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Simulation of β Transmutation by Decay Energetics

Syed Bahauddin Alam 1 ,Md. Nazmus Sakib, Md Sabbir Ahsan, Khaled Redwan, Imranul Kabir Chowdhury

Bangladesh University of Engineering and Technology (BUET), Dhaka1 baha [email protected]

Abstract —As energy sources are going to be diminished, ourfuture prognoses certainly run towards nuclear power as it isalready weighed as a safe and clean alternative energy. As,tralatitious waste disposal system is hazardous, ruminationabout nuclear waste management, treatment and processingvia adopting different physical and chemical technologies isof grave importance. Virility of nuclear waste needs to becontrolled and mitigated for safe industrial purposes andfuel consumptions. In this paper, physical explanations andsimulation of β transmutation by Decay Energetics has beengiven.

Index Terms —Q-value, Decay, Nucleon Separation Energy,Energetics, Tensor.

I. INTRODUCTION

The potential venturing of these waste [1]-[2] materialsfrom nuclear reactors and vindication initiations to a repos-itory in Nevada is of vital concern to Nevada residents.Radioactive wastes are innately unstable, exonerating energyin the form of radiation as they split up. Components of nuclear fuel cycle, which is the source of radioactive waste isshown. At Yucca Mountain in Nevada, many alternatives of nuclear waste have been contemplated with the most recentverdict for the plunging of 70,000 tons.The International

Atomic Energy Agency (IAEA) in Vienna should extendits responsibilities that now include nuclear nonproliferationand nuclear aegis to nuclear waste and it was ennobled in thesource Nuclear Waste: An International Problem and Eval-uating the Antarctic Continent as a Disposal Sight. But atpresent,it is seen that,waste disposal [3] is a great threat forenvironment. Now a days, The management of radioactivewastes is well diversied as well as complex subject, asthere are many sources of radioactivity, types of waste, andpossible ways to deal with the wastes including dispersal,storage, or burial [4]-[5]. But, at present environmentalhazards are observed by ocean disposal and disposed atMountain. Scientists Voice Concerns about Yucca Mountain

Repository. By that repository, global environment is con-taminating and scientists are thought of long-term factors,such as the inuence of climate change, the robustness of themetallic waste packages, and the impact of volcanic activityrequire detailed probing as well. So, instead of dumping ordisposal of nuclear waste into environment, the better optionis nuclear waste management and treatment so as to mitigateits radioactive virility by recycling and for further nuclearindustrialization. At present the treatment of nuclear wastesis a matter of great concern to the whole world. In this paper,

physical explanations and simulation of β transmutation byDecay Energetics has been given.

II. PHYSICAL SOLUTIONS OF NUCLEAR DECAYENERGETICS

In nuclear waste management [6], basic motive is toweaken the radoactive power of nuclear waste [7]. Thepurpose of weaken this waste power is as it can decay itsenergy as as fast as possible [8]. If it can be made weak,then its radiotoxicity will be lessen and this waste then wonteffect the environment and health. So, the motive goes tomitigate the radioactivity of nuclear waste via physical andchemical solutions as it can be made reusable and do notaffect the environment and public health.

1) Beta Decay Mechanism: Tensor Computation:

V f i = ψ∗

f V ψ i dV (1)

Integrand must have Even parity to give a non-zerointegral.

Here, V is scalar quantity and spatially-dependent termswhich are scalars i.e. independent of direction. Here is no

change in parity ψi and ψf both EVEN or both ODD i.e.same parity.Another process is, Fermi model assumed a pure Vectorinteraction. Gamow-Teller assumed a Tensor or Axial in-teraction. It takes into account the spins. Now, the Nuclearweak interaction is Vector-Axial. Its Strength is about 10− 6

of the Nuclear Strong force. In Fig. 1. Beta deacy andradioactivity has shown.

As the kinetic energy of the parent nucleus is zero,the radioactive decay energy must be disbursed among thekinetic energies of the products. So by using decay energyoperation, mitigation of the power of radiotoxic waste ispossible. The mass of decayed particle is much less than the

daughter nucleus Q. For that reason, if any radioactive wasteis done intervention by beta-decay operation, its toxicitywill be mitigated earlier. As the mass of decayed particleis much less than the daughter nucleus Q, by doing thatoperation treatment and conditioning is possible. In Fig. 2.Atomic Number vs. Q- Value has shown. In any nuclearwaste management plant, by using and varying excitednuclei produced by reactor through Q value variation as perequation above, as energy is varied so it can be processedand conditioned.

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Fig. 1. Beta deacy and radioactivity

Fig. 2. Atomic Number vs. Q- Value

A. Decay and Nucleon Separation EnergyThe decrease in the rest mass energy or increase in the

kinetic energy of the product nuclei can be dened as Qvalue of a nuclear reaction. For radioactive analysis Q valuecan be called as ’Disintegration Energy’. For α equation isas follows

Qα/c 2 = M (AZ P ) − [M (A − 4

Z − 2 D]2 − + m(42 )α] (2)

M (AZ P ) − [M (A − 4

Z − 2 D]2 − + 2 me + m(42 )α] (3)

M (AZ P ) − [M (A − 4

Z − 2 D ]2 − + M (42 He)] (4)

In Fig. 3. Refection coefcient vs separation betweenplates has shown.

In the above equations binding energies of two electronsin the He atom and in the daughter ion are several eVwhereas Q values is in the MeV range. For occurring of alpha decay,condition is,

M (AZ P ) > [M (A − 4

Z − 2 D ] + M (42 He)] (5)

The separation energy may be expressed as,

Fig. 3. Reection coefcient vs separation between plates

S n (AZ X ) = BE (A

Z X ) − BE (A − 1Z X ) (6)

The energy equivalent of the mass decrease is

S p(AZ Y ) = BE (A

Z Y ) − BE (A − 1Z − 1 X ) (7)

B. Q-Value for Radioactive Waste: β -Decay Process

By using Beta-decay process,waste treatment can be done.In Fig. 4. Refection coefcient vs separation between plateshas shown.

In general, a transition rate depends on (1) The count of directions that the changeover can occur ( density of nalstates).

(2)The intensity of the fundamental interaction inducingthe conversion i.e. the ”coupling” within the initial andterminal states.

In many processes, in the excited state one of the productnuclei is left decomposing by the emission of one or moregamma photons as the nucleus retroverts to its ground state.The mass of a nuclear atom amid its nucleus is heavier than

representing nuclear ground state nucleus by the measure[6] E ∗ /c 2 where E ∗ is the energizing energy of radioactivefactor. Q − value computing for a reactor separating aintersection nucleus, that is as equation

Q = [mn + M (AZ X ) − M (4

2 He ) − M (AZ X ∗ )]c2 (8)

M (AZ X )is the mass of an excited nucleus that is greater

than ground state atom M (AZ X ∗ )

If the decay energy Q were apportioned only amongst theDaughter atom and the beta particle, there would not be aambit of beta energies.

The decay energy of radioactive materials are obtainedfrom the above Q − value equation. Specially in equations

Qβ − /c 2 = M (AZ P ) − [M ([A

Z +1 D ]+) + mβ − + mυe ] (9)

Qβ − /c 2 M (AZ P ) − [M (A

Z +1 D ) − m e + mβ − + mυe ] (10)

For β − decay to occur spontaneously M (AZ P ) >

M (AZ +1 D ) for that reason Qβ − is positive.

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Fig. 4. Reection coefcient vs wavelength

Fig. 5. B.E vs. Mass Number for Carbon-12, Oxygen-16

For a decay to an energy level E ∗ the mass of the daughteratom is replaced by the mass of excited daughter M (A

Z +1 D ∗ )M (AZ +1 D ) + E ∗ /c 2 thus Qβ − for radioactive decay to an

excited level with energy E ∗ above zero level is as equation

Qβ − /c 2 = M (AZ P ) − M (A

Z +1 D ) − E ∗ /c 2 (11)

In Fig. 6. Reection coefcient vs separation betweenplates and in g. 7 Reection coefcient vs wavelength havebeen shown.

Fig. 6. B.E vs. Mass Number for overall variation

III. NUCLEAR B INDING E NERGY

In a reaction two or more entities X,Y come together toform a product Z.

X + Y > Z (12)

Binding energy is the energy emitted in such a reactionabbreviated by B.E.Condition:1If B.E.=(+)ve Reaction=ExothermicCondition:2If B.E.=(-)ve

Reaction=Endothermic

As in any reaction, the BE arises because of a change inthe mass of the reactants. The mass defect ∆ M is denedas the difference between the sum of initial masses arid thesum of the nal masses. In Fig. 5. B.E vs. Mass Number forCarbon-12, Oxygen-16 has shown. Alternatively, the B.E.can be viewed as the energy required to divide Z into itsconstituents. Here

∆ M =m

(Reactants ) −

m(Products ) (13)

The binding energy can then be computed as

B.E. = ∆ Mc2 (14)

that provided the masses of the reactants are known withsufcient accuracy. The formation of such a nucleus fromits constituents. The binding energy is determined from thechange of mass between the left and right-hand sides of thereactions. However, masses of nuclei are not available; onlyatomic masses are known with great accuracy. To examinethe energies involved with nuclear forces in the nucleus,

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consider the binding energy of a nucleus composed of Zprotons and N = AZ neutrons. Mass Defect in terms of atomic masses are

B.E.c2 =

ZBE 1 e

c2− M (A

Z X )+ ZM (11 H )+( A− Z )mn − B.E Ze /c 2

(15)In Fig. 6. B.E vs. Mass Number for overall radiation has

shown.However, the term involving electron binding energies can

be ignored for the two electron binding energies tend tocancel and electron binding energies are millions of timesless than the nuclear binding energy.

IV. CONCLUSIONS

As , there are effectual physical energetic solutions andprocesses in the laboratory, protection shield and wastemanagement cost is minor comparative to the transportation,disposal and burial of nuclear waste. Above all, as by

chemical and physical progression and component miningof radiotoxic element, the environmental hazard and healthrumination will be alleviated. Virility of nuclear waste needsto be controlled and mitigated for safe industrial purposesand fuel consumptions. In this paper, physical explanationsand simulation of β transmutation by Decay Energetics hasbeen given.

ACKNOWLEDGEMENTS

The authors are highly grateful to J. Kenneth Shultis and Richard E. Faw for the decay mechanism from their articlesand books.

R EFERENCES

[1] J. P. Tomain, ”Nuclear Waste Policy Act (1982)” available inhttp://www.enotes.com/major-acts-congress/nuclear-waste-policy-act.

[2] R. L. Murray, ”Radioactive Waste Storage and Disposal” Proceedingsof IEEE pp. 552-579, vol. 74, Issue 4, 1986.

[3] G. Butler, ”Nuclear Power Waste Management Issues” in Power Engineering Journal , pp. 207-212, Vol. 6, Issue 4, Aug 2002.

[4] F. Wicks, ”The nuclear waste problem and reconsideration of the oceandisposal option” in Energy Conversion Engoneering Conference , pp.801-803, 2002.

[5] M. A. Champ, H. D. Palmer. ”Overview of the comcept for oceanstorage of nuclear wastes” in Oceans02 MTS/IEEE , vol. 04, pp. 2105-2116, 2002.

[6] W. R. Wells, ”The development and management of nuclear wastetransportation research center” in Technology management: The newinternational language , p. 579, Portland, 1991,

[7] G. W. Philips, ”Applications of Compton Imaging in Nuclear Waste

Characterization and Treaty Verication” in Nuclear Science Sympo-seum, 1997, IEEE , vol. 1, pp. 362-364, 1997.

[8] l. Yi, ”The Experimental Research on the Impermeability of ReinforcedConcrete Used to the Nuclear Waste Cotainer”, in Professional Com-munication, IEEE transactions vlo. 49, pp. 325-334, 30 Nov 2006.

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