Dynamic Polarisability

Dynamic (frequency-dependent) polarisability, alpha(omega), over a range of frequencies.

The dynamicPolarisability module (run as Module::dynamicPolarisability{}) calculates the scalar dynamic polarisability \( \alpha_0(\omega) \) (and optionally the tensor part \( \alpha_2(\omega) \)) for a set of valence states, over a range of frequencies (or wavelengths), writing the results to screen and to plain-text files for plotting.

• For a single frequency (or a transition, or PNC), prefer the Second-Order Amplitudes module; this module is for frequency scans.
• The valence sum uses sum-over-states (method = SOS;) or mixed states (method = MS;; can be unstable near resonances).
• RPA (TDHF) may be re-solved at each frequency (rpa_omega), or held at its static value; likewise the core contribution (core_omega).
• The spectrum used for the sum-over-states can be adjusted: drop continuum states or specific states (spurious resonances), or replace low-lying spectrum states with the valence states.
• Structure radiation + normalisation may be added to the matrix elements of the sum via the StructureRadiation{} block (evaluated at w = 0; sum-over-states only).

Example:

Module::dynamicPolarisability{
  states = 6s;
  lambda_minmax = 600, 1800;
  num_steps = 40;
  filename = Cs_alpha.txt;
}

The calculations are performed by the Amplitudes library: see Amplitudes::sos_valence(), Amplitudes::ms_valence(), Amplitudes::sos_core(), and Amplitudes::ms_core() (the module, Module::dynamicPolarisability, builds the frequency-dependent matrix element tables and prints).

Available options (from ./ampsci -m dynamicPolarisability):

// Available Module::dynamicPolarisability options/blocks
Module::dynamicPolarisability{
  states;
    // Which states to calculate? (e.g., '7sp6d'). Must be a
    // subset of valence. By default, all valence states are
    // calculated.
  tensor;
    // Do tensor polarisability a2(w) (as well as a0)
    // [false]
  rpa;
    // Include RPA? [true]
  core_omega;
    // Frequency-dependent core? If true, core part
    // evaluated at each frequency. If false, core evaluated
    // once at w=0 [true]
  rpa_omega;
    // Frequency-dependent RPA? If true, RPA solved at each
    // frequency. If false, RPA solved once at w=0 [true]
  num_steps;
    // number of steps for dynamic polarisability [10]
  omega_minmax;
    // list (frequencies): omega_min, omega_max (in au)
    // [0.01, 0.1]
  lambda_minmax;
    // list (wavelengths, will override omega_minmax):
    // lambda_min, lambda_max (in nm) [600, 1800]
  method;
    // Method used for dynamic pol. for a0(w). Either 'SOS'
    // (sum-over-states) or 'MS' (mixed-states=TDHF). MS can
    // be unstable for dynamic pol. [SOS]
  replace_w_valence;
    // Replace corresponding spectrum states with valence
    // states - circumvents spectrum issue! [false]
  drop_continuum;
    // Discard states from the spectrum with e>0 - these can
    // cause spurious resonances [false]
  drop_states;
    // List. Discard these states from the spectrum for
    // sum-over-states []
  filename;
    // output filename for dynamic polarisability (a0_
    // and/or a2_ will be appended to start of filename)
    // [identity.txt (e.g., CsI.txt)]
  StructureRadiation{}
    // Options for structure radiation and normalisation. If
    // this block is included, SR+N is added to the
    // single-particle matrix elements of the sum-over-states
    // (evaluated at w = 0). Sum-over-states method only
}

(The StructureRadiation{} block takes the same options as in Second-Order Amplitudes, plus RPA_in_SR.)