New Reaction Rates
For Big Bang Nucleosynthesis



An evaluation of the 12 reaction rates most important for understanding the synthesis of elements in the Big Bang was made and published in M.S. Smith, L.H. Kawano, and R.A. Malaney, Astrophysical Journal Supplement Series 85 (1993) 219. The uncertainties of these reaction rates were also determined as functions of temperature. These are updates of rates previously given in the Caughlan and Fowler 1988 rate compilation. The valid temperature ranges of these new reaction rates are indicated with the rate, and vary from 0.01 < T9 < 2.0 to 0.01 < T9 < 100.0. We reproduce analytic expressions for these rates below, in FORTRAN formats similar to that in the Caughlan and Fowler 1988 compilation.

Units & Notation
T9 Temperature of the reactants in units of 109 K.
T9nm Notation for (T9)(n/m), [e.g. T932 = (T9)3/2].
f(j) Rate of the jth reaction in (cm3/moles)(N-1) /s, where N is the number of particles involved in the reaction. j corresponds to the numbering in the Caughlan and Fowler Compilation, except for p(n,gamma)d - which did not appear in that collection.
u(j) Rate Uncertainty (one sigma) of the jth reaction given in percentage.

p(n,gamma)d
Valid Temperature Range: 0.01 < T9 < 100.0 

      f(1)  = 4.742e+4*(1.-.8504*t912+.4895*t9-.09623*t932
     |                     +8.471e-3*t9*t9-2.80e-4*t9*t932)

      u(1)  = 7.0

d(p,gamma)3He
Valid Temperature Range: 0.01 < T9 < 6.0 
 

      f(4)  = 2.65e+3*t9m23*ex(-3.720/t913)
     |         *(1.+.112*t913+1.99*t923+1.56*t9+.162*t943+.324*t953)

      u(4)  = 10.0

d(d,n)3He
Valid Temperature Range: 0.01 < T9 < 2.0 

      f(7)  = 3.95e+8*t9m23*ex(-4.259/t913)
     |         *(1.+.098*t913+.765*t923+.525*t9+9.61e-3*t943+.0167*t953)

      u(7)  = 10.0

d(d,p)t
Valid Temperature Range: 0.01 < T9 < 2.0 

      f(8)  = 4.17e+8*t9m23*ex(-4.258/t913)
     |         *(1.+.098*t913+.518*t923+.355*t9-.010*t943-.018*t953)

      u(8)  = 10.0

3He(n,p)t
Valid Temperature Range: 0.01 < T9 < 6.0 

      f(10)  = 7.21e+8*(1.-.508*t912+.228*t9)

      u(10)  = 10.0

t(d,n)4He
Valid Temperature Range: 0.01 < T9 < 2.0 

      f(11)  = 1.063e+11*t9m23*ex(-4.559/t913-(t9/.0754)**2)
     |         *(1.+.092*t913-.375*t923-.242*t9+33.82*t943+55.42*t953)
     |         + 8.047e+8*t9m23*ex(-0.4857/t9)

      u(11)  = 8.0

3He(d,p)4He
Valid Temperature Range: 0.01 < T9 < 2.0 

      f(15)  = 5.021e+10*t9m23*ex(-7.144/t913-(t9/.270)**2)
     |         *(1.+.058*t913+.603*t923+.245*t9+6.97*t943+7.19*t953)
     |         + 5.212e+8/t912*ex(-1.762/t9)

      u(15)  = 8.0

3He(alpha,gamma)7Be
Valid Temperature Range: 0.01 < T9 < 2.0 

      t9f=t9/(1.0+0.1071*t9)
      t9f13=t9f**(1/3)
      t9f56=t9f**(5/6)

      f(24)  = 4.817e+6*t9m23*ex(-14.964/t913)
     |         *(1.+.0325*t913-1.04e-3*t923-2.37e-4*t9
     |             -8.11e-5*t943-4.69e-5*t953)
     |         + 5.938e+6*t9f56*t9m32*ex(-12.859/t9f13)

      t9b=t9+0.783
      t9b12=t9b**(1/2)
      t9b32=t9b**(3/2)
      if(t9.le.10) then
      u(24)  = 27.0 - 15.0*t9b12 + 4.0*t9b - 0.25*t9b32 - 0.02*t9b*t9b
      else
      u(24)=9.7
      endif

t(alpha,gamma)7Li
Valid Temperature Range: 0.01 < T9 < 2.0 

      t9e=t9/(1.0+0.1378*t9)
      t9e13=t9e**(1/3)
      t9e56=t9e**(5/6)
      
      f(22)  = 3.032e+5*t9m23*ex(-8.090/t913)
     |         *(1.+.0516*t913+.0229*t923+8.28e-3*t9
     |             -3.28e-4*t943-3.01e-4*t953)
     |         + 5.109e+5*t9e56*t9m32*ex(-8.068/t9e13)


      t9c=t9+0.0419
      t9c12=t9c**(1/2)
      t9c32=t9c**(3/2)
      if(t9.le.10) then
      u(22)  = 29.0 - 5.9*t9c12 - 7.2*t9c + 4.0*t9c32 - 0.56*t9c*t9c
      else
      u(22)=8.1
      endif

7Be(n,p)7Li
Valid Temperature Range: 0.01 < T9 < 20.0 

      t9a=t9/(1.0+13.076*t9)
      t9a32=t9a**(3/2)

      f(32)  = 2.675e+9*(1.-.560*t912+.179*t9-.0283*t932
     |        + 2.214e-3*t9*t9-6.851e-5*t9*t932)
     |        + 9.391e+8*t9a32*t9m32
     |        + 4.467e+7*t9m32*ex(-0.07486/t9)

      u(32)=9.0

7Li(p,alpha)4He
Valid Temperature Range: 0.01 < T9 < 2.0 

      t9d   = t9/(1.0+0.759*t9) 
      t9d13=t9d**(1/3)
      t9d56=t9d**(5/6)

      f(34)  = 1.096e+9*t9m23*ex(-8.472/t913)
     |         - 4.830e+8*t9d56*t9m32*ex(-8.472/t9d13)
     |         + 1.06e+10*t9m32*ex(-30.442/t9)
     |         + 1.56e+5*t9m23*ex((-8.472/t913)-(t9/1.696)**2)
     |           *(1.+.049*t913-2.498*t923+.860*t9+3.518*t943+3.08*t953)
     |         + 1.55e+6*t9m32*ex(-4.478/t9)

      u(34) = 8.0

Neutron Decay (Lifetime and uncertainty in seconds) 

      tau  = 888.54

      uncer_tau=0.42

Last modified January 21, 1999.

Any questions or comments should be directed to Michael Smith at msmith@mail.phy.ornl.gov