SLBW Resonance Format


The single-level Breit-Wigner equations can be written in the following form (which is the form used in NJOY, not the form from ENDF-102):

SLBW Equations

where

SLBW Equations

The resonance energies, J values, total widths, and partial widths are all given in the ENDF file; see ER, AJ, GT, GN, GG, and GF below. The actual resonance energy is different from the nominal Er value due to the "shift factors" S. The actual neutron width is different from GN due to the "penetrabilities" P. These two quantities are shown in the following:

SLBW Equations

SLBW Equations

The phase shifts in the SLBW formulas are given by

SLBW Equations

These quantities depend on rho=k*a and rho-hat=k*a-hat. There are several options for choosing the two characteristic lengths a and a-hat. The most common is to use AP from the file for the "scattering radius" a-hat and to compute the "channel radius" a based on the nuclear size, 0.123*AWRI1/3+0.08. Other options allow for using the scattering radius for a or for having an energy-dependent scattering radius.

At zero temperature, the resonance shapes in the SLBW formulas are given by

SLBW Equations

but for higher temperatures, we can use

SLBW Equations

This is a very fast way to generate Doppler-broadened cross sections from SLBW resonances, but the use of the BROADR module of NJOY is more general, and the psi-chi option of RECONR is rarely used.

The following quantities are defined for SLBW subsections:

SPI
spin I of the target nucleus.
AP
scattering radius in units of 10-12 cm.
NLS
number of l values (neutron orbital angular momentum) in this energy region. A set of resonances is given for each l.
AWRI
ratio of the mass of a praticular isotope to that of a neutron.
QX
Q value to be added to the incident particle's center-of-mass energy to determine the channel energy for use in the penetrability factor. Could be used for competition with discrete inelastic scattering, but this is not implemented in NJOY. QX will be zero unless LRX is nonzero.
L
value of l.
LRX
flag indicating whether this energy range contains a competitive width. Currently not implemented in NJOY.
NRS
number of resolved resonances for the current l value. (NRS<=600)
ER
resonance energy (in the laboratory system).
AJ
floating-point value for J (the total angular momentum of the resonance).
GT
resonance total width evaluated at the resonance energy ER.
GN
neutron width evaluated at the resonance energy ER.
GG
radiation width, a constant.
GF
fission width, a constant.
The structure of a subsection of SLBW data follows: 
        [MAT,2,151/0.,0.,0,0,NR,NP/Eint/AP(E)] TAB1  if NRO is not zero
        [MAT,2,151/SPI,AP,0,0,NLS,0] CONT
        [MAT,2,151/AWRI,QX,L,LRX,6*NRS,NRS/
                   ER_1,AJ_1,GT_1,GN_1,GG_1,GF_1,
                   ER_2,AJ_2,GT_2,GN_2,GG_2,GF_2,
                    ... for NRS resonances ...   ] LIST
           ... repeat LIST for NLS l values ...

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23 January 1998 T-2 Nuclear Information Service ryxm@lanl.gov