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

Segment 4: OPTICAL

The optical model parameter (OMP) segment is provided in two forms: full library (archival form) and shorter library with all single-energy potentials removed (user file). Currently, the user (archival) file contains 258 (258) po­tentials for incident neutrons, 98 (143) potentials for incident protons, 8 (11) for deuterons, 1 (26) for tritons, 3 (53) for 3He particles, and 10 (10) for in­cident a-particles. Of the neutron potentials, 229 are spherical potentials, 28 are coupled-channels potentials, and 1 is a vibrational model. There are 6 coupled-channels and 92 spherical potentials for incident protons in the user library, and a total of 5 dispersive optical potentials for incident neu­trons. Additions to the OMP library were made including new potentials from JENDL and from the Chinese Nuclear Data Center, as well as several new potentials from Bruyeres and Los Alamos. The new global potential for neutrons and protons from Koning and Delaroche [10] was incorporated, as were the new dispersive potentials from Capote. Where there are not enough experimental data to define phenomenological OM parameters, one has to resort either to global parameterizations or to new microscopic approaches. The semi-microscopic model developed at Bruyeres is now part of the OM segment, incorporating a revised version of the MOM code which relies on the Jeukenne, Lejeune, and Mahaux nuclear matter approach.

A compilation of 1708 deformation parameters (@2 and вз) for collective levels has been retrieved from the JENDL-3.2 evaluations, ENSDF and lit­erature to be used in direct reaction calculations. These deformations are in addition to those provided explicitly for the Coupled-Channels potentials in the OMP library.

Nuclear applications

The US ENDF/B-VI nuclear data library was released to the international community in the early 1990s (Dunford, 1992). An initial point of note is the development over many years of an internationally-accepted data format (ENDF-6), including the potential to accommodate uncertainties in the form of covariance matrices. Specific aims included the production of a self-consistent set of evaluated neutron cross sections, updated decay-data files (extracted from the ENSDF files, and supplemented with new measurements and theory), and the addition of charged — particle and high-energy reaction files. Many of the neutron-reaction cross sections were completely re-evaluated, including U(n, f), Pu(n, f) and the resonance

parameters for 235,238U and 239,241Pu. Adjustments were also made to the neutron-

capture cross sections of 151,153Eu, 165Ho and 197Au (latter as standard). Both the decay-data and fission-yield files of ENDF/B-VI have been supplemented with the beta and gamma energies and Pn values of Rudstam et al (1990 and 1993) and the chain yields derived by Wahl (1988). This resulting data base was tested in a series of decay-heat calculations and shown to reproduce the experimental results in a satisfactory manner (Rudstam and England, 1990). ENDF/B-VI gamma-ray data for the short-lived fission products were also augmented by spectra calculated from the gross theory for beta-strength functions to form mixed files of discrete and theoretical decay data (Katakura and England, 1991).

The Joint Evaluated File (JEF) is a collaborative project between member states of the NEA-OECD to produce a nuclear data library for industrial applications and research (Nordborg et al, 1992; Nordborg and Salvatores, 1994). Various decay-data files have been assembled by staff at the NEA Data Bank from other sources (particularly ENSDF, UKPADD-2 (Nichols, 1993) and UKHEDD-2 (Nichols, 1991)). This JEF-2.2 library consists of a general purpose file, radioactive decay — data files and fission-yield files. A number of adjustments were made to the JEF-2.2 decay-data starter files:

(a) mean beta and gamma energies of 109 short-lived fission products measured by Rudstam et al (1990) were added to the files;

(b) theoretical data were based on the p-n QRPA model of Hirsch et al (1992): 16 half-lives, 101 mean beta and gamma energies, and 32 Pn values.

The contents of the JEF-2.2 files have been summarised in hardcopy, and represent a definitive data set for nuclear applications (NEA-OECD, 1994 and 2000).

Efforts are underway to amalgamate the NEA fission (JEF) and fusion (EAF) data libraries, and to improve and expand the contents of the resulting files (Finck et al, 1997; Jacqmin et al, 2001; Bersillon et al, 2001). A Joint Evaluated Fission and Fusion project has been formulated to combine JEF and EAF database activities. Other sources of updated decay-data for JEFF-3 include NUBASE, ENSDF, UKPADD and UKHEDD. Various studies are also underway or completed to improve the contents of specific decay data files judged to be inadequate for fission and fusion reactor applications (e. g., Backhouse and Nichols, 1998; Nichols et al, 1999a and 1999b).

Other libraries have been developed for nuclear power applications that contain decay-data files. Staff at the Chinese Nuclear Data Centre, have assembled files of basic nuclear data and model parameters (Su Zongdi et al, 1994 and 1997). This nuclear parameter library (CENPL) contains atomic masses and constants for ground states, nuclear level properties and gamma-ray data extracted from ENSDF.

The JNDC-FP (Japanese Nuclear Data Committee — Fission Product) library contains decay and fission yield data for 1087 unstable and 142 stable fission products, and neutron cross-section data for 166 nuclides (Tasaka et al, 1990; Katakura et al, 2001). Recommended decay data include half-lives, branching ratios, and total beta and gamma-ray energies released per decay of every radionuclide. Significant emphasis has been placed on producing a comprehensive set of fission-product decay data, with the introduction of theoretical half-lives and mean energies for over 500 radionuclides with no known discrete decay data.

The contents of the various national and international decay-data files are difficult to summarise with respect to their technical origins (i. e., discrete decay-data or mean beta-decay measurements; file supplemented with calculated decay data from gross theory of в decay, microscopic analyses or p-n QRPA). Table 14 focuses on the fission-product nuclides to be found in the US ENDF/B-VI, JENDL-FP and JEF-2.2 libraries.

“Estimated decay energies” refers to a combination of data that originate from Rudstam et al (1990), Hirsch et al (1992) and others. The inclusion of estimated and theoretical decay data is considerably more extensive in US ENDF/B-VI and JENDL-FP than in JEF-2.2 (latter includes more recommended data based on direct measurements (with the concomitant problem of pandemonium (Hardy et al, 1977)).

Table 14: Evaluated decay-data libraries, 2000/2001: contents and origins of fission-product

decay energies (NEA-OECD, 2000; Katakura et al, 2001)

Fission products

ENDF/B-VI

JENDL-FP

JEF-2.2

Evaluated nuclides

891

1229

860

Radioactive nuclides

764

1087

730

Stable nuclides

127

142

130

Evaluated decay energies3

443c

536

611

Estimated decay energiesb

384c

551

119

a Evaluations of discrete decay data.

b Mean decay energies from gross measurements and theory.

c Some files contain both evaluated discrete data and estimated theoretical data (including continuum spectra).

d Uncertain — defined by number balance only.

Thermo-chemical Water Splitting

One mechanism that is being considered seriously for hydrogen production is thermo-chemical water splitting by the Iodine-Sulfur (IS) process. The IS process was originally proposed by the General Atomic Company in early 1970’s and is very promising because it involves only a few reaction steps. In this process Hydrogen — Iodide (HI) is produced by a cyclic chemical reaction chain utilizing Iodine, sulfur — dioxide and water; HI is then decomposed to produce hydrogen, releasing Iodine to the chemical reaction chain. Sulfuric acid, H2SO4, is generated in the process, which is vaporised and decomposed at a temperature of about 800 to 900 C to sulfur- dioxide, water and oxygen. The oxygen is released and sulfur-dioxide and water is returned to the reaction cycle. Laboratory scale experiments at Japan Atomic Energy Research Institute have demonstrated the feasibility of the IS process with continuous generation of hydrogen from water with recycling of the process material. An energy efficiency of 47% has been achieved in this process16.

B. Electrolysis

Water electrolysis at ambient pressure and temperature of 70 — 90 C is a common method for production of high purity hydrogen. However, it has been found that the demand for electricity decreases with increase of temperature. That is the electric energy required is much reduced for the electrolysis of steam at higher temperatures (800 C and above). High temperature electrolysis is a reverse reaction of the Solid-oxide Fuel Cell, where water is decomposed in the solid polymer electrolyte to hydrogen and oxygen. This method is at an early stage of development14.

Conclusion

There are several possibilities for direct utilization of heat from nuclear reactors. Nuclear desalination, district heating and industrial process heat are examples where this has been done, and these non-electric applications of nuclear power can be expanded in the future. It is also important to note that a wide range of temperatures, for low to high temperature applications, can be tailored for specific uses by different reactor types. Table IX shows the status of projects in several countries for non-electric applications of nuclear energy. The proposed applications are primarily for dual-purpose use but dedicated heating reactors are also being developed in China and Russia. Innovative applications are being explored with gas — cooled reactors because of their high temperatures. High temperature applications of nuclear energy, particularly for production of new fuel such as hydrogen, are in the laboratory stage now but have a great potential for the future3.

Cost-effectiveness is in general a crucial issue for non-electric applications of nuclear power. As nuclear power captures a larger share of the electricity market, the non-electric applications will also flourish. Until now, the non-electric applications are only a very small part of power production. For some applications, however, close proximity of the power plant to a population centre is needed (to reduce energy and/or product transmission losses) and this requires further public acceptance. Some large applications also require the development of infrastructure — heat-distribution networks for district heating and water distribution systems (water pipes and pumps) for fresh water. Many countries are exploring these possibilities of nuclear power. As mentioned in the text, there is a large market for non-electric applications of nuclear energy and it is hoped that someday this potential will be realized.

TABLE IX. PROSPECTIVE NUCLEAR PROJECTS FOR
NON-ELECTRIC APPLICATIONS

Country

Plant type or site

Location

Application^

Project status

Power,

MW(e)

Heat output, MW(th)

Bulgaria

WWER

Belene

E, DH

Design

2×1000

400

China

NHR-200

Daqing City

DH

Dormant

0

200

China

HTR-10

Tsinghua

University,

Beijing

Electricity/ high temp. applications

Achieved criticality in Dec. 2000

10

Japan

HTTR

Oarai

(JAERI)

High temp. process heat

Operating

0

30

Russia

RUTA

Apatity

DH / Air conditioning

Design

0

4×55

Russia

RUTA

Obninsk

DH

Design

0

55

Russia

ATEC-

200

E, DH

Design

50-180

70-40

Russia

VGM./ GT-MHR

P

Design

600

Russia

KLT-40

Floating

E, DH & Desalination

Regulatory

process

completed

35

150

Russia

AST-500

Voronez

DH

Construction

suspended

0

500

Russia

AST-500

Seversk

DH

Completed feasibility study, approval of the project by State regulatory authority is nearing completion

0

500

E: Electricity (Power), P: Steam supply for process heat, DH: Steam/Hot water supply for heating.

Refined Resonating Group Model and Standard. Neutron Cross Sections

Hartmut M. Hofmann[1]

Institute for Theoretical Physics, University of Erlangen-Nurnberg,

Erlangen, Germany

Textures given at the
Workshop on Nuclear Reaction Data and
Nuclexir Reactors: Physics, Design and Safety
Trieste, 25 February — 28 March 2002

LNS0520001

We describe in some detail the refined resonating group model and its application to light nuclei. Microscopic calculations employing real­istic nuclear forces are given for the reaction 3He(n, p). The extension to heavier nuclei is briefly discussed.

1 Introduction

The neutron standard cross sections cover a wide range of target masses from hydrogen to uranium. The high mass range is characterized by many over­lapping resonances, which cannot be understood individually. In contrast, the few-nucleon regime is dominated by well-developed, in general, broad resonances. The interpolation and to less extend extrapolation of data re­lies heavily on R-matrix analysis. This analysis has to fit a large number of parameters related to position and decay properties of resonances. Due to the limited number of data and their experimental errors, any additional input is highly welcome. Except for neutron scattering on the proton any of the standard cross sections involve few to many nucleon bound states. These many body systems can no more be treated exactly. The best model to treat scattering reactions of such systems proved the resonating group model (RGM) in its various modifications. Therefore we begin with a dis­cussion of the RGM.

The solution of the many-body problem is a long standing problem. The few-body community developed methods, which allow an exact solution of few-body problems, via sets of integral equations. In this way the 3-body problem is well under control, whereas the 4-body problem is still in its infancy. Hence, for systems containing four or more particles one has to rely on approximations or purely numerical methods. One of the most successful methods is the resonating group model (RGM), invented by Wheeler [1] more than 50 years ago in molecular physics. The basic idea was a resonant jump of a group of electrons from one (group of) atom(s) to another one.

This seminal idea sets already the framework for present day calculations: Starting from the known wave function of the fragments, the relative wave function between the fragments has to be determined e. g. via a variational principle. The basic idea, however, also sets the minimal scale for the cal­culation: a jump of a group of electrons needs at least two different states per fragment leading to coupled channels. Hence, an RGM calculation is basically a multi-channel calculation, which renders immediately the tech­nicality problem. This essential point of any RGM calculation is the key to an understanding of the various realisations of the basic idea. Besides the most simple cases, for which even exact solutions are possible, the RGM is always plagued with necessary, huge numerical efforts. Therefore, a dis­cussion about the various approaches has to be given. In most applications of the RGM till now, the evaluation of the many-body r-space integrals is the largest obstacle. It can only be overcome by using special functions, essentially Gaussians, for the internal wave functions of the fragments. Two basically different methods are well developed: One uses shell model tech­niques to perform the integration over the coordinates of the known internal wave functions leading to systems of integro-differential equations, whose kernels have to be calculated analytically. The other expands essentially all wave functions in terms of Gaussian functions and integrates over all Ja­cobian coordinates leading to systems of linear equations, whose matrices can be calculated via Fortran-programs. Since the latter is more suited for few-body systems and I’m more familiar with it, I will concentrate on this so-called refined resonanting group model (RRGM) introduced by Hacken — broich [2]. As detailed descriptions of the first method exist [3], I will not discuss it. I will, however, compare the advantages and disadvantages of both methods at various stages.

In order to allow the reader to find further applications of the RRGM, I will try to generalize the formal part from the nuclear physics examples I will give later on. Therefore I will first discuss the variational principle for the determination of the relative motion wave function. I will then demonstrate how the r-space integrals are calculated in the RRGM. The next two chapters deal with the treatment of the antisymmetriser and the evaluation of spin — isospin matrix elements. The last chapter, dealing with formal developments, demonstrates how the wave function itself is used by the evaluation of matrix elements of electric transition operators.

A chapter on various results from nuclear physics illustrates various points of the formal part and helps to understand the final part on possible exten­sions and also on the limitations of the model. Part of the work is already described previously [4]. Some repetition cannot be avoided in order to keep this article self-contained, so I will refer sometimes to ref. [4] for details.

Neutron Cross Sections

Uncertainties in the neutron-absorption cross sections of the fission products have only a marginal effect on decay-heat predictions for cooling times < 104 sec. Changes in decay heat at longer cooling times are dependent on the flux level and irradiation time, and no simple estimate can be made of the uncertainty in decay heat at these cooling times that arises from uncertainties in the cross-section data. Nevertheless, the conservative assumption is normally made that the desired accuracy of decay-heat calculations can be achieved with uncertainties in the cross sections of 10-30% for the important capture products over long decay times (leading up to 108 sec).

Institute for Transuranium Elements (ITU), Karlsruhe, Germany

‘Nuclides 2000: an Electronic Chart of the Nuclides’ has been developed and released as a CD-ROM by ITU, Karlsruhe. The Nuclide explorer gives access to the radionuclide decay data from JEF-2.2, using either a “Chart of the Nuclides’ or Segre display (Magill, 1999). Derived data include activities, gamma dose rates and annual limits of intake. There are additional features to this package, including background articles that describe various aspects of decay data and related historical publications.

‘Nuclides 2000’ allows the user to carry out decay calculations: starting from an initial mass or activity, the user can determine the masses, activities, radiotoxicities, gamma dose rates etc for all daughters at any time.

Contact ITU, Karlsruhe for further information:

Joseph Magill

Address: Institute for Transuranium Elements Postfach 2340 D-76125 Karlsruhe Germany

Tel: +49 7247 951366

Fax: +49 7247 951591

E-mail: magill@itu. fzk. de

More information on ‘Nuclides 2000’ is available on the Web (including direct purchase): http://www. nuclides. net/

The Italian experiences in decommissioning

First ENEL and then SOGIN have carried out a number of activities in the framework of the general decommissioning programs. They are both in-field activities and planning and designing activities. The current situation at the four NPP’s is the following:

Garigliano

• Reactor defuelling and off-site shipment of spent fuel: 1985 — 1987

• Radiological characterisation of plant systems, components and structures: 1990

• Safe Enclosure of Reactor building: 1990 — 1998

• Safe Enclosure of Turbine building: 1994 — 1995

• Treatment of low-level waste and retrieval/conditioning of intermediate — level and high-level waste: 1988 — 1999

• Dismantling and safe enclosure of existing Radwaste system, demolition of Off-gas stack and Safe Enclosure condition to be reached within the year 2003

Latina

• Reactor defuelling and off-site shipment of spent fuel: 1988 — 1991

• Radiological characterisation of plant systems, components and structures: 1992

• Decontamination and dismantling of systems and components: 1992 — 1996

• Decontamination of the spent fuel pool: 1996 — 1999

• Treatment of radioactive waste, dismantling of primary circuit ducts and components and Safe Enclosure condition to be reached within the year 2006

Trino

• Radiological characterisation of plant systems, components and structures: 1992 — 1994

• Reactor defuelling: 1991

• Temporary dry storage of spent fuel at plant site within the year 2003

• Safe Enclosure condition to be reached in the year 2007

Caorso

• Radiological characterisation of plant systems, components and structures: 1992 — 1995

• Reactor defuelling: 1998

• Temporary dry storage of spent fuel at plant site within the year 2004

• Safe Enclosure condition to be reached in the year 2009

Most of the above mentioned decommissioning activities (in particular at Garigliano and Latina sites) were carried out using experience and skill gained by Company personnel during plant operation, in particular:

■ headquarters personnel were involved in the design and licensing activities,

■ plant personnel, who operated the plant, were involved in the activities for plant operation termination and decontamination/dismantling activities.

Engineering and R&D Departments of ENEL were also involved in the development and design of special equipments and tools, used for waste retrieval and decontamination of structures.

After plants shutdown the plant staff were significantly reduced; part of the personnel were transferred to fossil power plants, and retired personnel were not replaced.

8. Conclusions

Some broad conclusions can be drawn from the issues that have been briefly discussed.

The first point is that decommissioning is mainly a management challenge. It is a complex and multi-faceted problem, whose optimum solution requires a multidisciplinary approach. Nuclear experts, therefore, should be highly interested in being involved in it without living this experience as a kind of tedious and dirty job that somebody else has to do.

From a technical standpoint it is a substantially mature technology, which may have, however, important margins of improvement. Application of new advanced technologies may lead to reduced doses to workers and reduced amount of wastes to be disposed, with consequential important economic advantages. It is also clear that the sooner the decommissioning is prepared (even during plant operation) the better it is. We might also say that decommissioning is something that should be addressed as early as in the plant design process, as currently imposed by utility requirements as EUR (European Utility Requirements) for advanced NPP’s. And it should be understood that the proof that decommissioning can be completed in reasonable time and economically may be a prerequisite for building new NPP’s.

From the financial standpoint, decommissioning is also a challenge, because it is a cost intensive activity without any important direct investment return, if we exclude site reuse and returns in terms of image for the utility or the region. Therefore, a correct funding scheme is very important to provide for all necessary funds at the end of the plant operating life.

International consensus and harmonization are needed in several areas. This need has been recognized only recently, in the last years, when a greater number of NPP’s have terminated their service life.

A decision making process transparent both to the politicians and to the public, who deserve the information they want in an activity that is finally for their assurance, is undoubtedly useful.

Finally, let me introduce an example of design of a modular inherently safe reactor, called MARS, developed since 1983 at the University “La Sapienza” of Rome, in which the decommissioning aspects have been taken into account since the beginning.

This design has been aimed at strongly simplifying the plant layout, the components construction and assembling on the site in order to reduce construction times and costs.

This effort has produced, as a parallel significant result, a huge simplification of all decommissioning activities. In particular, the basic design choices of the MARS plant affecting decommissioning are shown in Table 3. These choices produce the results shown in Table 4.

A quick sequence of pictures (figs. 4 to 6) is self-explaining of the decommissioning phases for this reactor.

[1] hmh@theorie3.physik. uni-erlangen. de

[2] mwherman@bnl. gov

[3] RIPL-2 studies focused on incident energies below 20 MeV, a typical limit for standard nuclear data files. However, new applications such as ADS, medical radioisotope production and radiation treatment re­quire reliable data at much higher energies (up to 1.5 GeV in the case of ADS). Most of the parameters available from RIPL-2 cannot be ex­trapolated to such high energies (e. g., temperature dependence of the GDR width). In particular, there should be consistency between statis­tical model calculations at low energies and the intra-nuclear cascade model commonly used at high energies.

[4] Adopted from a combination of Audi et al (1997), Takahashi et al (1973) and US ENDF/B-VI (Dunford, 1992); uncertainties are given in parentheses (for example, 0.13(2) means 0.13 ± 0.02).

Expressed in terms of incremental units of 10 keV starting from zero (first incremental energy step of continuum gamma spectra is from zero to 500 keV, as noted in parentheses).

+ Neutron spectrum adjusted to 0-1794 keV.

* Neutron spectrum adjusted to 0-620 keV.

[5] Croatia owns 50% of the Krsko 676 MWe Westinghouse PWR plant located in Slovenia.

* E, P and DH stand for electricity, process heat and district heating.

[7] Bruce A reactors are currently laid up; it is expected to start up in 2003.

[8]

Unit 1 was taken out of operation in 1988, unit 2 in 1990.

[9] maurizio. cumo@uniroma1.it

[10] 60 years is a limitation existing in the USA. In other countries this condition may last longer up to 100 years and more

[11] If a plant is allowed to sit idle for 30 years, for example, only about 1/50th of its original radioactivity from cobalt-60 will remain; after 50 years, some 1/1,000th will remain.

[12] Important in fusion devices also

[13] Fission products are also often found in nuclear reactors as a result of defects in the fuel cladding

[14] The clearance ‘’is the removal of material from a system of regulatory control provided that the radiological impact of these sources after removal from the system is sufficiently low as not to warrant any further control’’

Asymptotic contributions of the Hamiltonian

In order to determine the reaction matrix amn from eq. (2.24) and eq. (2.31) we need the matrix elements of H between regular and irregular Coulomb functions. Hence, we need matrix elements of H, eq. (2.18 — 2.19) between Fl, Gl and rv, respectively. Since FL and GL are not square-integrable functions, some care is necessary. In the discussion below eq. (2.41), FL and Gl, but obviously not GL, had to be solutions to the point-Coulomb Hamil­tonian, or to the total Hamiltonian for large separation of the fragments so that the identity operator from the antisymmetrizer between fragments could not lead to infinite contributions. Hence, one has to correct for the fact that Gl is not a solution in just this case.

All matrix elements of FL, containing Fl in the ket can be calculated using the expansion coefficients determined from eq. (4.2). Using eq. (2.29) the only critical matrix elements are < GHG > and < Г&HG >. Operating with the r. h.s. of eq. (2.41) onto GL we find that the regularisation factor TL can be factored out from all terms except the kinetic energy of the relative motion. Hence, it suffices to consider this term in detail.

Since there are no permutations across fragment boundaries we can restrict the discussion to just the relative coordinate. Omitting all unnecessary fac­tors we arrive at

Подпись: <9|^|9>image108[g(r)T (r)]

image109dr [g(r)T2(r)g//(r) — (g(r)T'(r))2] (4.4)

where the first term is already taken care of by g being a solution to the point-Coulomb Hamiltonian and the ’ denotes derivation with respect to r.

Taking into account eq. (4.2) we can write in the obvious notation < GHG > = 9mgn < XmHxn > —

mn

гж

-C (GT’fdr (4.5)

J 0

here gm denote the expansion coefficients of G and the constant C contains essentially the internal norm of the fragments.

In an analogous way we find

<XmHG > = gn <XmHXn > —

n

г ж

— C Xm(2G’T’ + GT") dr (4.6)

0

Note that the point Coulomb contribution has to be taken out of < xm H xn >. The correction terms of eqs. (4.5) and (4.6) sometimes exceed the expansion terms appreciably.

Now we have all the necessary ingredients to calculate the reactance ma­trix amn according to eq. (2.31). Since the Hamiltonian is symmetric, the eigenvalues ev, eq. (2.16), are real and therefore depending on the number of expansion functions Xv there are certain energies E for which the denomina­tor in eq. (2.21) or (2.31) vanishes. It is easy to convince oneself, that this factor is cancelled against a corresponding one in the numerator, see also ref. [2]. There could be a slight numerical problem, if the energy E is too close to one of the eigenvalues ev, due to division by a very small number or even zero. This difficulty can, however, be overcome quite easily by omitting the corresponding eigenvector rv, or by reducing the number of expansion functions just by one, so changing the eigenvalues ev slightly.

It can, however, not be excluded that accidentally the denominator in eqs. (2.21) or (2.31) becomes zero, without the existence of a physical resonance. Therefore it is argued [32, 33] that using a variational principle for e. g. the S — matrix, i. e. using complex scattering functions, this problem can be avoided. This might be true in practice, but there exist counter examples [34].

Since the position of the pole depends also on the regularization parameter в0, these accidental poles can always be avoided by changing f30, a procedure which needs only a small amount of computing time, compared to the calcu-

lation of the matrix elements as described in chapter 3.1. Also the measures taken to avoid division by a small number, discussed above, can be used.

Following along the general lines discussed in [5] it is possible to construct various variational principles, out of which the described K-matrix, K-1- matrix or the S-matrix, are just certain limiting cases. One can show that for all these different cases the matrix elements calculated so far suffice and it is only necessary to form the proper linear combinations [35]. So one could just use different methods to avoid spurious resonances. How to calculate the S-matrix and search for the complex energy poles of the S-matrix is described in [8].

Half-life

Radioactive decay is largely insensitive to conditions outside the nucleus (although not always so), and the resulting behaviour can be characterised by fixed modes of decay, transition energies and probabilities. The number of atoms decaying per unit time is the activity (A) given by the equation:

A = NX =

where N is the number of atoms at time t, X is the decay constant (probability that an atom will decay in unit time), and dN is the number of spontaneous nuclear transitions from that energy state in time interval dt. Activity is expressed in Becquerels (Bq) in which 1 Bq is one disintegration per second (dps). Integration of the above equation and substitution results in the expression:

N = N0e-Xt

where N0 is the number of atoms at time t = 0. Each radionuclide has a characteristic decay constant that is related to the half-life (t/2), the time taken for the number of original radionuclides to reduce by a factor of two:

ln2

The half-life of a radionuclide is a primary parameter in any radioactive decay process.

Liquid Metal-cooled Reactors

There has been renewed interest in recent years in liquid metal cooled reactors particularly for smaller sized designs and from a sustainable development point of view. They are significant because they can breed new fissile material and extend the potential of nuclear energy. Because of their fast neutron spectrum, which can be used as a burner or a breeder, they have also received recent attention for incinerating weapons plutonium, thorium utilization, partitioning and transmutation of actinides and burning nuclear waste. First used in Russian submarines, liquid lead and lead — bismuth have received worldwide attention in the last few years for power reactors and also for accelerator driven transmutation systems. Russia, India, and Japan have remained most active in recent years in liquid metal power reactor development14. The Republic of Korea is developing a pool-type sodium-cooled 150 MWe KALIMER plant with metal fuel and a passive safety decay heat removal system.

India: India’s sodium-cooled Fast Breeder Test Reactor (FBTR), has been operating in Kalpakkam for several years. It has a unique mixed uranium carbide — plutonium carbide fuel. It was designed for 40 MWt but has only recently reached a power level of 17.4 MWt. It has achieved a fuel burnup of 90 GWd/t. Thorium blankets have been used in the breeder reactor in Kalpakkam. A 500 MWe sodium — cooled pool type Prototype Fast Breeder Reactor (PFBR) design is under development, also for the Kalpakkam site. It will use U-Pu MOX fuel. The Preliminary Safety Analysis Report for this reactor is nearing completion.

Japan: The two sodium-cooled fast reactors, the Experimental Fast Reactor “Joyo” and the prototype fast breeder reactor “Monju” are not operating at this time. Joyo will start operation in 2003 with a new high-flux core, and Monju is waiting for governmental approval for improvement work for sodium leaks, leading to its eventual startup in 3 more years. However, several small and medium size designs are being developed in Japan, the most prominent one being the 50 — 100 MWe sodium — cooled fast reactor design known as Super Safe, Small and Simple (4S)15. In this reactor, Burnup of the core is controlled by the annular reflector surrounding the core, and a long life is achieved by the long length of the core and upward movement of the reflector. The Modular Double Pool (MDP) is another concept of 325 MWe sodium — cooled fast reactor, which has steam generator and secondary pumps in the sodium filled annular space between the primary and the secondary vessel thereby reducing the secondary piping system. Metallic fuel is used for both of these two designs. MDP has been designed to reduce the construction cost and improve reliability by factory manufacture of most components, and 4S has been designed to obtain a long life core. A concept of Multipurpose Fast Reactor (MPFR) has also been proposed which has liquid plutonium-Uranium metallic fueled core. It has 300MW thermal power and does not require fuel reloading16.

A Pb-Bi cooled Long-life, Safe, Simple, Small, Portable, proliferation-resistant reactor (LSPR)17 has also been proposed. This is a 35 MWe (150 MWt) integral type design where the steam generators are installed within the reactor vessel. Nitride fuel is used. Natural or depleted Uranium fuel assemblies are placed at the center of the core and Pu fuel assemblies at the outside. In this composition, the burnup will progress from the outer core into the inner blanket region.

Russian Federation: Russia’s experience in the construction and operation of sodium-cooled experimental and prototype fast reactors (the BR-10, BOR-60, BN — 350 in Kazakhstan and BN-600 with hybrid core) has been very good. Efforts have been directed towards further improving safety and reliability, and making the Liquid Metal Fast Reactors (LMFRs) economically competitive to other energy sources. While these efforts would take some time, LMFRs are being considered to burn weapons plutonium and minor actinides. The current main efforts in sodium cooled fast reactors in Russia have been the lifetime extension for BOR-60 and BN-600, decommissioning of BR-10 and designing BN-800. By 2010, Russia wants to complete construction of the BN-800 fast reactor at Beloyarsk. Russia has also developed three small sodium-cooled reactor designs: MBRU-1.5, MBRU-12 and BMN-170 for production of 1.5, 12 and 170 MWe of electricity18.

The design from Russia that has received the most recent attention is the BREST reactor, which uses lead coolant, uranium-plutonium mono-nitride fuel and indirect cycle for heat removal to a supercritical steam turbine. Owing to unique combination of the thermo-physical properties of the lead coolant and mono-nitride fuel, BREST can boast of a very high level of natural safety. Two conceptual designs have been developed for the 300 MWe and 1200 MWe BREST reactors. Figure 5

1100

Fig. 5. BREST-300 reactor. Vertical section

gives the schematic details of the 300 MWe BREST design. Russian fast reactor R&D activities are concentrating on advanced concepts with enhanced safety features and designs with alternative coolants, as well as on the development of the basic design, and experimental confirmation, of the lead cooled BREST-300 demonstration reactor with on-site closed fuel cycle19.

Studies of small fast spectrum reactor modules cooled by lead-bismuth eutectic are also being pursued. These designs, called SVBR-75/100, are based on the reactor operation experience with nuclear submarines. The designs could be used for electricity production, seawater desalination, or the utilization and transmutation of actinides. The SVBR-75 is a Pb-Bi cooled 75 MWe (268 MWt) fast reactor with two — circuits, the primary Pb-Bi circuit and the steam-water secondary loop20. Two other heat removal systems are provided for both scheduled and emergency cooling. The reactor operates for 8 years without refueling. Average fuel enrichment is 15.6%.

USA: Although the U. S. had a strong sodium cooled reactor program for many years, it has essentially halted. Recently, however, because of impetus in research for new generation of reactors, one innovative liquid metal cooled design called the Encapsulated Nuclear Heat Source (ENHS) has been proposed21. The ENHS is a Pb — Bi natural circulation cooled, 50 MWe (125 MWt), modular, fast reactor concept. It is designed that the fuel is installed sealed into the reactor module at the factory and transported to the site to be inserted into a secondary pool of Pb-Bi that contains the steam generators. Major components, such as the pool vessel and steam generators, are permanent and remain at the site while the reactor module is replaced every 15 or 20 years. The heat generated in the core is transferred through the primary coolant vessel wall to the secondary pool. The natural circulation avoids the need for active components but it requires a tall 19m primary vessel. A design with a lift pump reduces the height to 10m and reduces the coolant mass. The fuel considered is metallic Pu-U-Zr fuel with 11-12% of Pu. The peak fuel Burnup is approximately 105,000 MWD/t. The autonomous control and no fuel handling reduce the nuclear operations onsite to a minimum. Figure 6 gives a schematic description of ENHS.

Water/Steam Connections

Primary Pb-Bi

Secondary Pb-Bi

Primary Vessel of ENHS Module

TABLE VI. SOME MSR DESIGNS

Country

Design

Power

Primary circuit

Secondary

Circuit

Status

(MWt)

Coolant & Structure

Inlet/Outlet Temp C

USA

Aircraft

Reactor

Experiment

(ARE)

2.5

NaF

ZrF4UF4

Inconel

655/800

Helium

Operated in 1954 at ~750 C

USA

Molten Salt Reactor Experiment (MSRE)

8.0

LiFBeF2

ZrF4UF4

Hastalloy-

NM

632/654

LiFBeF2

Hastalloy-N

Operated during 1965­69

USA

Molten Salt Breeder Reactor (MSBR)

2250

LiFBeF2

ThF4UF4

Hastalloy-

NM

566/705

NaFNaBF4 Hastalloy — NM

Th-233 U fuel cycle. Design effort

discontinued in 1976

Japan

Fuji-II23

350

LiFBeF2

ThF4UF4

Hastalloy-

NM

566/705

NaFNaBF4 Hastalloy — NM

Conceptual

design

Russian

Federation

High

Temperature Molten Salt Reactor (MARS)

300

LiFBeF2

600/750

Air

Conceptual

Design

Russian

Federation

Gas-cooled Molten Salt Reactor

2000

LiFBeF2

ThF4UF4

600/750

NaFNaBF4

Designed especially for industrial applications

France

CCDP

2000

LiFBeF2

ThF4UF4

550/700

Plumbum

Conceptual

Design

China

MSGR

2250

NaFBeF2

Hastalloy-

NM

566/705

NaFNaBF4

Conceptual

design

Fig. 7. Schematic diagram of a molten salt reactor such as the MSRE21

Heat Removal

Fig. 8. Schematic diagram of a molten salt cooled reactor such as MARS