from mcdisp options  -ninit and -pinit)
   maxE            upper boundary for transition energy (meV) to be considered
                   (from mcdisp option -maxE)
on output
   int             total number of transitions
   u1             transition matrix element vector m1=<-|m-<m>|+>sqrt((n- - n+))

The module function must perform the following tasks:

1. check if the dimensions of vector Hxc (taken by mcphas from the number of interaction constant columns in mcphas.j) and MODPAR (taken by mcphas from the number of params in the single ion property file) agree with the module specifications. If the check fails the module function should exit the program with an appropriate error message
2. the module function should do a numbering of all possible single ion transitions and return the total number of transitions as an integer. Input file parameters params are supplied as a vector MODPAR and Lande factor as g_J and can be used for this purpose. The numbering will depend on the parameters ninit, pinit and maxE which are provided as input. These parameters have to be considered. IMPORTANT: the numbering scheme of transitions has to be the same for du1calc and all the corresponding d...1 functions for observables !
3. for the transition number tn the vector m1 is to be filled with ${\mathbf m1^s_{\alpha}}=\sqrt{(p_--p_+)}\langle -\vert\hat m^s_{\alpha}-\langle\hat m^s_{\alpha}\rangle_{\mathbf H,T}\vert+\rangle$. (note $\hat \mathbf m=2\hat \mathbf S+ \hat \mathbf L$).
4. If the energy of this transition is zero, i.e. $\Delta(tn)=0$ (diffuse scattering), the expression (230) would be zero because $(p_--p_+)$ vanishes. In this case the single ion module should calculate $(p_+/kT)$ instead of $(p_--p_+)$.
5. if $T<0$ all quantities should be evaluated assuming that all Boltzmann probabilities $p_i$ are zero except for the state number $n=(-T)$, for which the probability $p_n=1$.