Weak Interaction Rates

Weak Interaction Rates of sd-Shell Nuclei in Stellar Matter

by T. Oda, M. Hino, K. Muto, M. Takahara and K. Sato

Weak Interaction Rates of sd-Shell Nuclei in Stellar Matter Data by T. Oda, M. Hino, K. Muto, M. Takahara and K. Sato, Rate Tables for the Weak Processes of sd-Shell Nuclei in Stellar Matter; Atomic Data and Nuclear Data Tables, 56, 231-403 (1994).

Abstract The weak interaction rates in stellar matter are calculated for the sd-shell nuclei in the full-shell model configurations using the effective interaction of Wildenthal, taking into account the recent extensive compilations of experimental energy levels and Gamow-Teller beta decay rates. Based on camparisons between the present calculation and that of Fuller, Fowler and Newman (FFN), it is pointed out that correct treatment of nuclear structure effects is decisive in attaining reliable weak interaction rates in stellar matter. The weak rates are tabulated at the same grid points of density and temperature as those of FFN, for the ranges 10 < rho*Y_e < 10¹¹ and 0.01*10⁹ < T(K) < 30*10⁹.

The data file(1.238Mb) for A=1 and A=17-39 is available at (oda.txt ). Below is the explanation of the table, followed by a sample data set of A = 1.

Explanation of Table All weak interaction rates are tabulated in log₁₀lambda. In the table -100.00 means that the rate is smaller than 10^-100. Each pair of isobars is displayed on two pages. The first two pages of the Table list the weak interaction rates of a free nucleon in stellar mater.

Symbol Description

A Mass number

Z Proton number

N Neutron number

M Ground-state mass, with M(Z,N)-M(Z-1,N+1) given in the table in MeV

RHOYE log(rho*Y_e)(in g.cm^-3), where rho is the baryon density and Y_e is the ratio of the electron number to the baryon number

T9 Temperature in units of 10⁹ K

UF Fermi energy of eleotron and positron, including the rest mass (in MeV)

E-CAP Electron capture rate(s^-1)

E+DEC Positron decay rate(s^-1)

NEUE Neutrino energy loss rate (MeV.s^-1)

GAMRAY Gamma-ray heating rate (MeV.s^-1), tabulated separately for beta+direction (left) and beta-direction (right)

E+CAP Positron capture rate(s^-1)

E-DEC Electron decay rate(s^-1)

NEUEBAR Anti-neutrino energy loss rate (MeV.s^-1)

Symbol	Description
A	`Mass number`
Z	`Proton number`
N	`Neutron number`
M	`Ground-state mass, with M(Z,N)-M(Z-1,N+1) given in the table in MeV`
RHOYE	`log(rho*Y_e)(in g.cm^-3), where rho is the baryon density and Y_e is the ratio of the electron number to the baryon number`
T9	`Temperature in units of 10⁹ K`
UF	`Fermi energy of eleotron and positron, including the rest mass (in MeV)`
E-CAP	`Electron capture rate(s^-1)`
E+DEC	`Positron decay rate(s^-1)`
NEUE	`Neutrino energy loss rate (MeV.s^-1)`
GAMRAY	`Gamma-ray heating rate (MeV.s^-1), tabulated separately for beta+direction (left) and beta-direction (right)`
E+CAP	`Positron capture rate(s^-1)`
E-DEC	`Electron decay rate(s^-1)`
NEUEBAR	`Anti-neutrino energy loss rate (MeV.s^-1)`

Sample data set of A = 1


                                                                                                  

                                                                                                  

                           *********************   A =  1    ********************                 

                                                                                                  

                                                                                                  

                                                                                                  

                            N   1  ( Z= 0, N= 1 )   <--->  P   1  ( Z= 1, N= 0 )                  

                                                                                                  

                                                                                                  

                                    M (P   1) - M (N   1)  =   -0.782 MEV                         

                                                                                                  

                                                                                                  

                             ******* P   1 --> N   1  *******    ******* N   1 --> P   1  ********

                                                                                                  

   RHOYE     T9       UF     E-CAP    E+DEC     NEUE   GAMRAY     E+CAP    E-DEC  NEUEBAR   GAMRAY

     1.0   0.01    0.508  -100.000 -100.000 -100.000 -100.000  -100.000   -2.973   -3.291 -100.000

     1.0   0.10    0.453   -49.748 -100.000  -51.330 -100.000   -53.236   -2.973   -3.291 -100.000

     1.0   0.20    0.377   -29.587 -100.000  -30.861 -100.000   -26.546   -2.973   -3.291 -100.000

     1.0   0.40    0.205   -19.272 -100.000  -20.235 -100.000   -12.700   -2.973   -3.291 -100.000

     1.0   0.70    0.008   -14.030 -100.000  -14.735 -100.000    -6.995   -2.973   -3.291 -100.000

     1.0   1.00    0.000   -10.778 -100.000  -11.316 -100.000    -5.546   -2.973   -3.287 -100.000

     1.0   1.50    0.000    -8.003 -100.000   -8.346 -100.000    -4.326   -2.975   -3.217 -100.000

     1.0   2.00    0.000    -6.471 -100.000   -6.674 -100.000    -3.618   -2.979   -2.984 -100.000

     1.0   3.00    0.000    -4.728 -100.000   -4.733 -100.000    -2.750   -2.995   -2.305 -100.000

     1.0   5.00    0.000    -2.982 -100.000   -2.734 -100.000    -1.757   -3.038   -1.246 -100.000

     1.0  10.00    0.000    -1.048 -100.000   -0.464 -100.000    -0.429   -3.117    0.291 -100.000

     1.0  30.00    0.000     1.586 -100.000    2.682 -100.000     1.788   -3.211    2.929 -100.000

                                                                                                  

     2.0   0.01    0.510  -100.000 -100.000 -100.000 -100.000  -100.000   -2.973   -3.291 -100.000

     2.0   0.10    0.473   -48.747 -100.000  -50.328 -100.000   -54.237   -2.973   -3.291 -100.000

     2.0   0.20    0.416   -28.586 -100.000  -29.860 -100.000   -27.546   -2.973   -3.291 -100.000

     2.0   0.40    0.284   -18.272 -100.000  -19.235 -100.000   -13.700   -2.973   -3.291 -100.000

     2.0   0.70    0.065   -13.612 -100.000  -14.317 -100.000    -7.408   -2.973   -3.291 -100.000

     2.0   1.00    0.005   -10.757 -100.000  -11.294 -100.000    -5.568   -2.973   -3.287 -100.000

     2.0   1.50    0.000    -8.002 -100.000   -8.345 -100.000    -4.328   -2.975   -3.217 -100.000

     2.0   2.00    0.000    -6.471 -100.000   -6.674 -100.000    -3.618   -2.979   -2.985 -100.000

     2.0   3.00    0.000    -4.728 -100.000   -4.733 -100.000    -2.750   -2.995   -2.305 -100.000

     2.0   5.00    0.000    -2.982 -100.000   -2.734 -100.000    -1.757   -3.038   -1.246 -100.000

     2.0  10.00    0.000    -1.048 -100.000   -0.464 -100.000    -0.429   -3.117    0.291 -100.000

     2.0  30.00    0.000     1.586 -100.000    2.682 -100.000     1.788   -3.211    2.929 -100.000

                                                                                                  

     3.0   0.01    0.513  -100.000 -100.000 -100.000 -100.000  -100.000   -2.974   -3.292 -100.000

     3.0   0.10    0.493   -47.730 -100.000  -49.312 -100.000   -55.254   -2.973   -3.292 -100.000

     3.0   0.20    0.456   -27.580 -100.000  -28.855 -100.000   -28.552   -2.973   -3.292 -100.000

     3.0   0.40    0.364   -17.270 -100.000  -18.233 -100.000   -14.702   -2.973   -3.292 -100.000

     3.0   0.70    0.197   -12.662 -100.000  -13.367 -100.000    -8.357   -2.973   -3.291 -100.000

     3.0   1.00    0.046   -10.551 -100.000  -11.088 -100.000    -5.774   -2.973   -3.289 -100.000

     3.0   1.50    0.005    -7.987 -100.000   -8.330 -100.000    -4.342   -2.975   -3.219 -100.000

     3.0   2.00    0.001    -6.468 -100.000   -6.671 -100.000    -3.621   -2.979   -2.986 -100.000

     3.0   3.00    0.000    -4.728 -100.000   -4.732 -100.000    -2.750   -2.995   -2.306 -100.000

     3.0   5.00    0.000    -2.982 -100.000   -2.734 -100.000    -1.757   -3.038   -1.246 -100.000

     3.0  10.00    0.000    -1.048 -100.000   -0.464 -100.000    -0.429   -3.117    0.291 -100.000

     3.0  30.00    0.000     1.586 -100.000    2.682 -100.000     1.788   -3.211    2.929 -100.000

                                                                                                  

     4.0   0.01    0.523  -100.000 -100.000 -100.000 -100.000  -100.000   -2.976   -3.295 -100.000

     4.0   0.10    0.516   -46.570 -100.000  -48.151 -100.000   -56.414   -2.975   -3.295 -100.000

     4.0   0.20    0.498   -26.525 -100.000  -27.800 -100.000   -29.607   -2.975   -3.295 -100.000

     4.0   0.40    0.444   -16.253 -100.000  -17.215 -100.000   -15.720   -2.975   -3.294 -100.000

     4.0   0.70    0.337   -11.660 -100.000  -12.365 -100.000    -9.363   -2.975   -3.293 -100.000

     4.0   1.00    0.209    -9.729 -100.000  -10.266 -100.000    -6.596   -2.975   -3.293 -100.000

     4.0   1.50    0.047    -7.846 -100.000   -8.189 -100.000    -4.483   -2.975   -3.239 -100.000

     4.0   2.00    0.014    -6.436 -100.000   -6.639 -100.000    -3.652   -2.979   -3.002 -100.000

     4.0   3.00    0.004    -4.722 -100.000   -4.727 -100.000    -2.756   -2.995   -2.311 -100.000

     4.0   5.00    0.001    -2.981 -100.000   -2.733 -100.000    -1.758   -3.038   -1.247 -100.000

     4.0  10.00    0.000    -1.048 -100.000   -0.464 -100.000    -0.429   -3.117    0.291 -100.000

     4.0  30.00    0.000     1.586 -100.000    2.682 -100.000     1.788   -3.211    2.929 -100.000

                                                                                                  

     5.0   0.01    0.564  -100.000 -100.000 -100.000 -100.000  -100.000   -2.994   -3.325 -100.000

     5.0   0.10    0.563   -44.221 -100.000  -45.803 -100.000   -58.763   -2.994   -3.324 -100.000

     5.0   0.20    0.558   -25.023 -100.000  -26.297 -100.000   -31.110   -2.993   -3.323 -100.000

     5.0   0.40    0.537   -15.082 -100.000  -16.044 -100.000   -16.891   -2.992   -3.320 -100.000

     5.0   0.70    0.485   -10.596 -100.000  -11.301 -100.000   -10.429   -2.990   -3.315 -100.000

     5.0   1.00    0.413    -8.698 -100.000   -9.235 -100.000    -7.627   -2.988   -3.311 -100.000

     5.0   1.50    0.265    -7.112 -100.000   -7.455 -100.000    -5.215   -2.985   -3.296 -100.000

     5.0   2.00    0.128    -6.148 -100.000   -6.351 -100.000    -3.939   -2.985   -3.126 -100.000

     5.0   3.00    0.035    -4.669 -100.000   -4.673 -100.000    -2.808   -2.998   -2.358 -100.000

     5.0   5.00    0.009    -2.972 -100.000   -2.725 -100.000    -1.766   -3.039   -1.255 -100.000

     5.0  10.00    0.002    -1.047 -100.000   -0.463 -100.000    -0.430   -3.117    0.290 -100.000

     5.0  30.00    0.000     1.586 -100.000    2.682 -100.000     1.788   -3.211    2.929 -100.000

                                                                                                  

                                                                                                  

   RHOYE     T9       UF     E-CAP    E+DEC     NEUE   GAMRAY     E+CAP    E-DEC  NEUEBAR   GAMRAY

     6.0   0.01    0.726  -100.000 -100.000 -100.000 -100.000  -100.000   -3.155   -3.565 -100.000

     6.0   0.10    0.725   -36.027 -100.000  -37.609 -100.000   -66.957   -3.154   -3.563 -100.000

     6.0   0.20    0.724   -20.856 -100.000  -22.157 -100.000   -35.292   -3.152   -3.559 -100.000

     6.0   0.40    0.718   -12.808 -100.000  -13.770 -100.000   -19.165   -3.146   -3.545 -100.000

     6.0   0.70    0.700    -9.041 -100.000   -9.745 -100.000   -11.979   -3.130   -3.513 -100.000

     6.0   1.00    0.672    -7.394 -100.000   -7.931 -100.000    -8.930   -3.113   -3.482 -100.000

     6.0   1.50    0.604    -5.975 -100.000   -6.318 -100.000    -6.352   -3.085   -3.435 -100.000

     6.0   2.00    0.512    -5.181 -100.000   -5.384 -100.000    -4.903   -3.062   -3.373 -100.000

     6.0   3.00    0.299    -4.227 -100.000   -4.231 -100.000    -3.244   -3.037   -2.731 -100.000

     6.0   5.00    0.091    -2.890 -100.000   -2.642 -100.000    -1.846   -3.051   -1.335 -100.000

     6.0  10.00    0.020    -1.039 -100.000   -0.454 -100.000    -0.438   -3.120    0.281 -100.000

     6.0  30.00    0.002     1.587 -100.000    2.683 -100.000     1.788   -3.212    2.929 -100.000

                                                                                                  

     7.0   0.01    1.223   -45.935 -100.000  -48.522 -100.000  -100.000   -5.519   -6.798 -100.000

     7.0   0.10    1.222   -10.981 -100.000  -12.562 -100.000   -92.003   -5.461   -6.686 -100.000

     7.0   0.20    1.222    -8.296 -100.000   -9.570 -100.000   -47.837   -5.324   -6.442 -100.000

     7.0   0.40    1.219    -6.497 -100.000   -7.457 -100.000   -25.481   -5.006   -5.930 -100.000

     7.0   0.70    1.212    -5.372 -100.000   -6.071 -100.000   -15.663   -4.605   -5.340 -100.000

     7.0   1.00    1.200    -4.745 -100.000   -5.275 -100.000   -11.593   -4.312   -4.931 -100.000

     7.0   1.50    1.173    -4.079 -100.000   -4.414 -100.000    -8.263   -3.970   -4.476 -100.000

     7.0   2.00    1.133    -3.630 -100.000   -3.825 -100.000    -6.468   -3.742   -4.182 -100.000

     7.0   3.00    1.021    -3.023 -100.000   -3.022 -100.000    -4.455   -3.465   -3.640 -100.000

     7.0   5.00    0.698    -2.284 -100.000   -2.033 -100.000    -2.448   -3.222   -1.933 -100.000

     7.0  10.00    0.196    -0.951 -100.000   -0.366 -100.000    -0.524   -3.147    0.194 -100.000

     7.0  30.00    0.021     1.590 -100.000    2.686 -100.000     1.784   -3.213    2.926 -100.000

                                                                                                  

     8.0   0.01    2.447    -1.363 -100.000   -1.404 -100.000  -100.000 -100.000 -100.000 -100.000

     8.0   0.10    2.447    -1.363 -100.000   -1.403 -100.000  -100.000  -65.600  -67.194 -100.000

     8.0   0.20    2.446    -1.362 -100.000   -1.402 -100.000   -78.698  -35.638  -36.937 -100.000

     8.0   0.40    2.445    -1.358 -100.000   -1.395 -100.000   -40.930  -20.227  -21.241 -100.000

     8.0   0.70    2.442    -1.348 -100.000   -1.376 -100.000   -24.519  -13.315  -14.111 -100.000

     8.0   1.00    2.437    -1.333 -100.000   -1.348 -100.000   -17.823  -10.409  -11.080 -100.000

     8.0   1.50    2.424    -1.298 -100.000   -1.283 -100.000   -12.467   -8.035   -8.588 -100.000

     8.0   2.00    2.406    -1.253 -100.000   -1.201 -100.000    -9.675   -6.788   -7.274 -100.000

     8.0   3.00    2.355    -1.142 -100.000   -1.006 -100.000    -6.695   -5.477   -5.756 -100.000

     8.0   5.00    2.192    -0.889 -100.000   -0.588 -100.000    -3.950   -4.353   -3.424 -100.000

     8.0  10.00    1.493    -0.315 -100.000    0.279 -100.000    -1.167   -3.477   -0.453 -100.000

     8.0  30.00    0.209     1.621 -100.000    2.717 -100.000     1.754   -3.227    2.895 -100.000

                                                                                                  

     9.0   0.01    5.180     0.818 -100.000    1.317 -100.000  -100.000 -100.000 -100.000 -100.000

     9.0   0.10    5.180     0.818 -100.000    1.317 -100.000  -100.000 -100.000 -100.000 -100.000

     9.0   0.20    5.180     0.818 -100.000    1.317 -100.000  -100.000 -100.000 -100.000 -100.000

     9.0   0.40    5.180     0.818 -100.000    1.318 -100.000   -75.383  -54.681  -55.694 -100.000

     9.0   0.70    5.178     0.819 -100.000    1.320 -100.000   -44.219  -33.016  -33.812 -100.000

     9.0   1.00    5.176     0.821 -100.000    1.323 -100.000   -31.628  -24.214  -24.885 -100.000

     9.0   1.50    5.170     0.825 -100.000    1.330 -100.000   -21.694  -17.261  -17.815 -100.000

     9.0   2.00    5.161     0.830 -100.000    1.340 -100.000   -16.619  -13.731  -14.218 -100.000

     9.0   3.00    5.138     0.845 -100.000    1.367 -100.000   -11.370  -10.150  -10.430 -100.000

     9.0   5.00    5.062     0.890 -100.000    1.449 -100.000    -6.843   -7.225   -6.316 -100.000

     9.0  10.00    4.708     1.060 -100.000    1.746 -100.000    -2.783   -4.933   -2.071 -100.000

     9.0  30.00    1.972     1.908 -100.000    3.009 -100.000     1.464   -3.382    2.602 -100.000

                                                                                                  

    10.0   0.01   11.118     2.662 -100.000    3.570 -100.000  -100.000 -100.000 -100.000 -100.000

    10.0   0.10   11.118     2.662 -100.000    3.570 -100.000  -100.000 -100.000 -100.000 -100.000

    10.0   0.20   11.118     2.662 -100.000    3.570 -100.000  -100.000 -100.000 -100.000 -100.000

    10.0   0.40   11.118     2.662 -100.000    3.570 -100.000  -100.000 -100.000 -100.000 -100.000

    10.0   0.70   11.117     2.662 -100.000    3.570 -100.000   -86.979  -75.775  -76.571 -100.000

    10.0   1.00   11.116     2.662 -100.000    3.571 -100.000   -61.566  -54.152  -54.823 -100.000

    10.0   1.50   11.113     2.663 -100.000    3.572 -100.000   -41.663  -37.230  -37.784 -100.000

    10.0   2.00   11.109     2.664 -100.000    3.574 -100.000   -31.607  -28.719  -29.206 -100.000

    10.0   3.00   11.098     2.666 -100.000    3.578 -100.000   -21.384  -20.163  -20.444 -100.000

    10.0   5.00   11.063     2.675 -100.000    3.593 -100.000   -12.892  -13.274  -12.365 -100.000

    10.0  10.00   10.898     2.711 -100.000    3.659 -100.000    -5.903   -8.048   -5.190 -100.000

    10.0  30.00    9.163     2.992 -100.000    4.143 -100.000     0.263   -4.392    1.398 -100.000

                                                                                                  

    11.0   0.01   23.934     4.402 -100.000    5.675 -100.000  -100.000 -100.000 -100.000 -100.000

    11.0   0.10   23.934     4.402 -100.000    5.675 -100.000  -100.000 -100.000 -100.000 -100.000

    11.0   0.20   23.934     4.402 -100.000    5.675 -100.000  -100.000 -100.000 -100.000 -100.000

    11.0   0.40   23.934     4.402 -100.000    5.675 -100.000  -100.000 -100.000 -100.000 -100.000

    11.0   0.70   23.933     4.402 -100.000    5.676 -100.000  -100.000 -100.000 -100.000 -100.000

    11.0   1.00   23.933     4.402 -100.000    5.676 -100.000  -100.000 -100.000 -100.000 -100.000

    11.0   1.50   23.931     4.402 -100.000    5.676 -100.000   -84.730  -80.297  -80.851 -100.000

    11.0   2.00   23.930     4.403 -100.000    5.676 -100.000   -63.912  -61.025  -61.511 -100.000

    11.0   3.00   23.924     4.403 -100.000    5.677 -100.000   -42.930  -41.710  -41.991 -100.000

    11.0   5.00   23.908     4.405 -100.000    5.680 -100.000   -25.839  -26.221  -25.312 -100.000

    11.0  10.00   23.832     4.412 -100.000    5.693 -100.000   -12.421  -14.566  -11.708 -100.000

    11.0  30.00   23.015     4.485 -100.000    5.824 -100.000    -2.064   -6.702   -0.929 -100.000