Category Archives: WORKSHOP ON NUCLEAR REACTION DATA AND. NUCLEAR REACTORS:. PHYSICS, DESIGN AND SAFETY

Possible decommissioning strategies

Possible approaches to decommissioning a Nuclear Power Plant may be widely varied and the optimal choice is made on the bases of a number of parameters which, in most cases, are site specific or, at least, country specific. Therefore there is no single optimal approach for all facilities. Decommissioning process could be subdivided, in somewhat schematic way, into stages. There is no official definition of the different stages, each country using its own definitions which vary slightly to suit each case. We could mention, as an example, the IAEA Technical Reports Series N° 375, ‘’Safe Enclosure of Shut Down Nuclear Installations’’, 1995, which provides the following definitions:
"According to the definition of IAEA stages of decommissioning, the nuclear fuel or radioactive materials in the process systems as well as radioactive waters produced in normal operation is first removed by routine operation. Each of the three decommissioning stages of a nuclear plant can be defined by:

> the physical state of the plant and its equipment;

> the surveillance, inspections and tests necessitated by that state.

Stage 1

a) The first contamination barrier is kept as it was during operation but the mechanical opening systems are permanently blocked and sealed (valves, plugs etc.). The containment building is kept in a state appropriate to the remaining hazard. The atmosphere inside the containment building is subject to appropriate control. Access to the inside of the containment building is subject to monitoring and surveillance procedures.

b) The unit is under surveillance and the equipment necessary for monitoring radioactivity both inside the plant and in the area around it is kept in good condition and used when necessary and in accordance with national legal requirements. Inspections are carried out to check that the plant remains in good condition. If necessary, checks are carried out to see that there are no leaks in the first contamination barrier and the containment building.

Stage 2

a) The first contamination barrier is reduced to a minimum size (all parts easily dismantled are removed). The sealing of that barrier is reinforced by physical means and the biological shield is extended if necessary so that it completely surrounds the barrier. After decontamination to acceptable levels, the containment building and the nuclear ventilation systems may be modified or removed if they no longer play a role in radiological safety and, depending on the extent to which other equipment is removed decontaminated, access to the former containment building, if it is left standing, can be permitted. The non-radioactive parts of the plant (buildings or equipment) may be converted for new purposes.

b) Surveillance around the barrier can be relaxed but is desirable for periodic spot checks to be continued, as well as surveillance of the environment. External inspections of the sealed parts should be performed. Checks for leaks are no longer necessary on any remaining containment buildings.

Stage 3

All materials, equipment and part of the plant, the activity of which remains significant despite decontamination procedures are removed. In all remaining parts contamination has been reduced to acceptable levels. The plant is decommissioned (released) without restrictions. From the viewpoint of radiological protection, no further surveillance, inspection or tests are necessary.’ ’

Other terms that are widely used to describe the strategy adopted for the decommissioning are those that have been introduced in USA by the Nuclear Regulatory Commission (US NRC):

DECON (or one step dismantling):

In this strategy, all components and structures that are radioactive are cleaned or dismantled, packaged and transported to a low-level waste disposal site (if available) or stored temporarily on site. Once this task is completed, the facility can be used for another power plant or other purposes, without restrictions.

SAFSTOR (or Safe Storage):

In SAFSTOR, the nuclear plant is kept intact and placed in protective storage for a very long time (up to 60 years[10]), and afterwards it is dismantled. This method, which involves locking that part of the plant containing radioactive materials and monitoring it with an on-site security force, uses time as a decontaminating agent—that is, the radioactive atoms "decay" by emitting their extra energy to become non-radioactive or stable atoms. [11]Once radioactivity has decayed to low levels, the activity is the same as the one described above as DECON. All building structures and systems which are necessary for workers and public safety shall be maintained in service during the safe storage period. A pre-condition to reach the safe storage condition is that the fuel has been removed from the plant and that radioactive liquids have been drained from systems and components and then processed.

ENTOMBMENT:

The radioactive inventory is enclosed in a monolithic structure, e. g. concrete, to secure the public safety. The monolithic structure should ensure integrity for about 100 years to derive benefit from the decay of the nuclides. After the entombment period, all enclosed components are very low radioactive and the assumption should be that dismantling at that time can be performed in a “conventional” way. During entombment the plant remains under a nuclear license.

The 3 categories presented above are a crude schematization of various situations. The DECON strategy for example may imply a really “quick” decommissioning and dismantling, or a longer process, that might optimize the use of plant personnel and reduce costs associated with engulfing activities on site.

On the other side, the SAFSTOR option may really imply a simple “close and seal the door”, or a combination of immediate dismantling and safe store. In the latter case it may be considered the immediate dismantling of systems and buildings which are not, or only slightly, contaminated and a SAFSTOR strategy for the most radioactive portion of the plant. Also the safe storage period may range from 30 to more than 100 years, depending on a number of parameters and conditions that will be discussed later.

The third strategy (ENTOMBMENT) has never been applied yet to a NPP. There are several reasons for that. The first one is that the size of a NPP is too large to be simply entombed. A second reason is related to the fact that most power reactors will have radionuclides in concentrations exceeding the limits for unrestricted use even after 100 years and more and therefore this strategy cannot be successful. ENTOMBMENT is, however, a possible strategy for smaller reactors and for other small nuclear facilities.

Scattering of composite fragments

The RGM, however, usually deals with the much more complex case of the scattering of composite particles on each other. We will assume in the following, that the constituents interact via two-body forces, e. g. a short ranged nuclear force and the Coulomb force. An extension to three-body forces is straightforward and effects essentially only the treatment of the spin-isospin matrix elements. As alluded to in ref. [5], three body break-up channels pose a serious formal problem. Since for break-up channels the asymptotic wave function is not of the form of eq. (2.2), we have to neglect such channels. How they can be approximated is discussed in chapter 5.1.

With two-body forces alone, the Hamiltonian of an N-particle system can be split into

N 1

H(l,…,N)=’£Ti + -‘£/Vij (2-7)

i=1 i=j

where the centre of mass kinetic energy can be separated off by N 1 N

YTi = Tcm + Y (pi — pj)2 (2-8)

n=1 i<j

Here we assumed equal masses m for all the constituents, a restriction which can be removed, see ref. [7].

Due to our restriction we can decompose the translationally invariant part H’ of the Hamiltonian into the internal Hamiltonians of the two fragments, the relative motion one, and the interaction between nucleons being in different fragments

H (1,…,N) = Hi(l,…,Ni )+H2(Ni + 1,…,N)+Trei + Y, Vij

(2.9)

By adding and subtracting the point Coulomb interaction between the two fragments ZiZ2e2/Rrei the potential term becomes short ranged.

H'(1,…,N) = Hi(1,…,Ni)+H2(Ni + 1, … N) + Trel + ZZe2/Rrel + Vij — Zi Z2e2/Rrel (2.10)

ІЄ{ 1,…,N1}

^{N-l + W^N }

Here Rrel denotes the relative coordinate between the centres of mass of the two fragments. This decomposition of the Hamiltonian directs to an ansatz for the wave function in terms of an internal function of Hi and one of H2 and a relative motion function of type eq. (2.2). The total wave function is then a sum over channels formed out of the above functions properly antisymmetrised.

Nk

Фт = aY ф^ффз (2.11)

n=i

where A denotes the antisymmetriser, Nk the number of channels with chan­nel wave functions фсд described below and the relative motion wave function

«(Rrel) = $mn fm(Rrel) + amn gn(Rrel) + E bmnv Xnv (Rrel) (2.12)

V

The subscript m on фт indicates the boundary condition that only in channel m regular waves exist. The functions f and g are now regular and regularised

irregular Coulomb wavefunctions. How to use in — and outgoing waves and calculate the S-matrix directly is described in [8]. The sum n runs over physical channels, open or closed, and ’’distortion channels” without the standing wave terms. Such ’distortion channels” allow to take the distortion of the fragments in the interaction region into account, see the discussion in chapter 5.1. Sometimes they are called ’pseudo-inelastic” channels [3]. The coefficients amn and bmnv are variational parameters to be determined from

S(< ФтН’ — Ефт > ~amm) = 0 (2.13)

Подпись: Фт = Л < Подпись: dmn Fn + am Подпись: i G n + E bm Подпись: (2.14)
image016

To simplify the notation we combine the channel functions and the relative motion part into one symbol and write in the obvious notation

The Hamiltonian H’ can be diagonalised in the space spanned by all the Xnv. Let us assume this diagonalisation to be done, then we can switch to new square integrable functions rv with

< rv ЛГ^ >— dv^ and

(2.15)

< rv^^ЛТ^ >— 6v ^

(2.16)

Since H’ commutes with the antisymmetrizer Л it suffices to apply Л on one side, see also chapter 3.2.

In eq. (2.14) the eigenfunctions Г of the Hamiltonian can be used as

фт — Л e( dmn Fn + amn + E dmv Г v (2.17)

^ n V J

where now the variational parameters amn and dmv have to be determined from the set of variational equations

< GnHAFm > + E < GnHAGn’ > amn’

n’

< rvHAFm > + ‘У ] < rvHAGni > amn’

n’

Подпись:+ ^ ‘ < rvH ATv’ > dmv’ = 0

v’

image018 image019

with H = H’ — E. Since we prediagonalised the Hamiltonian only one term survives in the sum in eq. (2.19). Solving for dmv and taking eqs. (2.15, 2.16) into account we find

and inserting eq. (2.20) into eq. (2.18) yields

< Gn H Ag5 n’ > amn’ = — < <5n H AFm > (2.22)

n’

or in the obvious matrix notation

<GHG > aT = — <GHF > (2.23)

where aT denotes the transposed matrix a. This equation can easily be solved for a

a = — <GHF >T<GHG>-1 (2.24)

For known matrix elements of H, amn is known and via eq. (2.20) also dmv and hence the total wave function. Note that for a complete knowl­edge of the matrix a and the coefficients dmv the boundary condition of the total wavefunction фт has to run over all channels Nk. The expression for H (eq. (2.21)) indicates the close relationship of this approach to the quasiparticle method of Weinberg [9].

In general the reactance matrix amn in eq. (2.24) is not symmetric, therefore also the S-matrix given by the Caley transform

is not symmetric thus violating time-reversal invariance, even unitarity is not guaranteed. To enforce unitarity we have to have a symmetric reactance matrix a, which can be achieved by the so-called Kato correction [10]. In po­tential scattering the condition of stationarity leads to the same results [5]. For the scattering of composite systems, however, some integrals might di­verge, see the discussion below, so the more rigorous derivation [5] cannot be applied.

If we choose instead of eq. (2.17) another boundary condition as

Фт = A S (bmnFn + 5mnGn) + d! mvrv > (2.26)

^ n V J

then following along the lines of eqs. (2.17 — 2.24) we find

b = — <FHG >T< FHF>-1 (2.27)

again with an obviously unsymmetric matrix b. Since the boundary condi­tion should not affect observables, we should have

a = b-1 (2.28)

Therefore we can judge the quality of the calculation, by comparing the results of the two calculations. On the other hand we can follow the ideas of John [11] and insert the relation

< FHG >=< GHF >T + і 1 (2.29)

into eq. (2.28)

— < GHF >T< GHG >~l= — < FHF > GHF > + ^ l)

(2.30)

Multiplying by the transpose of the r. h.s of eq. (2.29) leads to [4]

a = —2(< FHiF > — < GHF >T < GHG >-1< GHF >) (2.31)

which is obviously symmetric. This expression has been derived as a second order correction in [2] and also in [5]. Analogously we find

Again from the comparison of the results for a and b we can judge the quality of the calculation. The most direct criterion of a ■ b being the unit matrix can easily fail near poles of a (resonances) or b without affecting physical observables. What remains to be done is the calculation of the matrix elements of H between F and G. For this purpose we need the channel wave function in eq. (2.11).

The ansatz for the internal wave functions is the most critical input. Because of the antisymmetrizer only two cases are realised in complicated systems: expansion in terms of harmonic oscillator wave functions or Gaussian func­tions and powers of r2, which can again be combined to harmonic oscillator functions. The difference of both expansions lies in the choice of parameters, a single oscillator frequency in one case, which allows to use the orthogonality of different functions, and a set of Gaussian width parameters, which allows to adjust the wave functions to different sizes of the fragments more easily. Therefore the harmonic oscillator expansion is well suited for the description of scattering of identical particles, or of the scattering of large nuclei on each other. In this case even algebraic methods can be used [12], [13]. Whereas the expansion in terms of Gaussians and powers of r2 can, in principle, be converted to harmonic oscillator functions, it becomes technically glumpy in more complicated cases, see the discussion in chapter 3. Since the sizes of light nuclei are quite different, we consider it, however, an advantage that different width parameters can be used.

Подпись: ФеН Подпись: ФІ ФІ Подпись: I J Подпись: (2.33)
image024

To clarify our ansatz we consider just one term in eq. (2.11). Here the channel function has the structure

where the square brackets indicate angular momentum coupling of the trans­lationally invariant wave functions fiJ1 of the two fragments to channel spin Se and the coupling of the orbital angular momentum l and the channel spin Se to the total angular momentum J. In case of a bound state calculation the coupling to good channel spin is usually omitted. Since all the latter examples are nuclear physics ones, I will consider in the sequel wave func­tions of light nuclei for the fragment wave functions, but we could also use the technique described below for describing electron scattering off atomic or molecular systems [14].

The individual fragment wave function consists of a spatial part and a spin
(-isospin)-part, which may contain an arbitrary number of clusters. We use the expression ’’cluster” only for groups of particles without internal orbital angular momenta, that means that in nuclear physics a cluster can, at most, contain 4 nucleons, two protons and two neutrons with opposite spin projections. In hadron physics, a typical cluster would be a baryon containing 3 quarks or a meson containing a quark-antiquark pair.

Подпись: Xh,int exp image026 Подпись: (2.34)

The spatial wave function of a cluster h consists of a single Gaussian function

with nh the number of particles inside the cluster h and the width parameter Ph. Clusters containing only one particle are described by h = 1. In hadron physics the spin-isospin function is coupled to good total spin and isospin, in nuclear physics this coupling is not necessary in most cases, because the antisymmetriser projects onto total singlet states anyhow. The cluster rel­ative functions Xlkrel contain, in addition to the Gaussian function, a solid spherical harmonic Yik of angular momentum lk

Xk, rei = exp(-7fcРІ)Yik (pk) (2.35)

Подпись: E s lj, S, a Подпись: Пс 11 Xa,h,int ,h=l Подпись: Пс —1 nYlk a,k,rel „ n=1 Подпись: nS,(T) Подпись: (2.36)

where pk denotes the Jacobi coordinate between the center-of-mass of cluster k + 1 and the center-of-mass of the clusters 1 to k, see fig. 1. The total wave function of a fragment is now a superposition of various combinations of internal and relative functions, e. g.

The spin-(-isospin) function HS,(T) is, in general, coupled to good spin (and may be coupled to good isospin). The set {lk} of orbital angular momenta between the clusters is denoted by lj, including the intermediate couplings. The sum a may run over different fragmentations, different sets of orbital angular momenta, e. g. ^-state admixtures, and different sets of width pa­rameters ph and Yk. The parameters (fah and Yak are determined from the Ritz variational principle together with the coefficients ClJs once the model space has been chosen. For this purpose one chooses the fragmentations and the set {lk} of angular momenta and the number of radial functions and asks for

Cluster 2

image033

Figure 1: Schematic illustration of the intercluster coordinates p used in eq. (2.35).

5<fiJlH'(1,…,Ni) — EAifiJl >=0 (2.37)

where Ai is the antisymmetriser of the N1 particles in fragment 1. Therefore, we assume in the following, that fiJl and fij2 are bound states in the chosen model space and fulfill the equations

HiAifii >= EiAifii > i = 1,2 (2.38)

фі can be the lowest state but also an excited one, see the example below.

We can now demonstrate that the functional of eq. (2.13) exists and that all integrals exist in a Riemannian sense. Let us consider a fragmentation into Ni particles in fragment 1 and the rest in fragment 2. Then we can write the total antisymmetriser A in the form

A = A3A1A2 ‘У ‘ signPs P3A1A2 (2.39)

P3

where P3 permutes particles across the fragment boundaries including P3 = id. Choosing the kinetic energy Ek in the channel k to be

with Ei, k from eq. (2.38), we can then decompose the operator in eq. (2.10)

as

H'(1,…,N) — E = (Hi(1,…,Ni) — ElM) + (H2(Nl + 1,…,N) — E2,k)

+ Vij — Z1Z2 e2 / Rrel

je{N1 + l,…,N }

+ Trel + ZiZ2(?/Rrel — Ek (2.41)

All the integrals necessary for evaluating eqs. (2.18 — 2.19) are now well behaved, terms containing only square integrable functions in bra or ket cannot lead to divergent integrals. Because of the exponential fall off of the bound state functions, the same is true for all terms in which channels of different fragmentations are connected. Again, due to the properties of the bound state functions, integrals containing identical fragmentations but a genuine exchange of particles between the fragments, i. e. P3 = id, are of short range. Hence, the only possibly critical terms involve channels with identical fragmentations in bra and ket of eq. (2.13) with no exchange across the fragment boundaries.

In this case the first line of eq. (2.41) contributes zero, because according to eq. (2.38) the internal functions are solutions of the internal Hamiltonian Hi to just that energy Ei, k. The potential in the second line of eq. (2.41) is by construction short ranged, hence also this integral is short ranged. The re­maining line in eq. (2.41) is the (point-Coulomb) Hamiltonian of relative mo­tion Hrel whose solutions are the well-known Coulomb wave functions [15]. If and only if the functions Fk and Gk in eq. (2.12) are eigenfunctions of Hrel to the energy Ek, the related integrals are finite, to be precise they are zero. This choice, however, implies that the threshold energies are fixed by the energies of the fragments Ei ^. Besides choosing a different potential, the only possibility to vary the threshold energies is to modify the model space for the Ritz variation.

Since we have now shown that all integrals in eq. (2.13) and therefore also in eqs. (2.18, 2.19) are short ranged, we expand the regular and regularised irregular (Coulomb) functions in terms of square integrable functions, for simplicity those chosen in eq. (2.12). Hence, we have to calculate matrix elements of the Hamiltonian, or just overlap matrix elements, between anti­symmetrized translationally invariant wavefunctions where the spatial part consists of a superposition of multi-dimensional Gaussian functions and solid
spherical harmonics. In the next chapter we will describe how to calculate a typical matrix element.

Sensitivity Studies

1.1.1. Fission products

image129 image130

Schmittroth (1976) studied the impact of the uncertainties in fission-product yields, half-lives, decay energies and the assignment of isomeric states. Thermal-neutron fission of 235U was considered in detail, and this assessment indicated that decay heat can be calculated to an accuracy of 7% or better for cooling times > 10 sec. The major sources of uncertainty at cooling times < 1000 sec arise from ill-defined decay energies and fission-product charge distributions. This work was extended further by Schmittroth and Schenter (1977) who undertook a sensitivity analysis of the calculated decay heat associated with the thermal fission of 235U and the fast fission of U and Pu. Both burst and 10 sec exposures were considered (Figs. 2 and 3).

Fig. 2. Total decay-heat uncertainties for thermal fission of 235U (Schmittroth and Schenter, 1977)

Подпись: PERCENT UNCERTAINTY
image132
image133

Fig. 3. Total decay-heat uncertainties for fast fission of 239Pu (Schmittroth and Schenter, 1977)

Schmittroth and Schenter were able to attribute the main sources of uncertainty in decay-heat summation calculations to existing uncertainties in the fission-product yields and decay energies. Uncertainties in fission-product half-lives were judged to be relatively unimportant for most cooling times in decay-heat calculations. Overall, decay energies were found to be the major source of decay-heat uncertainties, especially for short cooling times (< 100 sec). These studies underline the sensitivity of decay heat to the mean energies of decay; various efforts have been made to improve these data by measurement and theoretical modelling, as outlined in Section 5.

A similar sensitivity analysis has been made of the uncertainties in decay heat when using the nuclear data contained within the JEF-2.2 library (Storrer, 1994). The calculated decay heat is dominated by radionuclides with well-defined decay schemes for cooling times > 3 x 106 sec, while the largest contributions come from poorly-defined nuclides for cooling times < 3 x 105 sec. Finally, at cooling times less than ~10 sec, fission products based completely on theoretical data contribute approximately 25% to the resulting decay heat.

Developments of the gross theory of beta decay form the main source of decay data for poorly-defined radionuclides in the JNDC-FP and US ENDF/B-VI libraries (see Sections 5.3 and 5.5). Oyamatsu et al (1997) have undertaken extensive studies of the suitability of these data libraries in decay-heat calculations. Their sensitivity analyses were extremely detailed, and highlighted a series of specific inadequacies.

For example, Fig. 4 shows the variation in uncertainty of the total P+y decay heat as a function of cooling time, following the thermal-neutron fission of 235U:

(a) at short cooling times, the uncertainty in decay heat is dominated by uncertainties in specific independent yields and decay constants, although there is also a increasingly significant contribution from uncertainties in the decay energies up to 1000 sec cooling time;

(b) particular peaks in the uncertainty profile contain significant contributions from the uncertainties of specific parameters (see Table 4) — for example, peak 4 contains significant contributions from uncertainties in the decay energies of 93Sr and 102Tc, and peak 7 is dominated by uncertainties in the independent fission yields of 97,97mY.

These analyses are extremely informative for a wide range of fissioning nuclides, and a further example is given in Fig. 5 and Table 5, for the fast fission of 238Pu. Particular nuclear parameters appear regularly in the assessments (e. g., independent yields of 97Sr and 97mY in peak 1, decay constant for 101Zr in peaks 1 and 2, decay energies of 103Mo and 103Tc in peak 3, and cumulative yields for 102,102mNb in peak 4). The main contributors to the decay-heat uncertainties are highlighted in the tables with respect to each numbered peak, providing clear indications of the specific needs for improved fission-product data.

Nuclear Energy Agency (NEA) Data Bank

NEA On-line Services are open to registered scientific users in the seventeen member states of the NEA Data Bank. New users register via the on-line form at Web address www. nea. fr The site offers access to a wide range of databases (ENSDF, NSR, NUDAT, as well as experimental data (EXFOR), bibliographic reference to neutron induced reactions (CINDA), evaluated data files (including JEF, ENDF/B and JENDL) and the NEA Thermochemical Data Base (TDB)). All data libraries have on-line search and download facilities.

On-line services can be accessed through the Web at the following address: http://www. nea. fr/

For further information, contact: Pierre Nagel — Network & On-line-services

Telephone: +33 1 4524 1082

E-mail: nagel@nea. fr

References

Audi, G. and Wapstra, A. H. (1995) The 1995 update to the atomic mass evaluation, Nucl. Phys., A595, 409-480.

Audi, G., Bersillon, O., Blachot, J. and Wapstra, A. H. (1997) The NUBASE evaluation of nuclear and decay properties, Nucl. Phys., A624, 1-124.

Be, M. M., Duchemin, B. and Lame, J. (1996) An interactive database for decay data, Nucl. Instrum. Meth. Phys Res., A369, 523-526.

Heath, R. L. (1974) Gamma-ray spectrum catalogue, AEC Report ANC-1000-2.

Helmer, R. G., Gehrke, R. J., Davidson, J. R. and Mandler, J. W. (2000) Scientists, spectrometry and gamma-ray spectrum catalogues, 1957-2007, J. Radioanal. Nucl. Chem., 243, 109-117.

Konieczny, M., Weaver, D. R., Hale, D., Baynham, I., Tagziria, H. and Weaver, R. A. (1997) JEF-PC Version 2.0: a PC program for viewing evaluated and experimental data, pp 1063­1065 in Proc. Int. Conf. Nucl. Data for Science and Technology, Vol. 59, Editors: Reffo, G., Ventura, A. and Grandi, C., SIF, Bologna, Italy.

Los Arcos, J. M., Bailador, A., Gonzalez, A., Gonzalez, C., Gorostiza, C., Ortoz, F., Sanchez, E., Shaw, M. and Williart, A. (2000) The Spanish National Reference Database for Ionizing Radiations (BANDRRI), Appl. Radiat. Isot., 52, 335-340.

Magill, J. (1999) Nuclides 2000: an electronic Chart of the Nuclides — user’s guide, EUR 18737 EN, Office for Official Publications of the European Communities, Luxembourg, ISBN 92-828-6512-6.

Nouri, A., Nagel, P., Amah, F. Le C., Cunin, C., Patrouix, J., Rioland, O., Soppera, N. and Taton, B. (2001) JANIS: new software for nuclear data services, ND2001 Int. Conf. Nucl. Data for Science and Technology, 7-12 October 2001, Tsukuba, Japan.

APPENDIX B

B. 1 FISSION PRODUCTS AND DECAY CHAINS

B. 2 ACTINIDES AND DECAY CHAINS

Health warning: all data within this review (and particularly Appendix B) are subject to change.

—► P" decay

— ► p+ ,EC decay ->■ isomeric transition ->• P"n decay

—► P" decay

— У p+ ,EC decay —► isomeric transition

-> P"n decay

■> P" decay У P+ ,EC decay ->- isomeric transition > P’n decay

—► P’ decay

— ► p+ ,EC decay ->■ isomeric transition -> p"n decay

В.1.5 Fission products and decay chains

—► P" decay

— ► p+ ,EC decay

->■ isomeric transition

— > p’n decay

> P" decay

>- p+ ,EC decay ■> isomeric transition

> P’n decay

—————— ►- P" decay

——————— У p+,EC decay

——————— у isomeric transition

………………… > p"n decay

A

——————— ►

p" decay

————— ►

P+ ,EC decay

————— ►

isomeric transition

………………. >

P"n decay

В. 1.10 Fission products and decay chains

——————— P" decay

——————— у p+,EC decay

——————— >■ isomeric transition

………………… > P"n decay

A

——————— >• P" decay

——————— >- p+,EC decay

——————— >- isomeric transition

……………….. P’n decay

A


Xe*— ■’ Cs=^~ Be

Steal*

———— ► p" decay

———— ► p+,EC decay

———— у isomeric transition

———— > P"n decay

A

———— ► P" decay

———- >■ p+, EC decay

———— у isomeric transition

———— > P’n decay

A

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1.4s 3.63s

La— *• Cz-

(1.5s)

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The 7Li System

The 6Li(n, t) reaction is a standard neutron cross section from thermal en­ergies to I MeV [36]. In this energy range is a well developed § resonance

image115

Figure 6: Differential cross section of the reaction 3H(p, n)3He calculated for Ecm = 3.0 MeV. The data are for 4.101 MeV protons from Perry. The full line represents the R-matrix analysis, the dashed one the full calculation using the Bonn potential, the dot-dashed one the small calculation, and the dotted one the semi-realistic calculation. The open circles denote the full calculation with the 3P2 matrix element replaced by the corresponding R-matrix one, for details see [38].

around 2.40 MeV neutron energy [45]. An RGM calculation using realistic NN-forces is no more feasible. Even a calculation using a semi-realistic poten­tial form [26] poses a major task, due to the many possible fragmentations, like 4He-3H and 6Li-n for the standard reaction, but additional fragmen­tations 6Li (excited)-n, 5He-d and 5Li-(nn) [45] are necessary to reproduce the position of the § — resonance reasonably well [46, 26]. The the first task is to determine the internal wave functions of all fragments together with the excited states such that the many thresholds are reproduced reasonably well. As all effective forces share a reduced core, they tend to overbind, in case the model space is increased by using more and more width parame­ters or configurations with internal orbital angular momenta. Therefore any such calculation is a compromise between reproducing the size of the various fragments, the relative threshold energies and the total binding energy of the system, in this case the 7Li ground state § and first excited state , well below the 4He — 3H threshold. Increasing the model space too far, leads to overbinding and to tiny fragments, reducing the binding energy might yield too large fragments and then too strong interactions at low energies. Typ-

image116

Figure 7: As fig. 6, but data and R-matrix results (crosses) are compared and calcula­tions employing AV18 in the small model space (av18), adding negative parity distortion channels (av18n), for the large model space (av18-1) and adding negative parity distortion channels (av18n-1).

ical examples for the charge conjugate system 7Be are given in [47]. The potential is described in [26]. What can be achieved for the corresponding elastic scattering 6Li(n, n) is displayed in fig. 8, taken from [48].

It should be noted, however, that this effective potential overbinds neutron halo nuclei, like 6He and 8He [49].

To cure this problem a realistic NN interaction has to be used for the NN — P-wave configurations, see [49], whereas for the positive parities still the effective force [26] with the reduced core is taken. A calculation using this potential also in the 7Li-system is under way, see [50].

Modelling P» Decay

A serious lack of suitable decay data for many of the short-lived fission products has necessitated the adoption of theoretical half-lives and mean energies, based on a number of modelling methods that focus on the derivation of beta-strength functions. These models are outlined below.

(a) Gross theory: smooth beta-strength functions

The gross theory of P — decay has been used by Takahashi et al (1973) to predict beta — strength functions, and calculate the half-lives and other relevant decay parameters averaged over the final daughter states. The decay constant and average beta and gamma energies per disintegration can be expressed in terms of the sum of each partial decay to the ith final state of energy є:

a = ІA,

i=0

Ep= І A ^ )Ct

i=0 A

-Ey= єi

i=0

in which C. is the ratio of the average kinetic energy of the beta emission to the ith state to the maximum kinetic energy of the beta decay (Q — є).

The equation for A can be reformulated to include the beta-transition matrix element (Щ, &V):

n

A = ngQl M, f(E>).

2П i=0 n

where f is the integrated Fermi function, and E. is the maximum energy available for the emitted electron; П represents the transition operator, and gn is the coupling constant. A major assumption in the evolution of the gross theory is that the density of the final levels is sufficiently high to replace this summation with an integration function:

10

A = TT ЦЫ! ■ fn(g )|2 f(- Eg + l^lSg.

2K — Q n

in which |Mn(Eg)|2 is the product of the square of the transition matrix and the level density of the final states (also referred to as the beta-strength function, and sometimes denoted by the term Sp(E)). Similar manipulations can lead to gross theory expressions for the mean beta and gamma energies:

E в =-л — ГІІ gnl 2 ■ M n (Eg )| 2 Г mc 2(E -1) pE (- Eg +1 — E )2 F (E) dEdEg,

2П A — Q П 1

1 0 — E +1

Er=—r. j!|g a2. M n (Eg )| 2 mc2 (Q + Eg) J pE (- Eg +1 — E )2 F (E) dEdEg,

2П A — Q П 1

where F is the Fermi function, and p is the momentum of the electron. The beta — strength function is assumed to be smooth in this model; any structural features are deemed to be unimportant in deriving half-lives and mean energies.

The gross theory has been systematically applied to calculate P- decay half-lives, and these data compared with known experimental values (Table 8). Half-lives were predicted within a factor of 5 for 70% of 100 fission products with half-lives less than 1 min, and within a factor of 10 for 90% of the same set of fission products (Yoshida, 1977). Good agreement was also obtained for the mean beta and gamma energies, although the theory failed to predict these decay parameters for 82As and 92Rb (odd-odd nuclei).

Table 8: Mean beta-particle and gamma-ray energies for nuclides with Q > 4.5 MeV:

comparison of gross theory calculations with evaluated measurements (Yoshida, 1977)

Nuclide

Mean beta-i

^article energy (MeV)

Mean gamma-ray energy (MeV)

Half-life

(sec)

UK

evaluation

(1973)

US

evaluation

(1975)

Gross

theory

UK

evaluation

(1973)

US

evaluation

(1975)

Gross

theory

74Ga

1.072

1.070

1.350

3.043

3.040

2.471

500

76Ga

1.675

1.680

1.832

2.808

2.810

2.136

27

CO

о

>

2.468

2.523

2.584

0.554

0.606

0.347

17

82As

3.137

3.211

1.888

0.336

0.288

2.909

23

86Br

1.765

1.775

1.946

3.296

3.318

2.936

59

87Br

2.087

2.136

1.757

1.727

1.726

2.387

56

CO

CO

£

2.000

2.083

1.156

0.677

0.674

2.463

1100

90Rb

1.789

1.659

1.673

2.560

2.660

2.814

150

91Rb

1.320

1.334

1.533

2.871

2.733

2.533

59

92Rb

3.714

3.459

2.526

0.260

0.261

2.696

4.5

94y

1.193

1.717

1.039

1.043

0.986

2.417

1100

95y

1.713

1.745

0.968

0.523

0.488

2.111

650

97y

1.612

2.162

2.294

0.935

0.935

1.055

1.1

99Zr

1.586

1.621

1.651

0.794

0.794

0.719

2.4

Yoshida and Nakasima (1981) have used the gross theory to determine mean beta and gamma energies for fission products that undergo high-energy p — decay. Approximately 170 radionuclides with known half-lives and decay schemes were assessed in this manner (Q-values > 3 MeV), and the calculated mean energies were compared with available experimental data. There was a reasonable degree of overlap between theory and experiment for the mean beta energy data, but the mean gamma energies exhibited much less satisfactory agreement. This same approach was also adopted for a significant number of poorly-defined nuclides:

(i) measured half-lives, but unknown decay schemes;

(ii) unknown half-lives and decay schemes (as defined in 1980).

Nuclides in category (i) include some radionuclides that contribute significantly to decay heat at short cooling times (e. g., 89Br, 94Rb, 101Nb, 102Zr, 102Nb, 103Mo, 145Ba and 145La). Yoshida and Katakura (1986) combined a cascade gamma transition model with the gross theory of beta decay in a further attempt to improve predictions of the mean gamma energy data for short-lived fission products.

When all of the theoretical decay data were incorporated into decay-heat assessments, good agreement was observed between experiments and calculation (Figs. 15 and 16). Decay-heat measurements of Dickens et al (1980) have been compared with summation calculations in which theoretical mean energies were included. The original JNDC-FP decay-data library overestimated

Fig. 15. Beta energy emission rate after instantaneous pulse of thermal-neutron fission of 235U

Fig. 16. Photon energy emission rate after instantaneous pulse of thermal-neutron fission of

235U

the beta energy release and underestimated the gamma energy release; when the theoretical data were introduced, the decay-heat calculations reproduced the measurements extremely well.

Tachibana et al (1990) extended the gross theory by modifying the one-particle strength function and introducing the AQ0 term. When the Q-value is relatively small, the P — decay is sensitive to the forbiddenness of the transitions to the low-lying states, and the AQ0 term was used to modify the resulting strength functions of these nuclides (and others). Nakata et al (1995) have also refined the gross theory further for odd-odd nuclei, taking into account the selection rule for the beta transition to the ground state. This refined approach gives half-lives in better agreement with the experimental data than the values obtained by the unmodified gross theory (except for parents with a spin and parity of 1-). Furthermore, Nakata et al (1997) have taken the shell effects of the parent nuclei into consideration to produce the semi-gross theory of P- decay; the one-particle strength functions are dependent on the principal quantum numbers and spin-parity of the initial state of the decaying nuclide. This modification also involves raising the beta strengths to a level defined by the AQ0
term (subsequently referred to as Q0o) when the transitions to low-lying levels are highly forbidden.

Yoshida and Tachibana (2000) adopted the concept of Q00 to reproduce experimental half-lives:

0.25 Me V for even — even parent < 1.0 MeV forodd — A parent

1. 75 MeV forodd — odd parent

in which these Q00-values were subsequently multiplied by a parameter that depends on the even/odd properties of each nuclide to give the Q00-factor. The ratio between the calculated and experimental half-lives is given in Fig. 17 on a logarithmic scale; the best agreement is observed when the Q00-factor is unity. Similar analyses of the beta and gamma decay components indicate that a Q00-factor of approximately 0.4 is most appropriate for the calculation of the mean beta and gamma energies (Figs. 18 and 19).

INTERNATIONAL EFFORTS

Several countries and groups are working on innovative reactor technology development. However, to develop a cost-effective innovative reactor design a large amount of research is required, particularly for the design and testing of new fuel and other materials and the final demonstration. In the deregulated market no one company or even a country can afford to or willing to allocate the expenses necessary to bring a design to the market place. Hence international development and partnership may be required. From this perspective two efforts are already underway — the US-initiated Generation IV International Forum (GIF) and the IAEA-initiated International Project on Innovative Nuclear Reactors and Fuel Cycles (INPRO).

The time frame of interest to the GIF is two or three decades from now, and their goal is development of suitable technology for nuclear power (reliable and safe, sustainable, and economic). They also want to increase the assurance that the reactor system is a very unattractive and undesirable route for diversion or theft of weapons — usable materials. The US DOE has conducted wide-ranging discussions on the development of next-generation nuclear energy systems, engaging governments, industry and the research community of several countries. Ten countries have joined in this effort; they are Argentina, Brazil, Canada, France, Japan, Republic of Korea, South Africa, Switzerland, UK and the US. After long deliberations, the GIF has selected six areas for further research and collaboration among interested countries. These are gas-cooled fast reactor, molten salt reactor, liquid sodium metal-cooled reactor, lead alloy-cooled reactor, supercritical water-cooled reactor and very high temperature reactor systems.

The objective of INPRO is to support the safe, sustainable, economic and proliferation-resistant use of nuclear technology to meet the global energy needs of the 21st century. INPRO is mainly focusing on developing user’s requirements for nuclear power for the long term — fifty years time frame. As of January 2002, there were 13 members in INPRO: Argentina, Brazil, Canada, China, Germany, India, Republic of Korea, Russian Federation, Spain, Switzerland, The Netherlands, Turkey and the European Commission. The INPRO is developing a report to identify global user requirements for economics, safety, spent fuel and waste, non-proliferation and the environment, and establishing the criteria and methodologies for examination of nuclear reactor and fuel cycle technologies. The INPRO developed criteria are expected to be used by individual countries to assess their situation with respect to nuclear power introduction or expansion.

Conclusion

The global energy market is rapidly increasing and is expected to triple in about 50 years. Nuclear energy is free from greenhouse gas emissions and is excellent from an environmental perspective. In a closed cycle mode of operation, nuclear energy is almost an infinite source of energy; it could help improve the standard of living of all countries in the world. So nuclear power should expand, especially in developing countries, and could contribute to sustainable energy development for the world. With this in mind, many evolutionary designs of nuclear power plants have been developed to meet the high performance and the safety goals. The efficiency and economics of these new plants are excellent and are beginning to compete with other base load alternatives. These larger plants are currently being constructed in Japan, Republic of Korea and Taiwan, China. New small and medium sized designs are underway. They are of interest to many countries for many reasons. Due to population growth and demand for a higher standard of living, they are of primary importance to countries with a shortage of electric power and low grid capacity. Work is progressing on several innovative reactor and fuel cycle designs in several countries. However, these innovative, smaller reactor designs must be demonstrated in the near future because the time frame for the availability of commercial SMRs is very important as most developing countries can not wait for another two or three decades to increase their installed electricity generation capacities.

Many challenges remain for nuclear power to become an acceptable source of energy throughout the world. Notable among these are (1) implementing the disposal of high level waste, (2) making nuclear generated power economically competitive with fossil fuel alternatives in the deregulated market place, (3) continuing to assure non-proliferation and physical safety of nuclear plants, (4) developing economic reactors for small electricity grids and non-electric applications, and finally (5) continuing to assure the safety of nuclear reactors. The new evolutionary and innovative designs are responding to these challenges. Let us hope that the new surge of interest in nuclear power and the new activities that have been initiated in several countries will lead to a solution of the nuclear issues and provide adequate energy for all humanity.

Segment 7: FISSION

Fission is a new RIPL-2 segment, which retains the RIPL-1 recommendation and, in addition, includes global prescription for barriers and nuclear level densities at saddle points.

Fission barrier parameters for the trans-thorium nuclei were recommended by Maslov [5] and for the preactinides by Smirenkin [20]. The fission bar­rier parameters are strongly correlated with the corresponding level density description and the symmetry of the fission barriers should always be taken into account for the consistent description of the fission cross sections. For nuclei with Zj80 the liquid drop barriers described by Sierk’s code [21] are recommended with the addition of the ground-state shell corrections esti­mated by the Moeller-Nix (Segment 1) or the Mayer-Swiatecki (Segment 5) mass formulae. Sierk’s code provides fits to the fission barriers calculated using Yukawa-plus-exponential double folded nuclear energy, exact Coulomb diffuseness corrections, and diffuse-matter moments of inertia.

Another option is to predict the fission barriers and saddle point deforma­tions obtained within the Extended Thomas-Fermi plus Strutinsky Integral (ETFSI) method of Goriely. The ETFSI approach is a semi-classical ap­proximation to the Hartree-Fock method in which the shell corrections are calculated with the ’integral’ version of the Strutinsky theorem. BCS cor­rections are added with a delta-pairing force. Fission barriers are derived in terms of the SkSC4 Skyrme force on which the ETFSI-1 mass formula is based. Experimental primary barriers can be reproduced within plus or mi­nus 1.5 MeV (except for elements with Z < 87 which have barriers above 10

MeV). The present ETFSI compilation includes 2301 nuclei with 78<Z<120. Their masses range from slightly neutron deficient to very neutron rich nuclei (close to the calculated neutron drip line) up to A = 318. For each nucleus a maximum of two barriers are given (”inner” and ”outer”). In addition to these calculated barriers, the deformation parameters at the corresponding saddle points are also included. The nuclear shapes are limited to axially symmetrical deformations.

The ETFSI fission barriers are complemented with nuclear level densities (NLD) at the fission saddle points [22] for some 2300 nuclei with 78<Z<120. At each saddle point, the NLD is estimated within the statistical partition function approach. The NLD calculation is based on the realistic microscopic single-particle level scheme [11] determined by means of the HF-BCS mass model obtained with the MSk7 Skyrme force. For each saddle point, the single-particle level scheme is calculated consistently by the HF-BCS model constrained on the corresponding quadrupole, octupole and hexadecapole moments. The same pairing strength (within the constant-G approxima­tion) is used as for the NLD calculation at the ground-state equilibrium deformation (segment 5). No damping of the collective effects at increas­ing excitation energies is considered. The NLD for nuclei with left-right asymmetric fission barriers is increased by a factor of 2.

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APPENDIX A

NUCLEAR DATA: COMPUTERISED INFORMATION SYSTEMS

1. INTERNATIONAL INFORMATION SYSTEMS

1.1 Network of Nuclear Data Centres

The Nuclear Data Centres Network is a world-wide co-operation of nuclear data centres established under the auspices of the International Atomic Energy Agency (IAEA) to co-ordinate the collection, compilation and dissemination of nuclear data at an international level. Nearly all nuclear data required for energy, non-energy nuclear applications and basic science are covered, including nuclear cross sections, fission yields and decay data. The Network consists of four ‘core’ Nuclear Data Centres, and a group of regional, national and/or specialised data centres (second group compiles data from a restricted geographical region and/or for special data types (e. g., nuclear structure data, charged particle or photon induced reactions)). Essential links have been forged through the Network to establish communications between the producers and users of nuclear data. A brief summary is given below of the various communication links for nuclear data users, with listings of standard and Internet addresses.

1.1.1 Data centres

The four main data centres compile and exchange data in the CINDA and EXFOR systems, and maintain and exchange evaluated data files for nuclear reaction, structure and decay data. Evaluated data files include general purpose files as well as specialised data files (e. g., for fission products, activation, thermonuclear fusion, and dosimetry). These data centres compile and disseminate data to customers over a defined geographical area:

National Nuclear Data Centre: United States of America, and Canada;

Nuclear Energy Agency Data Bank: OECD countries in Western Europe and Japan;

Russian Nuclear Data Centre: former Soviet countries in Europe and Asia; IAEA Nuclear Data Section: all remaining countries in Eastern Europe, South and Central America, Asia, Africa and Australasia.

The reader can contact the responsible data centre (in their relevant geographical area) for further information, or retrieve data directly via the Internet using one of the addresses given below:

Centre name:

National Nuclear Data Centre

Nuclear Energy Agency Data Bank

Contact:

Address:

P. Oblozinsky Bldg. 197D Brookhaven National Laboratory PO Box 5000 Upton, NY 11973-5000 USA

C. Nordborg Le Seine St-Germain 12, boulevard des Iles 92130 Issy-les Moulineaux France

Telephone:

Fax:

E-mail:

World Wide Web: FTP file transfer:

+1 516 344 2902 +1 516 344 2806 nndc@bnl. gov http://www. nndc. bnl. gov bnlnd2 .dne. bnl. gov username: bnlndc (no password required)

+33 1 4524 1090 +33 1 4524 1110 nea@nea. fr http://www/nea. fr FTP file transfer Username: open Password: neadb

Centre name:

Nuclear Data Section

Russian Nuclear Data Centre

Contact:

Address:

A. L. Nichols IAEA

Wagramer Strasse 5, PO Box 100

A-1400 Vienna Austria

V. N. Manokhin

Leipunsky Institute of Physics and

Power Engineering

Centr Jadernykh Dannykh

Ploschad Bondarenko

249 020 Obninsk

Kaluga Region

Russia

Telephone:

Fax:

E-mail:

World Wide Web: FTP file transfer

+43 1 2600 21709 +43 1 26007

services@iaeand. iaea. org http ://www-nds. iaea. org username: ndsopen

+7 084 399 8982

+7 095 883 3112/7 095 230 2326

manokhin@ippe. rssi. ru

http://rndc. ippe. obninsk. ru

acjd. ippe. rssi. ru

username: cjd

Main decommissioning activities

The complete decommissioning process involves a number of stages (or activities) that shall be performed, even if the logical sequence may be changed according to the specific strategy.

Decommissioning Planning — The decommissioning planning is usually started while the plant is still operating. Some decision making process and some planning, associated with some cost evaluation shall be started well on time, since it is needed also for fund accumulation, that usually is performed during plant operation.

Post-Operation — It is the sum of the activities that are needed to maintain the safety of the plant even after the plant has been definitely shutdown. These activities are more relevant while the spent fuel is still present in the plant.

Characterization — The knowledge of the radioactive inventory in the systems, components and structures before start of decommissioning is a fundamental information to define strategy, costs, technologies and so on. Characterization is also an important process during plant dismantling in order to know exactly the content of the produced wastes. Finally, characterization is also an important, and complex activity to demonstrate that structures and systems, that have not been dismantled because no radioactive, are actually in this condition. In Table 2 a typical list of radioactive isotopes relevant to the decommissioning of NPP’s is reported.

Decontamination — It is an activity that is oriented to remove radioactivity from systems and structures, in order to release components, to reduce doses to workers and to reduce the volume of wastes. It is applied to floors, walls, piping, etc. and may be performed essentially with mechanical or chemical means.

Dismantling — It is the real demolition activity. It may be a rather simple and quick activity, using conventional tools, but it may also be a very complex activity in the case of highly radioactive parts, using remote cutting and other sophisticated tools.

Safe Storage — It is the period in which the plant is left in dormancy, waiting for the radioactive decay. The plant is not left without controls, but a number of activities are still needed and, in some cases, some maintenance and even construction activities are necessary to maintain the safety for the workers and the public.

Table 2 — Major radionuclides identified in facility characterization

NEUTRON ACTIVATION PRODUCTS FOUND IN NUCLEAR REACTORS4

H3 5

12,3

P-

C, O,S2

C14

5730

в —

G, M, S

Na22 2

2,6

EC, в+

0,51 — 1,28

O

Cl36

3,1 108

в -, EC

C

Ar39 2

269

в-

C

Ca41

1 10[12]

EC

C

Ca45

0,4

в-

C

V49 2

0,9

EC

S2

Mn54

0,9

EC, у

0,83

A, M, S

Fe55 2

2,7

EC

C, M, O, S2

Co57 2

0,7

EC, у

0,12 — 0,14

S2

Co60 2

5,3

в-, Y

1,2 — 1,3

C, M, O, S, Z

Ni59

7,5 10[13]

EC

C, M, O, S, Z

Ni63 2

100

в-

C, M, O, S2

Zn65

0,7

в +, Y, EC

0,51 — 1,12

A

Zr93

1,5 106

в —

O, Z

Nb94

2 104

в -, Y

0,70 — 0,87

M, O, S, Z

Mo93

3,5 103

EC, Y —

0,3

M

Ag108m

130

EC, Y

0,4 — 0,6 — 0,7

M, O, S

Ag110m

0,7

в -, Y

0,6 — 0,9

M, O, S

Ba133 2

10,7

EC, Y

0,08 — 0,36

C

Sm151

93

в -, Y

0,02

C

Eu152

13,4

в -, Y EC

0,1

C, G

Eu154

8,2

в-, Y

0,1 — 1,3

C, G

2. Major factors relevant to the decommissioning strategy and planning

Optimization of a decommissioning strategy is a rather complex process. The parameters to be considered can be grouped in 3 categories: technical, economical, socio-political.