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LAM-BIAS

Used to bias the decay length of unstable particles, the inelastic nuclear interaction length of hadrons, photons and muons and the direction of decay secondaries

The meaning of WHAT(1)...WHAT(6) depends on the value of SDUM. SDUM = DCDRBIAS and SDUM = DCY-DIRE are used to activate and define decay direction biasing; SDUM = GDECAY selects decay length biasing and inelastic nuclear interaction biasing; and if SDUM = blank, decay life biasing and inelastic nuclear interaction biasing are selected. Other LAM-BIAS cards with SDUM = DECPRI, DECALL, INEPRI, INEALL allow to restrict biasing to primary particles or to extend it also to further generations.

for SDUM = DCY-DIRE:

The decay secondary product direction is biased in a direction indicated by the user by means of a unit vector of components U, V, W (see Notes 4 and 5):

     WHAT(1) = U (x-direction cosine) of decay direction biasing
               Default: 0.0

     WHAT(2) = V (y-direction cosine) of decay direction biasing
               Default: 0.0)

     WHAT(3) = W (z-direction cosine) of decay direction biasing
               Default: 1.0

     WHAT(4) > 0.0: lambda for decay direction biasing. The degree of
               biasing decreases with increasing lambda (see Note 5).
             = 0.0: a user provided routine (UDCDRL, see (13)) is called at
               each decay event, to provide both direction and lambda for
               decay direction biasing
             < 0.0 : resets to default (lambda = 0.25)
               Default = 0.25

     WHAT(5) = not used

     WHAT(6) = not used

for SDUM = DCDRBIAS:

     WHAT(1) > 0.0: decay direction biasing is activated
             = 0.0: ignored
             < 0.0: decay direction biasing is switched off

     WHAT(2) = not used

     WHAT(3) = not used

     WHAT(4) = lower bound of the particle id-numbers (or corresponding name)
               for which decay direction biasing is to be applied
               ("From particle WHAT(4)...").
               Default = 1.0.

     WHAT(5) = upper bound of the particle id-numbers (or corresponding name)
               for which decay direction biasing is to be applied
               ("...to particle WHAT(5)...").
               Default = WHAT(4) if WHAT(4) > 0, 64 otherwise.

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

for all other SDUM's:

     WHAT(1): biasing parameter for decay length or life, applying only to
              unstable particles (with particle numbers >= 8). Its meaning
              differs depending on the value of SDUM, as explained in the
              following.

for SDUM = GDECAY:

     WHAT(1) < 0.0 : the mean DECAY LENGTH (in cm) of the particle in the
                     LABORATORY frame is set = |WHAT(1)| if smaller than
                     the physical decay length (otherwise it is left
                     unchanged). At the decay point sampled according to
                     the biased probability, Russian Roulette (i.e.
                     random choice) decides whether the particle actually
                     will survive or not after creation of the decay
                     products. The latter are created in any case and
                     their weight adjusted taking into account the ratio
                     between biased and physical survival probability.
             > 0.0 : the mean DECAY LENGTH (in cm) of the particle in the
                     LABORATORY frame is set = WHAT(1) if smaller than
                     the physical decay length (otherwise it is left
                     unchanged). Let P_u = unbiased probability and
                     P_b = biased probability: at the decay point sampled
                     according to P_b, the particle always survives
                     with a reduced weight W(1 - P_u/P_b), where W is the
                     current weight of the particle before the decay. Its
                     daughters are given a weight W P_u/P_b (as in
                     case WHAT(1) < 0.0).
             = 0.0 : ignored

for SDUM = blank:

     -1 < WHAT(1) < 0. : the mean LIFE of the particle in its REST frame
                         is REDUCED by a factor = |WHAT(1)|. At the decay
                         point sampled according to the biased
                         probability, Russian Roulette (i.e. random
                         choice) decides whether the particle actually
                         will survive or not after creation of the decay
                         products. The latter are created in any case and
                         their weight adjusted taking into account the
                         ratio between biased and physical survival
                         probability.
     0 < WHAT(1) < +1. : the mean LIFE of the particle in the REST frame
                         is REDUCED by a factor = |WHAT(1)|. At the decay
                         point sampled according to the biased
                         probability, the particle always survives with
                         a reduced weight. Its daughters are given the
                         same weight.
         |WHAT(1)| > 1 : a possible previously given biasing parameter
                         is reset to the default value (no biasing)
          WHAT(1) = 0  : ignored

     WHAT(2) : biasing factor for hadronic inelastic interactions
     -1 < WHAT(2) < 0. : the hadronic inelastic interaction length of the
                         particle is reduced by a factor |WHAT(2)|.
                         At the interaction point sampled according to
                         the biased probability, Russian Roulette (i.e.
                         random choice) decides whether the particle actually
                         will survive or not after creation of the
                         secondaries products. The latter are created in
                         any case and their weight adjusted taking into
                         account the ratio between biased and physical
                         survival probability.
     0. < WHAT(2) < 1. : the hadronic inelastic interaction length of the
                         particle is reduced by a factor WHAT(2),
                         At the interaction point sampled according to
                         the biased probability, the particle always
                         survives with a reduced weight. The secondaries
                         are created in any case and their weight
                         adjusted taking into account the ratio between
                         biased and physical survival probability.
                   = 0.0 : ignored

        |WHAT(2)| >= 1.0 : a possible previously set biasing factor is
                           reset to the default value of 1 (no biasing).

     WHAT(3) : If > 2.0 : number or name of the material to
                          which the inelastic biasing factor has to be applied.
                  < 0.0 : resets to the default a previously assigned value
                  = 0.0 : ignored if a value has been previously assigned to
                          a specific material, otherwise all materials (default)
               0.0 < WHAT(3) =< 2.0 : all materials.

     WHAT(4) = lower bound of the particle id-numbers (or corresponding name) for
               which decay or inelastic interaction biasing is to be applied
               ("From particle WHAT(4)...").
               Default = 1.0.

     WHAT(5) = upper bound of the particle id-numbers (or corresponding name) for
               which decay or inelastic interaction biasing is to be applied
               ("...to particle WHAT(5)...").
               Default = WHAT(4) if WHAT(4) > 0, 46 otherwise.

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

for SDUM = DECPRI, DECALL, INEPRI, INEALL:

     SDUM    = DECPRI: decay biasing, as requested by another LAM-BIAS card with
                       SDUM = GDECAY or blank, must be applied only to primary
                       particles.
             = DECALL: decay biasing, as requested by another LAM-BIAS card with
                       SDUM = GDECAY or blank, must be applied to all
                       generations (default).
             = INEPRI: inelastic hadronic interaction biasing, as requested by
                       another LAM-BIAS card with SDUM = blank, must be applied
                       only to primary particles.
             = INEALL: inelastic hadronic interaction biasing, as requested by
                       another LAM-BIAS card with SDUM = blank, must be applied
                       to all generations (default)

     Default (option LAM-BIAS not given): no decay length or inelastic
             interaction or decay direction biasing

Notes:

• 1) Option LAM-BIAS can be used for three different kinds of biasing: a) biasing of the particle decay length (or life), b) biasing of the direction of the decay secondaries, and c) biasing of the inelastic hadronic interaction length.

• 2) Depending on the SDUM value, two different kinds of biasing are applied to the particle decay length (or life). In both cases, the particle is transported to a distance sampled from an imposed (biased) exponential distribution: If WHAT(1) is positive, decay products are created, but the particle survives with its weight and the weight of its daughters is adjusted according to the ratio between the biased and the physical survival probability at the sampled distance. If WHAT(1) is negative, decay is performed and the weight of the daughters is set according to the biasing, but the survival of the primary particle is decided by Russian Roulette according to the biasing. Again, the weights are adjusted taking the bias into account.

• 3) The laboratory decay length corresponding to the selected mean decay life is obtained by multiplication by BETA*GAMMA*c.

• 4) Decay direction biasing is activated by a LAM-BIAS card with SDUM = DCDRBIAS. The direction of decay secondaries is sampled preferentially close to the direction specified by the user by means of a second LAM-BIAS card with SDUM = DCY-DIRE.

• 5) The biasing function for the decay direction is of the form exp{-[1-cos(theta)]/lambda} where theta is the polar angle between the sampled direction and the preferential direction (transformed to the centre of mass reference system). The degree of biasing is largest for small positive values of lambda (producing direction biasing strongly peaked along the direction of interest) and decreases with increasing lambda. Values of lambda >= 1.0 result essentially in no biasing.

• 6) Biasing of hadronic inelastic interaction length can be done either in one single material (indicated by WHAT(3)) or in all materials (default). No other possibility is foreseen for the moment.

• 7) When choosing the Russian Roulette alternative, it is suggested to set also a weight window (cards WW-FACTOr and WW-THRESh) in order to avoid too large weight fluctuations.

• 8) Reduction factors excessively large can result in an abnormal increase of the number of secondaries to be loaded on the stack, especially at high primary energies. In such cases, FLUKA issues a message that the secondary could not be loaded because of a lack of space. The weight adjustment is modified accordingly (therefore the results are not affected) but if the number of messages exceeds a certain limit, the run is terminated.

• 9) Biasing of the hadronic inelastic interaction length can be applied also to photons (provided option PHOTONUC is also requested) and muons (provided option MUPHOTON is also requested); actually, it is often a good idea to do this in order to increase the probability of photonuclear interaction.

• 10) For photons, a typical reduction factor of the hadronic inelastic interaction length is the order of 0.01-0.05 for a shower initiated by 1 GeV photons or electrons, and of 0.1-0.5 for one at 10 TeV.

Examples (number based):

 *...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+....8
 LAM-BIAS      -3.E+3        1.        1.       13.       16.        0.GDECAY
 *  The mean decay length of pions and kaons (particles 13, 14, 15 and 16)
 *  is set equal to 30 m. Survival of the decaying particle is decided by
 *  Russian Roulette.
 LAM-BIAS         0.0      0.02       11.        7.        0.        0.INEPRI
 *  The interaction length for nuclear inelastic interactions of primary
 *  photons (particle 7) is reduced by a factor 50 in material 11.
 *  (Note that such a large reduction factor is often necessary for photons,
 *  but generally is not recommended for hadrons). The photon survives after
 *  the nuclear interaction with a reduced weight.

The same examples, name based:

 *...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+....8
 LAM-BIAS      -3.E+3        1.        1.     PION+     KAON-        0.GDECAY
 *
 LAM-BIAS         0.0      0.02       11.    PHOTON        0.        0.INEPRI