98-Cf-250

 98-Cf-250 JAEA+      EVAL-FEB10 O.Iwamoto,T.Nakagawa,+           
                      DIST-MAY10                       20100318   
----JENDL-4.0         MATERIAL 9855                               
-----INCIDENT NEUTRON DATA                                        
------ENDF-6 FORMAT                                               
                                                                  
History                                                           
06-05 Resonance parameters were evaluated.                        
07-09 New theoretical calculation was done with CCONE code.       
      Data were compiled as JENDL/AC-2008/1/.                     
09-12 New theoretical calculation was done with CCONE code.       
10-02 Data of prompt gamma rays due to fission were given.        
10-03 Covariance data were added.                                 
                                                                  
                                                                  
MF= 1 General information                                         
  MT=452 Number of Neutrons per fission                           
    Sum of MT's = 455 and 456.                                    
                                                                  
  MT=455 Delayed neutron data                                     
    (same as JENDL-3.3)                                           
    Semi-empirical formula by Tuttle/2/.                          
                                                                  
  MT=456 Number of prompt neutrons per fission                    
    (same as JENDL-3.3)                                           
    Semi-empirical formula by Howerton/3/.                        
                                                                  
                                                                  
MF= 2 Resonance parameters                                        
  MT=151                                                          
  Resolved resonance parameters (MLBW: 1.0e-5 - 10.0 eV)          
    Measured resonance parameters were reported by Anufriev and   
    Sivukha/4/ and Danon et al./5,6/ The present parameters were  
    determined from these results. A negative resonance was       
    assumed to reproduce thermal cross sections:                  
       capture = 2019+-178 /7,8/                                  
       fission =  112+-99  /5/                                    
                                                                  
  Unresolved resonance parameters (10 eV - 100 keV)               
    Parameters (URP) were determined with ASREP code/9/ so as to  
    reproduce the cross sections in this energy region. URP are   
    used only for self-shielding calculations.                    
                                                                  
                                                                  
     Thermal cross sections and resonance integrals (at 300K)     
    -------------------------------------------------------       
                    0.0253 eV    reson. integ.(*)                 
                     (barns)       (barns)                        
    -------------------------------------------------------       
    total           2131.9                                        
    elastic            2.25                                       
    fission          112.0            133                         
    capture         2017.7          11900                         
    -------------------------------------------------------       
      (*) In the energy range from 0.5 eV to 10 MeV.              
                                                                  
                                                                  
MF= 3 Neutron cross sections                                      
  Cross sections above the resolved resonance region were         
  calculated with CCONE code/10/.                                 
                                                                  
  MT= 1 Total cross section                                       
    The cross section was calculated with CC OMP of Soukhovitskii 
    et al./11/                                                    
                                                                  
  MT=18 Fission cross section                                     
    The experimental data of Danon et al./5/ were used to         
    determine the parameters in the CCONE calculation.            
                                                                  
                                                                  
MF= 4 Angular distributions of secondary neutrons                 
  MT=2 Elastic scattering                                         
    Calculated with CCONE code/10/.                               
                                                                  
  MT=18 Fission                                                   
    Isotropic distributions in the laboratory system were assumed.
                                                                  
                                                                  
MF= 5 Energy distributions of secondary neutrons                  
  MT=18 Prompt neutrons                                           
    Calculated with CCONE code/10/.                               
                                                                  
                                                                  
MF= 6 Energy-angle distributions                                  
    Calculated with CCONE code/10/.                               
    Distributions from fission (MT=18) are not included.          
                                                                  
                                                                  
MF=12 Photon production multiplicities                            
  MT=18 Fission                                                   
    Calculated from the total energy released by the prompt       
    gamma-rays due to fission which was estimated from its        
    systematics, and the average energy of gamma-rays.            
                                                                  
                                                                  
MF=14 Photon angular distributions                                
  MT=18 Fission                                                   
    Isotoropic distributions were assumed.                        
                                                                  
                                                                  
MF=15 Continuous photon energy spectra                            
  MT=18 Fission                                                   
    Experimental data measured by Verbinski et al./12/ for        
    Pu-239 thermal fission were adopted.                          
                                                                  
                                                                  
MF=31 Covariances of average number of neutrons per fission       
  MT=452 Number of neutrons per fission                           
    Sum of covariances for MT=455 and MT=456.                     
                                                                  
  MT=455                                                          
    Error of 15% was assumed.                                     
                                                                  
  MT=456                                                          
    Covariance was obtained by fitting a linear function to the   
    data at 0.0 and 5.0 MeV with an uncertainty of 10%.           
                                                                  
                                                                  
MF=32 Covariances of resonance parameters                         
  MT=151 Resolved resonance parameterss                           
    Format of LCOMP=0 was adopted.                                
                                                                  
    Uncertainties of parameters were taken from Mughabghab /13/.  
    For the parameters without any information on uncertainty,    
    the following uncertainties were assumed:                     
       Resonance energy    0.1 %                                  
       Neutron width       10 %                                   
       Capture width       10 %                                   
       Fission width       90 %                                   
                                                                  
    They were further modified by considering experimental data   
    of the fission and capture cross sections at the thermal      
    neutron energy.                                               
                                                                  
                                                                  
MF=33 Covariances of neutron cross sections                       
  Covariances were given to all the cross sections by using       
  KALMAN code/14/ and the covariances of model parameters         
  used in the cross-section calculations.                         
                                                                  
  In the resolved resonance region, the following standard        
  deviations were added to the contributions from resonance       
  parameters:                                                     
       Elastic scattering  20 %                                   
                                                                  
                                                                  
MF=34 Covariances for Angular Distributions                       
  MT=2 Elastic scattering                                         
    Covariances were given only to P1 components.                 
                                                                  
                                                                  
MF=35 Covariances for Energy Distributions                        
  MT=18 Fission spectra                                           
    Estimated with CCONE and KALMAN codes.                        
                                                                  
                                                                  
***************************************************************** 
  Calculation with CCONE code                                     
***************************************************************** 
                                                                  
  Models and parameters used in the CCONE/10/ calculation         
  1) Coupled channel optical model                                
     Levels in the rotational band were included. Optical model   
     potential and coupled levels are shown in Table 1.           
                                                                  
  2) Two-component exciton model/15/                              
    * Global parametrization of Koning-Duijvestijn/16/            
      was used.                                                   
    * Gamma emission channel/17/ was added to simulate direct     
      and semi-direct capture reaction.                           
                                                                  
  3) Hauser-Feshbach statistical model                            
    * Moldauer width fluctuation correction/18/ was included.     
    * Neutron, gamma and fission decay channel were included.     
    * Transmission coefficients of neutrons were taken from       
      coupled channel calculation in Table 1.                     
    * The level scheme of the target is shown in Table 2.         
    * Level density formula of constant temperature and Fermi-gas 
      model were used with shell energy correction and collective 
      enhancement factor. Parameters are shown in Table 3.        
    * Fission channel:                                            
      Double humped fission barriers were assumed.                
      Fission barrier penetrabilities were calculated with        
      Hill-Wheler formula/19/. Fission barrier parameters were    
      shown in Table 4. Transition state model was used and       
      continuum levels are assumed above the saddles. The level   
      density parameters for inner and outer saddles are shown in 
      Tables 5 and 6, respectively.                               
    * Gamma-ray strength function of Kopecky et al/20/,/21/       
      was used. The prameters are shown in Table 7.               
                                                                  
                                                                  
------------------------------------------------------------------
                              Tables                              
------------------------------------------------------------------
                                                                  
Table 1. Coupled channel calculation                              
  --------------------------------------------------              
  * rigid rotor model was applied                                 
  * coupled levels = 0,1,2,3,4 (see Table 2)                      
  * optical potential parameters /11/                             
    Volume:                                                       
      V_0       = 49.97    MeV                                    
      lambda_HF = 0.01004  1/MeV                                  
      C_viso    = 15.9     MeV                                    
      A_v       = 12.04    MeV                                    
      B_v       = 81.36    MeV                                    
      E_a       = 385      MeV                                    
      r_v       = 1.2568   fm                                     
      a_v       = 0.633    fm                                     
    Surface:                                                      
      W_0       = 17.2     MeV                                    
      B_s       = 11.19    MeV                                    
      C_s       = 0.01361  1/MeV                                  
      C_wiso    = 23.5     MeV                                    
      r_s       = 1.1803   fm                                     
      a_s       = 0.601    fm                                     
    Spin-orbit:                                                   
      V_so      = 5.75     MeV                                    
      lambda_so = 0.005    1/MeV                                  
      W_so      = -3.1     MeV                                    
      B_so      = 160      MeV                                    
      r_so      = 1.1214   fm                                     
      a_so      = 0.59     fm                                     
    Coulomb:                                                      
      C_coul    = 1.3                                             
      r_c       = 1.2452   fm                                     
      a_c       = 0.545    fm                                     
    Deformation:                                                  
      beta_2    = 0.213                                           
      beta_4    = 0.066                                           
      beta_6    = 0.0015                                          
                                                                  
  * Calculated strength function                                  
    S0= 1.34e-4 S1= 3.08e-4 R'=  9.14 fm (En=1 keV)               
  --------------------------------------------------              
                                                                  
Table 2. Level Scheme of Cf-250                                   
  -------------------                                             
  No.  Ex(MeV)   J PI                                             
  -------------------                                             
   0  0.00000   0  +  *                                           
   1  0.04272   2  +  *                                           
   2  0.14189   4  +  *                                           
   3  0.29623   6  +  *                                           
   4  0.50000   8  +  *                                           
  -------------------                                             
  *) Coupled levels in CC calculation                             
                                                                  
Table 3. Level density parameters                                 
  --------------------------------------------------------        
  Nuclide      a*    Pair  Eshell       T      E0  Ematch         
            1/MeV     MeV     MeV     MeV     MeV     MeV         
  --------------------------------------------------------        
   Cf-251 19.2285  0.7574  1.2773  0.3926 -0.9361  3.0632         
   Cf-250 19.1626  1.5179  1.0208  0.3974 -0.1838  3.8400         
   Cf-249 19.0966  0.7605  0.7689  0.3773 -0.6847  2.7641         
   Cf-248 19.0305  1.5240  0.7495  0.3921 -0.0631  3.7096         
   Cf-247 18.9645  0.7635  0.5924  0.3748 -0.6176  2.6898         
  --------------------------------------------------------        
                                                                  
Table 4. Fission barrier parameters                               
  ----------------------------------------                        
  Nuclide     V_A    hw_A     V_B    hw_B                         
              MeV     MeV     MeV     MeV                         
  ----------------------------------------                        
   Cf-251   6.200   0.800   5.000   0.600                         
   Cf-250   6.200   1.040   5.400   0.600                         
   Cf-249   6.700   1.200   5.900   0.800                         
   Cf-248   6.200   1.040   5.400   0.600                         
   Cf-247   6.700   1.000   5.900   0.800                         
  ----------------------------------------                        
                                                                  
Table 5. Level density above inner saddle                         
  --------------------------------------------------------        
  Nuclide      a*    Pair  Eshell       T      E0  Ematch         
            1/MeV     MeV     MeV     MeV     MeV     MeV         
  --------------------------------------------------------        
   Cf-251 21.5360  0.8837  2.5000  0.3208 -1.5294  2.8837         
   Cf-250 21.4621  1.7709  2.5000  0.2827 -0.1068  3.2709         
   Cf-249 20.0514  0.8872  2.5000  0.3486 -1.7837  3.0872         
   Cf-248 21.3142  1.7780  2.5000  0.3226 -0.6352  3.7780         
   Cf-247 21.2402  0.8908  2.5000  0.3232 -1.5224  2.8908         
  --------------------------------------------------------        
                                                                  
Table 6. Level density above outer saddle                         
  --------------------------------------------------------        
  Nuclide      a*    Pair  Eshell       T      E0  Ematch         
            1/MeV     MeV     MeV     MeV     MeV     MeV         
  --------------------------------------------------------        
   Cf-251 21.5360  0.8837  1.0000  0.3488 -0.8268  2.8837         
   Cf-250 21.4621  1.7709  0.9600  0.3499  0.0610  3.7709         
   Cf-249 20.0514  0.8872  0.9200  0.3794 -1.0059  3.0872         
   Cf-248 21.3142  1.7780  0.8800  0.3522  0.0693  3.7780         
   Cf-247 21.2402  0.8908  0.8400  0.3533 -0.8173  2.8908         
  --------------------------------------------------------        
                                                                  
Table 7. Gamma-ray strength function for Cf-251                   
  --------------------------------------------------------        
  K0 = 1.700   E0 = 4.500 (MeV)                                   
  * E1: ER = 11.36 (MeV) EG = 2.69 (MeV) SIG = 256.28 (mb)        
        ER = 14.26 (MeV) EG = 4.16 (MeV) SIG = 512.55 (mb)        
  * M1: ER =  6.50 (MeV) EG = 4.00 (MeV) SIG =   2.02 (mb)        
  * E2: ER =  9.99 (MeV) EG = 3.10 (MeV) SIG =   7.35 (mb)        
  --------------------------------------------------------        
                                                                  
                                                                  
References                                                        
 1) O.Iwamoto et al.: J. Nucl. Sci. Technol., 46, 510 (2009).     
 2) R.J.Tuttle: INDC(NDS)-107/G+Special, p.29 (1979).             
 3) R.J.Howerton: Nucl. Sci. Eng., 62, 438 (1977).                
 4) V.A.Anufriev, V.I.Sivukha: Sov. At. Energy, 74, 69 (1993).    
 5) Y.Danon et al.: Nucl. Sci. Eng., 109, 341 (1991).             
 6) Y.Danon et al.: 1994 Gatlinburg, Vol. 1, p.245 (1994).        
 7) J.Halperin et al.: ORNL-4706, p.47 (1971).                    
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    (1978).                                                       
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11) E.Sh.Soukhovitskii et al.: Phys. Rev. C72, 024604 (2005).     
12) V.V.Verbinski et al.: Phys. Rev., C7, 1173 (1973).            
13) S.F.Mughabghab: "Atlas of Neutron Resonances," Elsevier       
   (2006).                                                        
14) T.Kawano, K.Shibata, JAERI-Data/Code 97-037 (1997) in         
    Japanese.                                                     
15) C.Kalbach: Phys. Rev. C33, 818 (1986).                        
16) A.J.Koning, M.C.Duijvestijn: Nucl. Phys. A744, 15 (2004).     
17) J.M.Akkermans, H.Gruppelaar: Phys. Lett. 157B, 95 (1985).     
18) P.A.Moldauer: Nucl. Phys. A344, 185 (1980).                   
19) D.L.Hill, J.A.Wheeler: Phys. Rev. 89, 1102 (1953).            
20) J.Kopecky, M.Uhl: Phys. Rev. C41, 1941 (1990).                
21) J.Kopecky, M.Uhl, R.E.Chrien: Phys. Rev. C47, 312 (1990).