[mesa-users] ni56 beta decay rate is function of temperature? and goes to 0 for logT < 8?
Bill Paxton
paxton at kitp.ucsb.edu
Wed Oct 23 15:10:01 EDT 2013
Stan,
Thanks for your explanation. We've got some work to do! You caution against using tables and mention better alternatives -- can use suggest how we should implement those in MESA? Would you like to share your KEPLER implementation with us? ;D
-Bill
On Oct 23, 2013, at 11:35 AM, Stan Woosley wrote:
> 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 10:37 AM, Bill Paxton <paxton at kitp.ucsb.edu> wrote:
>
>> 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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