version 7.1 Coulomb Fission Oleg Tarasov 1 2

version 7.1 Coulomb Fission Oleg Tarasov 1 2

version 7.1 Coulomb Fission Oleg Tarasov 1 2 1,2 National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824-1321, USA Flerov Laboratory of Nuclear Reactions, JINR, 141980, Dubna, Moscow Region, Russia next Fission spontaneous fission; photofission; Coulomb (electro-magnetic) and electron fission; fusion-fission (fast fission, quasifission); fission induced by nuclear reactions (proton-induced, spallation and etc). 1. 2. 3. 4. 5. However from the point of view of the LISE++ code only the following fission reactions are interesting to simulate fragment transmission through a fragment-separator: Coulomb (electromagnetic) fission; fusion-fission; abrasion-fission (spallation in inverse kinematics). In the development of this new reaction mechanism in the LISE++ framework it is possible to distinguish the following principal directions: * Kinematics of reaction products; * Production cross-section of fragments * Spectrometer tuning to the fragment of interest to produce maximal rate (or purification). next Fission fragment kinematics at intermediate and high energies The kinematics of the fission process is characterized by the fact that the velocity vectors of the fission residues populate a narrow shell of a sphere in the frame of the fissioning nucleus. The radius of this sphere Vf is defined by the Coulomb repulsion between both fission fragments. In the case of reactions induced by relativistic heavy ions, the transformation into the laboratory frame leads to an ellipsoidal distribution which will characterize the angular distribution of fission residues [Ben02, Amb96] (see Figure). Two different methods for fission fragment kinematics are available in LISE++: MCmethod and DistrMethod. DistrMethod is the fast analytical method applied to calculate the fragment transmission through all optical blocks of the spectrometer. MCmethod (Monte Carlo) has been developed for a qualitative analysis of fission fragment kinematics and utilized in the Kinematics calculator. References: 2) P.Armbruster et al., Z.Phys.A355 (1996) 191. 1) J.Benlliure et al., Nucl.Phys. A628 (1998) 458.

3) M.Bernas, et al., Nucl.Phys.A725 (2003) 213. Fig.a) Schematic view of the experimental parameters shaping the measured velocity spectrum in the frame of the fissioning system. Vf the fission-fragment velocity. b) Velocity spectrum of 128Te in the frame of the fissioning system. The velocity V = 0 refers to the projectile frame 2).next Fission kinematics by Monte Carlo method All Allreaction reactionsettings settings(projectile, (projectile,target, target,setting settingfragment) fragment)and andexcitation excitationenergies energiescan canbe beentered enteredininthe the Kinematics calculator dialog. In the 2D fragment plot dialog (see Figure) it was possible to set: Kinematics calculator dialog. In the 2D fragment plot dialog (see Figure) it was possible to set: The energy, horizontal and vertical angular emittances; The angular acceptance shape; The horizontal and vertical angular values and their variance; The center of energy silts and their size in %. Fig. The 2D fragment plot dialog. Initial excitation energy of fissioning nucleus 238 U is equal to 50 MeV next Fission kinematics by Monte Carlo method

2D-plots Ax(horizontal component of the angle in the laboratory frame) versus Energy per nucleon of 132 Sn final fragment after 238U(600MeV/u) fission. Acceptances settings are shown in previous page figure. The left picture represents case of using target thickness (Pb 4mm ), the right plot was got in the case of a zero thickness target. Initial excitation energy of fissioning nucleus 238U is equal 50 MeV. next Projections next Fission kinematics by LISE analytical Distribution method The forward intensity matrix after cutting by a horizontal rectangle shape acceptance equal to 12mrad.mrad. The forwardenergy matrix. The Monte Carlo method is a powerful tool for modeling, but sometimes the amount of time spent to get enough statistics makes it more beneficial to use fast analytical methods. next Spectrometer settings in the case of fission The two new settings mode (left peak and right peak) have been developed for the case of fission reactions (see screen-shot of the dialog). The default method to tune the spectrometer in the fission case is right peak (as on more intense peak). Figure. Horizontal spatial selection of fission fragments by the slits S1. The spectrometer is set to next the right peak of 130Te momentum distribution. Coulomb fission fragment production cross-sections 1. The program assumes that the reaction takes place in middle of the target. Therefore the first step is the calculation of the primary beam energy in the middle of the target. 2. Total fission cross-section and average excitation energy: a. Calculation of differential electromagnetic crosssection. b. Deexcitation fission function d f/d(E*). c. Calculation of statistical parameters of the deexcitation fission function: mean value , and area f. 3. Calculation of an initial fission cross-section matrix (CSinit) of production crosssections excited fragments using the semi-empirical model 1). The code takes into account unbound nuclei as well for this stage of the calculations. 4. Post-scission nucleon emission. The code calculates five final cross-section matrices using the CSinit matrix. Use of the LisFus method 2) define the number of post-scission nucleons is a big advantage of the LISE++ code which allows to observe shell effects in the TKE distribution, and enables the user to estimate qualitatively the final fission

fragment faster. All four stages together take no more than 5 seconds! References 1. J.Benlliure et al., Nuclear Physics A 628 (1998) 458-478. 2. O.Tarasov and D.Bazin, NIM B204 (2003) 174-178. 3. M.G.Itkis et al., Yad.Fiz. 43 (1986) 1125. 4. M.G.Itkis et al., Fiz.Elem.Chastits At.Yadra 19 (1988) 701. next Electromagnetic Electromagneticexcitation excitation A well-known review of the processes generated by the electromagnetic interaction in relativistic nuclear, and atomic collisions, by C.Bertulani and G.Baur [Physics Report 163 (1988) 299-408] has been used to obtain the excitation energy function for fission. The d iffe r e n t i a l c r o s s - s e c t i o n fo r e le c t r o m a g n e t ic e x c i t a t io n is g iv e n b y : d em n E 1 dE E E1 nE2 E E2 ,1 E2 ,2 w it h n E 1 , n E 2 b e in g t h e n u m b e r o f e q u iv a le n t p h o t o n s f o r e le c t r ic d ip o le and q u a d r u p o le e x c it a t io n s E1 E2 r e s p e c t iv e ly . , , i a r e t h e p h o t o n

a b s o r p t io n c r o s s - s e c t io n s f o r g ia n t E 1 a n d E 2 e x c it a t io n s , w h e r e f o r E 2 e x c it a t io n s i= 1 d e n o t e s is o s c a la r a n d i= 2 d e n o te s is o v e c t o r g ia n t q u a d r u p o le re so n a n ce s. M u lt ip le e x c it a t io n s of th e q u a d r u p o le r e s o n a n c e s a r e n e g le c t e d . Figure. Top left: Differential cross-sections of GDR (red solid curve), GQR(IS) (blue dashed curve), and GQR(IV) (black dot curve) excitations in 238U as calculated from the equivalent photon spectrum representing a 208Pb projectile nucleus at 600 MeV/u. The green dot-dashed curve is obtained by summing-up the different contributions. Bottom left: Equivalent photon number per unit projectile charge, for E1, M1, and E2 radiation. Top right: Deexcitation channels for 238U nuclei at 600 MeV/u excited by a lead target. The solid red curve represents fission decay. The blue dashed line represents 1n-decay channel, black dotted and green dotdashed curves respectively 2n- and 3n-decay channels. Bottom right: The same as the top right but for the probabilities. next A semi-empirical model of the fission-fragment properties T he has but num com com L I S E + + c o d e u s e s a s e m i- e m p ir ic a l m o d e l o f J . B e n lliu r e [ B e n 9 8 ] w h ic h s o m e s im ila r itie s w it h p r e v io u s ly p u b lis h e d a p p r o a c h e s , e .g . [I tk 8 6 , It k 8 8 ], in c o n t r a s t t o t h o s e , B . s m o d e l d e s c r ib e s t h e f is s io n p r o p e r t ie s o f a la r g e b e r o f f is s io n in g n u c le i o n a w id e r a n g e o f e x c ita t io n e n e r g ie s . T h e p e t it io n b e t w e e n e v a p o r a t io n o f d if f e r e n t lig h t p a r t ic le s a n d f is s io n is p u te d w ith t h e L is F u s e v a p o r a t io n m o d e l. F o r a g iv e n e x c ita t io n e n e r g y E , t h e y ie ld Y ( E , N ) o f f is s io n f r a g m e n ts w it h n e u t r o n n u m b e r N is c a lc u la te d b y th e s ta tis t ic a l w e ig h t o f t r a n s itio n s ta te s a b o v e th e c o n d it io n a l p o t e n t ia l b a r r ie r : N E V U dU N Y E , N 0 N CN N 0

, N E V U dU N 0 w h e r e V ( N ) is t h e h e ig h t o f th e c o n d it io n a l p o t e n t ia l b a r r ie r f o r a g iv e n m a s s a s y m m e t r ic d e f o r m a t io n , N is t h e le v e l d e n s it y f o r a n e n e r g y U a b o v e t h is p o te n tia l a n d N C N is th e n e u t r o n n u m b e r o f t h e f is s io n in g n u c le u s . T h e t o ta l p o t e n t ia l e n e r g y a t t h e f is s io n b a r r ie r ( s e e F ig u r e ) is g iv e n b y t h e s u m o f f iv e c o n t r ib u t io n s : V N N V sh , 1 N V sh , 1 N CN V sh , 2 N V sh , 2 N CN V mac N Figure. LISEs calculation of potential energy at the fission barrier for 238U, as a function of mass asymmetry expressed by the neutron number. N w h e r e V m a c is t h e s y m m e t r ic c o m p o n e n t d e f in e d b y t h e liq u id - d r o p d e s c r ip t io n b y m e a n s o f a p a r a b o lic f u n c t io n . T h is p a r a b o la is m o d u la t e d b y t w o n e u t r o n s h e lls , lo c a t e d a t m a s s a s y m m e t r ie s c o r r e s p o n d i n g t o t h e n e u t r o n s h e lls V s h ,1 a n d V s h ,2 in t h e d a u g h t e r f r a g m e n t s . References [Ben98] J.Benlliure et al., Nuclear Physics A 628 (1998) 458-478. [Itk86] M.G.Itkis et al., Yad.Fiz. 43 (1986) 1125. [Itk88] M.G.Itkis et al., Fiz.Elem.Chastits At.Yadra 19 (1988) 701. next Pairing corrections Pairing (or odd-even) corrections have been done in the code in accordance with [Ben98]. Odd-even corrections can be turned off in the Fission properties dialog. Using the Fission cross-section plot (summary) button the crosssection distributions versus

the fragment neutron number, atomic number and mass for different excitation energies can be plotted (see Figure). Left top plot represent cross-section distributions without oddeven corrections and post-scission nucleon emission. Figure. Calculated fission fragment production cross-sections for different excitation energies. Crosssections were normalized to 1 mb. Left top plot: Initial distributions (without odd-even corrections and post-scission nucleon emission) versus the fragment neutron number. Left bottom: Final (after using oddeven corrections and post-scission nucleon emission) cross-section distributions versus the fragment neutron number. Right top: Final cross-section distributions versus the fragment atomic number. Right top: Final cross-section distributions versus the fragment mass. next Post-scission nucleon emission: Fission cross-section matrix T Th he e f i fsi ss sioion n c cr or os ss s- s- se ec ct iot ion n m ma at rtirxi x r er ep pr er es se en nt st s a an n a ar rrar ay y o of ff l fol oa at tv va al ulue es s ( 3( 32 2 b bi t ist s) )o of fd dimime en ns sioion n ( Z( Zmma ax x N Nmma ax x) ) w wh he er er e Z Zmma ax x isis t ht he e mma ax xi mimu umm Z Z p po os ss sibibl ele t ot o b be e u us se ed d inin t ht he e c co od de e ( 1( 13 30 0) )a an nd d N Nmma ax x i si s t ht he e mma ax ximi mu umm n nu ummb be er ro of fn ne eu ut rtor on ns s inin a an n e elelemme en nt t p po os ss sibibl el e inin t ht he e c co od de e ( 2( 20 00 0) .) . T Th he e c cl al as ss s F Fisiss sioion nC CS S r er es sp po on ns si bi blele f of or r f i fsi ss sioion n f rfar ag gmme en nt t p pr or od du uc ct i toion n c cr or os ss s- s- se ec ct iot ion ns s h ha as s 6 6 F FC CS SMM w wh hi ci ch h a ar er e k ke ep pt ti ni n t ht he e mme emmo or yr y. .T Th he es se e mma at rtirci ce es s c co on nt at ai nin t ht he e f of olloll ow wining g v va alulue es s f of or re ea ac ch h isiso ot ot op pe e: : 1 1. .F Fi nina al l f rfar ag gmme en nt t p pr or od du uc ct iot ion n c cr or os ss s- s- se ec ct i toi on ns s, , 2 2. .E Ex xc cit ite ed d f rfar ag gmme en nt tp pr or od du u- c ct iot ion n c cr or os ss s- s- se ec ct i toion ns s, , 3 3. .d dA A_ _o ou ut , t , 4 4. .d dA A_ _i nin, , 5 5. .d dN N_ _o ou ut , t , 6 6. .d dN N_ _inin. . C Co ou ul ol ommb b f i fsi ss sioion n s sc ch he emma at i tci c i si s s sh ho ow wn n ini n F Figigu ur er e, ,w wh he er er e A A* *i si s t ht he e e ex xc cit ite ed d f rfar ag gmme en nt , t ,a an nd d A Af ft ht he e f inf ina al lf rfar ag gmme en nt ti ni n g gr or ou un nd d s st at at et e. .T Th he en n d dA A = = A A* *- -A Af fi si s t ht he e n nu ummb be er ro of fe emmi t itt et ed d n nu uc cl el eo on ns s, ,a an nd d d dN N isis t ht he e n nu ummb be er ro of fe emmit itt et ed d n ne eu ut rtor on ns s f rfor omm t ht he e e ex xc ci t iet ed d n nu uc cleleu us s. .L Le et st s d de ef inf ine e d dA A_ _inin, ,d dA A_ _o ou ut ta as s: : 1 1. . d dA A_ _i ni n isis t ht he e v va alulue e u us se ed d o on nlyly f of or rt ht he e f inf ina al lf rfar ag gm me en nt ta an nd d e eq qu ua al lt ot o a av ve er ar ag ge e n nu ummb be er r o on n n nu uc cl el eo on ns s e emmit itt et ed d b by y e ex xc cit ite ed d f rfar ag gmme en nt st s t ot o g ge et tt ht he e f ifni na al lf rf ar ag gmme en nt t A A A A dA dA dAdA _ _in in( A( A ) ) A A A A 2 2. . d dA A_ _o ou ut t isis t ht he e v va alulue e u us se ed d o on nl yl y f of or r t ht he e e ex xc cit ite ed d f rfar ag gmme en nt t a an nd d e eq qu ua al lt ot o a av ve er ar ag ge e n nu ummb be er r o on n n nu uc cl eleo on ns s e emmit itt et ed d b by y t ht he e e ex xc ci tiet ed d f rf ar ag gmme en nt t j A A3* 3* A A3 f j3 fj dA dA3 j3 j dAdA _ _outout ( A( A3* )* ) j 3 j A A3* 3* A A3 f j3 fj f 3 f 3 j * 3 j* 3 j j

j f 3 f 3 * 3 j* 3 j 3 j 3 j f 3 f 3 j j next Post-scission nucleon emission: excitation energy Ifth e o p tio n ta k e fr o m s y s te m a tic iss e tin th e E x c ita tio n e n e r g y

b o xo fth e 2 D fr a g m e n tp lo td ia lo g ,th e n th e e x c ita tio n p e n e r g yo fth efr a g m e n tsista k e na sth es u m o fth ee x c ita tio ne n e

r g ya b o v eth eb a r r ie ra n din tr in s ice x c ita tio ne n e rg y E B e n 9 8 ]: d iis d s[ TXE E C * E D * E A * B E x x x f d x x

x f d is is /1 / w h e r e B th e h e ig h to fth e fis s io n b a r r ie r ,a n d E sp a r a m e te r iz e d in th e fo llo w in g w a y[W il8 6 ]: f

d is fis d si 2 2 E 3 .53 Z A 34 .25 . d C N CN dis is CN CN /2 / T h efin a le x c ita tio ne n e r g yisa ttr ib u te dtoth efis s io np r o p o r tio

n a llytoth e irle v e ld e n s ityp a r a m e te r sb a s in go nth e r m a l e q u ilib r iu m a so n e a p p r o a c h e ss c is s io n [B is 7 0 ],o rin o

th e rw o r d s ,th e n u c le a rte m p e r a tu r e so fC *& D *fr a g m e n tsa r e e q u a l T ( C * )= T ( D * ) .W e r e fe rto th is T X E m

e th o d a s d is s ip a te d e n e r g y m e th o d . T h eu s e rc a ns e le c t th es e c o n da lte rn a tiv ed e fin itio no f th eto ta le x c ita tio ne n

e r g y( Q v a lu e m e th o d )b yH .R .F a u s t [F a u 0 2 ]in th e F is s io n p r o p e r tie s d ia lo g : 2 2 f A a TXE E *

a Q x C * D * x C * D * /3 / w h e r e a n d a re th e le v e ld e n s ityp a r a m e te r sfo rth e e x c ite d fr a g m e n tC *a n d D *

,Q isth e r e a c tio n Q v a lu e ,a n df is m C * D * C *a D *a th e c o n s ta n tc o n n e c tin g fr a g m e n te x c ita tio n a n d Q v a lu e .T

h e v a lu e fo rf w a se s t im a te d to b e e q u a lto 0 .0 0 4 5 [F a u 0 2 ]. t e R e f e r e n c e : [B e n 9 8 ] [F a u 0 2 ] [W il8 6 ]

J .B e n lliu r e e ta l.,N u c l.P h y s .A 6 2 8 ( 1 9 9 8 )4 5 8 4 7 8 . n H .R .F a u s t,E u r .P h y s .J . A 1 4 ( 2 0 0 2 )4 5 9 4 6 8

. F a u s h y . 0 0 2 4 5 9 B .D . W iilk in s e ta l. ,P r o c . In t.S y m p o s iu m N u c l.F is s io n ,H e a v y Io n In d u c e d R e a c

tio n s ,W .S c h r o d e r ,e d .H a r w o o d 1 9 8 6 . . . c . y s c n e next Post-scission nucleon emission Red solid curve: calculated mean number of evaporated nucleons as a function of the excited fission-fragment atomic number in fission of the excited nucleus 238U with excitation energy equal to 15.4mrad.MeV. Red dot-dashed curve: calculated mean number of evaporated neutrons as a function of the excited fission-fragment atomic number in fission of the excited nucleus 238U with exc.energy equal to 80mrad.MeV. Blue dot-dashed curve: calculated charge change as a function of the excited fission-fragment atomic number in fission of the excited nucleus 238U with excitation energy equal to 80mrad.MeV. Calculated number of evaporated neutrons for/from final/excited fission tin fragment and calculated charge change as a function of the fission-fragment mass number in fission of the excited nucleus 238U with excitation energy equal to 80mrad.MeV. next LISEs plots for Coulomb fission mode Cross Sections Calculated fission fragment differential cross sections for the fissile nucleus 238U for excitation energies: left 12 MeV, right 80 MeV. The total fission cross-section is normalized to 10mrad.mb.

next LISEs plots for Coulomb fission mode Total Kinetic Energy Calculated kinetic energies of both final fragments for the fissile nucleus energies: left 15.4 MeV, right 80 MeV. 238 U for excitation next LISEs plots for Coulomb fission mode Number of emitted nucleons (dA,dN,dZ) Calculated number of emitted nucleons from one excited fragment for the fissile nucleus excitation energies: left 15.4 MeV, right 80 MeV. 238 U next Comparisons with experimental data Cross Sections (1) Experimental production crosssection of cesium isotopes (black squares) with a uranium beam (1GeV/u) in a lead target [Enq99]. Cross sections calculated with the TXE method to set 1 (Qvalue). See details on plots. Fragmentation parameterization EPAX2.15 is shown by blue dotted-dash line. [Enq99] T. Enqvist et al., Nucl.Phys. A658 (1999) 47-66. next Comparisons with experimental data Cross Sections (2) Experimental (black solid squares) integrated nuclearcharge (left plot) and neutron number (right plot) crosssections for EM fission of 238 U(1GeV/u) in a lead target [Enq99]. See details for calculation curves in plots. The

Dissipated energy TXE method (0) was used for calculations. [Sch00] K.-H.Schmidt et al., Nucl.Phys. A665 (2000) 221-267. next Comparisons with experimental data Total Kinetic Energy The total kinetic energy as a function of the nuclear charge of the fission fragments. Experimental (black circles) values of every element correspond to fission of 233U having passed the lead target at 420 MeV/u [Sch00]. Calculations were done the excitation energy equal to 13.1 MeV what corresponds to the average energy of the EM fission excitation function in the reaction 233 U(420mrad.MeV/u)+ Pb. See details for calculated curves in plots [Sch00] K.-H.Schmidt et al., Nucl.Phys. A665 (2000) 221-267. next Comparison of different calculation methods LISE++ Monte Carlo 2D-plot Energy-X of the fission-fragment 100Zr in the reaction 238U(920MeV/u)+Pb(5g/cm2). Angular transmission of the fragment is 100%. 2D-plot Energy-X of the fission-fragment 100Zr in the reaction 238U(920MeV/u)+Pb(5g/cm2). Angular acceptances: H= 20 & V =20 mrad. Angular transmission of the fragment is 33.6%. next Comparison of different calculation methods Mocadi* 2D-plot Energy-X of the fission-fragment 100Zr in the reaction 238U(920MeV/u)+Pb(5g/cm2). Angular transmission of the fragment is 100%. 2D-plot Energy-X of the fission-fragment 100Zr in the reaction 238U(920MeV/u)+Pb(5g/cm2). Angular acceptances: H= 20 & V =20 mrad. * the MOCADI code: http://www-linux.gsi.de/~weick/mocadi/ next Projections (Comparison of different calculation methods) LISE++ DistrMethod

LISE++ MCmethod MOCADI next Short-term plans for fission Reconsider the secondary reactions calculation mechanism in the target in case of Coulomb fission Use more points (now just one point) for the EM fission excitation function in the fission-fragment production cross-sections Incorporate the new model of fission-fragment yields prediction of V.A.Rubcheya & J.yst as alternative to Benliures model Development of the abrasion-fission (nuclear fission) mechanism in the code Incorporation of Atomic Mass Evaluation (AME2003) database for more precise mass calculations next Thank You for Your attention! Register in LISEs sites to get information about new versions of the code http://dnr080.jinr.ru/lise or http://www.nscl.msu.edu/lise Acknowledgements Acknowledgements Theauthors authorsthank thank Dr.mrad. Dr.mrad. lexandraGade Gade for forcarefully carefullyproof proofreading readingthe themanual. manual. The AAlexandra Further, the authors gratefully acknowledge Dr.mrad.Helmut Weicks fruitful remarks, his Further, the authors gratefully acknowledge Dr.mrad.Helmut Weicks fruitful remarks, his careful checking checking LISE++ LISE++ calculations calculations inin fission fission fragment fragment kinematics, kinematics, and and MOCADI MOCADI careful calculations performed by him to compare with LISE

simulations. calculations performed by him to compare with LISE simulations. TheLISE++ LISE++authors authorsthank thankProf.mrad. Prof.mrad.CC arlosBertulani Bertulanifor forthe thehelp helpinindeveloping developingEM EMcrosscrossThe arlos sectionsprocedures proceduresininthe theprogram. program. sections Weare aregrateful gratefultotoProf.mrad. Prof.mrad.BBrad radSherrill Sherrillfor forcontinuous continuoussupport supportand andguidance. guidance.Fruitful Fruitful We discussionswith withProf.mrad. Prof.mrad.MM ichaelThoennessen Thoennessenare aregratefully gratefullyacknowledged. acknowledged. discussions ichael next

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