90-Th-231

 90-Th-231 JAEA+      EVAL-FEB10 O.Iwamoto, T.Nakagawa, et al.    
                      DIST-MAY10                       20100303   
----JENDL-4.0         MATERIAL 9037                               
-----INCIDENT NEUTRON DATA                                        
------ENDF-6 FORMAT                                               
                                                                  
History                                                           
07-10 Theoretical calculation was performed with CCONE code.      
07-11 Data were compiled as JENDL/AC-2008/1/.                     
10-02 Data of prompt gamma rays due to fission were given.        
10-03 Covariance data were given.                                 
                                                                  
                                                                  
MF=1 General information                                          
  MT=452 Number of Neutrons per fission                           
    Sum of MT's=455 and 456.                                      
                                                                  
  MT=455 Delayed neutron data                                     
    Estimated from systematics by Tuttle/2/, Benedetti et al./3/  
    and Waldo et al./4/                                           
                                                                  
  MT=456 Number of prompt neutrons per fission                    
    Estimated from Howerton's systematics/5/.                     
                                                                  
                                                                  
MF= 2 Resonance parameters                                        
  MT=151                                                          
  No resonance parameters are given.                              
                                                                  
                                                                  
     Thermal cross sections and resonance integrals (at 300K)     
    -------------------------------------------------------       
                    0.0253 eV    reson. integ.(*)                 
                     (barns)       (barns)                        
    -------------------------------------------------------       
    total             1683.2                                      
    elastic             12.03                                     
    fission             40.01        282                          
    capture           1630.8         725                          
    -------------------------------------------------------       
      (*) In the energy range from 0.5 eV to 10 MeV.              
                                                                  
                                                                  
MF= 3 Neutron cross sections                                      
  Below 0.33 eV:                                                  
    * Elastic scattering cross section is 12.0 b calculated from  
      scattering radius of 9.779 fm/6/.                           
    * Fission cross section is in the 1/v shape.                  
      Cross section of 40 b at 0.0253 eV was assumed from         
      systematics.                                                
    * Capture cross section is in the 1/v shape.                  
      CCONE calculation was extrapolated to 1.0e-5 eV.            
      Cross section at 0.0253 eV is 1630 b.                       
                                                                  
  Above 0.33 eV:                                                  
    Cross sections calculated with CCONE code/6/ were adopted.    
                                                                  
  MT= 1 Total cross section                                       
    The cross section was calculated with CC OMP of Soukhovitskii 
    et al./7/.                                                    
                                                                  
                                                                  
MF= 4 Angular distributions of secondary neutrons                 
  MT=2  Elastic scattering                                        
    Calculated with CCONE code/6/.                                
                                                                  
  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/6/.                                
                                                                  
                                                                  
MF= 6 Energy-angle distributions                                  
    Calculated with CCONE code/6/.                                
    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./8/ for         
    U-235 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   
    at 0.0 and 5.0 MeV with an uncertainty of 5%.                 
                                                                  
                                                                  
MF=33 Covariances of neutron cross sections                       
  Covariances were given to all the cross sections by using       
  KALMAN code/9/ and the covariances of model parameters          
  used in the cross-section calculations.                         
                                                                  
  For the following cross sections, standard deviations in the    
  energy region below 0.3 eV were assumed as follows:             
                                                                  
     Total               87 %                                     
     Elastic scattering  90 %                                     
     Fission             90 %                                     
     Capture             90 %                                     
                                                                  
                                                                  
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/6/ 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/10/                              
    * Global parametrization of Koning-Duijvestijn/11/            
      was used.                                                   
    * Gamma emission channel/12/ was added to simulate direct     
      and semi-direct capture reaction.                           
                                                                  
  3) Hauser-Feshbach statistical model                            
    * Moldauer width fluctuation correction/13/ 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/14/. 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/15/,/16/       
      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 (see Table 2)                        
  * optical potential parameters /7/                              
    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= 0.87e-4 S1= 2.05e-4 R'=  9.78 fm (En=1 keV)               
  --------------------------------------------------              
                                                                  
Table 2. Level Scheme of Th-231                                   
  -------------------                                             
  No.  Ex(MeV)   J PI                                             
  -------------------                                             
   0  0.00000  5/2 +  *                                           
   1  0.04195  7/2 +  *                                           
   2  0.09613  9/2 +  *                                           
   3  0.16194 11/2 +  *                                           
   4  0.18571  5/2 -                                              
   5  0.20531  7/2 -                                              
   6  0.22140  3/2 +                                              
   7  0.23689  9/2 -                                              
   8  0.24088  5/2 +                                              
   9  0.24758  1/2 +                                              
  10  0.27218  3/2 +                                              
  11  0.27542  7/2 +                                              
  12  0.27780 11/2 -                                              
  13  0.30174  5/2 +                                              
  14  0.31708  5/2 +                                              
  15  0.32491  9/2 +                                              
  16  0.33400 13/2 -                                              
  17  0.35151  7/2 +                                              
  18  0.37758  7/2 +                                              
  19  0.38569 11/2 +                                              
  20  0.38783  7/2 -                                              
  -------------------                                             
  *) Coupled levels in CC calculation                             
                                                                  
Table 3. Level density parameters                                 
  --------------------------------------------------------        
  Nuclide      a*    Pair  Eshell       T      E0  Ematch         
            1/MeV     MeV     MeV     MeV     MeV     MeV         
  --------------------------------------------------------        
   Th-232 18.7786  1.5757  3.3953  0.3835 -0.2200  3.9949         
   Th-231 18.7090  0.7895  3.3191  0.3770 -0.9082  3.0943         
   Th-230 18.6395  1.5825  3.2401  0.4059 -0.4442  4.2813         
   Th-229 17.7702  0.7930  3.2566  0.4327 -1.4313  3.7239         
   Th-228 17.7035  1.5894  3.0590  0.3964 -0.1539  3.9563         
  --------------------------------------------------------        
                                                                  
Table 4. Fission barrier parameters                               
  ----------------------------------------                        
  Nuclide     V_A    hw_A     V_B    hw_B                         
              MeV     MeV     MeV     MeV                         
  ----------------------------------------                        
   Th-232   5.800   1.040   5.950   0.500                         
   Th-231   6.000   0.800   6.000   0.600                         
   Th-230   5.500   1.040   5.950   0.600                         
   Th-229   5.500   0.800   6.000   0.520                         
   Th-228   3.900   1.040   6.400   0.600                         
  ----------------------------------------                        
                                                                  
Table 5. Level density above inner saddle                         
  --------------------------------------------------------        
  Nuclide      a*    Pair  Eshell       T      E0  Ematch         
            1/MeV     MeV     MeV     MeV     MeV     MeV         
  --------------------------------------------------------        
   Th-232 20.1263  1.8383  2.6000  0.3319 -0.5731  3.8383         
   Th-231 19.6937  0.9211  2.6000  0.3507 -1.7165  3.1211         
   Th-230 19.9772  1.8463  2.6000  0.3332 -0.5651  3.8463         
   Th-229 19.9026  0.9251  2.6000  0.3339 -1.4862  2.9251         
   Th-228 19.8280  1.8543  2.6000  0.3346 -0.5570  3.8543         
  --------------------------------------------------------        
                                                                  
Table 6. Level density above outer saddle                         
  --------------------------------------------------------        
  Nuclide      a*    Pair  Eshell       T      E0  Ematch         
            1/MeV     MeV     MeV     MeV     MeV     MeV         
  --------------------------------------------------------        
   Th-232 20.5756  1.8383 -0.1400  0.3595  0.2690  3.6883         
   Th-231 19.6937  0.9211 -0.1800  0.3963 -0.9457  3.1211         
   Th-230 19.9772  1.8463 -0.2200  0.3786  0.1497  3.8463         
   Th-229 19.9026  0.9251 -0.2600  0.3799 -0.7708  2.9251         
   Th-228 19.8280  1.8543 -0.3000  0.3812  0.1590  3.8543         
  --------------------------------------------------------        
                                                                  
Table 7. Gamma-ray strength function for Th-232                   
  --------------------------------------------------------        
  K0 = 1.502   E0 = 4.500 (MeV)                                   
  * E1: ER = 11.03 (MeV) EG = 2.71 (MeV) SIG = 302.00 (mb)        
        ER = 13.87 (MeV) EG = 4.77 (MeV) SIG = 449.00 (mb)        
  * M1: ER =  6.67 (MeV) EG = 4.00 (MeV) SIG =   2.79 (mb)        
  * E2: ER = 10.25 (MeV) EG = 3.33 (MeV) SIG =   6.25 (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) G.Benedetti et al.: Nucl. Sci. Eng., 80, 379 (1982).          
 4) R.Waldo et al.: Phys. Rev., C23, 1113 (1981).                 
 5) R.J.Howerton: Nucl. Sci. Eng., 62, 438 (1977).                
 6) O.Iwamoto: J. Nucl. Sci. Technol., 44, 687 (2007).            
 7) E.Sh.Soukhovitskii et al.: Phys. Rev. C72, 024604 (2005).     
 8) V.V.Verbinski et al.: Phys. Rev., C7, 1173 (1973).            
 9) T.Kawano, K.Shibata, JAERI-Data/Code 97-037 (1997) in         
    Japanese.                                                     
10) C.Kalbach: Phys. Rev. C33, 818 (1986).                        
11) A.J.Koning, M.C.Duijvestijn: Nucl. Phys. A744, 15 (2004).     
12) J.M.Akkermans, H.Gruppelaar: Phys. Lett. 157B, 95 (1985).     
13) P.A.Moldauer: Nucl. Phys. A344, 185 (1980).                   
14) D.L.Hill, J.A.Wheeler: Phys. Rev. 89, 1102 (1953).            
15) J.Kopecky, M.Uhl: Phys. Rev. C41, 1941 (1990).                
16) J.Kopecky, M.Uhl, R.E.Chrien: Phys. Rev. C47, 312 (1990).