External module function

In order to calculate neutron intensities for phonon scattering the external single ion module has to provide the transition matrix elements of the phonon displacement in units of Å, which for the transition i (=1,2,3) is usually given by: , with for the different spatial directions and is the mass of the oscillating atom (compare section 11).

Note, that in this expression the sum over the different equally spaced phonon levels (of the harmonic oscillator) in the single ion susceptibility is already done. If the levels are not equally spaced, such as by interaction with other degrees of freedom, one has to take into account each transition separately by the expression .

The format to be used is:

extern "C" int dP1(int & tn,double & T,Vector & Hxc,Vector & Hext,double * g_J,Vector & MODPAR, char ** sipffilename,ComplexVector & p1,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 (normally =3 for the unperturbed atomic Einstein oscillator in three independent spatial directions, but may be larger if coupling of phonons to other degrees of freedom such as CEF is treated on a quantum mechanical level in the module) P1 transition matrix element vector of the phonon displacement for an Einstein oscillator p1=hbar/sqrt(2m hbar Delta), or more general if phonon levels are not equally spaced: P1=<-|P-<P>|+>sqrt((p- - p+))The module function must perform the following tasks:

- 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 - 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 !* - for the transition number tn the vector p1 is to be filled with the displacement transition matrix elements (Å) or more general .
- If the energy of this transition is zero, i.e. (diffuse scattering), the above expression would be zero because vanishes. In this case the single ion module should calculate instead of .
- if all quantities should be evaluated assuming that all Boltzmann probabilities are zero except for the state number , for which the probability .

Martin Rotter 2017-01-10