40-Zr- 93

 40-ZR- 93 JNDC       EVAL-MAR90 JNDC FP NUCLEAR DATA W.G.        
                      DIST-MAR02 REV2-FEB02            20020222   
----JENDL-3.3         MATERIAL 4034                               
-----INCIDENT NEUTRON DATA                                        
------ENDF-6 FORMAT                                               
                                                                  
   ===========================================================    
   JENDL-3.2 data were automatically transformed to JENDL-3.3.    
    Interpolation of spectra: 22 (unit base interpolation)        
    (3,251) deleted, T-matrix of (4,2) deleted, and others.       
   ===========================================================    
                                                                  
HISTORY                                                           
84-10 EVALUATION FOR JENDL-2 WAS MADE BY JNDC FPND W.G./1/        
90-03 MODIFICATION FOR JENDL-3 WAS MADE/2/.                       
                                                                  
MF = 1  GENERAL INFORMATION                                       
  MT=451 COMMENTS AND DICTIONARY                                  
                                                                  
MF = 2  RESONANCE PARAMETERS                                      
  MT=151 RESOLVED AND UNRESOLVED RESONANCE PARAMETERS             
  RESOLVED RESONANCE REGION (MLBW FORMULA) : BELOW 1.7 KEV        
    RESONANCE PARAMETERS WERE NEWLY EVALUATED AS FOLLOWS:         
    RESONANCE ENERGIES, NEUTRON WIDTHS AND RADIATION WIDTHS WERE  
    MAINLY TAKEN FROM THE MEASUREMENT OF MACKLIN/3/ UP TO 6.1 KEV.
    NEUTRON WIDTHS NOT MEASURED WERE DETERMINED FROM CAPTURE AREA 
    DATA, AND TOTAL AND RADIATION WIDTHS OF MACKLIN ET AL./4/     
    AVERAGE RADIATION WIDTHS WERE DEDUCED TO BE 0.145 EV FOR      
    S-WAVE RESONANCES, AND 0.250 EV FOR P-WAVE RESONANCES.  TOTAL 
    SPIN J OF SOME RESONANCES WAS TENTATIVELY ESTIMATED WITH A    
    RANDOM NUMBER METHOD.  NEUTRON ORBITAL ANGULAR MOMENTUM L OF  
    SOME RESONANCES WAS ESTIMATED WITH A METHOD OF BOLLINGER AND  
    THOMAS/5/.  SCATTERING RADIUS WAS BASED ON THE SYSTEMATICS OF 
    MEASURED VALUES FOR NEIGHBORING NUCLIDES.  A NEGATIVE         
    RESONANCE WAS ADDED SO AS TO REPRODUCE THE THERMAL CAPTURE    
    CROSS SECTION GIVEN BY MUGHABGHAB ET AL./6/                   
                                                                  
  UNRESOLVED RESONANCE REGION : 1.7 KEV - 100 KEV                 
    UNRESOLVED RESONANCE PARAMETERS WERE ADOPTED FROM JENDL-2.    
    THE NEUTRON STRENGTH FUNCTIONS, S0, S1 AND S2 WERE CALCULATED 
    WITH OPTICAL MODEL CODE CASTHY/7/.  THE OBSERVED LEVEL SPACING
    WAS DETERMINED TO REPRODUCE THE CAPTURE CROSS SECTION         
    CALCULATED WITH CASTHY.  THE EFFECTIVE SCATTERING RADIUS WAS  
    OBTAINED FROM FITTING TO THE CALCULATED TOTAL CROSS SECTION AT
    100 KEV.                                                      
                                                                  
  TYPICAL VALUES OF THE PARAMETERS AT 70 KEV:                     
    S0 = 0.370E-4, S1 = 5.480E-4, S2 = 0.360E-4, SG = 5.31E-4,    
    GG = 0.200 EV, R  = 6.734 FM.                                 
                                                                  
  CALCULATED 2200-M/S CROSS SECTIONS AND RES. INTEGRALS (BARNS)   
                     2200 M/S               RES. INTEG.           
      TOTAL           7.892                    -                  
      ELASTIC         5.653                    -                  
      CAPTURE         2.239                    18.2               
                                                                  
MF = 3  NEUTRON CROSS SECTIONS                                    
  BELOW 100 KEV, RESONANCE PARAMETERS WERE GIVEN.                 
  ABOVE 100 KEV, THE SPHERICAL OPTICAL AND STATISTICAL MODEL      
  CALCULATION WAS PERFORMED WITH CASTHY, BY TAKING ACCOUNT OF     
  COMPETING REACTIONS, OF WHICH CROSS SECTIONS WERE CALCULATED    
  WITH PEGASUS/8/ STANDING ON A PREEQUILIBRIUM AND MULTI-STEP     
  EVAPORATION MODEL.  THE OMP'S FOR NEUTRON GIVEN IN TABLE 1 WERE 
  DETERMINED BY IIJIMA AND KAWAI/9/ TO REPRODUCE A SYSTEMATIC     
  TREND OF THE TOTAL CROSS SECTION.  THE OMP'S FOR CHARGED        
  PARTICLES ARE AS FOLLOWS:                                       
     PROTON   = PEREY/10/                                         
     ALPHA    = HUIZENGA AND IGO/11/                              
     DEUTERON = LOHR AND HAEBERLI/12/                             
     HELIUM-3 AND TRITON = BECCHETTI AND GREENLEES/13/            
  PARAMETERS FOR THE COMPOSITE LEVEL DENSITY FORMULA OF GILBERT   
  AND CAMERON/14/ WERE EVALUATED BY IIJIMA ET AL./15/  MORE       
  EXTENSIVE DETERMINATION AND MODIFICATION WERE MADE IN THE       
  PRESENT WORK.  TABLE 2 SHOWS THE LEVEL DENSITY PARAMETERS USED  
  IN THE PRESENT CALCULATION.  ENERGY DEPENDENCE OF SPIN CUT-OFF  
  PARAMETER IN THE ENERGY RANGE BELOW E-JOINT IS DUE TO GRUPPELAAR
  /16/.                                                           
                                                                  
  MT = 1  TOTAL                                                   
    SPHERICAL OPTICAL MODEL CALCULATION WAS ADOPTED.              
                                                                  
  MT = 2  ELASTIC SCATTERING                                      
    CALCULATED AS (TOTAL - SUM OF PARTIAL CROSS SECTIONS).        
                                                                  
  MT = 4, 51 - 91  INELASTIC SCATTERING                           
    SPHERICAL OPTICAL AND STATISTICAL MODEL CALCULATION WAS       
    ADOPTED.  THE LEVEL SCHEME WAS TAKEN FROM REF./17/            
                                                                  
           NO.      ENERGY(MEV)    SPIN-PARITY                    
           GR.       0.0            5/2 +                         
            1        0.2671         3/2 +                         
            2        0.9490         1/2 +                         
            3        1.4231         3/2 +                         
            4        1.4800         7/2 +                         
            5        1.6000         9/2 +                         
            6        1.6500         5/2 +                         
            7        1.9200         1/2 +                         
            8        2.0400        11/2 -                         
            9        2.0800         9/2 +                         
           10        2.1000         1/2 +                         
      LEVELS ABOVE 2.18 MEV WERE ASSUMED TO BE OVERLAPPING.       
                                                                  
  MT = 102  CAPTURE                                               
    SPHERICAL OPTICAL AND STATISTICAL MODEL CALCULATION WITH      
    CASTHY WAS ADOPTED.  DIRECT AND SEMI-DIRECT CAPTURE CROSS     
    SECTIONS WERE ESTIMATED ACCORDING TO THE PROCEDURE OF BENZI   
    AND REFFO/18/ AND NORMALIZED TO 1 MILLI-BARN AT 14 MEV.       
                                                                  
    THE GAMMA-RAY STRENGTH FUNCTION (5.35E-04) WAS DETERMINED FROM
    THE SYSTEMATICS OF RADIATION WIDTH (0.20 EV) AND THE AVERAGE  
    S-WAVE RESONANCE LEVEL SPACING (374 EV) CALCULATED FROM THE   
    LEVEL DENSITY PARAMETERS.                                     
                                                                  
  MT = 16  (N,2N) CROSS SECTION                                   
  MT = 17  (N,3N) CROSS SECTION                                   
  MT = 22  (N,N'A) CROSS SECTION                                  
  MT = 28  (N,N'P) CROSS SECTION                                  
  MT = 32  (N,N'D) CROSS SECTION                                  
  MT = 33  (N,N'T) CROSS SECTION                                  
  MT =103  (N,P) CROSS SECTION                                    
  MT =104  (N,D) CROSS SECTION                                    
  MT =105  (N,T) CROSS SECTION                                    
  MT =107  (N,ALPHA) CROSS SECTION                                
    THESE REACTION CROSS SECTIONS WERE CALCULATED WITH THE        
    PREEQUILIBRIUM AND MULTI-STEP EVAPORATION MODEL CODE PEGASUS. 
                                                                  
    THE KALBACH'S CONSTANT K (= 178.4) WAS ESTIMATED BY THE       
    FORMULA DERIVED FROM KIKUCHI-KAWAI'S FORMALISM/19/ AND LEVEL  
    DENSITY PARAMETERS.                                           
                                                                  
    FINALLY, THE (N,P) AND (N,ALPHA) CROSS SECTIONS WERE          
    NORMALIZED TO THE FOLLOWING VALUES AT 14.5 MEV:               
      (N,P)         12.70  MB (SYSTEMATICS OF FORREST/20/)        
      (N,ALPHA)      3.79  MB (SYSTEMATICS OF FORREST)            
                                                                  
  MT = 251  MU-BAR                                                
    CALCULATED WITH CASTHY.                                       
                                                                  
MF = 4  ANGULAR DISTRIBUTIONS OF SECONDARY NEUTRONS               
  LEGENDRE POLYNOMIAL COEFFICIENTS FOR ANGULAR DISTRIBUTIONS ARE  
  GIVEN IN THE CENTER-OF-MASS SYSTEM FOR MT=2 AND DISCRETE INELAS-
  TIC LEVELS, AND IN THE LABORATORY SYSTEM FOR MT=91.  THEY WERE  
  CALCULATED WITH CASTHY.  FOR OTHER REACTIONS, ISOTROPIC DISTRI- 
  BUTIONS IN THE LABORATORY SYSTEM WERE ASSUMED.                  
                                                                  
MF = 5  ENERGY DISTRIBUTIONS OF SECONDARY NEUTRONS                
  ENERGY DISTRIBUTIONS OF SECONDARY NEUTRONS WERE CALCULATED WITH 
  PEGASUS FOR INELASTIC SCATTERING TO OVERLAPPING LEVELS AND FOR  
  OTHER NEUTRON EMITTING REACTIONS.                               
                                                                  
TABLE 1  NEUTRON OPTICAL POTENTIAL PARAMETERS                     
                                                                  
                DEPTH (MEV)       RADIUS(FM)    DIFFUSENESS(FM)   
         ----------------------   ------------  ---------------   
        V  = 46.0-0.25E           R0 = 5.893    A0 = 0.62         
        WS = 7.0                  RS = 6.393    AS = 0.35         
        VSO= 7.0                  RSO= 5.893    ASO= 0.62         
  THE FORM OF SURFACE ABSORPTION PART IS DER. WOODS-SAXON TYPE.   
                                                                  
TABLE 2  LEVEL DENSITY PARAMETERS                                 
                                                                  
 NUCLIDE  SYST A(1/MEV)  T(MEV)    C(1/MEV)  EX(MEV)   PAIRING    
 ---------------------------------------------------------------  
 38-SR- 89     9.380E+00 8.200E-01 5.043E-01 4.642E+00 1.240E+00  
 38-SR- 90     9.940E+00 8.530E-01 3.795E-01 6.252E+00 1.960E+00  
 38-SR- 91     1.090E+01 8.100E-01 1.103E+00 5.625E+00 1.240E+00  
 38-SR- 92  *  1.288E+01 7.065E-01 2.515E-01 6.391E+00 2.360E+00  
                                                                  
 39-Y - 90     1.027E+01 6.770E-01 1.716E+00 2.209E+00 0.0        
 39-Y - 91     1.050E+01 7.140E-01 8.362E-01 3.521E+00 7.200E-01  
 39-Y - 92     1.012E+01 7.629E-01 2.480E+00 3.191E+00 0.0        
 39-Y - 93     1.150E+01 8.053E-01 1.740E+00 5.854E+00 1.120E+00  
                                                                  
 40-ZR- 91     1.036E+01 8.000E-01 7.822E-01 5.057E+00 1.200E+00  
 40-ZR- 92     1.088E+01 8.192E-01 5.122E-01 6.429E+00 1.920E+00  
 40-ZR- 93     1.298E+01 7.000E-01 1.273E+00 5.183E+00 1.200E+00  
 40-ZR- 94     1.275E+01 7.530E-01 4.411E-01 7.019E+00 2.320E+00  
 ---------------------------------------------------------------  
  SYST:  * = LDP'S WERE DETERMINED FROM SYSTEMATICS.              
                                                                  
 SPIN CUTOFF PARAMETERS WERE CALCULATED AS 0.146*SQRT(A)*A**(2/3).
 IN THE CASTHY CALCULATION, SPIN CUTOFF FACTORS AT 0 MEV WERE     
 ASSUMED TO BE 6.100 FOR ZR- 93 AND 5.524 FOR ZR- 94.             
                                                                  
REFERENCES                                                        
 1) AOKI, T. ET AL.: PROC. INT. CONF. ON NUCLEAR DATA FOR BASIC   
    AND APPLIED SCIENCE, SANTA FE., VOL. 2, P.1627 (1985).        
 2) KAWAI, M. ET AL.: PROC. INT. CONF. ON NUCLEAR DATA FOR SCIENCE
    AND TECHNOLOGY, MITO, P. 569 (1988).                          
 3) MACKLIN, R.L. ET AL.: NUCL. SCI. ENG., 92, 525 (1986).        
 4) MACKLIN, R.L. : ASTROPHYS. SPACE SCI., 115, 71 (1985).        
 5) BOLLINGER, L.M. AND THOMAS, G.E.: PHYS. REV., 171,1293(1968). 
 6) MUGHABGHAB, S.F. ET AL.: "NEUTRON CROSS SECTIONS, VOL. I,     
    PART A", ACADEMIC PRESS (1981).                               
 7) IGARASI, S.: J. NUCL. SCI. TECHNOL., 12, 67 (1975).           
 8) IIJIMA, S. ET AL.: JAERI-M 87-025, P. 337 (1987).             
 9) IIJIMA, S. AND KAWAI, M.: J. NUCL. SCI. TECHNOL., 20, 77      
    (1983).                                                       
10) PEREY, F.G: PHYS. REV. 131, 745 (1963).                       
11) HUIZENGA, J.R. AND IGO, G.: NUCL. PHYS. 29, 462 (1962).       
12) LOHR, J.M. AND HAEBERLI, W.: NUCL. PHYS. A232, 381 (1974).    
13) BECCHETTI, F.D., JR. AND GREENLEES, G.W.: POLARIZATION        
    PHENOMENA IN NUCLEAR REACTIONS ((EDS) H.H. BARSHALL AND       
    W. HAEBERLI), P. 682, THE UNIVERSITY OF WISCONSIN PRESS.      
    (1971).                                                       
14) GILBERT, A. AND CAMERON, A.G.W.: CAN. J. PHYS., 43, 1446      
    (1965).                                                       
15) IIJIMA, S., ET AL.: J. NUCL. SCI. TECHNOL. 21, 10 (1984).     
16) GRUPPELAAR, H.: ECN-13 (1977).                                
17) LEDERER, C.M., ET AL.: "TABLE OF ISOTOPES, 7TH ED.", WILEY-   
    INTERSCIENCE PUBLICATION (1978).                              
18) BENZI, V. AND REFFO, G.: CCDN-NW/10 (1969).                   
19) KIKUCHI, K. AND KAWAI, M.: "NUCLEAR MATTER AND NUCLEAR        
    REACTIONS", NORTH HOLLAND (1968).                             
20) FORREST, R.A.: AERE-R 12419 (1986).