Formal Specifications for File 1 Fission Nu-bars


The following is based on ENDF-102,
Data Formats and Procedures for the
Evaluated Nuclear Data File ENDF-6.

This page describes MT=452, 456, and 455 from File 1.

Number of Neutrons per Fission, nu-bar (MT=452)

If the material fissions, then a section specifying the average total number of neutrons per fission, nu-bar (MT=452), must be given. This format applies to both particle-induced and spontaneous fission, each in its designated sublibrary. Values of nu-bar may be tabulated a function of energy or represented by coefficients provided for the following polynomial expansion of nu-bar(E):

nu-bar polynomial

where
nu-bar(E)
the average total (prompt plus delayed) number of neutrons per fission produced by neutrons of incident energy E (eV),
Cn
the nth coefficient, and
NC
the number of terms in the polynomial.
MT=452 for an energy-dependent neutron multiplicity cannot be represented by a polynomial expansion when MT=455 and MT=456 are utilized in the file.

Formats

The structure of this section depends on whether the data are given in tabulated form or as a polynomial expansion. The following quantities are defined:

ZA,AWR
standard material charge and mass parameters
LNU
flag to specify the representation used:
  • LNU=1, polynomial representation has been used, or
  • LNU=2, tabulated representation.
NC
count of the number of terms used in the polynomial expansion. Up to 4.
Cn
coefficients of the polynomial. There are NC coefficients given.
NR
number of interpolation ranges used to tabulate values of nu-bar(E).
NP
total number of energy points used to tabulate nu-bar>(E).
nu-bar(E)
average total number of neutrons per fission.

If LNU=1, the structure of a section is 

        [MAT, 1, 452/ ZA, AWR, 0, LNU, 0, 0] HEAD   LNU=1
        [MAT, 1, 452/ 0., 0., 0, 0, NC, 0/ C1, C2, ... CNC] LIST
        [MAT, 1, 0/ 0.0, 0.0, 0, 0, 0, 0] SEND

If LNU=2, the structure of the section is 
        [MAT, 1, 452/ ZA, AWR, 0, LNU, 0, 0] HEAD   LNU=2
        [MAT, 1, 452/ 0., 0., 0, 0, NR, NP/ Eint/ nu-bar(E)] TAB1
        [MAT, 1, 0/ 0.0, 0.0, 0, 0, 0, 0] SEND

For spontaneous fission, the polynomial representation (LNU=1) is used with NC=1. There is no energy dependence.

The polynomial form for particle-induced nu-bar is only used when neither prompt nor delayed nu-bar values are given.

Delayed Neutron Data, nu-bar-d (MT=455)

This section describes the delayed neutrons resulting from either particle induced or spontaneous fission. The average total number of delayed neutron precursors emitted per fission, nu-bar-d, is given, along with the decay constants lambdai for each precursor family. The fraction of delayed neutrons generated for each family is given in MT=455 of File 5. The energy distribution of the neutrons associated with each precursor family are also given in File 5.

For particle induced fission, the total number of delayed neutrons is given as a function of energy in tabulated form (LNU=2), just as for MT=452. For spontaneous fission, the polynomial representation (LNU=1) is used with NC=1, just as for MT=452.

Formats

The following quantities are defined:

ZA,AWR
standard material charge and mass parameters
LNU
flag to specify the representation used:
  • LNU=1, polynomial representation has been used, or
  • LNU=2, tabulated representation.
NC
count of the number of terms used in the polynomial expansion. If used, it is 1.
NR
number of interpolation ranges used to tabulate values of nu-bar-d(E).
NP
total number of energy points used to tabulate nu-bar-d>(E).
nu-bar-d(E)
average total number of delayed neutrons per fission.
NNF
number of precursor families considered.
lambdai
decay constant (sec-1) for the ith precursor.
The structure when values of nu-bar-d are tabulated (LNU=2) is: 
        [MAT, 1, 455/ ZA, AWR, 0, LNU, 0, 0] HEAD   LNU=2
        [MAT, 1, 455/ 0., 0., 0, 0, NNF, 0/ lambda1, lambda2, ...] LIST
        [MAT, 1, 455/ 0., 0., 0, 0, NR, NP/ Eint/ nu-bar-d(E)] TAB1
        [MAT, 1, 0/ 0.0, 0.0, 0, 0, 0, 0] SEND

If LNU=1 (spontaneous fission), the structure of the section is: 
        [MAT, 1, 455/ ZA, AWR, 0, LNU, 0, 0] HEAD   LNU=1
        [MAT, 1, 455/ 0., 0., 0, 0, NNF, 0/ lambda1, lambda2, ...] LIST
        [MAT, 1, 455/ 0., 0., 0, 0, NC, 0/ nu-bar-d] TAB1  NC=1
        [MAT, 1, 0/ 0.0, 0.0, 0, 0, 0, 0] SEND

If MT=455 is used, then MT=456 must also be used, as well as MT=452.

Number of Prompt Neutrons per Fission, nu-bar-p (MT=456)

If the material fissions, a section specifying the average number of prompt neutrons per fission, nu-bar-p (MT=456), can be given using formats identical to MT=452. For particle-induced fission, nu-bar-p is given as a function of incident particle energy. The prompt nu-bar for spontaneous fission can also be given using MT=456, but there is no energy dependence.

The following quantities are defined:

ZA,AWR
standard material charge and mass parameters
LNU
flag to specify the representation used:
  • LNU=1, polynomial representation has been used, or
  • LNU=2, tabulated representation.
NC
count of the number of terms used in the polynomial expansion. If used, it is 1.
NR
number of interpolation ranges used to tabulate values of nu-bar(E).
NP
total number of energy points used to tabulate nu-bar-p>(E).
nu-bar-p(E)
average number of prompt neutrons per fission.

If LNU=2, the structure of the section is 

        [MAT, 1, 456/ ZA, AWR, 0, LNU, 0, 0] HEAD   LNU=2
        [MAT, 1, 456/ 0., 0., 0, 0, NR, NP/ Eint/ nu-bar-p(E)] TAB1
        [MAT, 1, 0/ 0.0, 0.0, 0, 0, 0, 0] SEND

If LNU=1 (spontaneous fission), the structure of a section is 
        [MAT, 1, 456/ ZA, AWR, 0, LNU, 0, 0] HEAD   LNU=1
        [MAT, 1, 456/ 0., 0., 0, 0, NC, 0/ nu-bar-p] LIST  NC=1
        [MAT, 1, 0/ 0.0, 0.0, 0, 0, 0, 0] SEND

For spontaneous fission, the polynomial representation (LNU=1) is used with NC=1. There is no energy dependence.

If MT=456 is specified, then MT=455 must also be specified, as well as MT=452.

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15 December 2012 T-2 Nuclear Information Service ryxm@lanl.gov