next up previous contents
Next: ISO Up: ATSP2K manual Previous: BIOTR   Contents

Subsections


HFS

Introduction

The atomic hyperfine splitting is determined by the hyperfine interaction constant ${A_J}$ and ${B_J}$. In strong external magnetic fields, the splitting is also affected by the off-diagonal hyperfine constants ${A_{J,J-1}, B_{J,J-1}, B_{J,J-2}}$. The hyperfine program computes the magnetic dipole and electric quadrupole constants from MCHF wave functions. The program requires that the orbitals of a single configuration from the initial and final state to be mutually orthogonal.

hfs Program Structure

The program structure is shown on Figure  7.37. The configurations are analyzed for orthogonality (cfgn(), cfg01()). factr() computes a table of logarithms of factorials. readwt() reads the weight from .l or .j file. A number of $L_{j}, S_{j}, L_{k}, S_{k}$ and $J$ dependent factors are determined in lsjfact(). The wave functions are read in readwfn(). The one-electron active radial integrals are determined in radial1() and radial2(). multwt() multiplies the weights of configuration $j$ and $k$. setup() transforms the occupation and coupling for a configuration pair in a format suitable for use by tensor(), which evaluates the reduced matrix element between arbitrarily LS coupled configurations.

Figure 7.37: hfs program structure.
\begin{figure}\begin{center}
\centerline{\psfig{figure=tex/fig/hfs_main.epsi}}\end{center}\end{figure}

Input data

The user provides the following input data:
  1. Name of state
    This program requires that the name of the sate, denoted here as <name>, to be specified. The program expects expects all data from <name>.c, <name>.w and either of <name>.l, or <name>.j.

  2. Type
    The following options are provided; For the last option all needed input data is in the configuration input file <name>.c .

  3. Hyperfine parameters
    The hyperfine parameters $a_{l},a_{d},a_{c}$ and $b_{q}$ can be printed out. (meaningful for pure LS terms).

  4. Input
    The program can use wave function expansion from either an MCHF or CI calculation.

  5. Number
    Specifies the particular states for which the $A$ and $B$ factors to be calculated (when <name>.j contains more than one state).

  6. Print-out
    In a calculation of the $A$ and $B$ factors, values of the $A^{orb},A^{dip}, A^{cont}$, and $B$ terms are written to the file <name>.h. Full print-out prints the values of coefficients and radial matrix elements as well as the contribution to the different $A$ and $B$ factors for every pair of configurations.

  7. Tolerance for printing
    In the case of a full print-out it is possible to set a tolerance for printing. If the contribution to a term is less than the tolerance, then it will not be printed.

  8. Nuclear data
    The user provides: which are experimental values.

File IO

The input files are described in Chapter  13.16.

The output is written to a file <name>.h . If a full print-out is requested, the program outputs the following data from equations (46) and (47) for a pair of configurations $j$ and $k$.

  1. $J$ $J'$
    The $J$ values for which the matrix element has been calculated.

  2. Weight
    The configuration weight $c_{j}c_{k}$.

  3. Coeff
    The coefficient coef$(\rho,\sigma)$.

  4. Radial matrix elements
    Values of the radial matrix elements $\mbox{rad}({\rho},{\sigma}),
({\mu}\vert{\mu}')^{n_{1}}$ and $({\nu}\vert{\nu}')^{n_{2}} $

  5. A(MHz), B(MHz)
    The contribution in MHz to the different $A$ and $B$ factors from this pair of configurations.


next up previous contents
Next: ISO Up: ATSP2K manual Previous: BIOTR   Contents
2001-10-11