The Effect of Core-Polarization on Nucleon-Nucleon. Realistic Potential Parameters in. Doubly-Magic Nucleus 40 Ca

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1 Adv. Suds hor. Phs., Vo. 8, 04, o. 0, HIKARI Ld, hp://dx.do.org/0.988/sp h Effc of Cor-Poro o Nuco-Nuco Rsc Po Prrs Dou-Mgc Nucus 40 C Md Aus Fcu of Scc, Phscs Dpr- 04 h Uvrs, Sud Ar & A- Uvrs, ord Coprgh 04 Md Aus. hs s op ccss rc dsrud udr h Crv Coos Aruo Lcs, whch prs ursrcd us, dsruo, d rproduco du, provdd h org work s propr cd. Asrc o sud h cor-poro ffc o rsc uco uco po prrs, h sc cro scrg for fcors h dou gc ucus 40 C sd o croscopc hor s pod. Hghr rg xcos fro s-sh cor ors d so fro h vc p-sh o hghr owd ors up o hω r cosdrd for cor-poro ccuos. h rsc Mchg hr Yukw po for N-N rcos for h cor-poro horc ccuos o cosdrd. PACS : 5.0.Dh Kwords: Nucr po, Sh od, Cor-Poro. hs ppr s prford durg h sc v 0-0 o h Uvrs, Phscs Dpr, Sud Ar.. Iroduco h org of h ucr forc s cr pro of ucr phscs. I hs og hsor sc Yukw H. Yukw,95 proposd h sc o-po xchg po OPEP of h rg of h po Copo wv gh.

2 448 Md Aus h cro scrg procss c xpd ccordg o h frs Borpproxo s xchg of vru phoo crrg ou q w h cro d h ucus. Dfors, r. d Wck, 966;.O. Nwo, 975. Accordg o hs pproxo, h rco of h cro wh h chrg dsruo of h ucus s cosdrd s xchg of vru phoo wh ro gur ou og h drco of h ou-rsfr q, hs s cd Couo or ogud scrg. O h ohr hd, h rco of h cro wh h sp d curr dsruos of h ucus gvs rs o h rsvrs scrg. For h r p, h procss s cosdrd s xchg of vru phoo wh gur ou ± og q drco. As cosquc of pr d rvrs vrc, o crc upos c hv ogud copo, wh oh crc d gc upos c hv rsvrs copos. Rd. hv surd h gc for fcors of h p-sh uc 6 L, 7 L, 9 B, 0 B, B, d 4 N gh-rg cro scrg hghr ou rsfr Rd., 97. h scrg fro hos uc ws dod h ocup ou. h sc cro scrg for fcor of soscr d sovcor uc C d 6 O hs sudd Md Aus., 0.h rsus dc h o rproduc h xpr d h dxur fro hghr ors d h cor poro ffc shoud roducd. Ecro scrg for fcor wh cor-poro ffc for gv d posv pr ss of C hs sudd Huss, 00. I h ow q-rgo h rsus show good gr wh h xpr d. Nd N. Ad, 00 hs sudd sc d sc cro scrg for fcors for h sr pr ss of psh uc 6 L, 7 L, 9 B, 0 B, d B h fr work of h -prcs sh od. Erg xcos up o 6 hω r cosdrd for cor-poro ccuo, wh MSDI s rsdu rco. h rsus showd good gr wh h xpr d ow q-rgo d h vrg of Couo for fcor C vus co ou 90% of h vrg xpr vu wh h cor-poro ffcs r cudd. Cor-poro ffcs o Couo for fcor C svr scd p-sh uc 7 L, 0 B, C, C hv dscussd Rdh R.A. Rdh., 00 Corporo ccuo s foud ss oh h rso srghs d ou rsfr dpdc of for fcors. A good gr wh h surd d ws od. h go of h prs ppr s o us h rsc ffcv uco-uco NN rco s rsdu rco o ccu h cor-poro cp ffcs hough croscopc hor whch cos sh od wv fucos d hgh xd ss usg dus NN prrs. W w dscuss h cor-poro ffcs o h sc cro scrg ogud for fcors for h ow g ss of dou gc ucus 40 C. h NN rco dopd h prs sud s rsc rco w wo ucos, h Mchg hr Yukw po. hs rco s usd s h rsdu rco w ucos h cor, d ucos xcd o hghr ors.

3 Effc of cor-poro 449 h drvo of cp ffcs wh hghr cofguro h frs ordr pruro hor d h wo-od rx s of hr pr of h rsc rco: cr, sp or d srog sor forc w roducd. A copur progr s wr usg FORRAN 90 gug o cud rsc rco MY h org cod Ur, 009 whch ccus h od spc for fcors ro-ordr.. Fors For cosd-sh uc, h srucur of h ow-g xcd ss r sudd hrough prc-ho ods whch r -Dcoff Approxo DA. Accordg o DA, h groud s s rd s dpd prc od cosd sh, wh h xcd ss of cosd-sh uc r dscrd s r coo of prc-ho xco whch s crd xco of uco fro h cosd fd sh o hghr uoccupd sh vg ho wh h cosd sh. h rsdu rco usd hs ppr s h Mchg su of hr-rg Yukw MY po k fro rf. Brsch.,977. hs po s drvd fro h fg of prrd hr Yukw rd dpd for of cr, spor d sor forcs wh h hroc oscor rx of Rd sof-cor po Rd, R V V V Y r / R so c V Y r / R S r r V V r Y r / R S V c, V so d V r cr, sp-or d sor prs of h MY po, rspcv. h vr r s rv coords for h dsc w h rcg wo prcs, d Yr s Yukw fuco, S s h sor opror d V, R prrs h k spc vus ccordg o h MY po copo d h ch of h wo-od rco, gv wh h prrs of Rd k fro rf. Ar., 98. h ucr ogud d rsvrs for fcors r xprssd r of rducd rx s of cro scrg opror s Brow, 985 F 4π η f f f η q f f q Z f M c. q Ff. s q F 4 ˆ

4 450 Md Aus whr h rp-r s h h rx s r rducd oh gur ou, d sosp, d η sc h ogud L, rsvrs crc, d rsvrs gc oprors, rspcv. h s wo r q.0 r h corrco fcors of h cr of ss c. d f uco s f.s gv W, 96, rspcv q 4A Fc. q F f. s 5 q pq A 5 whr p 0.4 f, s h oscor gh prr or s prr, d, A s ucr ss ur. For crogc rcos,,0 d f whch gvs M 0, whr Z N Z 6 h -prc ss rx rducd sp-sosp spc c wr rs of sg-prc rx s Do d Sck, 984 ˆ η ˆ η χ 7 whr f f χ s h gvcor h od fro h dgoo of h DA Ho rx h prsc of h MY po. h ss d r h sg-prc wv fucos of d f ss, rspcv. h ogud Couo scrg cos fro h rco of h cro wh h chrg dsruo of h ucus. h ogud opror s dfd s So., 994 L L r r r M q M M qr ˆ ρ d 8 wh 0,,, L r M M qr qr YM rˆ 8 whr qr s h sphrc Bss fuco, Y M rˆ s h sphrc hrocs fucos, d ˆ ρ r s h ucr chrg ds opror whch s gv wh r r r ˆ ρ δ 9

5 Effc of cor-poro 45 τ, τ 9 h rducd sg-prc rx of h ogud opror c wr s r Y qr L, ˆ ˆ 0 whr h rducd rx s of h sphrc hrocs s gv Brussrd d Guds, 977 r Y / 0 / 4 ˆ / π So, q.0 c wr s L qr C P,,, ˆ, h rx s of h rd sg-prc wv fuco c sovd c s D Fors d Wck, 966 ; ; F / /!!!! / / /!!!! 0 / 0 qr whr q, s h g fuco d F s h cofu hprgorc fuco, dfd s Arfk, 970 L! ; ; F β α β α β α β α 4 I our ccuo of h for fcor, h groud s wv fuco s odfd o cud dxur fro hghr cofguros, whch s vr por o dd or dgr of cocv, s foows,989. δ γ 5 whr γ d δ r xg prrs wh δ γ. hs xso h groud s wv fuco w odf o h rd pr of h rducd sg-prc rx, wh h gur pr s s uchgd

6 45 Md Aus. Rsus d Dscusso h groud s of h dou gc ucus 40 C s, 0, 0 ssud o for h cosd s /, p /, p /, d 5/, s / d d / shs. h ss xpcd o os srog xcd fro cosd-sh r r coos whch o uco hs rsd o hghr shs f 7/, p /, p / d f 5/, forg pur sg-prc-ho s. h rsug vus of h puds r usd o ccu h rducd prc rx s of h cro scrg for fcors whch r fucos of h ou rsfrs q r ccordg o quo 7. h rducd sg-prc rx of ogud opror s ccud ccordg o q.. h squrd for fcors for h ogud s ccud ccordg o q. 4, whch ks o cosdro h corrcos for h cr of ss oo d h f s of h uco. π Our DA ccuos for h gv pr 0 ss, Ex MV,6. 58 d 5,4. 49, prdc h rg gvus 9.7, d 5.08 MV, rspcv. h do prc-ho cofguro for hs ss s f 7/ d / -. Fg. shows h ogud C for fcor for h soscr s Ex6.58 MV 40 C ucus. h ccuo of h for fcor h frwork of DA s show h dshd curv. h sod curv shows h ffc of h ddo of or cocv o hs s h odfco of h groud s wv fuco o cud p-f shs wh γ-0.4, s w s kg h cor poro ffcs o ccou roducg ffcv chrgs ff p δp fr p, ff δ fr, whr δ p.08 d δ 0.6 wh dus NN prrs of MY whch ds o vr w dscrpo wh h xpr d k fro rf. Ioh., 970. Fg. shows h ogud C5 for fcor for h soscr 5 s Ex4.49 MV 40 C ucus. h dshd curv shows h ccuo of h for fcor usg h vus of h fr proo d uro chrgs, h frwork of DA. Adxur of hghr cofguros fro p-f shs wh γ-0.96 s w s kg h cor poro ffcs o ccou roducg ffcv chrg of proo o ff p δ p fr p,whr δ p.5 wh dus NN prrs of MY, producs ovr gr wh h d k fro rf. [4]Ioh., 970 s show h sod curv. As s Fgs d, ccordg o DA od h groud s s ucorrd. I our work, h corro h groud s s ddd cudg dxur fro hghr hroc oscor ors usg xg prr, γ. Fro h prs work w cocud h h for fcor rsus of -Dcoff Approxo rqur so hc, hrfor h ccuo of for fcor for h groud s wv fuco s odfd o cud dxur fro hghr cofguros usg xg prr, γ. Aso, o hc our ccuo for h π

7 Effc of cor-poro 45 ogud for fcors, cor poro ffcs r k o ccou gvg h ucos ffcv vus o hr chrgs d g-fcor whch r dffr fro h of hr fr vus whch d o dus h NN po prrs. hs odfco h groud s wv fuco hcs h for fcor horc curvs xc. I h furhr work w pg o sud h cro scrg for fcors of su cosd-sh uc usg DA h prsc of rc rco usg ohr NN-rsc po such s CD-Bo d Prs pos. Rfrcs [] H. Yukw, Proc Mh. Phs. Soc. p 7, []. Dfors, r. d Wck; Adv.Phs.5, 966 [].O. Nwo, h crogc rco ucr spcroscop, Norh- Hod 975. [4] Rd, R.F Frosch d M.R.Yr Phs. Rv. 44, [5] Aus Md,. UK.. Phscs vo. 54, N. 4 0 [6] Huss, M.Sc.hss, Uvrs of Bghdd 00 [7] N. Ad, Ph.D. hss, Uvrs of Bghdd 00. [8] R.A. Rdh, A.A. Aduh, Z.A. Dkh, N.M. Ad, Nuc. Phs. A696,4400. [9] Ur,"Ecro scrg fro copx uc", pr A, Acdc 65- H. Prss, Nw York 009. [0] Brsch, G.,.. Nuc. Phs. A84, [] Rd, R. A. Phs. 50, [] Ar, N.,. Nuc. Phs. A98, [] Brow, B.A.,. Phs. Rv. C, [4] W, R. S. Nuc. Phs. 40, [5] Do,.W., d I. Sck. Rv. Mod. Phs. 56, [6] So,.,. Phs. Rv. C49,, [7] Brussrd, P.., d P.W.M. Gud. Sh-Mod Appcos Nucr Spcroscop Norh Hod, Asrd 977. [8] D Fors,., d. D. Wck. Adv. Phs. 5,966 [9] Arfk, G. " Mhc Mhods for Phscss ", d do, AP, Nw York 970. [0], I. Phs. Rv. C9, [] Ioh, K.,. Phs. Rv. C,8970.

8 454 Md Aus MY copo Irco ch R 0.5 f R 0.4 f R *.44 f V V V V c Sg-v Sg-odd rp-v rp-odd V so rp-v rp-odd V rp-v rp-odd :-h prrs of MY po whch f o h oscor rx s of Rd sof-cor k fro rf. [Ar, 98] *R 0.7 f for sor pr o MY copo V c Irco ch Sg-v Sg-odd rp-v rp-odd R 0. f R 0.4 f R *.85 f V V V V so rp-v rp-odd V rp-v rp-odd :-h dus prrs of MY po whch f o h oscor rx s for rco chs.

9 Effc of cor-poro 455 E- D Ioh DA γ DA γ0.4, P.08, 0.6 E-4 F L q E-5 E-6 E-7 0 qf - Fg h ogud C for fcor for 0s E MV 40 C ucus cudg h ffc of cor poro wh dus NN prrs- sod,whr h dshd s h DA ccuo. D r k fro rf. Ioh., 970 χ E- D Ioh DAγ DAγ 0.96, p.5 E-4 F L q E-5 E-6 0 q f - Fg h ogud C5 for fcor for 5 0s E MV 40 C ucus cudg h ffc of cor poro wh dus NN prrs- sod,whr h dshd s h DA ccuo. D r k fro rf. Ioh., 970 Rcvd: Mrch 9, 04 χ