c===========================================================================
c     fitting formula for e-e bremsstrahlung gaunt factor
c
c                 n_e
c      g_e-e= ------------ theta_e J(theta_e,u)
c              n_j (Z_j)^2
c                     
c                      Sqrt(3)
c      J(theta_e,u)=------------- u^2 exp(u) I(theta_e,u)
c                   10 Sqrt(2)Pi
c     
c                 k_B T          T[K]
c     theta_e = ---------- = --------------
c                 mc^2        5.9299 x 10^9
c
c     We give an analytic fitting formula for J(theta_e,u).
c     The range of the fitting is
c
c                 -4.0 <= log theta_e <=-1.3
c                 -4.0 <= log u       <=1.0         
c     
c     Function jfit(logth,logu) returns the fitting result 
c                                            of J(log(theta_e),log(u)). 
c 
c===========================================================================

      real*8 function jfit(logth,logu)
      implicit real*8(a-z)
      real a(1:121)
c
      data a/
     $     3.15847E+00,  2.46819E-02, -2.11118E-02,  1.24009E-02,
     $     -5.41633E-03,  1.70070E-03, -3.05111E-04, -1.21721E-04,
     $     1.77611E-04, -2.05480E-05, -3.58754E-05,
     $     -2.52430E+00,  1.03924E-01, -8.53821E-02,  4.73623E-02,
     $     -1.91406E-02,  5.39773E-03, -7.26681E-04, -7.47266E-04,
     $     8.73517E-04, -6.92284E-05, -1.80305E-04,
     $     4.04877E-01,  1.98935E-01, -1.52444E-01,  7.51656E-02,
     $     -2.58034E-02,  4.13361E-03,  4.67015E-03, -2.20675E-03,
     $     -2.67582E-03,  2.95254E-05,  1.40751E-03,
     $     6.13466E-01,  2.18843E-01, -1.45660E-01,  5.07201E-02,
     $     -2.23048E-03, -1.14273E-02,  1.24789E-02, -2.74351E-03,
     $     -4.57871E-03, -1.70374E-04,  2.06757E-03,
     $     6.28867E-01,  1.20482E-01, -4.63705E-02, -2.25247E-02,
     $     5.07325E-02, -3.23280E-02, -1.16976E-02, -1.00402E-03,
     $     2.96622E-02, -5.43191E-04, -1.23098E-02,
     $     3.29441E-01, -4.82390E-02,  8.16592E-02, -8.17151E-02,
     $     5.94414E-02, -2.19399E-02, -1.13488E-02, -2.38863E-03,
     $     1.89850E-02,  2.50978E-03, -8.81767E-03,
     $     -1.71486E-01, -1.20811E-01,  9.87296E-02, -4.59297E-02,
     $     -2.11247E-02,  1.76310E-02,  6.31446E-02, -2.28987E-03,
     $     -8.84093E-02,  4.45570E-03,  3.46210E-02,
     $     -3.68685E-01, -4.46133E-04, -3.24743E-02,  5.05096E-02,
     $     -5.05387E-02,  2.23352E-02,  1.33830E-02,  7.79323E-03,
     $     -2.93629E-02, -2.80083E-03,  1.23727E-02,
     $     -7.59200E-02,  8.88749E-02, -8.82637E-02,  5.58818E-02,
     $     9.20453E-03, -4.59817E-03, -8.54735E-02,  7.98332E-03,
     $     1.02966E-01, -5.68093E-03, -4.04801E-02,
     $     1.60187E-01,  2.50320E-02, -7.52221E-03, -9.11885E-03,
     $     1.67321E-02, -8.24286E-03, -6.47349E-03, -3.80435E-03,
     $     1.38957E-02,  1.10618E-03, -5.68689E-03,
     $     8.37729E-02, -1.28900E-02,  1.99419E-02, -1.71348E-02,
     $     -3.47663E-03, -3.90032E-04,  3.72266E-02, -4.25035E-03,
     $     -4.22093E-02,  2.33625E-03,  1.66733E-02/
      
      the     = (logth+2.65)/1.35
      u       = (logu+1.50)/2.50
      
      
      jfit =(A(1)+A(2)*the+A(3)*the**2+A(4)*the**3+A(5)*the**4
     *     +A(6)*the**5+A(7)*the**6+A(8)*the**7
     *     +A(9)*the**8+A(10)*the**9+A(11)*the**10)
      
     *     +(A(12)+A(13)*the+A(14)*the**2+A(15)*the**3+A(16)*the**4
     *     +A(17)*the**5+A(18)*the**6+A(19)*the**7
     *     +A(20)*the**8+A(21)*the**9+A(22)*the**10)*u
      
     *     +(A(23)+A(24)*the+A(25)*the**2+A(26)*the**3+A(27)*the**4
     *     +A(28)*the**5+A(29)*the**6+A(30)*the**7
     *     +A(31)*the**8+A(32)*the**9+A(33)*the**10)*u**(+2)
      
     *     +(A(34)+A(35)*the+A(36)*the**2+A(37)*the**3+A(38)*the**4
     *     +A(39)*the**5+A(40)*the**6+A(41)*the**7
     *     +A(42)*the**8+A(43)*the**9+A(44)*the**10)*u**(+3)
      
     *     +(A(45)+A(46)*the+A(47)*the**2+A(48)*the**3+A(49)*the**4
     *     +A(50)*the**5+A(51)*the**6+A(52)*the**7
     *     +A(53)*the**8+A(54)*the**9+A(55)*the**10)*u**(+4)
      
     *     +(A(56)+A(57)*the+A(58)*the**2+A(59)*the**3+A(60)*the**4
     *     +A(61)*the**5+A(62)*the**6+A(63)*the**7
     *     +A(64)*the**8+A(65)*the**9+A(66)*the**10)*u**(+5)
      
     *     +(A(67)+A(68)*the+A(69)*the**2+A(70)*the**3+A(71)*the**4
     *     +A(72)*the**5+A(73)*the**6+A(74)*the**7
     *     +A(75)*the**8+A(76)*the**9+A(77)*the**10)*u**(+6)
      
     *     +(A(78)+A(79)*the+A(80)*the**2+A(81)*the**3+A(82)*the**4
     *     +A(83)*the**5+A(84)*the**6+A(85)*the**7
     *     +A(86)*the**8+A(87)*the**9+A(88)*the**10)*u**(+7)
      
     *     +(A(89)+A(90)*the+A(91)*the**2+A(92)*the**3+A(93)*the**4
     *     +A(94)*the**5+A(95)*the**6+A(96)*the**7
     *     +A(97)*the**8+A(98)*the**9+A(99)*the**10)*u**(+8)
      
     *     +(A(100)+A(101)*the+A(102)*the**2+A(103)*the**3+A(104)*the**4
     *     +A(105)*the**5+A(106)*the**6+A(107)*the**7
     *     +A(108)*the**8+A(109)*the**9+A(110)*the**10)*u**(+9)
      
     *     +(A(111)+A(112)*the+A(113)*the**2+A(114)*the**3+A(115)*the**4
     *     +A(116)*the**5+A(117)*the**6+A(118)*the**7
     *     +A(119)*the**8+A(120)*the**9+A(121)*the**10)*u**(+10)
      
      return
      end