Schopper, H.

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Marz 1965". ,f,..KFK 313Institut für ExperiITlentelle KernphysikThe charge dependent nuclear interaction and FerITli n-.a ri..-",.,eleITlents of ß decayH. SchopperKERNFORSCHUNGSZEHTRUfIJ KlI.RLSRUHEMar:: 1965 KFK 313Institut ~Ur Experi~entel_e KernphysikThe cna~ge jepende~~ ~~cle3~ lnter3c:i~n ~ni Fermi matrixH Schoppe.o:Gesellschaft _uc KernLors~hun~ ~ b H. KarlsruheThe charge dependent nuclpqr interqcti~n and Fermi matrixelements of B decayIf charge indepennpnce of ~uclear f~rce3 were v~lid the Fer-mi matrix eleme~ts M~ ~f D T = ~ 1 8 transitions w~uld va-"'1nish. Theref'f')re deviatio~s f'rf'r:: -:::he.rge ir..depenjen::e can befound by determining MF f'rf'~ J-y circ~lqr po~alizatior.. cnr-~elation or S asym~etries fr~~ pola~ized r..~~lei.Blin Stnyl~ anj Le To~rneux [1J nave introducej the rhargedependent r..uclear p~te~tia1~!/:")~-n( 1 )(n ~ (\[ -r(, '-'+1 ,.i) +~ - 3 3Charge indepenien~e ir::p~ies r = q = r = s = (' and forr1 rpe~dent onc has r sWith this potential Slin-Stoyp and Novakovic [21, r ,L3 i de-rived the ff')11owing Exrrcs3i~r..3 :f')r ?er~i ~atrix ele~entsNa 24 . " 0,012 1 .. h,7 3, h,7lv ............ - P + r. ~'.4 41 IvJ-r-, ().49 (p-q) + (' .. 93 (r-s;: =l'Se 44 IV'! ,'-" 2h, (p-q) 0,40 (r-s): ~ lp =]Vir.. r::;2 ~v'~ :~~ C',01r::; o "'r; (lJ+q) ~ , .L7 ( .... \= - \ <; Qc + r.s;In addi ti on ~rovakovL' r31 has rel8- ted p ani r to the mass"4 .' -'.dL ferenc:e oetween 1\.1"- "lnd jhL~ ~:rld oot2ins(2 )(3 )( 4 )- 222,~ P + 17.~ r 1.370New precise meqsurements of the 8-y circular polarizationcorrelation of Ha 24 and A41 by 3ehrens and Schopper [4J to-n 44 S2 ( h T bl )gether with older data for oC qnd Mn \see t.e 8 emake ~ determination of p q, rand s possible. This can beactieved in the follovlin; ',','ay. Co~r;tining eq. (1) ;:tnd (6)one obt8ins6.7 + C',C'2(- S, 92:0,3 ,= ,II _c, 7+0 -z,\,. ~', - 5/ <.0The 8mbiguity origina~es frG~ t~~ ;act ttat expe.imentallyonly the sign of Mp/M GT ca~ to de~prm:ned. Since the signof rv']~rr' is not ;,cncwn qlso the sign o:G M~ remains ur,deterrr;in-u_ed. Theoreti~al ca:culations [~J i~di~a~e that the signs ofMp f(")r 3,-,4 4 and fv'ln~2 2,Y'P c(")t!- nec::",tlv, This will be takenfor gra~ted [(")1' toe 2ubseqJent analysis.p..dding and subtra .:::tir:.r; (3 ) Et~d I S \ ~.- i '? 1cl ~e ~. , I" 1. 7+fl ~ ;: I , '-t..:..\ ... r;I _ ,(le' - 3 .. ":;' \.\ ! /P - 1 9r xJ 2"'+n( ,I <:G\ - 1- - •'-- /2s±6! I c, 41 , ) ,)) ;[ I "', ), ~ ,,,-) ~ .. ? "q - ..L ':;is ::; l x .J.. ,T~'S) '- 0(3 )(9), -3If p = - 6.7 x ~ConA fin:ls='irst relation(10)7.'T'n' p "a1'u'e If'\J 1'::-_7 "Y', "C""'T ,'!,","''; ~,;-1~eOr"pn- Wl'th yo "'s.J..~ V,J.. \ ~, .... ,J ..L,. J" J " '..A ,,-,_ ",,~ ~ • _ "24 ~ '\ded'Jced :rrl':'l the lJ~, r'J.c-:'8, \\'he::ec>s lS--'!, = 17 is ::ao small.+-" rr (,,41\This implips ,h8t "',2,,\ ) >C. It 11:0U~C~ bc: very ir..terestingto explqiu this err.~ricial :4esJlt cy nuclo0: ~odel cqlcu12-':iOES.In order t!J 44Se:~ust oe includejc Ca~bi~in~ eq. (4) ~nd (S) givQ~q == ') C''''c: + (' IV",',,. IS = (J,01 cc, + Ci, C<J4-,- 3 -As a check L~e value of s may be put into eq. (9) and oneabtA-insq =<nThe upper valu.e a~recs \';i t.h thatborates that M~(~ ') ~s positiv.l'44deduced 1":'or1. Se ~nd CO:CTO-Summarizing ~ne can state that all jat~ ~re consistent anda re8.sl"\nable set of p~ rarr:et ers 'vlf"\uld t'9lr"3 p = -6,7 + r .9 Cl 2 ln3r 6,7 + r:,3-lo3q 5~ + /' -.!r-.13 ....... 1 :' + 4== ':: -1.-'---' C -=These DL<.iTJbers sr.ow "::'h~t there is a def"inite devi8.tion fror.12harge independence. Als' charge sy~metry is violated al-though "'L,n a lesser jeg-ree (since IIII<lql J 1:~\<.lsl).In additi~n an ~~pre:lablp spin dependence is :~und. sincerand s are ~f the same order of ~ag~itude than p and q.~ltm8n and ~a~Donald [El ~ave derived p) T, q, and s from14 14the enercy level shifts and the ft values of thr ~ , N ,14 +-C sys0em. Data of the p-p and r~-p scattering are ~lsouspd. Our val~es of p and r agree nicely with their case 11.These authors, however find negative values lrr q and s.It is not quite ...:lea~· if ttis disc:epqncy csn be asc:!"ibedt~ 8. sign a~biguity.Of course, the quantitative results f~r tne pgrameters p,q,r and s shnulJ no: be t~ken toc serious since eq. (2) to(6) have been de~ivpj on the bqsis of ~ pqrticula~ nucl~a~model. However, it see~s ~h~t the Fer~i ~qtrix elementscannot be explained er.tirel:i" by 0rdirl':t::' y Coulo;'L; e:'_ects.- 4 -B-y c.:irc.A.syIT,IYJet Y>ypc~'~ Re';:' erenee2 4Na '41,0"1,7 + 0,':'~) + (3ehre~s .qnd SchJpper[4]11 )1S:' " -O,i)l + 0 013~<~"~ 1:)2 -'),029 + r:,C:03[I, -,L;-l E.2ehr~n~~ rt.2~~opper,r r l'nL " ~== ],1 ~ 0; ~. 7 (1 S'! ~ .8.1 J 12 ~ 2(1 ( 1~12J L.~.M8.nn et 8,1 , Ptys ~cc L~ 9, 39S (1064)

The charge dependent nuclear interaction and Fermi matrix elements of β decay

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The charge dependent nuclear interaction and Fermi matrix elements of β decay

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