USRYIELD

Summary

Defines a detector to score a double differential particle yield around an extended or a point target ​​

​

See also USRBDX

The full definition of the detector may require two successive cards (the second card, identified by the character “ & ” in any column from 71 to 78 (or in the last field in case of free format input), must be given unless the corresponding defaults are acceptable to the user)
First card:
For SDUM = anything but BEAMDEF:

WHAT(1) =
\(i_e + i_a \times 100 + i_4 \times 10000\), where \(i_e\) and \(i_a\) indicate the two physical quantities with respect to which the double differential yield is calculated.
If \(i_e > 0\), the yield will be analysed in linear intervals with respect to the first quantity; if \(i_e < 0\), the yield distribution will be binned logarithmically.
(Note that for rapidity​, pseudo-rapidity​ and Feynman-x​ logarithmic intervals are not available and will be forced to linear if requested).
For the second quantity, indicated by \(i_a\), only one interval will be considered.

\(|i_e|\) or \(|i_a|\)

= 1

: kinetic energy​ in GeV

= 2

: total momentum in GeV/c

= 3

: rapidity in the lab frame​ (only linear scoring available)

= 4

: rapidity in the c.m.s. frame​ (only linear scoring available)

= 5

: pseudo-rapidity in the lab frame (only linear scoring available)

= 6

: pseudo-rapidity in the c.m.s. frame (only linear scoring available)

= 7

: Feynman-x in the lab frame (\(E/E_{beam}\))​ (only linear scoring available)

= 8

: Feynman-x in the c.m.s. frame (only linear scoring available)

= 9

: transverse momentum​ in GeV/c

= 10

: transverse mass​ in GeV

= 11

: longitudinal momentum​ in the lab frame (in GeV/c)

= 12

: longitudinal momentum in the c.m.s. frame (in GeV/c)

= 13

: total energy in GeV

= 14

: polar angle​ in the lab frame (see Note 6)

= 15

: polar angle in the c.m.s. frame (see Note 6)

= 16

: square transverse momentum​ in (GeV/c)\(^2\)

= 17

: \(1/(2\pi\sin\theta)\) weighted angle​ in the lab frame (see Note 6)

= 18

: \(1/(2\pi p_{T})\) weighted transverse momentum​ in GeV/c

= 19

: ratio laboratory momentum​/beam momentum

= 20

: transverse kinetic energy​

= 21

: excitation energy​

= 22

: particle charge​

= 23

: particle LET​

= 24

: like 14, but with input in degrees rather than in radians (see Note 6)

= 25

: like 15, but with input in degrees rather than in radians (see Note 6)

= 26

: laboratory kinetic energy/nucleon​

= 27

: laboratory momentum/nucleon​

= 28

: particle baryonic charge​

= 29

: four-momentum transfer -t​

= 30

: c.m.s. longitudinal Feynman-x​ (only linear scoring available)

= 31

: excited mass squared​

= 32

: excited mass squared/s

= 33

: time (s)​

= 34

: \(sin\) weighted angle in the lab frame (see Note 6)

\(|i_e|\) or \(|i_a|\)

= 35

: total momentum (GeV/c) in the c.m.s. frame

= 36

: total energy (GeV) in the c.m.s. frame

= 37

: like 17, but with input in degrees rather than in radians (see Note 6)

= 38

: like 34, but with input in degrees rather than in radians (see Note 6)

\(i_4\)

= 0

: group-wise scoring for low energy neutrons

= \(\pm\)1

: point-wise scoring for low energy neutrons
WHAT(2) > 0.0:

number or name of the (generalised) particle type to be scored.

< -800.0 and WHAT(4) = -1.0 and WHAT(5) = -2: the (generalised) particles of type IJ entering an inelastic hadronic interaction are scored by setting WHAT(2) = -1000 -IJ​

Default

= 201.0  (all particles)

WHAT(3) =

logical output unit:

> 0.0:

formatted data are written on WHAT(3) unit

< 0.0:
unformatted data are written on |WHAT(3)| unit
Values of |WHAT(3)| < 21.0 should be avoided (with the exception of +11).
Default

= 11.0  (standard output unit)​

WHAT(4) > 0.0:

number or name of the first region defining the boundary (upstream region)

= -1.0

and WHAT(5) = -2.0: the yield of particles emerging from inelastic hadronic interactions is scored

Default

= -1.0

WHAT(5) > 0.0:

number or name of the second region defining the boundary (downstream region)

= -2.0

and WHAT(4) = -1.0: the yield of particles emerging from inelastic hadronic interactions is scored

Default

= -2.0

WHAT(6) =

normalisation factor (the results will be divided by WHAT(6))

SDUM

= any character string (not containing “ & ”) identifying the yield detector (max. 10 characters)​

Continuation card:​
WHAT(1) =

Upper limit of the scoring interval for the first quantity

Default

= beam momentum value in case \(|i_e|\) =1 or2, no default otherwise!

WHAT(2) =

Lower limit of the scoring interval for the first quantity

Default

= 0.0  if linear binning, 0.001 otherwise. Note that these values might not be meaningful for all available quantities.

WHAT(3) =

number of scoring intervals for the first quantity

Default

= 50.0

WHAT(4) =

Upper scoring limit for the second quantity

Default

:  no default!

WHAT(5) =

Lower scoring limit for the second quantity

Default

= 0.0

WHAT(6) =

\(ix_a + ix_m \times 100\), where \(ix_a\) indicates the kind of yield or cross section desired and \(ix_m\) the target material (if needed in order to calculate cross section or particle LET, otherwise \(ix_m = 0\)). Cross sections are obtained from yields multiplying the latter ones by the microscopic inelastic cross section of the beam particle at beam energy on the selected material. See Note 4 in case of a thick target​

\(ix_a\)

= 1:

plain double differential cross section​ \({ \frac{\mathrm{d}^2 \sigma}{\mathrm{d} x_1 \mathrm{d} x_2}}\), where \(x_1\), \(x_2\) are the first and second

quantity

\(ix_a\)

= 2:

invariant cross section​ \({ E \frac{\mathrm{d}^3 \sigma}{\mathrm{d} p^3}}\)

\(ix_a\)

= 3:

plain double differential yield​ \({ \frac{\mathrm{d}^2 N}{\mathrm{d} x_1 \mathrm{d} x_2}}\), where \(x_1\), \(x_2\) are the first and second quantity

\(ix_a\)

= 4:

double differential yield \({ \frac{\mathrm{d}^2 (x_2 N)}{\mathrm{d} x_1 \mathrm{d} x_2}}\) where \(x_1\), \(x_2\) are the first and second quantity

\(ix_a\)

= 5:

double differential yield \({ \frac{\mathrm{d}^2 (x_1 N)}{\mathrm{d} x_1 \mathrm{d} x_2}}\), where \(x_1\), \(x_2\) are the first and second quantity

\(ix_a\)

= 6:

double differential fluence yield \({ \frac{1}{\cos\theta} \frac{\mathrm{d}^2 N}{\mathrm{d} x_1 \mathrm{d} x_2}}\) where \(x_1\), \(x_2\) are the first and second

quantity, and \(\theta\) is the angle between the particle direction and the NORMAL TO THE

SURFACE. The same \(\theta\) is also used for \(x_1\) or \(x_2\) if the laboratory polar angle (14 or 24)

is requested

\(ix_a\)

= 7:

double differential yield \({ \frac{\mathrm{d}^2 (x_2^2 N)}{\mathrm{d} x_1 \mathrm{d} x_2}}\) where \(x_1\), \(x_2\) are the first and second quantity

\(ix_a\)

= 8:

double differential yield \({ \frac{\mathrm{d}^2 (x_1^2 N)}{\mathrm{d} x_1 \mathrm{d} x_2}}\) where \(x_1\), \(x_2\) are the first and second quantity

\(ix_a\)

= 9:

double differential yield \({ \frac{\mathrm{d}^2 N}{x_2 \mathrm{d} x_1 \mathrm{d} x_2}}\) where \(x_1\), \(x_2\) are the first and second quantity

\(ix_a\)

= 10:

double differential yield \({ \frac{\mathrm{d}^2 N}{x_1 \mathrm{d} x_1 \mathrm{d} x_2}}\) where \(x_1\), \(x_2\) are the first and second quantity

\(ix_a\)

= 11:

double differential yield \({ \frac{\mathrm{d}^2 N}{\mathrm{d} \frac{x_1}{x_2} \mathrm{d} x_2}}\) where \(x_1\), \(x_2\) are the first and second quantity

\(ix_a\)

= 12:

double differential yield \({ \frac{\mathrm{d}^2 (x_1 \sqrt{x_1^2 - x_2^2} N)}{\mathrm{d} x_1 \mathrm{d} x_2}}\) where \(x_1\), \(x_2\) are the first and second quantity

\(ix_a\)

= 13:

double differential yield \({ \frac{\mathrm{d}^2 ((x_1^2 + x_2^2)N)}{\mathrm{d} x_1 \mathrm{d} x_2}}\) where \(x_1\), \(x_2\) are the first and second quantity

\(ix_a\)

= 14:

double differential yield \({ \frac{\mathrm{d}^2 ((x_1 + x_2^2) N)}{\pi \mathrm{d} x_1 \mathrm{d} x_2}}\) where \(x_1\), \(x_2\) are the first and second quantity

\(ix_a\)

= 15:

double differential yield \({ \frac{\mathrm{d}^2 ((x_1^2 + x_2) N)}{\pi \mathrm{d} x_1 \mathrm{d} x_2}}\) where \(x_1\), \(x_2\) are the first and second quantity

\(ix_a\)

= 16:

double differential weighted fluence yield \({ \frac{1}{\cos\theta} \frac{\mathrm{d}^2 (x_2 N)}{\mathrm{d} x_1 \mathrm{d} x_2}}\) where \(x_1\), \(x_2\) are the first and

second quantity, and \(\theta\) is the angle between the particle direction and the NORMAL

TO THE SURFACE. The same \(\theta\) is also used for \(x_1\) or \(x_2\) if the laboratory polar angle

(14 or 24) is requested

\(ix_a\)

= 26:

double differential weighted fluence yield \({ \frac{1}{\cos\theta} \frac{\mathrm{d}^2 (x_1 N)}{\mathrm{d} x_1 \mathrm{d} x_2}}\) where \(x_1\), \(x_2\) are the first and

second quantity, and \(\theta\) is the angle between the particle direction and the NORMAL

TO THE SURFACE. The same \(\theta\) is also used for \(x_1\) or \(x_2\) if the laboratory polar angle

(14 or 24) is requested

\(ix_a\)

> 52:

as per \(ix_a\) = (\(ix_a\) - 50), but double differential cross section instead of yield,

for instance \(ix_a\) = 59 is \({ \frac{\mathrm{d}^2 \sigma}{x_2 \mathrm{d} x_1 \mathrm{d} x_2}}\),

while note that \(ix_a\) = 53 (that is \({ \frac{\mathrm{d}^2 \sigma}{\mathrm{d} x_1 \mathrm{d} x_2}}\)) coincides with \(ix_a\) = 1

\(ix_m\)

= material number of the target for cross section or LET calculations (default: HYDROGEN).

In case of scoring as a function of LET, it must be a material actually assigned to some

geometry region (and this way initialised by the code).
Default

= 1.0  (plain double differential cross section — but see Note 4)

SDUM

= “ & ” in any position in column 71 to 78 (or in the last field if free format is used)

For SDUM = BEAMDEF:

projectile particle index, or corresponding name

Default

= IJBEAM  (beam particle)

target particle index, or corresponding name (used by the code to define the c.m.s. frame)

Default

= 1.0  (proton)

projectile momentum​

Default

= PBEAM  (beam momentum)

WHAT(4,5,6) = projectile direction cosines​
Default

= UBEAM, VBEAM, WBEAM  (beam direction cosines)​

Default

(option USRYIELD not given): no yield estimator detector is defined


Notes

  1. While option USRBDX calculates angular distributions with respect to the normal​ to the boundary at the point of crossing, USRYIELD distributions are calculated with respect to a fixed direction (the beam direction, or a different direction specified by the user with SDUM = BEAMDEF).

  2. When scoring thick-target yields​, the angle considered is that between the direction of the particle at the point where it crosses the target surface and the beam direction (or a different direction specified by the user, see Note 1). The target surface​ is defined as the boundary between two regions (positive values of WHAT(4) and WHAT(5) of the first USRYIELD card).

  3. Point-target yields​, i.e. yields of particles emerging from inelastic hadronic interactions ​ with single nuclei (including hadronic interactions by ions and real or virtual photons), are scored by setting WHAT(4) = -1.0 and WHAT(5)= -2.0 in the first USRYIELD card). As an alternative, the corresponding cross sections can be calculated, depending on the value of WHAT(6) in the continuation card. In addition, if WHAT(2) in the same card is < -800.0, the distributions of particles entering the inelastic hadronic interactions​ can be scored.

  4. Calculating a cross section has little meaning in case of a thick target. Cross sections are obtained from yields by multiplying by the microscopic inelastic cross section of the beam particle at beam energy on the selected material.

  5. Differential yields (or cross sections) are scored over any desired number of intervals for what concerns the first quantity, but over only one interval for the second quantity. However, the results are always expressed as second derivatives (or third derivatives in the case of invariant cross sections​), and not as interval-integrated yields. In order to obtain more intervals for the second quantity, the user must define further USRYIELD detectors.

  6. In the case of polar angle​ quantities (\(|i_e|\) or \(|i_a| = 14,15,17,24,25,34,37,38\)) the differential yield is always referred to solid angle in steradian, although input is specified in radian or degrees.

  7. When scoring yields as a function of LET​, the intervals will be in keV/(\(\mu\)m g/cm\(^3\)), and the histogram will be normalized, as usual, to the unit interval of the first and second quantities.

  8. A USRYIELD card with SDUM = BEAMDEF, if given, does not refer to a particular detector, but modifies the reference projectile or target parameters for all USRYIELD detectors of the current run. No continuation card has to be given after one with SDUM = BEAMDEF.

  9. The logical output unit for the estimator results (WHAT(3) of the first USRYIELD card) can be any one of the following:

    • the standard output​ unit 11: estimator results will be written on the same file as the standard FLUKA output.

    • a pre-connected unit​ (via a symbolic link on most UNIX systems, ASSIGN under VMS, or equivalent commands on other systems)

    • a file opened with the FLUKA command OPEN

    • a file opened with a Fortran OPEN statement in a user-written initialisation routine such as USRINI​, USRGLO​ or SOURCE​ (see USRINI: USeR INItialisation, USRGLO: USeR GLObal settings, SOURCE: user-written source)

    • a dynamically opened file, with a default name assigned by the Fortran compiler (typically fort.xx or ftn.xx, with xx equal to the chosen logical output unit number).

    The results of several USRYIELD detectors in a same FLUKA run can be written on the same file, but of course only if they are all in the same mode (all formatted, or all unformatted).

    It is also possible in principle to write on the same file the results of different kinds of estimators (USRBDX, USRBIN, etc.) but this is not recommended, especially in the case of an unformatted file, because it would make very difficult any reading and analysis.

  10. Not all \(38 \times 38\) combinations of quantities are accepted by the code, nor are they all meaningful (for instance one could run successfully by setting in the first USRYIELD card WHAT(1) with \(i_a = i_e\), but the result would have no physical meaning).

  11. When scoring neutron yield with energy as the first quantity, and the requested energy interval structure overlaps with that of the low energy neutron groups, interval boundaries are forced to coincide with group boundaries and no interval can be smaller than the corresponding group. Actually, the program uses the requested energy limits and number of intervals to estimate the desired interval width. The number of intervals above the upper limit of the first low-energy neutron group is recalculated according to such width. To preserve the requested upper energy limit, the width of the first interval above the low energy group may be smaller than that of the others.
    Note that the lowest energy limit of the last neutron group is \(10^{-14}\) GeV (\(10^{-5}\) eV) for the 260 data set.
    All group energy boundaries are listed in Table 10.1 on.
  12. If the scored yield with energy as the first quantity is that of a generalised particle​ which includes neutrons (e.g. ALL-PART, ALL-NEUT, NUCLEONS, NUC&PI+-, HAD-NEUT, and even ENERGY), the spectrum is presented in two separate tables. One table refers to all non-neutron particles and to neutrons with energies > 20 MeV. The second table refers only to neutrons with energy < 20 MeV, and its interval structure is that of the neutron energy groups.
    In case an interval crosses 20 MeV, it will include the contribution of neutrons with energy > 20 MeV and not that of neutrons with energy < 20 MeV.

  13. A program Usysuw is available with the normal FLUKA code distribution in directory $FLUPRO/flutil. Usysuw reads USRYIELD results in binary form from several runs and allows to compute standard deviations. It returns differential and cumulative fluence, with the corresponding percent errors, in a file, and differential fluence in another file formatted for easy plotting. It also returns a binary file that can be read out in turn by Usysuw. The content of this file is statistically equivalent to that of the sum of the files used to obtain it, and it can replace them to be combined with further output files if desired (the Usysuw program takes care of giving it the appropriate weight).

  14. The maximum number of yield detectors detectors​ that the user can define is 1000.

Example (number based):

*...+....1....+....2....+....3....+....4....+....5....+....6....+....7...+...8
USRYIELD      1399.0       13.      21.0       3.0       2.0       1.0TotPi+(E)
USRYIELD        50.0     0.001     100.03.14159265       0.0       3.0 &
* Score double differential yield of positive pions going from region 3 to
* region 2 with a polar angle between 0 and pi with respect to the beam
* direction. Energy distribution is in 100 logarithmic intervals between 1 MeV
* and 50 GeV. Normalisation factor = 1. Results are written formatted on
* unit 21.

The same example, name based:

*...+....1....+....2....+....3....+....4....+....5....+....6....+....7...+...8
USRYIELD      1399.0     PION+      21.0  ThirdReg  RegioTwo       1.0TotPi+(E)
USRYIELD        50.0     0.001     100.03.14159265       0.0       3.0 &