Nuclear Phenomenology: A Conceptual Proposal for High School Teaching
aa r X i v : . [ phy s i c s . e d - ph ] M a y Nu lear Phenomenology: A Con eptual Proposal for High S hool Tea hingJ.D. Dantas and M.A.M. Souza ∗ Departamento de Físi a, Universidade Federal da Paraíba,Caixa Postal 5008, 58051-970 João Pessoa, Paraíba, BrasilThe dis overy of atomi nu leus by E. Rutherford, at the beginning of the twentieth entury,was the Nu lear Physi s original landmark. From then, a series of experiments in whi h beams ofparti les omposed of neutrons, protons and others, brought to ollide with a nu leus in order tounravel its stru ture or produ e arti(cid:28) ial elements through nu lear transmutation, were triggered.With the development of experimental equipment, a number of other nu lear phenomena havebeen observed, su h as beta de ay, nu lear (cid:28)ssion and fusion, Möesbauer e(cid:27)e t, et . In view ofthe global politi al and e onomi lands ape and the ontemporary edu ational trends, this worksuggest alternative topi s in nu lear physi s that an be dis ussed at the on eptual level in highs hool tea hing, where the main fo us lies in the histori al and te hnologi al importan e of su hphenomena in so iety.PACS numbers:I. INTRODUCTIONThe XX entury was marked by the appearan e of oneof the physi s largest bran hes, the Modern Physi s. Themain te hnologi al progresses of the modern world aredue, partly, to the appearan e of the Quantum Me han-i s and the Relativity Theory that were used as base todes ribe a series of phenomena in the atomi and nu- lear s ale. As example we have the super ondu tivity,des ribed by the BCS theory [1℄, whi h has been ex-tremely e(cid:27)e tive in the sear h for more e(cid:30) ient systemsin information transmission. We also have ountless pro-gresses in Medi ine, whi h an be in the instrumentalpoint of view, for diagnosis with image pro essing equip-ment, su h as magneti resonan e, or a lini al point ofview, through radiotherapy treatments. Besides the im-portant medi al ontributions, the Nu lear Physi s servesas theoreti al ba kground for other knowledge areas su has Astrophysi s and some rami(cid:28) ations of Cosmology.The obje tive of this work is to show that some themesof Nu lear Physi s an be treated at a on eptual level inhigh s hool tea hing. It is an e(cid:27)ort in the sear h of ex-plaining phenomena of great histori al importan e andpra ti al usefulness in the modern world, a ording toTerrazzan proposal [2℄, that defends the Physi s urri u-lum modernization by means of the urrent s ien e devel-opment as a need to reate ons ious itizens apable totransform the reality. This was emphasized by Aubre ht[3℄ in the Modern Physi s tea hing onferen e in April of1986, at FERMILAB (Fermi National A elerator Labo-ratory), Batavia, Illinois, where was defended the in lu-sion of physi s resear h topi s in high s hool tea hing. Aninteresting text about literature review dealing with thetheme modern and ontemporary physi s in high s hool an be found at [4℄.Some authors have elaborated proposals of edu ational ∗ emails:msouza(cid:28)si a.ufpb.br/ m.a.m.souza.ufpbgmail. om methodology for themes of Modern Physi s in high s hooltea hing, like quantum me hani s [5℄ and restri ted rel-ativity [6℄. In this arti le, initially, we will dis uss theedu ational motivation for the proposal of the on ep-tual tea hing on nu lear phenomenology, whose themes,su h as nu lear (cid:28)ssion and fusion, already do part of the urrent menu. In subsequent se tions, we will debate thephenomena on eptual stru ture that an be treated inHigh S hool.II. EDUCATIONAL MOTIVATIONThe Nu lear Physi s has a prominen e role in the ur-rent s ienti(cid:28) s enario, and even in the international e o-nomi poli y, on erning the uranium enri hment for mil-itary purposes or for ele tri energy produ tion; whatturns it into an important subje t in the edu ationalpoint of view. This work suggests the study of some phe-nomena in the nu lear s ale that an be treated qualita-tively in the lass room at high s hool level, for method-ologi al and pra ti al (cid:28)nalities.These are phenomena of high histori al importan e,whi h have appli ations in other knowledge areas. Whatis intended here is not to reformulate the ourse programof Modern Physi s, but to make use of a theoreti al ba k-ground that an ontribute to the student's formation inepistemologi al level.Although su h on epts have an extremely omplexquantitative des ription, till ertain point rooted to anempiri analysis, it is possible to turn them qualitativelysimple without needing to appeal to advan ed mathemat-i al formulations, staying, however, its te hni al har-a ter. The student of medium level, at the beginning,would not have many di(cid:30) ulties in understanding the nu- lear dynami s, on e, when penetrating in this subje t,some ontents that serve as prerequisites for su h un-derstanding were already seen, partly in the dis iplinesof Chemistry, like the atom on ept, spin, ions, bondenergy, mass and atomi number, and also in the owndis ipline of Physi s, in the topi s related to Ele tromag-netism, Restri ted Relativity and Quantum Me hani s.The student who has studied Chemi al Rea tionswon't have di(cid:30) ulties in understanding how a nu learrea tion is pro essed, on e the notation used to des ribeboth is identi al. On the other hand, it is important thatthe tea her, as mediator of knowledge, is able to ontex-tualize the ontents supplied with the student's daily life;all the nu lear pro esses are sus eptible to a pra ti al ap-pli ation, and an be extended to other knowledge areas.It an stand out, among them, the geologi al dating withthe use of isotope radioa tive of C or U , in Geog-raphy and Geology. We have the dosimetry in medi altreatments by Cs ( , or the indu tion of geneti mu-tations in ertain organisms in Biology, in addition tothe possibility of an international so io-politi al analy-sis on the impa t of the use of nu lear weapons and thehandling of nu lear garbage. An experien e of tea hingon these last two issues was made in Holland by Eijkel-hof et al [7℄, on whi h was in luded in the urri ulumstru ture of Physi s, a unit alled "Nu lear Weapons andSe urity", where 65 per ent of students agreed that thetopi should be in orporated to Physi s urri ulum, al-though the administrative members of the s hools havepositioned themselves against in lusionThe radiologi al a ident in Goiânia [8, 9, 10℄ onseptember , , an be dis ussed, where , kg of esium hloride, a salt obtained from the esium , on-tained in a oated apsule with steel and lead of a radio-therapy equipment, was released ontaminating people, the most with external body ontamination. Ofthese, people had on rete body ontamination in-ternal and external, oming to develop symptoms su has nausea, vomiting, diarrhea, et , being just medi ated.Other were hospitalized, of whi h needed to gothrough intensive treatment; from these, four did not re-sist and ended up dying. While leaning the ity , tons of atomi waste were olle ted, separated in boxes and drums, whi h will remain as a risk sour eto the environment for years.In general, the Nu lear Phenomenology is a ri h topi and of great potential in the edu ational ontext. Followsas suggestion the approa h of the next topi s.III. HISTORICALThe des ription of the matter stru ture is an old prob-lem whi h goes ba k to Classi al Antiquity. In an ientGree e, Leu ippus and Demo ritus defended the ideathat all things were formed by bodies, to whi h theygave the name of Atoms. These were onsidered indivis-ible, rigid and impenetrable, equipped with an in essantmovement in va uum [11℄.Although the ideas on erning the atomism have beenabandoned and obs ured by the hur h in the MiddleAges, at the beginning of the nineteenth entury, thehypotheses on the atomi onstitution of matter returned to gain strength with J. Dalton, where these have beenused to explain hemi al rea tions and its basi laws [11℄.At the end of the nineteenth entury, with the dis ov-ery of athodi rays and the determination of its natureas onstituted by negative ele tri harges and the obser-vations about the radiation emitted by ertain atoms byBe querel and Curie have led to a new formulation of thematter onstitution. The fa t that atoms of a hemi alelement su(cid:27)er a transmutation of atoms from another el-ement through the issuan e of parti les with negative orpositive harge, led to onje ture that the atoms shouldbe made of these two types of parti les, being the nega-tive harges the ele trons [12℄.Experien es with X-ray and atoms intera tion by C.G.Barkla ( ) led to the on lusive on(cid:28)rmation of ele -trons existing inside atoms, where those were numeri- ally in the order of half the atomi weight of the atom( ≈ A = 2 ). Assumptions about the nature of positive harges ould not be made due to di(cid:30) ulties in analyz-ing the properties of these parti les in the gas dis hargetubes, through the issue arising from radioa tive sub-stan es, whi h did not have the uniformity of the nega-tive harges [12℄.Assuming that the atoms are seen in nature as ele -tri ally neutral, it was expe ted that the amount of pos-itive harge was identi al to the number of ele trons inthe atom. Another point observed is that the ele tronsmasses, determined by R.A. Millikan in 1908(me = 0;9108:10??27g ), is mu h smaller than the mass of theHydrogen atom (the lightest of nature), whi h leads tothe on lusion that most of the atom mass is on the pos-itive harges, later identi(cid:28)ed as protons [13℄. The atomwas not indivisible anymore, now had parts ele tri allya tive, leading to the development of atomi models inorder to explain the atomi stability of whi h stood outthe model of J.J. Thonson and E. Rutherford.J.J. Thonson proposed a model in whi h the ele tronswere uniformly distributed in a positively harged sphere,with a radius around − m, whi h at the time wastaken as the atom standard size. This model be ameknown as the plum pudding. The ollapse of this modelis asso iated with the theoreti al results expe ted for thes attering of parti les by a few atoms, whi h were in starkdisagreement with the experiment. This model was notable to explain the high angles of de(cid:29)e tion aused by theparti les when they pass through a thin sheet of gold.E. Rutherford and his assistants Geiger and Mardsendid, in the year 1909, a series of experiments in whi hwere observed large angles of s attering [14℄. The resultobtained by the resear h group led the formulation ofRutherford`s atom model in whi h the atoms were seenas mini-planetary systems, with the ore at the enterand ele trons orbiting around it. The idea was simple,the high deviations su(cid:27)ered by alpha parti les would onlybe possible if the spreader enter had an ele tri repul-sive (cid:28)eld extremely high. Sin e the parti les had positive harge, they are doubly ionized helium atoms, the retros attering was a result of a frontal ollision with a verypositive region and of high mass, whi h was alled nu lei[15℄.FIG. 1: Experiment done by Rutherford showing the highdeviations ( β ) su(cid:27)ered by parti les α when they pass througha sheet of gold and are dete ted in a (cid:29)i ker s reen.The dis overy of the nu leus was the (cid:28)rst milestone ofNu lear Physi s. The possibility of obtaining informa-tion about the atomi stru ture by means of ollisionswith sub-nu lear parti les opened a range of possibilitiesin the sear h for understanding and applying energy in-volved in the rea tions with baryoni matter, as well asknowledge on the ore internal stru tures. Doors werebeing open to a new area of knowledge in whi h theexperimental results ould only be a hieved by ollisionme hanisms. With the theories of Quantum Me hani sof W. Heisenberg and E. S hrödinger and the relativisti version of P. Dira , a more pre ise theoreti al des riptionabout nu lear pro esses an be obtained, resulting in themost modern theories of Quantum Chromodynami s D.Politzer, F. Wil zek and D. Gross and ele troweak theoryof S. Weinberg, A. Salam and S. Glashow, whi h uni(cid:28)esthe ele tromagneti intera tion with the Fermi theory forweak intera tion through the a tion of (cid:28)elds (cid:28)lled by ve -tor bosons.IV. NUCLEAR PHENOMENOLOGYThe nu lear dynami s is a omplex me hanism, whereall the des ription is related to the laws of onservation,of symmetries and to the Quantum s attering formalism,besides the fa t that many of the theoreti al models pro-posed to explain the behavior of the nu leus are stru -tured into experimental basis. Next, we will present abrief and qualitative approa h of a limited number of phe-nomena that were hosen be ause of its unquestionableimportan e, either from a histori al perspe tive, eitherfrom the te hni al sophisti ation and pra ti al appli a-bility.A. Alpha de ay and Nu lear TransmutationWe will begin with the alpha de ay pro ess. This pro- ess is dire tly linked to radioa tive transitions experi- en ed by unstable nu leus, where o urs the emission of α parti le in the sear h for stability. The nature of theseparti les has been demonstrated previously, our interestin this pro ess of de ay is related to the e(cid:27)e t of quantumtunneling or transmission through the potential barriers.This is an extremely omplex pro ess from the point ofview that a urate results are related to quantum prob-abilities, spe i(cid:28) ally with the probability that the alphaparti le is formed in the ore plus the probability of it rossing the potential barrier of the latter [16℄. So thatthe pro ess an be treated as a problem of ollision, itis assumed, for al ulation purposes, a foreign parti lealready formed whi h is to be atta hed to the ore of de-parture. In this ontext, just al ulate the probability ofalpha parti le going through the potential barrier of thenu leus. This is a lassi problem of modern physi s. SeeFig. 2.FIG. 2: Potential of the nu leus generated by ele trostati intera tion and that must be rossed by the alpha parti le.From the appli ation point of view, the alpha de ayserved as basis for the a omplishment of the (cid:28)rst nu- lear rea tions, espe ially in the me hanism of arti(cid:28) ialnu lear transmutation aused by ollision of ores and α parti le. In , E. Rutherford was the (cid:28)rst to use theseparti les as proje tiles, at the expense of having high en-ergy and momentum [17℄. There was however a problem,most of the α parti les should be diverted due to the highele tri (cid:28)eld generated by the target, drasti ally redu ingthe probability of a rea tion. The solution to this prob-lem was the use of light nu leus whi h drasti ally redu esthe repulsive oulomb for es in reasing the probabilityof a possible rea tion [12℄. The rea tions alpha-protonalpha-neutron, where we have the emission, by the resid-ual nu leus, from a proton and a neutron respe tively,are the most signi(cid:28) ant examples of this me hanism. Inthe (cid:28)rst rea tion we had a nu leus of nitrogen atom beingbombarded by an α parti le a ording to the equation: N + He → [ F ] → O + H (1)The elements on the left represent the reagents, the oneson the right the ompound nu leus followed by de ay tothe proton and residual nu leus.The alpha-neutron rea tion is very important histor-i ally, be ause it brought the dis overy of the neutron,what led to the a eptan e of a ore omposed by pro-tons and neutrons, abandoning the old model that postu-lates the existen e of ele trons inside the nu leus, sin ethis model had a number of limitations, starting withthe un ertainty prin iple whi h showed that an ele tron on(cid:28)ned in a region in the order of the nu lear diametershould have an energy around MeV with the observedexperimental value of energy for ele trons in beta de aywas MeV. Besides the magneti dipole moment of the ore is three times smaller than the dipole moment of anele tron [13℄. The rea tion is based on the ollision of α parti le with a beryllium nu leus: Be + He → [ C ] → C + n (2)The result of this rea tion provides as residual nu leus arbon and a neutron.Both rea tions an be explained from the lassi al the-ory of inelasti ollisions with the in rease, however, ofthe rest energy for ea h reagent given by Einstein equa-tion E = m c , sin e the levels of energy involved stilldo not require a deeper relativisti treatment. The pro- ess of transmutation is very useful be ause it allows the reation of arti(cid:28) ial ompounds, "eliminating", in parts,the need for exploitation of natural resour es.Another interesting appli ation of the alpha de ay anbe observed within the smoke dete tors ((cid:28)re alarm),where is used the radioa tive element alled ameri ium- , whi h has half life of years. Smoke dete tor de-vi es are low ost and are widely used in ommer ial andresidential buildings. It is omposed of two parts, a sen-sor to sense the smoke and an ele troni ampaign. Thereare two types of dete tors: the photoele tri and the ion-ization ones. For pra ti al purposes, within the ontextof this work, we will sti k to the ionization dete tors.Within these dete tors we have an ionization hamberwhi h has in its interior × − g of Ameri ium- ,whi h equals , mi ro urie, this amount of ameri iumsu(cid:27)ers approximately thousand nu lear transmuta-tions per se ond and in ea h is emitted an α parti le.The ionization hamber onsists in two plates subje t toa potential di(cid:27)eren e, as an be seen in Fig. 3FIG. 3: S hedule of ionization hamber operation of a smokedete tor.The α parti le ionize the atoms of oxygen and nitrogenfrom the air inside the hamber. The ele trons released in this pro ess are attra ted to the positively harged plateand the positive atoms are attra ted to the plate withnegative harge, establishing therefore an ele tri urrentbetween two plates originated from the ele trons and ionsmovement. In a situation of (cid:28)re, the smoke parti les enterthe ionization hamber, rea t with the ions, making themneutrons, interrupting the urrent between the plates.The dete tor senses the drop in urrent and triggers thealarm. B. Beta de ayIn , J. Chadwi k was the (cid:28)rst to observe exper-imentally, through measurements performed with mag-neti spe trometers, that the nu leus ould emit ele trons[16℄. These initial observations led to believe that theele trons were, su h as protons, the onstituents of thenu leus, whi h was later refuted by the dis overy of theneutron. This, su h as the alpha de ay, is about a pro e-dure of radioa tive transition between states of some un-stable nu lei with the emission of high energy ele trons,whi h was alled beta de ay. The original theory of betade ay had serious problems be ause it ould not handlethe energy spe trum observed experimentally and ouldnot be ommitted by a single ele tron. In , W. Paulipostulated the existen e of the neutrino, a parti le thatwas also emitted in de ay, without harge and mass andspin / ; the existen e of a parti le devoid of mass, withnull harge and spin momentum / was ne essary topreserve the prin iples of energy and angular momentum onservation. A more pre ise theory was only proposedin by E. Fermi [18℄, in whi h on ludes a new typeof intera tion, the weak intera tion.Years later this theory was enhan ed with the work ofR. Feynman and M. Gell-Mann [19℄, where a onsistentrelativisti treatment from the Dira equation was usedto des ribe the Fermi intera tion. Inside the nu leus thebeta de ay an be expressed by the following rea tions: p → n + e + + ν ( .a ) n → p + e − + ¯ ν ( .b )The equations show the positive and negative beta de aywith the emission of a positron and a neutrino or theemission of an ele tron and an anti-neutrino, respe tively.FIG. 4: beta de ay(Z → atomi number and A → number ofmass): a) initial state of the nu leus before the de ay. b)Nu leus after the emission of ele tron.The appli ations of this de ay me hanism are presentin a lass of important phenomena, whi h extend fromthe human physiology, in the medi ine, to the develop-ment of spa e te hnology and industrial te hnology. Inthe last ase, we have the use of Promethium, the hemi- al element of atomi number , whi h is found at roomtemperature at solid state. It is used as an emitter ofbeta parti les in the onstru tion of thi k meter, withinthe metrology of pre ision in the onstru tion of the lo kdials and pointers. In the aerospa e industry is used tomanufa ture mi ro batteries for long periods and pos-sibly as a portable sour e of X-rays and heat in spa eprobes and arti(cid:28) ial satellites [20℄.An interesting phenomenon that involves the betaemission o urs inside the human body, this radiationpro edure is responsible for the fun tioning of the heartmus le. In the human blood, is diluted about mg ofpotassium- ( K ( ), whi h is a radioa tive isotope ofpotassium- , this on entration is enough to the eje tionof beta parti les. Within the heart, there are two avi-ties, alled left and right auri le, the (cid:28)rst has the fun tionof pumping blood into the pulmonary ir ulation and these ond is responsible for distributing blood enri hed withoxygen to all parts of the body, are endowed with ellsand beam of nerve (cid:28)bers alled the sino-atrial node andBa hman beam respe tively. The potassium diluted inthe blood, inside these avities, su(cid:27)ers disintegration byele trons emission (beta parti les), when these ele trons ollide with the nerve terminations of the heart avitieswalls, generate a stimulus that leads the heart mus le to ontra t and grow in a determined rhythm, so that theblood is pumped to all parts of the body.C. Möessbauer E(cid:27)e tFollowing the line of rea tion indu ed by gamma rays,another me hanism gets prominent alled absorption bynu lear resonan e or Möessbauer e(cid:27)e t. The des riptionis as follows: after absorbing a photon, the nu leus getsto the ex ited state, the line width asso iated with thisstate is given, a ording to the un ertainty prin iple, by Γ = ~ /τ , where τ represents the average life of the state.After this period, the nu leus de ays by emission of anew γ photon, su(cid:27)ering a retreat. The entral idea isthat the energy transferred to the ore of the absorptionmust be equal to the re oil energy in the issue, fore astinga resonant state.Till now, we have onsidered the ore of a free atom,the problem hanges on(cid:28)guration for the ase in whi hthe atom is onne ted to a rystal network. Due tothe onne tions with the network, the ore an absorb aphoton without retreat, it says that resonant absorptionwithout re oil o urred, what is pre isely the Möessbauere(cid:27)e t. The fa t that the atom an perform harmoni vi-brations along three freedom degrees, where the energyasso iated with the os illation modes is quantized andgiven by ǫ = ~ ω , where ω is the network os illation fre- quen y and the value of ǫ represents the vibrations quan-tum alled phonon, making that, in the eje tion pro ess,the re oil energy get transferred to the network in theform of os illations, ontributing to temperature raisingof the same, given that this phenomenon only o urs ifthe re oil energy is greater than the energy of the netquantum os illation, generating a state of ex itement init. If the re oil energy is less than ~ ω , the network annot be ex ited, performing as a bu(cid:27)er; o urs, therefore,an eje tion without re oil. This e(cid:27)e t is widely used inastrophysi s, the lines of the Möessbauer e(cid:27)e t spe trumprovides a pre ise hara terization of the elements that ompose the interstellar matter [16℄.Other appli ations of Möessbauer spe tros opy lie instru tural hara terization of some proteins, in the hem-i al omposition of meteorites. In industry, an be usedto study the stru ture of alloys and geology for geologi aldating of erami s [21, 22, 23℄.D. Strong Nu lear For eAs major ontribution of the ollision me hanisms, thenu lear physi s is rooted in the hara terization of thestrong nu lear for e; this is the for e responsible for on-ne ting protons and neutrons inside the atom nu leusand, onsequently, ensure the stability of the ore andthe hadroni matter; is the for e of greater intensity innature, whi h justi(cid:28)es alling it strong intera tion. Thehadroni intera tion an be des ribed from the neutron-proton dispersion at high energy. This pro ess is de-s ribed in terms of the bounded energy of the deuteron,whi h is a nu leus omposed of one proton and one neu-tron. The problem is physi ally treated with quantumprin iples of intera tion between two bodies.The results of s attering experiments between nu leonsshow the following properties about the nu leon intera -tion: ) the property of saturation, ie a single nu leon an only intera t with a restri ted number of nu leons; ) the independen e of the harge, ie the nu lear for esare symmetri al in relation to the harge, the intensityof intera tion a rea tion ( nn ) is identi al to a rea tion( pp ); ) the presen e of ex hange for es. In quantumme hani s, when two parti les intera t mutually, thereis always a state in whi h one property an be shared,produ ing an ex hange intera tion between to the nu le-ons. Heisenberg supposed that this property would bethe harge [26℄.The property of energy ex hange is losely linked tothe mesoni theory of nu lear for es, proposed by theJapanese physi ist H. Yukawa in that, in analogywith the ele tromagneti intera tion mediated by the ex- hange of photons, assumed that the hadroni intera -tion between nu leons would be result of the ex hangeof one meson π . The fa t that this parti le have mass,allowed the des ription of this intera tion as short-range.Moreover, the mesons have harge ( π − , π + ) or may beele tri ally neutral ( π ), needed requirement to, in anintera tion, the involved parti les harge get ex hanged.Expli itly in this pro ess, a proton an be ome a neutronand vi e versa. See Fig. 5.FIG. 5: Feynman diagram for illustrating the intera tion be-tween a proton and a neutron by ex hanging a meson.The greater appli ation of the strong nu lear for e o - urs in the nu lear (cid:28)ssion rea tors, used to produ e ele -tri ity; where the uranium, when bombarded by neu-trons, absorb these parti les and be ome unstable, su(cid:27)er-ing a split ( reating two new lighter atoms). The energy orresponding to the strong nu lear for e that united theprotons and neutrons in the nu leus of uranium is re-leased as kineti energy from both residual nu lei. Thisenergy an be used within the rea tor of a nu lear plantor an be used for war purposes, su h as the atomi bomb,with devastating e(cid:27)e ts.E. Nu lear (cid:28)ssionThere are two rea tion me hanisms in Nu lear Physi sthat are intrinsi ally linked, they are: the moderation ofneutrons and nu lear (cid:28)ssion. In O. Hahn and F.Strassmann [25℄ dis overed nu lear (cid:28)ssion; Liese Meitnerand R. O. Fris h [26℄ interpreted the (cid:28)rst time the me ha-nism of the pro ess and then N. Bohr and J. Wheeler [27℄proposed a theoreti al treatment based on the model ofthe liquid drop. Finally, only in 1942 E. Fermi, managethe (cid:28)rst ontrolled hain rea tion [16℄.The pro ess of nu lear (cid:28)ssion is the result of a dynami instability of the nu leus, whi h results in its splittinginto two residual nu lei with a high release of energy.For nu lei with
Z > , there is the possibility of spon-taneous (cid:28)ssion to o ur without an external agent a t-ing [25℄. However, for pra ti al purposes, the pro essof (cid:28)ssion indu ed in nu lei with Z ≈ (uranium 233,for example) generated in nu lear rea tors, as in Fig. 6,presents bigger e(cid:30) ien y. The me hanism is based onthe apture of a neutron by a uranium nu leus througha ollision, although there is the possibility to promotethe (cid:28)ssion of a uranium nu leus through ollisions withhigh-energy parti les, protons, deuterons and γ rays [26℄.The neutrons energy generated in nu lear rea tionsand in the (cid:28)ssion pro ess is in the order of MeV [25℄,ie, they are extremely fast, what makes hard its ap-ture by other nu lei of uranium involved in the rea tion.To get a hain rea tion, the neutrons must be thermal-ized, or moderate, from the ollisions with other nu lei FIG. 6: S hedule of nu lear (cid:28)ssion in a rea tor where the orerelease neutrons that an be aptured by other non (cid:28)ssile thatafter fell to U ( , or are absorbed by (cid:28)ssionable materialand indu e (cid:28)ssion.(su h as graphite, beryllium, et .). With the de rease ofits speed, in reases the probability of a rea tion with auranium nu leus, whi h must be to (cid:28)ssioned, releasingneutrons that will be moderated and aptured by othernu lei, starting a hain rea tion. This pro ess is used inthermonu lear rea tors for power plants to produ e ele -tri ity and manufa ture of mass destru tion weapons likethe atomi bomb.F. Enri hment of UraniumThe International Energy Overview 2007 (IEO2007),published by the International Energy Agen y (IEA) es-timates a growth of in world onsumption of the var-ious forms of energy between the period 2004 and 2030.A ording to the report, all energy used worldwide willgrow from × Btu (British Thermal Unit) in 2004to × ( Btu in 2030. For nu lear energy, the aver-age onsumption should grow . in that period, withgreater on entration in developing ountries, whose es-timated demand is of . .In this s enario, the uranium enri hment plants gainimportan e, whose related resear hes worry about tomake it feasible, from the e onomi , so ial, environmen-tal points of view, among others, the pro esses for fuelprodu tion, from the prospe ting of ore to the (cid:28)nal trans-portation of radioa tive waste.Uranium found in nature, under the form of uraniumdioxide ( UO ), is omposed of approximately . ofthe isotope U and . of U . The latter, unlike the U , is a (cid:28)ssile material, , in other words, that su(cid:27)ers(cid:28)ssion only aused by low energy neutrons (thermal neu-trons). The enri hment of uranium onsists, therefore, inthe in reasing of U on entration that, in the fuels ofthe rea tors, should be − . An atomi bomb, on theother hand, is built with uranium enri hed to .One of the isotopes separation pro esses - the gaseousdi(cid:27)usion - onsists in transforming UO into uraniumhexa(cid:29)uoride gas ( UF ) and to make this gas spreadtrough porous plates, separating the ( UF ) of the( UF ). This pro edure was used in the United Statesduring the last world war, for large s ale produ tion ofhighly enri hed uranium. Another pro ess that have in-dustrial prominen e is the ultra entrifugation, in whi hdo to rotate the gas UF in a ylinder at high speed; asa result, the UF is on entrated on the ylinder wall,while the UF ) remains in the enter [24, 30℄.G. Nu lear Rea torsNu lear rea tors are systems in whi h, ontrolled, nu- lear rea tions are produ ed in hain to release energy.The physi s of rea tors basi ally study the phenomenarelated to the behavior of neutrons in a set of spe ialmedium materials, arranged in appropriate quantitiesand geometries. The rea tors are lassi(cid:28)ed by several fa -tors: building materials, fuel, geometry, purpose of use,among others. We an, however, for simpli ity, sharethem in two groups: thermal rea tors, that use modera-tors to redu e the energy (speed) of neutrons and rapidrea tors, using neutrons without moderate them [24, 30℄.The essential parts in a rea tor are: an a tive orewith the fuel element - usually uranium - where the (cid:28)s-sion rea tion is kept, A moderator - water or graphite -to redu e the energy of neutrons, a re(cid:29)e tor to avoid itsexhaust, a ooler to remove the heat generated in onse-quen e of the (cid:28)ssions, and a shield to blo k the passageof penetrating radiation [31℄.We treated the thermal (cid:28)ssion rea tor parti ularly,whose purpose an be lead the rea tion of nu lear (cid:28)ssionfor use in resear h or for onversion and use of energyin new form (rea tor power). The fun tion of a rea torin a power system is to onvert energy from (cid:28)ssion tothermal energy, preparing the subsequent onversion ofthermal energy into ele tri al energy. The (cid:28)ssion energyis onverted into kineti energy of the (cid:28)ssion fragments,and the immediate result is the in rease in the internalenergy of the material fuel and moderator. In a nu learplant, the in rease of internal energy generates steam,whi h triggers a turbine (outside the rea tor), making anele tri generator [32℄, as seen in Fig. 7.FIG. 7: Simpli(cid:28)ed s heme of a Thermonu lear Power Plant.A (cid:28)ssion produ ed by a neutron releases new neutrons apable of produ ing new (cid:28)ssions. For ea h neutron ab-sorbed, about 2:5 new neutrons are released. It is ne es-sary then that at least one of neutrons released ause a new (cid:28)ssion, to establish the desired hain rea tion. Therate of rea tion is ontrolled inserting or removing (bars ontrol) - of boron or admium - whi h absorb neutronswithout su(cid:27)ering further rea tions. These bars are alsoset as se urity devi es.H. Nu lear fusionThe last ase to be addressed is nu lear fusion. Wehave seen previously that heavy ores ould (cid:28)ssion by a ollision with neutrons, liberating a great deal of energy.The me hanism of fusion is almost the reverse: fast andlight nu leus an ollide and merge to form heavier nu lei,where a onsiderable amount of energy is released in thispro ess.This energy is asso iated with dissipation of heat, de-pends dire tly on the masses of the partners involved inthe rea tion and their properties are related to nu learmatter, ie, for fusion to o ur some requirements mustbe ful(cid:28)lled by the partners involved in the pro ess: the kineti energy of the nu lei rea tion must be large toallow the in rease of penetration probability in Coulombbarrier, this pro ess o urs in very light nu lei at a tem-perature of a 107K, where the atoms are fully ionizedforeshadowing a state of plasma [16℄; the matter den-sity in the temperatures involved in the fusion rea tion,must be extremely high.The interior of the stars, in parti ular the sun, has awhole propitious s enario to this type of rea tion, thedensity of the sun interior is approximately g/cm at a temperature of , . K . The Fig. 8 representsthe fusion rea tion of hydrogen helium that o urs insidethe stars and that was present at the beginning of theformation of the universe in primary nu leosynthesis [33℄. H + H → H + e + + ν + 0 , ( .a ) H + H → He + γ + 5 , ( .b ) He + He → He + 2H + γ + 12 , ( .c v − n − a2