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MULSOPT

Sets the tracking conditions for multiple Coulomb scattering (MCS), for both FLUKA and EMF particles. Can also be used to activate single scattering.

See also EMFFIX, FLUKAFIX, MCSTHRES, STEPSIZE

For SDUM = anything except GLOBAL/GLOBEMF/GLOBHAD:

     WHAT(1) : controls the step optimisation for multiple Coulomb scattering,
               and the number of (possible) single scatterings on a material
               by material basis
            <= -1.0 : a possible previous request of optimisation is cancelled
                      and the number of single scatterings in the materials
                      indicated by WHAT(4)-WHAT(6) is reset to the default value
                      (i.e. 0, or the global default possibly set previously by
                      this option with SDUM = GLOBAL/GLOBHAD/GLOBEMF)
              =  0.0 : ignored
              = I0 + I1*10 + I2*100000
                (with 0=< I0 =<1, 0=< I1 <10000, 0 =< I2 < 10000):
                I0 >= 1  : the optimisation is activated
                I1  - 1  = number of single scattering steps for hadrons and muons
                           in the materials indicated by WHAT(4)-WHAT(6)
                I1  = 0  : ignored
                I2  - 1  = number of single scattering steps for electrons and
                           positrons in the materials indicated by WHAT(4)-WHAT(6)
                I2  = 0  : ignored

              Default: -1.0 (no multiple scattering optimisation and no single
                           scattering)

     WHAT(2) :
     |WHAT(2)| = 1.0: spin-relativistic corrections are activated for
                      hadrons and muons at the 1st Born approximation
                      level
     |WHAT(2)| = 2.0: spin-relativistic corrections are activated for
                      hadrons and muons at the 2nd Born approximation
                      level
      WHAT(2)  < 0.0: nuclear finite size effects are activated.
              = -3.0: nuclear finite size effects (form factors) are
                      considered but not the spin-relativistic effects
      WHAT(2) >= 3.0: multiple scattering for hadrons and muons is
                      completely suppressed
              Default: 0.0 (no corrections)

     WHAT(3) :
     |WHAT(3)| = 1.0: spin-relativistic corrections are activated for
                      e+ and e- at the 1st Born approximation level
     |WHAT(3)| = 2.0: spin-relativistic corrections are activated for
                      e+ and e- at the 2nd Born approximation level
      WHAT(3)  < 0.0: nuclear finite size effects are activated
      WHAT(3) >= 3.0: multiple scattering for e+ and e- is completely
                      suppressed
              Default: 0.0 (no corrections)

     WHAT(4) = lower bound of the indices of the materials, or corresponding
               name, in which the corrections are activated
               ("From material WHAT(4)...")
               Default = 3.0

     WHAT(5) = upper bound of the indices of the materials, or corresponding
               name, in which the corrections are activated
               ("... to material WHAT(5)...")
               Default = WHAT(4)

     WHAT(6) = step length in assigning indices
               ("...in steps of WHAT(6)")
               Default: 1.0

      SDUM   = FANO-ON : Fano correction for inelastic interactions
                         on atomic electrons switched on (for the moment
                         only for charged hadrons and muons)
               FANO-OFF: Fano correction for inelastic interactions on
                         atomic electrons is switched off
               MLSH-ON : Moliere screening angle on for hadrons and muons
               MLSH-OFF: Moliere screening angle for hadrons and muons as
                         modified by Berger & Seltzer for electrons
               Default:  Fano correction on, original Moliere screening
                         angle for hadrons on

     Default (option MULSOPT not given): no MCS optimisation

For SDUM=GLOBAL/GLOBEMF/GLOBHAD: (GLOBEMF restricts the input value use to the EM part, GLOBHAD to the hadron and muon part)

     WHAT(1) : controls the minimum MCS step size used by the boundary approach
               algorithm for electron/positrons and charged heavy
               particles (in the multiple scattering routine)
 0.2 > WHAT(1) >= 0.0 : ignored
       WHAT(1) >= 0.2 : the minimum step size is set equal to the size
                        corresponding to B=5 in Moliere theory,
                        multiplied by WHAT(1)
               <  0.0 : the minimum step is reset to default
               Default: WHAT(1) = 1 (maximum accuracy)

     WHAT(2) : index of step stretching factor tabulation to be used
               by the electron/positron transport algorithm when
               approaching a boundary.
               The values of the index implemented for the moment are 1,2,3,4.
               Values 11,12,13,14 cause the sensing algorithm to multiply
               the range/mcs step rather than the current step.
               Values 101,111,102,112,103,113,104,114 have the additional
               effect of making the algorithm resample as unphysical any
               step cut at a boundary and "reflected" from the boundary.
               = 0.0 : ignored
               < 0.0 : the tabulation index is reset to default
               Default: WHAT(2) = 1 (maximum accuracy)

     WHAT(3) : controls the optimal step to be used by the optimisation
               option (and to some extent by the hadron/muon boundary approach
               algorithm).
 0.2 > WHAT(3) >= 0.0 : ignored
       WHAT(3) >= 0.2 : the minimum step size is set equal to the size corresponding
                        to B = 5 in Molière theory [Mol47,Mol48,Mol55,Bet53],
                        multiplied by WHAT(3)
               <  0.0 : the minimum step is reset to its default value
               Default: minimum step equal to that corresponding to B=5,
                        multiplied by 20

     WHAT(4) > 0: single scattering option activated at boundaries or
                  for too short steps
             < 0: resets to default
             = 0: ignored
               Default: single scattering not activated

     WHAT(5):  (meaningful only if single scattering is activated at
               boundaries and when step is too short: see WHAT(4) above)
             > 0: single scattering option activated for energies too small
                  for Molière theory to apply
             < 0: not activated
             = 0: ignored
               Default: not activated

     WHAT(6):  (meaningful only if single scattering  is activated at
               boundaries and when step is too short: see WHAT(4) above)
             > 0: number of single scatterings to be performed when
               crossing a boundary
             = 0: ignored
             < 0: resets the default
               Default: 1

Notes:

• 1) When optimisation is requested, the program always makes the minimum step for which the Molière theory of multiple scattering is applicable. Optimisation via MULSOPT is available only for charged hadrons and muons. For electrons and positrons, option EMFFIX is recommended. The correction for the nuclear finite size has been implemented using simple Thomas-Fermi form factors according to Tsai [Tsa74]. The user can provide more sophisticated values by supplying a function FORMFU which must return the square of the nuclear form factor. (See details in (13)).

• 2) Complete suppression of multiple scattering can be useful in some particular cases, for instance when replacing a gas of extremely low density by a gas of the same composition but of much larger density in order to increase the frequency of inelastic interactions or bremsstrahlung reactions (of course, the results must then be scaled by the density ratio). In such a case, one should also select the biased density so that
• 3) no re-interaction of secondaries can take place.

• 4) Runs for which the nuclear form factor is taken into account and/or the 2nd Born approximation is requested are very CPU-time consuming at low energy (but not at high energy).

• 5) Setting WHAT(6) > 1000.0 with SDUM = GLOBAL, GLOBHAD or GLOBEMF, replaces systematically multiple scattering with single scattering everywhere. This choice is generally extremely demanding in CPU time, except for particles of very low energy (a few keV), which have a very short history anyway. In such cases, the single scattering option is even recommended ([Fas01]).

Example 1 (number based):

 * Activate spin-relativistic corrections and nuclear finite size effects
 * for heavy charged particles in the first Born approximation.
 * Activate spin-relativistic corrections but not nuclear size effects
 * for electrons and positrons in materials 5, 10 and 15
 *...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+....8
 MULSOPT          1.0      -1.0       2.0       5.0      15.0       5.0

The same example, name based:

 *...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+....8
 MULSOPT          1.0      -1.0       2.0  BERYLLIU      GOLD       5.0

Example 2:

 * Maximum accuracy requested for the electron step size used in the boundary
 * approach and in the optimisation algorithm. Single scattering activated for
 * electrons at boundary crossing and when the step is too short for Moliere
 * (but not when the energy is too low for Moliere). Boundaries will be
 * crossed with 2 single scatterings.
 *...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+....8
 MULSOPT          1.0       1.0       1.0       1.0       0.0       2. GLOBEMF

Example 3:

 * Single scattering activated everywhere for all charged particles
 *...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+....8
 MULSOPT          0.0       0.0       0.0       1.0       1.0 99999999.GLOBAL