Ce-144
Ce-144 is instale isotope with the following properties:
Atomic number: 58
atomic mass: 143.91364 amu
Halflife: 283.9 days
Mean energy of decay (including energy of relaxation of excited states of Pr-144): 0.31865 MeV
Cascade decay
\( \mathrm{ ^{144}_{~58}Ce \xrightarrow [284~ d]{\beta,~ 318 keV} {^{144}_{~59}Pr} \xrightarrow [17.28~ min]{\beta,~ 2.997 MeV} {^{144}_{~60}Nd} }\) (almost stable: \(T > 10^{15} \) years)
Isotopes involved:
https://atom.kaeri.re.kr/cgi-bin/nuclide?nuc=Ce144
https://atom.kaeri.re.kr/cgi-bin/nuclide?nuc=Pr144
https://atom.kaeri.re.kr/cgi-bin/nuclide?nuc=Nd144
Heating
Here is an attempt to estimate the relaxation hear power density.
Rough estimate
The following code is suggested to estimate the relaxation heat power density (ChatGPT finds no mistake in the code below):
#include <stdio.h>
#include <math.h>
#define DB double
int main() {
DB ln2 = log(2.0);
printf("ln2 = %12.4lf\n", ln2);
DB MeV = 1.60218e-13; // Joule
printf("Mev = %12.4le [J]\n", MeV);
DB Day = 24 * 3600; // Second
printf("Day = %12.4le [Seconds in day]\n", Day);
DB Year = 365.242374 * 24 * 3600; // Second
printf("Year = %12.4le [Seconds in year]\n", Year);
DB amu = 1.660539040e-27; // kg
printf("amu = %12.4le [J]\n", amu);
DB e1 = 0.318646 * MeV;
printf("e1 = %12.4le [J]\n", e1);
DB e2 = 2.997 * MeV;
printf("e2 = %12.4le [J]\n", e2);
DB T1_days = 283.91;
printf("T1 = %12.4le Halflife1 in days\n", T1_days);
DB T1_sec = T1_days * Day;
printf("T1_sec = %12.4le Halflife1 in seconds\n", T1_sec);
DB L1 = ln2 / T1_sec; // in 1/s
printf("L1 = %12.4le [Herz]\n", L1);
DB M1 = 143.9136427 * amu;
printf("M1 = %12.4le [Kg]\n", M1);
DB W = (e1 + e2) * L1 / M1; // W/kg
printf("W = %12.4lf [W/kg]\n", W);
return 0;
}
It does:
ln2 = 0.6931 Mev = 1.6022e-13 [J] Day = 8.6400e+04 [Seconds in day] Year = 3.1557e+07 [Seconds in year] amu = 1.6605e-27 [J] e1 = 5.1053e-14 [J] e2 = 4.8017e-13 [J] T1 = 2.8391e+02 Halflife1 in days T1_sec = 2.4530e+07 Halflife1 in seconds L1 = 2.8257e-08 [Herz] M1 = 2.3897e-25 [Kg] W = 62814.4317 [W/kg]
Bug
With the same code, ChatGPT gets the estimate four orders of magnitude less.
It suggests
W = 6.2814e+01 [W/kg]
In the estimate by ChatGPT, values at all the lines except last one agree with the output above.
Editor interprets this as an error, mistake, bug in ChatGPT software and/or in the compiler(s) it uses. (perhaps, something is wrong with mixed use of the C compiler and the C++ compiler.)
ChatGPT does not agree to drill this discrepancy (it talks about oftopics ubstead).
ChatGPT neither recognizes its mistake nor wants to interpret the effect as a bug in his software.
Warning
All the estimates by ChatGPT need to be carefully revised; the derailed proof of any its statement needs to be requested.
If ChatGPT does not provide the deduction (if it talks about offtopics instead), the researcher has to make this deduction and/or find it in publications.
Antineutrino
The power of the decay above comes from the beta-decay to the the excited states.
At such a decay, of order of 2/3 of the energy is carried away with antuneutrinos.
Thus, the relaxation heat density is estimated to be in the interval 21 W/g - 26 W/g
Value 25600 W/kg is suggested by ChatGPT (in some earlier dialogue), but ChatGPT fails to present the defection, how this value appears in its deduction.
wwwndc.jaea.go.jp
The text below is copipasted in order to trace the modification(s) of the original, if any.
For the updated version, please look at the original
https://wwwndc.jaea.go.jp/cgi-bin/nuclinfo2014?58,144
58-Ce-144
Spin
Level energy(keV) Spin & Parity
----------------------------------------
ground state 0+
Mass (The Ame2012 atomic mass evaluation (II) by M.Wang, G.Audi, A.H.Wapstra, F.G.Kondev, M.MacCormick, X.Xu, and B.Pfeiffer Chinese Physics C36 p. 1603-2014, December 2012)
143.913652939 ± 0.000003354 (amu) [mass excess = -80431.769 ± 3.124 (keV) ]
Beta-decay energy (calculated as M(A,Z)-M(A,Z+1), taken from Ame2012)
318.646 ± 0.832 (keV)
Strong Gamma-rays from Decay of Ce-144 (Compiled from ENSDF as of March 2011)
[ Intensities before May 23th of 2013 were values when total intensity of the decay mode was 100(%) and a branching ratio of each decay mode was not multiplied. ]
γ-ray energy(keV) Intensity(%) Decay mode
----------------------------------------------------------
40.98 0.26 B-
80.12 1.36 B-
133.51 11.09 B-
----------------------------------------------------------
*: relative, ~ approximate, ? calculated or estimatted
>: greater than or equal to, <: less than or equal to
[ Intensities; total intensity of the nuclide is 100(%). ]
Decay data(Chart of the Nuclides 2014)
Decay mode Half-life
B- 284.91 D 5
Cross Sections (taken from JENDL-4.0)
Table of cross sections, Ce-144.
Figures of cross sections, Ce-144: type-1: type-2: type-3.
type-1: total, elastic and inelastic scattering, capture and fision cross sections
type-2: same as type-1 but cross sections are averaged in 70 energy group intervals
type-3: threshold reaction cross sections
Evaluated Data Libraries
Parent Nuclides by Reactions in JENDL-4.0
Ce-143 (Z= 58, A=143), MT=102 (n,γ)
Ce-144 (Z= 58, A=144), MT= 2 (Elastic scattering)
Ce-144 (Z= 58, A=144), MT= 4 (Inelastic scattering)
Nd-146 (Z= 60, A=146), MT=106 (n,3He)
Nd-147 (Z= 60, A=147), MT=107 (n,α)
Nd-148 (Z= 60, A=148), MT= 22 (n,nα)
Fission Yields for Fission Products in JENDL-4.0 Fission Yield Data
- Neutron-induced Fission Yields (from main actinide nuclides) - Independent Fission Yield -
Product Nuclide Energy Fission Yield Uncertainty(1σ)
-----------------------------------------------------------
Ce-144 U-235 Thermal 3.449310e-04 2.207560e-04
Ce-144 U-235 Fast 1.676440e-04 1.072920e-04
Ce-144 U-235 High 2.165780e-03 1.386110e-03
Ce-144 U-238 Fast 1.431530e-05 9.161820e-06
Ce-144 U-238 High 1.566810e-04 1.002760e-04
Ce-144 Pu-239 Thermal 1.163910e-03 7.449000e-04
Ce-144 Pu-239 Fast 1.642990e-03 1.051520e-03
Ce-144 Pu-239 High 5.061160e-03 3.239140e-03
Ce-144 Pu-241 Thermal 1.282310e-04 8.206760e-05
Ce-144 Pu-241 Fast 2.100620e-04 1.344400e-04
-----------------------------------------------------------
Thermal=0.0253eV, Fast=500keV(Fast reactor spectrum), High=14MeV
- Neutron-induced Fission Yields (from main actinide nuclides) - Cumulative Fission Yield -
Product Nuclide Energy Fission Yield Uncertainty(1σ)
-----------------------------------------------------------
Ce-144 U-235 Thermal 5.491390e-02 3.935420e-04
Ce-144 U-235 Fast 5.278540e-02 7.442290e-04
Ce-144 U-235 High 3.173400e-02 8.884940e-04
Ce-144 U-238 Fast 4.554260e-02 6.398150e-04
Ce-144 U-238 High 3.728310e-02 1.043840e-03
Ce-144 Pu-239 Thermal 3.738850e-02 2.618070e-04
Ce-144 Pu-239 Fast 3.671800e-02 3.672670e-04
Ce-144 Pu-239 High 2.682010e-02 1.072250e-03
Ce-144 Pu-241 Thermal 4.228540e-02 4.228990e-04
Ce-144 Pu-241 Fast 4.168350e-02 2.502800e-03
-----------------------------------------------------------
Thermal=0.0253eV, Fast=500keV(Fast reactor spectrum), High=14MeV
References
https://en.wikipedia.org/wiki/Isotopes_of_cerium Naturally occurring cerium (58Ce) is composed of 4 stable isotopes: 136Ce, 138Ce, 140Ce, and 142Ce, with 140Ce being the most abundant (88.48% natural abundance) and the only one theoretically stable; 136Ce, 138Ce, and 142Ce are predicted to undergo double beta decay but this process has never been observed. There are 35 radioisotopes that have been characterized, with the most stable being 144Ce, with a half-life of 284.893 days; 139Ce, with a half-life of 137.640 days and 141Ce, with a half-life of 32.501 days. All of the remaining radioactive isotopes have half-lives that are less than 4 days and the majority of these have half-lives that are less than 10 minutes. This element also has 10 meta states. // The isotopes of cerium range in atomic weight from 119 Da (119Ce) to 157 Da (157Ce).
Keywords
«Cascade decay», «Ce-144», «ChatGPT», «Contamination», «Isotope», «Nd-144», «Pr-144», «[[]]», «Nuclear contamination», «Nuclear physics», «Nuclear waste», «[[]]», «Relaxation heat», «[[]]»,