• Nuclear Engineering and Technology
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• v.54 no.1
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• pp.275-282
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• 2022

The aim of this work is to develop the fractional Bateman equations, which can model memory effects in successive isotopes transformations. Such memory effects have been previously reported in the alpha decay, which exhibits a non-Markovian behavior. Since there are radioactive decay series with consecutive alpha decays, it is convenient to include the mentioned memory effects, developing the fractional Bateman Equations, which can reproduce the standard ones when the fractional order is equal to one. The proposed fractional model preserves the mathematical shape and the symmetry of the standard equations, being the only difference the presence of the Mittag-Leffler function, instead of the exponential one. This last is a very important result, because allows the implementation of the proposed fractional model in burnup and activation codes in a straightforward way. Numerical experiments show that the proposed equations predict high decay rates for small time values, in comparison with the standard equations, which have high decay rates for large times. This work represents a novelty approach to the theory of successive transformations, and opens the possibility to study properties of the Bateman equation from a fractional approach.

• Journal of Radiation Protection and Research
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• v.39 no.4
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• pp.159-167
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• 2014

In Korea, July 2012, the law as called 'Act on Safety Control of Radioactive Rays Around Living Environment' was implemented to control the consumer product containing Naturally Occurring Radioactive Material (NORM), but, there are no appropriate database and effective dose calculation system. The aim of this study was to develop evaluation technique of the exposure dose with the use of the consumer products containing NORM and to understand the characteristics of the exposed dose according to the radiation type and energy. For the evaluate of exposure dose, the ICRP reference phantom was simulated by the MCNPX code based on Monte Carlo method, and the minimum, medium, maximum energy of alphas, betas, gammas from the representative NORM of Uranium decay series were used as the source term in the simulation. The annual effective doses were calculated by the exposure scenario of the consumer product usage time and position. Short range of the alpha and beta rays are mostly delivered the dose to the skin. On the other hand, the gamma rays mostly delivered the similar dose to all of the organs. The results of the annual effective dose with $1Bq{\cdot}g^{-1}$ radioactive stone-bed and 10% radioactive concentration were employed with the usage time of 7 hours 50 minute per day, the maximum annual effective dose of alphas, betas, gammas were calculated 0.0222, 0.0836, $0.0101mSv{\cdot}y^{-1}$, respectively.

• The Bulletin of The Korean Astronomical Society
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• v.45 no.1
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• pp.36.1-36.1
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• 2020

The progenitor of Type Ia supernovae (SNe Ia) is mainly believed to be a carbon/oxygen white dwarf (WD) with non-degenerate (single degenerate) or another WD companion (double degenerate). However, there is little observational evidence of their progenitor system. Recent studies suggest that shock-breakout cooling emission after the explosion can constrain the size of the progenitor system. To do so, we obtained a optical/Near-IR light curve of SN 2019ein, a normal but slightly sub-luminous type Ia supernova, from the very early phase using our high-cadence observation of Intensive Monitoring Survey of Nearby Galaxies (IMSNG). Assuming the expanding fireball model, the simple power-law fitting of the early part of the light curve gives power indices of 1.91 (B) and 2.09 (R) implying radioactive decay of 56Ni is the dominant energy source. By comparison with the expected light curve of the cooling emission, the early observation provides us an upper limit of the companion size of R∗≤1R⊙. This result suggests that we can exclude a large companion such as red giants, which is consistent with the previous study.