Within the Collider section, the Impact section can be used to specify information about the impact parameter, defined as the distance in fm of the two straight lines that the center of masses of the nuclei travel on. The separation of the two colliding nuclei is by default along the x-axis. If the Impact section is not specified, default values here below will be used, e.g. the impact parameter will be set to 0 fm.

Warning: Note that there are no safeguards to prevent you from specifying negative impact parameters. The value chosen here is simply the x-component of \(\mathbf{b}\). The result will be that the projectile and target will have switched position in x.

Max — double, optional, default = 0.0

Like Range: [0.0, Max]. Note that if both Range and Max are specified, Max takes precedence (in fm).

Random_Reaction_Plane — bool, optional, default = false

Rotate the direction of the separation of the two nuclei due to the impact parameter with a uniform random angle in the x-y plane.

Range — list of two doubles, optional, default = [0.0,0.0]

A list of minimal and maximal impact parameters in fm between which \(b\) should be chosen. The order of these is not important.

Sample — string, optional, default = "quadratic"

Distribution according to which the impact parameter is sampled. Possible alternatives:

"uniform" → use uniform sampling of the impact parameter (uniform in \(b\): \(dP(b) = db\))
"quadratic" → use areal (aka quadratic) input sampling (the probability of an input parameter range is proportional to the area corresponding to that range, uniform in \(b^2\): \(dP(b) = b\,db\)).
"custom" → creates a custom distribution of piecewise linear functions based on the provided impact parameter Values and the corresponding Yields (likelihood of that impact parameter value to be sampled). This distribution is used to randomly sample the impact parameter using rejection sampling. Note that both these keys, Values and Yields are required when using Sample: "custom".

Value — double, optional, default = 0.0

Fixed value for the impact parameter in fm.

Attention: If this value is set, all further Impact keys are ignored.

Custom sampling

Values — list of doubles, required

Impact parameter Values in fm used to build the custom distribution. Each element of Values corresponds to an element of Yields, these are connected through piecewise linear functions to create the distribution. Must be same length as Yields. This key can be omitted if Sample is not set to "custom".

Yields — list of doubles, required

Each element of Yields indicates the likelihood of sampling the corresponding impact parameter in Values. Between the specified points of Values and Yields, linear interpolation is used to build the custom distribution. Yields must be same length as Values. It does not need to be normed. This key can be omitted if Sample is not set to "custom".

Configuring the Impact Parameter

The impact parameter can be configured to have a fixed value in the Collider subsection of Modi. In addition, the initial distance of the nuclei in \(z\)-direction is assigned a specific value. This does not affect the time at which the nuclei will collide, but only changes the start time of the simulation as the nuclei are further apart when the simulation begins.

Modi:
    Collider:
        Impact:
            Value: 0.1

The impact parameter may further be sampled within a certain impact parameter range. By default, a quadratic distribution is used for the sampling. However, this may be set to "uniform" if necessary.

Modi:
    Collider:
        Impact:
            Sample: "quadratic"
            Range: [3.0, 6.0]

A custom impact parameter distribution based on a set of Values and Yields, can be configured as follows:

Modi:
    Collider:
        Impact:
            Sample: "custom"
            Values: [0.0, 3.0, 6.0, 9.0]
            Yields: [0.000000, 2.999525, 5.959843, 6.995699]