Reich-Moore Resonance Format


The Reich-Moore equations can be written in the following form:

RM Equations 1

where the I symbol stands for an element of the inverse of the complex R-matrix, and

RM Equations 2

The elements of the complex R-matrix are given by

RM Equations 3

In these equations, "c" stands for the fission channel (two are allowed), "r" indexes the resonances belonging to a particular spin sequence l,J, and the other symbols have the same meanings as for the SLBW representation.

When fission is not present, the R matrix reduces to a simple R function, and the matrix inversion normally required to get the script-I quantities reduces to a simple inversion of a complex value.

As is the MLBW case, the summation over J runs over the range

RM Equations 4

The term d of lJ in the expressions for the total and elastic cross sections is used to account for the possibility of an additional contribution to the potential scattering cross section from the second channel spin. It is unity if there is a second J value equal to J, and zero otherwise. This is just a slightly different approach for making the correction discussed in connection with the MLBW method.

The following quantities are defined for the Reich-Moore representation:

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.
NLSC
number of l values that must be used to converge the calculation with repsect to the incident l value in order to obtain accurate elastic angular distributions.
AWRI
ratio of the mass of a praticular isotope to that of a neutron.
APL
the l-dependent scattering radius. If zero, use APL=AP.
L
value of l.
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).
GN
neutron width evaluated at the resonance energy ER.
GG
radiation width.
GFA,GFB
partial fission widths.
The format used for a subsection of Reich-Moore parameters is as 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,NLSC] CONT
        [MAT,2,151/AWRI,APL,L,0,6*NRS,NRS/
                   ER_1,AJ_1,GN_1,GG_1,GFA_1,GFB_1,
                   ER_2,AJ_2,GN_2,GG_2,GFA_2,GFB_2,
                    ... for NRS resonances ...   ] LIST
           ... repeat LIST for NLS l values ...

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14 February 1998 T-2 Nuclear Information Service ryxm@lanl.gov