The dependence of prompt neutron yield on fragment mass ν(A) of photofission of actinide nuclei ²³²Th, ²³⁵U and ²³⁸U in the giant dipole resonance energy range has been parameterized. This allows us to describe the observed changes of saw-tooth behavior of neutron yield from the light and heavy fragments using few energy and nucleon composition dependent free parameters and to predict ν(A) for Pu isotopes.Выполнена параметризация зависимости выходов мгновенных нейтронов от массы осколков ν(A) фотоделения актинидных ядер ²³²Th, ²³⁵U и ²³⁸U для области энергий гигантского дипольного резонанса. Это позволяет описать наблюдаемые изменения пилообразного поведения выхода нейтронов из легкого и тяжелого осколков небольшим числом свободных параметров в зависимости от энергии и нуклонного состава и предсказать ν(A) для изотопов Pu .Виконана параметризацiя залежностi виходiв миттєвих нейтронiв вiд маси уламкiв ν(A) фотоподiлу актинiдних ядер ²³²Th, ²³⁵U і ²³⁸U для областi енергiй гiгантського дипольного резонансу. Це дозволяє описати спостережуванi змiни пилкоподiбної поведiнки виходiв нейтронiв з легкого i важкого уламкiв невеликим числом вiльних параметрiв у залежностi вiд енергiї та нуклонного складу, а також передбачити ν(A) для iзотопiв Pu 

Kibkalo, Yu.V.

Lengyel, A.I.

Maslyuk, V.T.

Parlag, O.O.

Romanyuk, M.I.

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

PARAMETRIZATION OF PROMPT NEUTRON YIELDSFROM PHOTOFISSION FRAGMENTS OF ACTINIDENUCLEI FOR THE GIANT DIPOLE RESONANCE ENERGYRANGEA. I.Lengyel1, O.O.Parlag1, V.T.Maslyuk1, Yu.V.Kibkalo2 ,M. I.Romanyuk11Institute of Electron Physics, 88000, Uzhhorod, Ukraine2Institute for Nuclear Research, National Academy of Sciences of Ukraine, 03680, Kiev, Ukraine(Received June 25, 2013)The dependence of prompt neutron yield on fragment mass (A) of photossion of actinide nuclei 232Th, 235U and238U in the giant dipole resonance energy range has been parameterized. This allows us to describe the observedchanges of saw-tooth behavior of neutron yield from the light and heavy fragments using few energy and nucleoncomposition dependent free parameters and to predict (A) for Pu isotopes.PACS: 24.75.+1, 25.85.-w, 25.85. Ec, 25.85. Ca1. INTRODUCTIONInformation about the dependence of prompt neu-trons yield on ssion fragments mass (A) plays animportant role for both quantitative understanding ofthe dynamics of the ssion process and a number ofpractical applications. Direct measurement of (A)is very dicult. Historically, the experimental data(A) and model descriptions exist for spontaneousssion of 244;248Cm, 252Cf [1] and neutron ssion of233U [2], 235U [3], 237Np [4], 239Pu [5].However, new challenges associated with the de-velopment of technologies for closed nuclear fuel cy-cle, hybrid reactors, simulation of radiation shieldingof accelerators and nuclear material monitoring [6-9]require data on multiplicity of prompt neutrons afterphotossion of wide class of actinide nuclei for thegiant dipole resonance energy range, up to 30MeV .The same data are also used to obtain the massand charge distribution of actinide nuclei ssion prod-ucts and to convert the secondary fragments (prod-ucts) yields into the primary ones. Typically, to esti-mate the number of neutrons (A), emitted by corre-sponding ssion fragments of atomic mass A the phe-nomenological Wahl method [10] is applied, which iswidely used till present for estimation of (A) duringneutron- and gamma-induced ssion [11, 12]. How-ever, this method does not reect the complex struc-ture of sawtooth-like (A) dependence due to nuclearshells eect.So far there is only information about the aver-age number of neutrons emitted by two conjugatedfragments and there is no information on photossionneutron emission curves. Primarily, this is due to ex-perimental diculties of time-span or direct neutronmeasurements in photossion experiments. However,in principle, neutron emission curves can be obtainedcombining the measurement of fragments mass dis-tribution and post-ssion neutrons.Calculations of (A) for 238U photossion [13]based on the parameters of asymmetric fragmentsmass distribution and the average total neutron yieldhtoti provide only qualitative, approximate reectionof saw-tooth behavior (see dash-dot line in Figs.2 and4).There is, however, another, more advancedmethod to determine the neutron emission curves(A), based only on the mass distribution of ssionfragments and products using the so-called Terrelltechnique [14]. This method was used to calculateprompt neutron yields (A) at photossion of 232Th,235U and 238U [15, 16], based on technique [14, 17]and data from the primary [18, 19] and secondary[20, 21] mass distributions of photossion fragments.The question is whether it is possible to identifysome of the basic laws using the results of calculationsdepending on such parameters of actinides photos-sion as charge, mass, photon energy, shell charac-teristics. According to the results, one can param-eterize neutron yields depending on the mass of ac-tinide photossion fragments and other parametersthat would reproduce the complex structure of saw-tooth behavior and allow to predict the dependenceof (A) for the photossion of a wide class of actinidenuclei. This is the task of extreme interest.Corresponding author E-mail address: parlag.oleg@gmail.com12 ISSN 1562-6016 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2014, N5 (93).Series: Nuclear Physics Investigations (63), p.12-17.2. PARAMETRIZATION OF (A) ANDRESULT OF CALCULATIONA recent analysis [22, 23] of experimental data onneutron yields from fragments of thermal neutron s-sion of 233U , 235U , 239Pu and spontaneous ssion of252Cf showed that for a detailed account of "saw-tooth" particularity of dependence of ssion neutronyield on the mass the ecient tool is the value ofR(A), introduced by Wahl [24], which is dened asR(A) =L;H(A)F (A); (1)where L;H(A) - prompt neutron yield of light andheavy fragment mass respectively, F (A) - total neu-tron yield, A - fragment mass and consists of severalsegments to reect the observed features, dependingon the complexity of the experimental behavior ofR(A). Therefore, the whole range of fragments masswas divided for more then 2 x 4 segments (comparewith solid broken line in Fig.4.2.39 [25]).We have known the experimental values ofL;H(A) and F (A), where AH is the heavy fragmentmass. Values F (AL), where AL is the light fragmentmass, are the reected points to the values of F (AH)."Experimental" values of R(A) (with errors) can bedetermined using formula (1) from experimental val-ues of L;H(A), F (AH) and F (AL).Model function R(A) is chosen as a linear functionfor each segment:RLi(A) = aLi + bLi(A AHN ) ; (2)RHi(A) = 1 RLi(A AHN ) (3)for light and heavy fragments, respectively, i - num-ber of the segment, aLi; bLi, ALN - parameters,AHN = Af  ALN , Af - mass of compound nucleus.The total number of parameters can be signi-cantly reduced taking into account the boundary con-ditions. Thus the phenomenological analysis of s-sion of 233U , 235U , 239Pu and 252Cf showed thatthe chosen parameterization and established regular-ities allow to describe observed change of saw-toothbehavior of neutron yield from light and heavy s-sion fragments [23]. Based on the established lawsthe possible neutron emission curves for 237Np(n; f)ssion were predicted.To parameterize photo-neutron emission andidentify general prediction patterns we will act ina similar way. For this we use the well-known re-sults of (A) calculation for the photossion of 232Th,235U and 238U at bremsstrahlung boundary energiesof 12:::30MeV [15, 16].However, prompt neutrons emission curves ob-tained from the calculations in [15, 16] is not pre-cise enough (Figs. 2-4 here) to describe all the ob-served features of R(A) functions built using thesedata. So there is no sense to try to describe them ad-equately using complicated function with more than22 segments. Here, using the same methodology wesimulate the behavior of neutrons from photossionof 232Th, 235U and 238U actinides depending on theenergy and nucleon composition in the giant dipoleresonance energy range.Let us simplify this task and divide the mass inter-val of light and heavy fragments for the function R(A)into two segments. The number of unknown parame-ters is also reduced while keeping the model eciency.As a result, we get the following picture (Fig.1).Fig.1. An example of R(A) function. The segmentsI-II and III-IV correspond to our parameterizationLet us consider some features of R(A) function.At the point of symmetric ssion A0 = AF =2;R(A0) = 0:5 and R(ALN ) = 0:5 [23], where ALNis determined from tting.Kink points Amin, A1 and A2 are chosen fromphysical considerations and experiment: Amin = 130corresponds to the mass of nearly magic nucleus frag-ment associated with spherical shells Z = 50 andN = 82, where ssion neutron yield is minimal. Thenmaximum neutron ssion yield for light fragmentswill match point A1, which is symmetrical to Aminrelative to A0, A1 = 2A0  Amin.The kink point A2 corresponds to the averagefragment mass of light fragments, A2 = hALi =AF   hAHi, where hAHi = 138 [26-28].The parameters ai, bi and ALN are determined bycalculating the function R(A) for 4 segments I...IV(see Fig.1). The number of free parameters can bereduced using the conditionsa1 = R(ALN ) = 0:5 ; (4)a2 = a1 + (b1   b2)(A2  ALN ) : (5)The dependence of bi slopes on excitation energyis noticed on the gure for R(A), so to study this de-pendence we have chosen bi = xi + yE . Thus, weneed to determine ALN , bi, xi and y parameters forseveral hundred "experimental" points.The value of ALN varies signicantly with changesof actinide mass, at least for neutron-induced actinidession (Fig.4) [23]. Therefore, we chose a similar pa-rameterizationALN =  80 +B(A0) : (6)13To take even-even and even-odd eect into accountwe introduce the factor1  c( 1)N : (7)As a result bi slopes will look asbj = (xj + yE)[1  c( 1)N ] ;j = 1:2; N = AF   ZF : (8)We calculate the function R(A) for the photos-sion of actinides 232Th, 235U and 238U according to(1)-(10) by tting of 406 "experimental" values ofR(A).Using the least squares method 5 parameters weredened to satisfactorily describe the characteristic"saw-tooth" behavior of prompt neutrons from thephotossion of actinides with A = 232:::238 a:m:u:Calculated parameters of R(A) function are:Parameter Value Errorx1 2:69  10 2 0:62  10 2x2 3:86  10 2 0:69  10 2y  0:108  10 2 0:047  10 2c 0:215  10 2 0:061  10 2B 1:45 0:04The results of R(A) calculation are shown inFigs. 2-4 (solid curve).The curves for prompt neutrons yield L;H(A) canbe calculated with help of formula (1).The results of L;H(A) calculation are shown inFigs. 2-4 (dashed curve). As can be seen from the g-ures the calculated values for prompt neutrons yieldare everywhere within the errors.These observations allow to estimate the possiblevalues of ssion neutrons yield from light and heavyfragments with known total yields just through themass distributions of ssion fragments using the mod-ied Terrell method [14].Fig.2. Results of calculation ofL;H(A) (dashed line) and R(A)function (solid curve) of a) 232Th,b) 235U and c) 238U photossionwith bremsstrahlung maximum energy12MeV . Dash-dot line - Brosa calcu-lation [13]. Squares - F (A), circles -L;H(A), up triangles - R(A)14Fig.3. Results of calculation ofL;H(A) (dash line) and R(A) function(solid curve) of 235U photossion withbremsstrahlung maximum energy of a)15, b) 20 and c) 30MeV . Squares -F (A), circles - L;H(A), up triangles -R(A)Fig.4. Results of calculation ofL;H(A) (dash line) and R(A) function(solid curve) of 238U photossion withbremsstrahlung maximum energy of a)15, b) 20 and c) 30MeV . Dash-dotline - Brosa calculation [13]. Squares- F (A), circles - L;H(A), up triangles- R(A)15With R(A) function parameterization,which fairly well reproduces the characteris-tic features of its behavior, we can calcu-late the expected values of prompt neutronsyield for other actinides, such as 239Pu or240Pu. Calculation results are shown in Fig.5.Fig.5. The result of R(A) functions calculationfor 232Th, 235U , 238U photossion (solid curve),and predictions for 239Pu and 240Pu photossion(dotted line) at the bremsstrahlung maximum energy12MeV3. CONCLUSIONSThus, to determine the photossion yield for theseactinides we need to know the value F (A), whichis determined by the general empirical formula, forexample [27], or with its experimental values, calcu-lated on the basis of the mass distributions of s-sion products [30]. This technique allows fast andecient calculation of photossion yield for not veryheavy nuclei in the excitation energy range up to 2nthreshold, avoiding cumbersome calculations by Ter-rell method [14].References1. V.Kalinin, V.Dushin, F.-J. Hambsch, et al. Measure-ments of prompt neutron multiplicity distributions incorrelation with mass-energy distribution of ssionfragments in spontaneous ssion of 252Cf , 244Cmand 248Cm // Journal of Nuclear Science and Tech-nology. 2002, v. 35, N2, p. 250-253.2. K.Nishio, M.Nakashima, I.Kimura, Y.Nakagome.Multi-parametric measurement of prompt neutronsand ssion fragments for 233U(nth; f) // Journalof Nuclear Science and Technology. 1998, v. 35, N9,p. 631-642.3. K.Nishio, I. Kimura. Measurement of Level DensityParameters of Fission Fragments Following ThermalNeutron Induced Fission of Uranium-235 // Journalof Nuclear Science and Technology. 1997, v. 34, N5,p. 439-444.4. 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Series Physics. 2008, N23,p. 58-63 (in Ukrainian).ÏÀÐÀÌÅÒÐÈÇÀÖÈß ÂÛÕÎÄÎÂ ÌÃÍÎÂÅÍÍÛÕ ÍÅÉÒÐÎÍÎÂ ÈÇ ÎÑÊÎËÊÎÂÔÎÒÎÄÅËÅÍÈß ÀÊÒÈÍÈÄÎÂ ÄËß ÎÁËÀÑÒÈ ÝÍÅÐÃÈÉ ÃÈÃÀÍÒÑÊÎÃÎÄÈÏÎËÜÍÎÃÎ ÐÅÇÎÍÀÍÑÀÀ.È.Ëåíäüåë, Î.À.Ïàðëàã, Â.Ò.Ìàñëþê, Þ.Â.Êèáêàëî , Í.È.ÐîìàíþêÂûïîëíåíà ïàðàìåòðèçàöèÿ çàâèñèìîñòè âûõîäîâ ìãíîâåííûõ íåéòðîíîâ îò ìàññû îñêîëêîâ (A) ôî-òîäåëåíèÿ àêòèíèäíûõ ÿäåð 232Th, 235U è 238U äëÿ îáëàñòè ýíåðãèé ãèãàíòñêîãî äèïîëüíîãî ðåçîíàíñà.Ýòî ïîçâîëÿåò îïèñàòü íàáëþäàåìûå èçìåíåíèÿ ïèëîîáðàçíîãî ïîâåäåíèÿ âûõîäà íåéòðîíîâ èç ëåãêîãîè òÿæåëîãî îñêîëêîâ íåáîëüøèì ÷èñëîì ñâîáîäíûõ ïàðàìåòðîâ â çàâèñèìîñòè îò ýíåðãèè è íóêëîííîãîñîñòàâà è ïðåäñêàçàòü (A) äëÿ èçîòîïîâ Pu.ÏÀÐÀÌÅÒÐÈÇÀÖIß ÂÈÕÎÄIÂ ÌÈÒÒÂÈÕ ÍÅÉÒÐÎÍIÂ Ç ÓËÀÌÊIÂÔÎÒÎÏÎÄIËÓ ÀÊÒÈÍIÄIÂ ÄËß ÎÁËÀÑÒI ÅÍÅÐÃIÉ ÃIÃÀÍÒÑÜÊÎÃÎÄÈÏÎËÜÍÎÃÎ ÐÅÇÎÍÀÍÑÓÎ. I.Ëåíäåë, Î.Î.Ïàðëàã, Â.Ò.Ìàñëþê, Þ.Â.Êiáêàëî , Ì. I.ÐîìàíþêÂèêîíàíà ïàðàìåòðèçàöiÿ çàëåæíîñòi âèõîäiâ ìèòò¹âèõ íåéòðîíiâ âiä ìàñè óëàìêiâ (A) ôîòîïîäiëóàêòèíiäíèõ ÿäåð 232Th, 235U i 238U äëÿ îáëàñòi åíåðãié ãiãàíòñüêîãî äèïîëüíîãî ðåçîíàíñó. Öå äîçâîëÿ¹îïèñàòè ñïîñòåðåæóâàíi çìiíè ïèëêîïîäiáíî¨ ïîâåäiíêè âèõîäiâ íåéòðîíiâ ç ëåãêîãî i âàæêîãî óëàìêiâíåâåëèêèì ÷èñëîì âiëüíèõ ïàðàìåòðiâ ó çàëåæíîñòi âiä åíåðãi¨ òà íóêëîííîãî ñêëàäó, à òàêîæ ïåðåä-áà÷èòè (A) äëÿ içîòîïiâ Pu.17

Parametrization of prompt neutron yields from photofission fragments of actinide nuclei for the giant dipole resonance energy range

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Parametrization of prompt neutron yields from photofission fragments of actinide nuclei for the giant dipole resonance energy range

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