figures \[fig:ratecompare\] and \[fig:rate12\].

As an alternative to QCT calculations, we tested J-extrapolation techniques, using the form of @depristo79 generally used by astrophysicists (see for example @lamda, section 6). We found that even if it reproduces the interference pattern, the extrapolation systematically underestimates the rates, for $J_1\ge
20$. Hence, QCT rates are more precise in the average.

  --------- ------------------ ------------------ ------------- -------------------
                                                                

   $J_{1}$   $T = 10 \rm K\;$   $T = 20 \rm K\;$   $T = 50 \rm   $T = 100 \rm K\;$
                                                      K\;$      

                                                                

                                                                

      1         2.03(-11)          1.59(-11)        1.32(-11)        1.24(-11)

      2         4.94(-11)          4.83(-11)        6.23(-11)        8.04(-11)

      3         1.20(-11)          1.04(-11)        8.23(-12)        7.43(-12)

      4         2.25(-11)          2.57(-11)        2.85(-11)        2.87(-11)

      5         7.01(-12)          6.80(-12)        5.62(-12)        4.77(-12)

      6         9.15(-12)          1.18(-11)        1.42(-11)        1.38(-11)

      7         3.14(-12)          3.40(-12)        3.46(-12)        3.26(-12)

      8         2.45(-12)          3.71(-12)        5.92(-12)        6.61(-12)

      9         1.63(-12)          1.63(-12)        1.95(-12)        2.18(-12)

     10         5.35(-13)          8.13(-13)        2.00(-12)        2.96(-12)

     11         7.81(-13)          7.01(-13)        9.42(-13)        1.36(-12)

     12         1.37(-13)          1.58(-13)        6.17(-13)        1.32(-12)

     13         2.74(-13)          2.51(-13)        4.17(-13)        8.26(-13)

     14         4.14(-14)          4.65(-14)        2.24(-13)        6.28(-13)

     15         7.63(-14)          8.26(-14)        1.76(-13)        4.85(-13)
  --------- ------------------ ------------------ ------------- -------------------

  : [$\mathrm{HC_3N}$]{}– para-[$\rm H_2$]{} s($J=0$)collisions. Quantum deexcitation rates in $\mathrm{cm^3\,s^{-1}}$, for $J_1'=0$, for successive initial $J_1$ and for various temperatures. Powers of ten are denoted in parenthesis.[]{data-label="tab:rates"}

[llcccc]{} &\
$J_{1}'$ &$J_{1}$& $T = 10 \rm K\;$ & 