Calculation of Effective Resonance Integrals
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1 Clculo of ffecve Resoce egrls S.B. Borzkov FLNP JNR Du Russ Clculo of e effecve oce egrl wc cludes e rel eerg deedece of euro flux des d correco o e euro cure e smle s eeded for ccure flux deermo d euro cvo lss o e RN d BR- M fcles. s well kow euros re dvded o erml oce d fs euros. erco of e oce euros w e ucldes s descred oce egrl: d J were s e cdmum order wc roxmel eul o.5 ev -rdve cross-seco. Te vlues of e oce egrls for dffere ucldes re eed e dooks look for exmle []. Bu s deermo s sed o e ssumo oce euro flux des oes o recrocl fuco from eerg Ferm secrum. A rel secrum dffers from Ferm secrum. For exmle euro flux des from RN d BR-M fcles s ex ecul: mxmum for erml euros es s e eerg of -5 mev d oce flux des deeds o eerg ccordg e ex formul: were α =.5 -. s e euro flux des ev. ffecve oce egrls dffer from e vlues e dook. A frs em o clcule effec of euro secrum o e ws mde de Core e l. []. Te roduce e effecve oce for ever uclde. erg of e effecve oce s close o e eerg of e srog rel oce w smll eerg. Te cross-seco s dvded o wo rs: oe r oes /v low d oer r s deermed e oce. Te gve e ex formul for e effecve oce egrl:.9 eff.9 eff
2 .5 Te fcor.9 s eul o e exso Some ers go e euro secrum from BR- fcl ws vesged cvo meod []. Te clculos ccordg o formule ve ee mde. Te meod of more correc clculos for effecve oce egrls s roosed s work. ver uclde s lo of oces. our me oe c crr ou clculos wc clude umer of oces. Te ccure descro of erco of e oce euros w e ucle s sow e ex formul. Numer of rdocve ucle wc ered durg sor me of rrdo s eul o: dn d d rr ex Te e effecve oce egrl s eul o: d ex 5 Oe c es receve f d s exso s eul o J. A frs we clcule e vlue of α wou cludg of euro cure. Neuro oces re descred e Bre-Wger formul: Were k k g r A.97 - euro momeum cm - us eerg s ev A A omc weg for e rge ucle r s e oce eerg - euro d rdve wds s e ol oce wd g sscl weg wc deeds o rge ucleus s d oce ol momeum. We c dvde cure cross-seco o wo rs logous o e work []:.5 Te frs erm desc l from erml cross-seco ccordg o /v low k g r 7 - erml euro cure cross-seco. Secod erm desc cross-seco from osve oces.
3 For rrow oces oe c eglgle e euro wd s eerg deedece. We c roduce e vlue r x d rewre : Here g J k Te oce re s: g 8 k x x - s e cross-seco e oce mxmum. A d 9 x x Te ro o e oce egrl from oe oce s eul o: Te ul of e clculos w kr r..5 r d r kr.97 r.87 r s e ex formul: k.5 g r Bu s exso does o clude e euo of e euro flux e smle. We eed o clcule e egrl 5 o comuer. We ve wre e code wc clcules e effecve oce egrls w rel eerg deedece for euro flux des d smle ckess. Te clculos of e oce form deedece from e emerure d smle ckess Te rge ucle ke r e erml moo wc ffecs e ure of euro erco w em d leds o gger oce wd. Te cure cross-seco s eul o x r were x Accordg o Bee d Plcek: r k B T A - Doler wd.
4 d x x ex Te rol for euro cure smle w e ckess : x N d P ex cos N s e umer of e rge ucle e volume u. For ver smle N P 5 Te oce self-soro fcor s P P G. Te clculos of e fuco x d G s e comlex sk. Ts sk euvle o e clculo of e ex egrl []: x d G ex 7 were N. Tese fcors ve ee clculed for ever oce serel. Te oce rmeers ve ee ke from [5]. So e fl exso for e effecve oce egrl s: r v eff G. 8 Te fuco ψθх ve ee clculed e Pde roxmo meod []. 8 8 x x x x x x x 9 s formul d exsos for e coeffces re ke from [8].
5 <G> Ps X Fg. Te fuco x for dffere vlues of θ. Au cm Fg. Te uls of clculos for verge G fcor s fuco of gold fol ckess. 5
6 eff To o G fcors oe eed o clcule e egrl 7. Te egro s ee mde Smso meod. Te fcor verged o umer of oces eff. T G ve ee clculed. Our uls re comred w e uls of e oer works d w e exermel d o e rsmsso of e oce euros roug e gold fols [78]. Au Fol ckess cm Fg.. Te clculed vlues of e effecve oce egrl s fuco of e fol ckess for dffere vlues of e rmeer α. Cocluso. Te rogrm for clculos of e effecve oce egrls wc cludes e rel eerg deedece of e flux des d smle ckess s creed. Refereces. T.S. Belov e l. Rdve cure of e euros: Te dook M. ergoomzd 98 Russ.. De Core e l. Jourl of Rdolcl d Nucler Cemsr v. No V. F. Peedov A.D. Rogov JNR Sor Commucos 75-9 Du 99.. G.M. Roe Te Asoro of Neuro Doler Brodeed Resoces KAPL S.. Sukoruck e l. Tles of Neuro Resoce Prmeers Ldol-Borse Num. D d Fucol Reloss Scece d Tecolog Grou V. suvolume B ed. H. Scoer Srger R.S. Kesvmur R. Hrs Nucl. Sc. g. v O. Scerkov H. Hrd Jourl of Nucler Scece d Tecolog v. 9 No H.T. Puog e l. Aled Rdo d sooes v
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