MULSOPT¶

Summary

Sets the tracking conditions for multiple Coulomb scattering (MCS), for both hadrons/muons and \(e^+\)\(e^-\). Can also be used to activate single scattering.

See also EMFFIX, FLUKAFIX, MCSTHRES, STEPSIZE

For SDUM ≠ GLOBAL, GLOBEMF, GLOBHAD:

WHAT(1) :: controls the step optimisation for multiple Coulomb scattering (see Note 1) and the number of 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 the MULSOPT option with SDUM = GLOBAL/GLOBHAD/GLOBEMF)
= 0.0:: ignored

= \({\texttt{i}}_0 + {\texttt{i}}_1 \times {\texttt{10}} + {\texttt{i}}_2 \times {\texttt{100000}}\), with \({\texttt{0}} \leq {\texttt{i}}_0 \leq {\texttt{1}}\), \({\texttt{0}} \leq {\texttt{i}}_1 \leq {\texttt{10000}}\), \({\texttt{0}} \leq {\texttt{i}}_2 \leq {\texttt{10000}}\):

\({\texttt{i}}_0 \geq {\texttt{1}}\) : the optimisation is activated

\({\texttt{i}}_1 - {\texttt{1}}\) = number of single scattering steps for hadrons and muons in the materials indicated by WHAT(4)–WHAT(6)

\({\texttt{i}}_1\) = 0 : ignored

\({\texttt{i}}_2 - {\texttt{1}}\) = number of single scattering steps for electrons and positrons in the materials indicated by WHAT(4)–WHAT(6)

\(i_2\) = 0 : ignored

Default

= -1.0 (no multiple scattering optimisation and no single scattering)

1.0: spin-relativistic corrections are activated for charged hadrons and muons at the 1\(^{st}\) Born approximation level

2.0: spin-relativistic corrections are activated for hadrons and muons at the 2\(^{nd}\) Born approximation level

WHAT(2) < 0.0:

nuclear finite size effects (form factors) are activated (see Note 2).

= -3.0:

nuclear finite size effects are considered but not the spin-relativistic effects

≥ 3.0:

multiple scattering for hadrons and muons is completely suppressed (see Note 3).

Default

= 0.0 (no corrections)

1.0: spin-relativistic corrections activated for \(\rm{e}^{\pm}\) in the 1\(^{st}\) Born approximation

2.0: spin-relativistic corrections activated for \(\rm{e}^{\pm}\) in the 2\(^{nd}\) Born approximation

WHAT(3) < 0.0:

nuclear finite size effects are activated

≥ 3.0:

multiple scattering for \(e^+\) and \(e^-\) is completely suppressed

Default

= 0.0 (no corrections)

lower bound of the indices of the materials, or corresponding name, in which the corrections are activated

(“From material ``WHAT(4)``…”)

Default

= 3.0

upper bound of the indices of the materials, or corresponding name, in which the corrections are activated

(“…to material ``WHAT(5)``…”)

Default

= WHAT(4)

step length in assigning indices.

(“…in steps of ``WHAT(6)`` ”)

Default

= 1.0

SDUM

= FANO–ON: Fano correction for inelastic interactions of charged hadrons and muons on atomic electrons [Fan54] is switched on

=: FANO–OFF: Fano correction for inelastic interactions of charged hadrons and muons on atomic electrons is switched off

=: MLSH–ON: Original Molière screening angle on for hadrons and muons

=: MLSH–OFF: Molière screening angle for hadrons and muons as modified by Berger & Seltzer for \(e^+\)\(e^-\) (not recommended)
Default: : Fano correction on, original Molière screening angle for hadrons on
Default: (option MULSOPT not given): no MCS optimisation

For SDUM = GLOBAL, GLOBEMF, GLOBHAD:

(GLOBEMF restricts the input value to \(e^+\)\(e^-\), GLOBHAD to charged hadrons and muons)

WHAT(1) :: controls the minimum MCS step size used by the boundary approach algorithm for \(e^+\)\(e^-\) and charged heavy particles
≥ 0.0: and < 0.2: ignored
≥ 0.2:: the minimum step size is set equal to the size corresponding to B = 5 in Molière theory, multiplied by WHAT(1)
< 0.0:: the minimum step size is reset to default
Default: = 1.0 (maximum accuracy)
WHAT(2) :: index of step stretching factor tabulation to be used by the electron/positron transport algorithm when approaching a boundary.

Only for experts! Not for the normal user

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: = 1.0 (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).

Only for experts! Not for the normal user
≥ 0.0: and < 0.2: ignored
≥ 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 size equal to that corresponding to B = 5, multiplied by 20.0
WHAT(4) > 0.0:: single scattering option activated at boundaries or for too short steps
< 0.0:: resets to default
= 0.0:: ignored
Default: : single scattering is not activated
WHAT(5): (meaningful only if single scattering is activated at boundaries and when the step is too short: see WHAT(4) above)
> 0.0:: single scattering option activated for energies too small for Molière theory to apply
< 0.0:: single scattering is not activated
= 0.0:: ignored
Default: : single scattering is not activated
WHAT(6): (meaningful only if single scattering is activated at boundaries and when step is too short: see WHAT(4) above)
> 0.0:: number of single scatterings to be performed when crossing a boundary. To replace multiple scattering with single scattering everywhere, see Note 5.
= 0.0:: ignored
< 0.0:: resets the default
Default: = 1.0

Notes

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 FORMFU: nuclear FORM Factor User-defined.
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 cases, one should also select the biased density so that no re-interaction of secondaries can take place.
Runs in which the nuclear form factor is taken into account and/or the 2\(^{nd}\) Born approximation is requested are very CPU-time consuming at low energy (but not at high energy).
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....+...
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....+...
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....+...
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....+...
MULSOPT          0.0       0.0       0.0       1.0       1.0 99999999.GLOBAL