[mesa-users] ni56 beta decay rate is function of temperature? and goes to 0 for logT < 8?
Stan Woosley
woosley at ucolick.org
Wed Oct 23 15:28:29 EDT 2013
Resending what I sent to Bill earlier today - Stan
Bill,
You have to stick in the low T value for all weak decays
where a laboratory rate is known. Fuller's rates (or Langanke's
or Ito's) are not for use at low T.
Unless the decay rate depends on ionization state, and electron capture
nuclei often do, you use the laboratory rate as a lower bound for the actual
decay. Some terrestrially unstable nuclei are stable in cosmic rays
for example. But usually at T less than about 10**6, at least the
most tightly bound atomic electrons are there and that is what matters.
You also have to keep track of any low lying states and their
effect on the weak decay rate, a prime example being 26Al.
Also a caution on using tables, especially log tables, for rates.
They often interpolate poorly. What you really must use is
a) For nuclei with charged particle channels - the S-factor
b) For weak rates, values that have the leading order Fermi integral
terms divided out.
You want a table where things don't vary much - just an overall
adjustment factor to a rate that has the leading order T and rho
dependence already built in.
Unless you do this, fits are much more accurate than tables.
Stan
On Oct 23, 2013, at 11:39 AM, Josiah Schwab <jwschwab at berkeley.edu> wrote:
> Hi Bill,
>
> I'm pretty sure that your confusion is because these weak tables are
> calculated for fully ionized Ni-56, but your intuition for Ni-decay is
> from SNe ejecta where the nickel is only lightly ionized.
>
> If I have a little free time later, I can give a more thorough answer,
> but I don't think you should worry about this (not a bug).
>
> Josiah
>
> Bill Paxton writes:
>
>> Hi,
>>
>> My turn to ask a question -- I have a model that manages to get ni56 up to regions of lower temperature compared to the usual places where it lives, i.e., where logT < 8 rather than the usual logT > 9. I was surprised to see the ni56 sticking around for a years when logT < 8.0, so I took a look at the weakreactions.tables in mesa/data/weaklib_data. You can find the table for ni56 beta decay by searching for "lbeta+ positron emission; ni56 co56". The values in the table are log10 of decay rate. The columns are temperatures in T9 = T*10^-9. Up at the high T9 end the rates are very large, while down at the low end, including my case of T9 = 0.1, they effectively go to zero.
>>
>> ni56 co56 by positron emission and electron capture; LMP
>> T9 0.01 0.10 0.20 0.40 0.70 1.00 1.50 2.00 3.00 5.00 10.00 30.00
>> lYeRho lbeta+ positron emission; ni56 co56
>> 1 -99.999 -99.999 -69.740 -35.714 -21.132 -15.299 -10.760 -8.472 -6.021 -3.557 -1.373 -0.071
>> 2 -99.999 -99.999 -69.740 -35.714 -21.132 -15.299 -10.760 -8.472 -6.021 -3.557 -1.373 -0.071
>> 3 -99.999 -99.999 -69.740 -35.714 -21.132 -15.299 -10.760 -8.472 -6.021 -3.557 -1.373 -0.071
>> 4 -99.999 -99.999 -69.740 -35.714 -21.132 -15.299 -10.760 -8.472 -6.021 -3.557 -1.373 -0.071
>> 5 -99.999 -99.999 -69.740 -35.714 -21.132 -15.299 -10.760 -8.472 -6.021 -3.557 -1.373 -0.071
>> 6 -99.999 -99.999 -69.740 -35.714 -21.132 -15.299 -10.760 -8.472 -6.020 -3.556 -1.373 -0.071
>> 7 -99.999 -99.999 -69.740 -35.714 -21.132 -15.299 -10.760 -8.472 -6.019 -3.553 -1.370 -0.071
>> 8 -99.999 -99.999 -69.740 -35.714 -21.132 -15.299 -10.760 -8.472 -6.019 -3.551 -1.358 -0.068
>> 9 -99.999 -99.999 -69.740 -35.714 -21.132 -15.299 -10.760 -8.472 -6.019 -3.551 -1.354 -0.049
>> 10 -99.999 -99.999 -69.740 -35.714 -21.132 -15.299 -10.760 -8.472 -6.019 -3.551 -1.354 -0.028
>> 11 -99.999 -99.999 -69.740 -35.714 -21.132 -15.299 -10.760 -8.472 -6.019 -3.551 -1.354 -0.027
>>
>>
>>
>> I had expected to find something more like what I find for mg20 beta decay where the rates are (almost) independent of T.
>>
>> mg20 na20 by positron emission and electron capture; OHMT
>> T9 0.01 0.10 0.20 0.40 0.70 1.00 1.50 2.00 3.00 5.00 10.00 30.00
>> lYeRho lbeta+ positron emission; mg20 na20
>> 1 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.765 0.766 0.799 1.382
>> 2 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.765 0.766 0.799 1.382
>> 3 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.765 0.766 0.799 1.382
>> 4 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.765 0.766 0.799 1.382
>> 5 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.799 1.382
>> 6 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.800 1.382
>> 7 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.768 0.802 1.382
>> 8 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.769 0.811 1.385
>> 9 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.769 0.814 1.406
>> 10 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.766 0.769 0.814 1.429
>>
>>
>> I thought this might be a bug in the preprocessor that builds the weakreactions.tables file from the separate sources. The ni56 => co56 reaction rates come from "LMP",
>> LMP: K. Langanke, G. Martínez-Pinedo / Nuclear Physics A 673 (2000) 481–508
>> so I checked that input file (mesa/weaklib/preprocessor/input_data/lmp.data). But I found the "-99.999" entries for beta decay rates there too.
>>
>> neg. daughter ni56 z=28 n=28 a=56 q= -1.6240
>> pos. daughter co56 z=27 n=29 a=56 q= 1.6240
>> +++ ni56 --> co56 +++ --- co56 --> ni56 ---
>> t9 lrho uf lbeta+ leps- lrnu lbeta- leps+ lrnubar
>> 0.01 1.0 -0.003 -99.999 -8.684 -9.066 -99.999 -99.999 -99.999
>> 0.10 1.0 -0.058 -99.999 -9.164 -9.537 -99.999 -99.999 -99.999
>> 0.20 1.0 -0.134 -69.740 -9.291 -9.652 -69.759 -74.128 -70.327
>> 0.40 1.0 -0.306 -35.714 -9.387 -9.722 -37.930 -38.276 -38.162
>> 0.70 1.0 -0.503 -21.132 -8.777 -9.063 -24.300 -23.078 -23.182
>> 1.00 1.0 -0.511 -15.299 -7.439 -7.669 -18.824 -17.809 -17.866
>>
>>
>> What's the story here? Is ni56 stable to beta decay at logT < 8? ;p Curiouser and curiouser.
>>
>> Thanks,
>> Bill
>>
>>
>>
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