Hybrid R-Function Resonance Format


The Hybrid R-Function approach treats elastic scattering as a multilevel cross section using formulas similar to those given for the Reich-Moore representation, except that fission is absent:

Hybrid Equations 1

where the U function is now a scalar and doesn't require the matrix inversion of the Reich-Moore approach,

Hybrid Equations 2

The R function itself is given by

Hybrid Equations 3

where R0 is a complex background R function and P is a penetrability factor. The background R function can either be read in or set to zero. The penetrability and shift factors are computed from the scattering radius or channel radius as for the SLBW approach. The phase shifts can be computed from the scattering radius as in the SLBW approach, or they can be read in from an optical model calculation. The latter allows this format to be used for charged-particle channels.

The other reactions are treated with formulas similar to those of the SLBW method.

Note that resonance parameters are given explicitly for all three quantum numbers l, s, and J. No correction to the potential scattering cross section for repeated J values is needed.

The following quantities are defined for Hybrid R-Function subsections:

SPI
spin I of the target nucleus.
LAD
flag indicating whether these parameters can be used to compute angular distributions: LAD=0 do not use; LAD=1, can be used if desired.
NGRE
number of radiative capture reactions (0 or 1).
NFRE
number of fission reactions (0 or 1).
NIRE
number of inelastic scattering reactions (0 to 4).
NCRE
number of charged-particle reactions (0 to 4). A maximum of four partial reactions is allowed; that is, NIRE+NCRE can vary from 0 to 4.
MTRE1, MTRE2, MTRE3, MTRE4
MT value for each of the four inelastic or charged particle reactions being represented. Nine possible values are allowed for these MT numbers, and if present, they must be given in the following order: 51 (n,n_1), 52 (n,n_2), 53 (n,n_3), 54 (n,n_4), 103 (n,p), 104 (n,d), 105 (n,t), 106 (n,3He), 107 (n,alpha). Use zeros for the unspecified MTRE values if fewer than four are specified.
GG
energy-independent partial width for capture, Gamma-gamma. This value should be zero if NGRE=0.
GF
energy-independent partial width for fission, Gamma-f. This value should be zero if NFRE=0.
GRE1,GRE2,GRE3,GRE4
partial widths for each of the four specified reactions evaluated at the resonance energy ER.
GE
eliminated width GE=GG+GF+GRE1+GRE2+GRE3+GRE4 evaluted at ER.
QRE1,QRE2,QRE3,QRE4
Q value for each of the four possible reactions, positive for an exothermic reaction. Use the negative of the level excitation energy for an inelastic reaction. Use zero for an unused channel.
ALRE1,ALRE2,ALRE3,ALRE4
exit l-value for each of the four possible reactions. Use zero for an unused channel. These quantities are needed for the penetrability factors of the exit reaction widths and are floating-point numbers with integer values.
AS
the channel spin s.
AC
the channel radius (units of 10-12 cm).
AWRIC
mass ratio for a charged-particle exit channel.
PCP(E)
charged-particle penetrability as a function of the neutron's laboratory energy. Four such function will be supplied for each of the NCRE charged-particle reactions, one for each of the four possible l values, 0, 1, 2, or 3. If the penetrability for a particular l value is not actually required, zeros should be supplied.
NLS
number of l values for which resonance parameters are given.
NLSC
number of l values that must be used to converge the calculation of the scattering angular distribution at the highest energy covered. NLSC must be greater than or equal to NLS and can have values up to 20.
NSS
number of different s values (channel spin) for a given l value.
NJS
number of different J values for a given pair of l and s values.
NLSJ
number of resonances in the channel specified by l, s, and J. This can be zero, signifying a non-resonant "phase shift only" channel. Such channels can be included, because they contribute to the potential scattering and the angular distribution. However, they may be omitted if the potential scattering is adjusted in File 3, and if the angular distributions are specified in a way other than be calculation form R-Function formulas, i.e., in File 4.
LBK
a flag to signal the presence of a background R function in a particular channel, lsJ.
RR0(E)
real part of the complex background R function. Present if LBK=1.
IR0(E)
imaginary part of the complex background R function. Present if LBK=1.
LPS
flag to signal the presence of complex optical-model phase shifts to be used instead of the hard-sphere values.
RPS(E)
real part of the complex phase shift. Present if LPS=1.
IPS(E)
imaginary part of the complex phase shift. Present if LPS=1.
The structure of a subsection for the Hybrid R-Function format follows: 
        [MAT,2,151/SPI,0.0,LAD,0,NLS,NLSC] CONT
        [MAT,2,151/0.0,0.0,NGRE,NFRE,NIRE,NCRE] CONT
        [MAT,2,151/0.0,0.0,MTRE1,MTRE2,MTRE3,MTRE4] CONT
        [MAT,2,151/0.0,0.0,0,0,4,0/QRE1,QRE2,QRE3,QRE4] LIST

          If NCRE is greater than zero, give a record
        [MAT,2,151/AWRIC,0.0,0,0,NR,NP/Eint/PCP(E)] TAB1
          for each of the four l values 0-3 for the first 
          of the NCRE reactions, then the four l values 
          for the second, etc., until all NCRE reactions 
          have been given.  A total of 4*NCRE TAB1 records
          are given.

          Start the loop over NLS values of L here
        [MAT,2,151/AWRI,0.0,L,0,NSS,0] CONT
 
          Start the loop over NSS values of AS (channel spin) here
        [MAT,2,151/AS,0.0,0,0,NJS,0] CONT

          Start the loop over NJS values of J for this L,AS pair here
        [MAT,2,151/AJ,AC,LBK,LPS,12*NLSJ,NLSJ/
                   ER_1,GN_1,GG_1,GF_1,GRE1_1,GRE2_1,
                   GRE3_1,GRE4_1,ALRE1,ALRE2,ALRE3_1,ALRE4_1,
                   ER_2,GN_2,GG_2,GF_2,GRE1_2,GRE2_2,
                    ... for NLSJ resonances ...   ] LIST

          If LBK=1, give the complex background R function
        [MAT,2,151/0.0,0.0,0,0,NR,NP/Eint/RR0(E)] TAB1
        [MAT,2,151/0.0,0.0,0,0,NR,NP/Eint/IR0(E)] TAB1

          If LPS=1, give the complex optical-model phase shift
        [MAT,2,151/0.0,0.0,0,0,NR,NP/Eint/RPS(E)] TAB1
        [MAT,2,151/0.0,0.0,0,0,NR,NP/Eint/IPS(E)] TAB1

          Continue the loop over the NJS values of J for this L,AS pair

          Continue the loop over the NSS values of AS for this L

          Continue the loop over the NLS values of L

NEXT
INDEX

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