HVTH: Quyn GVHD: TS. V Xun nCHNG 1: S CN THIT CA CC MU HT NHNI. L DO XUT HIN CC MU HT NHNCho n nay chng ta cha xy dng c mt l thuyt hon chnh gii thch ton din v ng n tt c cc s liu thc nghim v ht nhn. Cc vn lin quan n l thuyt ht nhn c th phn thnh hai loi l cu trc ht nhn v phn ng ht nhn. Tuy nhin, khi xy dng l thuyt ht nhn ta vp phi 3 kh khn chnh l:+ Khng bit chnh xc v lc tng tc gia cc nucleon trong ht nhn. + S lng cc phng trnh miu t s chuyn ng ca cc nucleon trong ht nhn rt ln.+ Khng th quan nim ht nhn nh mt mi trng v m lin tc. trnh cc kh khn trn ngi ta phi xy dng cc mu ht nhn, trong ht nhn c thay bng mt h vt l no c kh nng miu t cc tnh cht ca ht nhn vi cch gii thch ton hc n gin c th chp nhn c. Mu ht nhn cn gii thch c cc tnh cht c bn ca cc trng thi ht nhn nh spin, chn l, momen t, momen t cc in, cc tnh cht ca cc trng thi kch thch , m trc tin l ph kch thch ca ht nhn, v cc tnh cht ng lc hc ca ht nhn nh xc sut phng gamma ca cc mc kch thch ca ht nhn. Mi mu ht nhn ch gii thch c mt s tnh cht ca ht nhn, do c nhiu mu ht nhn khc nhau.II. PHN LOI CC MU HT NHNMi mu gii thch mt s tnh cht v ht nhn. Cha c mu no c th gii thch ton din cc hin tng ht nhn. Chnh v vy cc mu ring l vn c song song tn ti.C s xy dng mu ht nhn l gi thuyt v s c lp ca mt tp hp no cc bc t do ca ht nhn. Cc bc t do ca ht nhn c chia lm hai loi l : bc t do mt ht m t s chuyn ng ca cc ht ring bit, v bc t do tp th m t s chuyn ng ca mt s ln ht. Mt cch tng ng, mu ht nhn cng c phn thnhhai loi l mu tp th v mu mt ht, ngoi ra cn c mu suy rng, l tng hp hai mu ni trn. II.1 Mu tp th-1-HVTH: Quyn GVHD: TS. V Xun nMu tp th l mu da trn cc bc t do tp th ca nhiu ht v cn c gi l mu tng tc mnh gia cc ht. Mu ny th hin cc hiu ng tp th trong ht nhn khi qung ng t do ca cc ht trong ht nhn rt b so vi kch thc ht nhn. iu cng tng ng vi khi nim cho rng cc ht bn trong ht nhn tng tc mnh vi nhau v vi mt s t ht bn cnh. Vi ngha mu tp th coi ht nhn nh mt git cht lng hay mt vt rn. Mu tp th gm mu git cht lng v mu ht nhn khng c dng hnh cu. II.2 Mu mt htMu mt ht da trn cc bc t do ca mt ht v c gi l mu cc ht c lp. Trong mu ny, qung ng t do ca cc ht ln hn kch thc ht nhn, tc l mt ht chuyn ng c lp trong mt th nng trung bnh no . Mu mt ht gm mu v khng c tng tc d v mu v c tnh n hiu ng cp. II.3 Mu suy rngMu suy rng tnh n cc tnh cht chuyn ng c lp ln tnh cht chuyn ng tp th ca cc ht trong ht nhn. Mu ny gm mu suy rng vi lin kt yu v mu suy rng vi lin kt mnh.Hai gi thit c bn ca mu suy rng l:+ Dng cn bng ca ht nhn xa cc s magic l dng elipxoit trn xoay.+ Chuyn ng tp th trong c chuyn ng dao ng v chuyn ng quay khng ph hoi dng ca h th ht nhn.-2-HVTH: Quyn GVHD: TS. V Xun nIII. S TNG QUT M T CU TRC HT NHNHnh 1: S tng qut m t cu trc ht nhn-3-HVTH: Quyn GVHD: TS. V Xun nCHNG 2 : MU GIT CHT LNGI. KHI NIMMu git cht lng l mu in hnh nht ca cc mu tng tc mnh (mu tp th). Trong mu git cht lng, cc nucleon c xem l tng tc mnh vi nhau ging nh cc phn t trong mt git cht lng. Mt nucleon cho thng xuyn va chm vi cc nucleon khc bn trong ht nhn, qung ng t do trung bnh ca n nh hn nhiu so vi bn knh ht nhn. S chuyn ng zic zc thng xuyn nh th gi cho chng ta hnh nh v s chuyn ng nhit hn lon ca cc phn t trong mt git cht lng.Mu gt gi thit rng cc nucleon va chm thng xuyn vi nhau v ht nhn phc hp c thi gian sng di trong cc phn ng ht nhn. Mu git cho php chng ta thit lp c s tng quan ca nhiu s kin v khi lng v nng lng lin kt ca ht nhn; n rt tin ch trong vic gii thch s phn hch v cc phn ng ht nhn.Theo mu ny th ht nhn l mt git cht lng hnh cu mang in v khng nn c. Cc phn t to nn cht ht nhn l cc nucleon ch tng tc vi nhng nucleon bn cnh. Nhng chuyn ng ring l ca tng nucleon khng gy cc tnh cht ca nhn. Ch c nhng tng tc mnh ca cc nucleon mi to nn cc tnh cht ca ht nhn.Trong tt c cc mu ht nhn, mu git l mu n gin nht. Mu git do N.Bohr ra nm 1936. Tuy n gin nhng mu git c ng dng hiu qu trong vic gii thch nhiu tnh cht ca ht nhn v phn ng ht nhn.II. C s xy dng mu git cht lngMu git cht lng ca ht nhn c xy dng trn c s ging nhau gia ht nhn v git cht lng. l:II.1 Tnh khng chu nn ca ht nhn v git cht lngMt ht nhn khng ph thuc s khi lng A, tc l khng ph thuc vo kch thc ht nhn, v bng c 1014 g/cm3. Git cht lng tuy c mt b hn nhng cng khng ph thuc vo kch thc ca n. l tnh khng chunn ca ht nhn v git cht lng.Mt ht nhn l mt hng s, khng i vi mi ht nhn.38 333 300310 /4 443 3A A An nucleon cmV rR rA -4-HVTH: Quyn GVHD: TS. V Xun n38 24 14 3. 10 .1, 66.10 10 /nn m g cm i vi cht lng th mt cng khng ph thuc vo kch thc ca n (tnh khng th nn c ca cht lng). II.1 Tnh bo ha ca cc lc tng tcNng lng lin kt trung bnh trn mt nucleon tuy c thay i theo s khi lng A nhng dao ng trong khong t 7,4 MeV n 8,6 MeV, vi gi tr trung bnh khong 7,6 MeV. iu cho thy mt nucleon trong ht nhn khng tng tc vi tt c cc nucleon cn li m ch tng tc vi mt s hu hn cc nucleon gn n. Hin tng ny xut pht t tnh bo ha ca lc ht nhn. Git cht lng cng c tnh cht tng t. Trong mt git cht lng cc phn t tng tc vi nhau bng cc lc tc dng gn, ngha l mi phn t ch tc dng vi mt s phn t gn n. Cc phn t nm trn b mt ca git cht lng ch lin kt mt pha vi cc phn t khc. V vy pha cn li s to nn mt sc cng b mt.Nucleon b mtHnh 2 : Cc nucleon cha bn trong ht nhn.Da vo cc c tnh ging nhau m N. Bohr v J. Frenkel xy dng mu git cht lng. Mu git cht lng coi ht nhn l mt git cht lng mang in tch v khng nn c. Cc phn t to nn ht nhn l cc nucleon, chng tng tc vi cc nucleon bn cnh. Nng lng lin kt ca ht nhn gm nng lng th tch, nng lng b mt v nng lng Coulomb, tng ng vi 3 s hng u trong cng thc bn thc nghim Weizsacker (1.60). Phm vi ng dng ca mu git cht lng l miu t nng lng lin kt trung bnh ca ht nhn l hm ca A v Z, kho st cc dao ng b mt ca cc ht nhn hnh cu v gii thch nh tnh qu trnh phn hch ht nhn.III. NG DNG CA MU GIT CHT LNG-5-HVTH: Quyn GVHD: TS. V Xun nIII.1M t nng lng lin kt ca ht nhnCng thc bn thc nghim Weizsacker: ( )22/3 21/31( , ) ( ) 12lk lkZ AE A Z A A Z EA A Ba s hng u ca cng thc (1) c th c gii thch trn c s mu git cht lng. S hng th nht tng ng vi nng lng khi. i vi mt git nc, nhit lng cn thit n bay hi t l vi nhit bay hi. Nhit ny t l vi nng lng chuyn ng ca cc phn t to nn git nc. Cng nh vy, mt ht nhn mun tch thnh cc nucleon ring bit phi c cung cp mt nng lng thng c nng lng lin kt gia cc nucleon. Nng lng lin kt bng tng cc nng nng lng lin kt ca tng nucleon, bng A, trong l nng lng lin kt trung bnh ca nucleon trong ht nhn. S hng th hai tng ng vi nng lng mt. i vi mt git nc ta c sc cng mt ngoi. i vi ht nhn cng tng t nh vy, cc nucleon trn b mt ht nhn ch chu sc ht v pha trong v pha ngoi khng c cht ht nhn na. V vy nng lng lin kt ca ht nhn phi tr i mt lng t l vi din tch b mt ht nhn, tc l t l vi A2/3. S hng th ba tng ng vi nng lng y tnh in Coulomb. Ht nhn l mt git cht lng tch in dng. Lc tng tc tnh in trong ht nhn c gi tr dng v lm gim lc lin kt. Nng lng Coulomb t l vi bnh phng s proton Z2 v t l nghch vi kch thc ht nhn A1/3, ngha l t l vi 21/3ZA.Hai s hng cui ca cng thc (1) khng c gii thch trong khun kh mu git cht lng m phi tnh n vai tr ca s cc nucleon, tnh i xng ca Z v N, v tnh chn l ca s nucleon trong ht nhn. Ni khc i, hai s hng c miu t bi mu v ht nhn.III.2Tnh khi lng ca ht nhnT cng thc nng lng lin kt (1) c th nhn c khi lng ht nhn nh sau:-6-HVTH: Quyn GVHD: TS. V Xun n( ) ( , )p n lkM Zm A Z m E A Z + ( ) ( )22/3 21/31( , ) ( ) 22p n lk lkZ AM Zm A Z m E A Z A A Z EA A + + + + Cng thc bn thc nghim (2) cho php tnh bt c khi lng ca ht nhn no vi A, Z, mp v mn cho trc vi sai s tng i khng vt qu 10-4.Cng thc (2) biu din s ph thuc khi lng ht nhn vo in tch Z v s khi lng A. i vi cc ht nhn ng khi, khi lng M ch ph thuc vo Z v bin thin theo hm parabole (hnh 3). Hnh 3 : Cc ht ng khi vi A l. Cc ht nhn phn r v+ chuyn v ht nhn bn nht c khi lng b nht ng vi in tch Zo.Trn hnh 3, khi lng cc tiu ti gi tr Zo ng vi ht nhn bn nht. Gi tr Zo c xc nh bng cch ly o hm khi lng M theo Z i vi A c nh v cho o hm ny bng 0:0 3/ 21, 98 0, 015AZA+Trong cng thc bn thc nghim th s hng hiu chnh trong nng lng lin kt l:-7-HVTH: Quyn GVHD: TS. V Xun nTrn hnh 3 ht nhn c khi lng M(Zo) l ht nhn bn nht trong s cc ht nhn ng khi vi A l. Do vi A l th lkE = 0 theo cng thc (1) nn M(Z) l hm n tr theo Z, do i vi mi gi tr A ch c mt gi tr Zo tng ng vi ht nhn ng khi bn. Ht nhn vi Z = Zo + 1 nhnh bn phi ca parabole c khi lng ln hn M(Zo) nn phn r+ chuyn v ht nhn ny. Ht nhn ng khi vi Z = Zo 1 nhnh bn tri ca parabole cng c khi lng ln hn M(Zo) v phn r chuyn v ht nhn bn. Cng tng t nh vy, ht nhn (A, Zo + 2) phn r+ chuyn v ht nhn (A, Zo+ 1) v ht nhn (A, Zo 2) phn r chuyn v ht nhn (A, Zo 1). V d vi A = 25 th Zo = 12, l ht nhn bn 12Mg25; vi A = 43 th Zo = 20, l ht nhn bn 20Ca43, . . .i vi ht nhn ng khi vi A chn, khi lng M(Z) l hm lng tr v s hng lkE trong cng thc (1) nhn hai gi tr khc nhau i vi cc ht nhn chn-chn v l - l. Khi khi lng M khi A khng i c miu t bi hai ng parabole th hin trn hnh 4.Hnh 4 : Cc ht nhn ng khi vi A chn. Hnh 4a ng vi ccht nhn l - l khng bn cn cc ht nhn chn - chn bn. Hnh 4bng vi cc ht nhn l-l bn cn cc ht nhn chn - chn khng bn.Trn hnh 4a, ng parabole di ng vi cc ht nhn bn hn, l cc ht nhn vi Z chn, cn ng parabole trn ng vi cc ht nhn km bn hn, l cc ht nhn vi Z l. T hnh 4a thy rng cc ht nhn cnh nhau trn cng mt parabole -8-HVTH: Quyn GVHD: TS. V Xun nkhc nhau v Z n 2 n v v tn ti mt vi ht nhn bn i vi cc ht nhn ng khi chn - chn. l do s chuyn i ht nhn vi in tch Zo + 2 hay Zo 2 thnh ht nhn vi in tch Zo +1 hay Zo 1 b cm v mt nng lng cn s chuyn i trc tip bng phn r b kp t ht nhn Zo + 2 hay Zo 2 sang ht nhn Zo c xc sut rt b, coi nh khng th xy ra. Mt khc mi ht nhn trn parabole trn c hai ht nhn nh hn vi in tch cch 1 nm parabole di nn tt c ht nhn ng khi l-l u khng bn, tr bn ht nhn 1H2, 3Li6, 5B10 v 7N14.Bn ht nhn ny thuc trng hp c minh ha trn hnh 4b, khi ht nhn l - l bn cn ht nhn chn-chn khng bn. V d vi ht nhn l - l 7N14 do cc ht nhn chn - chn 6C14 v 8O14 chuyn thnh.III.3Kho st cc dao ng b mt ca ht nhn hnh cuTa hy xem xt s kch thch cc bc t do kh d ca git cht lng ht nhn. Trong trng thi t do, ngha l khng b kch thch, git cht lng c dng hnh cu. trng thi kch thch, git cht lng khng b nn nhng c th thay i dng hnh hc, do cc bc t do b kch thch s tng ng vi cc dao ng b mt.Hnh 5 : Git cht lng c dng hnh cu (hnh a). Dao ng t cc (hnh b) v dao ng bt cc (hnh c) ca git cht lng.L thuyt phi lng t ca cc dao ng b b mt ca git cht lng t do pht trin trc khi c l thuyt lng t. Theo l thuyt ny th tn s thp nht quad ng vi cc dao ng ring t cc, khi git cht lng c dng hnh ellipsoid cng hay dt (hnh 5b). Tn s cao hn oct ng vi cc dao ng bt cc, khi git cht lng c dng hnh qu l (hnh 5c). Cc dao ng ring khc tng ng vi cc bin dng phc tp hn v c tn s cao hn. Khi chuyn sang l thuyt lng t th cc dao ng ring ca ht nhn c lng t ha. Vic lng t ha khng lm thay i cc tn s ring -9-HVTH: Quyn GVHD: TS. V Xun nnhng cc ph nng lng v momen ng lng ca cc trng thi dao ng kch thch tr thnh gin on. Khi cc nng lng dao ng t cc v bt cc nhn cc gi tr sau:quad quad quadE n h ; oct oct octE n h(3)Trong nquad v noct l s cc lng t t cc v bt cc, ng thi nquad, noct = 1, 2, . . . Mi lng t t cc c spin J = 2 v chn l dng, cn mi lng t bt cc c spin J = 3 v chn l m. S dng cng thc Weizsacker (1) c th tnh c nng lng ca lng t t cc bng:( )1/ 230 4quadA MeV hLng t bt cc c nng lng c hai ln nng lng lng t t cc vi cng mt gi tr A. Cc cng thc (3) v (4) ph hp vi thc nghim i vi cc mc thp nht khi nquad = 1, 2 v noct = 1. By gi ta hy xem xt mu git cht lng miu t cc mc nng lng thp nht nh th no. Nu mc c bn c c trng 0+ th mc kch thch th nht l mc 2+ c nng lng tnh theo cng thc (4). Mc 3 tip theo s c nng lng gp i. Gn mc 3 l ba mc nm rt gn nhau tng ng vi trng thi kch thch ca hai lng t t cc vi cc c trng 0+, 2+ v 4+. Ch rng khi cng hai vector 2r vi 2r ta c vector tng cng vi cc ln 0, 1, 2, 3, 4, nhng cc trng thi 1+ v 3+ b cm do cc lng t kch thch (3) tun theo thng k Bose.Tin on v vic mc kch thch u tin c c trng 2+ c thc hin hu nh i vi tt c cc ht nhn chn-chn. Tuy nhin nng lng ca mc ny thp hn gi tr tnh theo cng thc (4). Chng hn mc 2+ i vi ht nhn 28Ni60 c nng lng 1,3 MeV trong khi tnh ton cho nng lng 3 MeV. rt nhiu ht nhn chn - chn cng thy c b ba 0+, 2+ v 4+ nm mc nng lng cao hn hai ln so vi mc kch thch u tin (hnh 2.4). V cui cng hu nh tt c cc ht nhn chn -chn u c mc 3- c gii thch do kch thch bt cc.Trong mu git cht lng cn c bc t do ring do dao ng ca ton b khi lng cc neutron i vi ton b khi lng cc proton. Vi gi thuyt ny ta coi ht nhn gm hai git cht lng neutron v proton trn vi nhau. Khi kch thch bc t do ny, ht nhn tr thnh mt t cc in, ngha l b phn cc. Kch thch phn cc ng -10-HVTH: Quyn GVHD: TS. V Xun nvi s thay i cu trc bn trong ht nhn. Do nng lng kch thch kh ln, c 15 - 20 MeV i vi cc ht nhn nng v 20 - 25 MeV i vi cc ht nhn nh.III.4Gii thch nh tnh qu trnh phn hch ht nhnNgay sau khi pht hin ra hin tng phn hch, Niels Bohr v John Wheeler pht trin thnh mu git ht nhn, da trn s tng t gia ht nhn v mt git cht lng tch in gii thch nhng c im ch yu ca qu trnh phn hch. Hnh (6) cho thy qu trnh phn hch c din ra nh th no theo quan im . Khi mt ht nhn nng (gi s l 92U235) hp th mt ntrn chm, nh trn hnh 6a, ntrn ny ri vo mt ging th gn lin vi lc ht nhn mnh tc dng bn trong ht nhn v chuyn ha thnh ht nhn trng thi kch thch. Nng lng kch thch m ntrn chm a vo ht nhn ng bng cng cn thit bt mt ntrn ra khi ht nhn , tc l bng nng lng lin kt n ca ntrn . Hnh 6b cho thy rng ht nhn ging nh mt git cht lng tch in dao ng mnh. Sm hay mun g ri cng s pht trin thnh hnh tht c chai ngn v bt u tch xa dn ra thnh hai khi cu tch in. Nu cc iu kin l thch hp th lc y tnh in gia hai khi cu s buc chng tch ra xa nhau v lm t ch tht c chai. Hai mnh vn cn mang mt s nng lng kch thch cn d ri bay ra xa nhau. Nh vy, s phn hch xy ra.-11-HVTH: Quyn GVHD: TS. V Xun nHnh 6 : C ch phn hch IV.HN CH CA MU GIT CHT LNGMu git cht lng khng gii thch y cc s hng trong cng thc bn thc nghim v khi lng v nng lng lin kt ca ht nhn, khng cung cp c cc s liu nh lng v cc trng thi kch thch ca ht nhnNgoi ra, cn mt lot cc vn m mu git cht lng cha cp n, l cc c trng c bit ca cc trng thi c bn v kch thch ca ht nhn nh nng lnglin kt,spin,moment tvtnhchn l,cc tnh cht ca phnr alpha v beta Mu git cht lng b hn ch trong vic m t tnh cht ca ht nhn c lien quan n vai tr ca nucleon v s bin thin tun hon ca chng.Thiu st chnh ca mu git cht lng l s ph kch thch t, khng tnh n cc tnh cht ring bit ca tng ht nhn cng nh khng th gii thch cc momen t cc ca cc trng thi kch thch u tin.-12-HVTH: Quyn GVHD: TS. V Xun nCHNG 3: MU KH FERMII. LDO A RA MU KH FERMITa bit rng: mt phm vi gn ng nht nh th nng lng lin kt ring v mt ht nhn c s khi A l c lp.Tnh cht ca kh l tng: cc phn t kh bn trong cht kh l tng c qung ng t do trung bnh rt ln, iu ny c th xem nh cc phn t kh l tng khng tng tc vi nhau.T , chng ta c th gi thit rng: cc nucleon chuyn ng mt cch t do bn trong ht nhn (gi thit ny hp l i vi cc ht nhn nng). Mt cch gn ng, t mi pha mt ca nucleon l nh nhau. Do nh hng ca cc lc vi cc hng khc nhau gy ra bi cc nucleon bn cnh trit tiu ln nhau. iu ny c ngha l lc trung bnhtcng bi mt nucleonangchuyn ngbn trong ht nhn l bng khng. II. NI DUNG MU KH FERMITrong mu kh Fermi, cc proton v cc neutron- gi chung l cc nucleon c tha nhn l hai h c lp nhau, mi h di chuyn t do bn trong th tch ca ht nhn theo nguyn l loi tr Pauli.Hnh 7 : H th ca proton v ntron trong ht nhn.-13-HVTH: Quyn GVHD: TS. V Xun n Tnh ton su ca h th Cc mc nng lng c chim y t y ca ging th. Mc nng lng cao nht cchimycgi lmcnnglngFermi EFvcnglngl 2F Fp ME , y M l khi lng ca nucleon. Trong phm vi th tch V, s trng thi c ng lng t p p+ dp c cho bi mt yu t trng thi.Ta c th tnh s trng thi ht kh d xut pht t mt quan st khng gian pha: yu t nh nht ca khng gian pha, ta c:3.K pdVdV h VK: th tch ht nhn.Vp: th tch khng gian xung lng.i vi ht nm trong yu t th tch dVK c xung lng nm trong khong p p + dp th dVp c tnh theo cng thc:24 .pdV p dp Th tch khng gian pha: 24 .K p KdV dVdV p dpV Mt yu t trng thi:2 23 3 2 34( ) .2K Kp dpV p dpV dVdn np dph h hMi trng thi nng lng c th cha hai Fermion cng loi: chng ta c ( s dng 02Fpn dn ):32 3( )3nF Kp VNh v 32 3( ).3pF Kp VZhCc neutron v proton tng ng vi th tch ht nhn:3 304 4.3 3KV R r A Ta c th tnh c xung lng pF v ch rng :2.2FFpEm-14-HVTH: Quyn GVHD: TS. V Xun nTa c:13094nFNpA r _ ,h v 1309.4pFZpA r _

,hTa cng c:2232094 2nFNEA mr _ ,h v 223209.4 2pFZEA mr _ ,hNu t:n pm m m v r0= 1,4fm th ta nhn c nng lng cc i ca nucleon trong ht nhn:2338, 6nFNEA _ , MeV, 2338, 6pFZEA _ , Mev.i vi cc ht nhn nh c 12N ZA A , th EF= 24 MeV.i vi cc ht nhn nng, t s trn l:0, 445ZA v0, 555NA . T y ta s tnh c cc mc nng lng Fermi tng ng l:26nFE MeV v23 .pFE MeV Ta bit rng: su ca h th c tnh bng tng nng lng Fermi tng ng ca tng loi nucleon v nng lng tch ca cc nucleon, ngha l:0n n nF SV E E +v 0n n nF SV E E +Nng lng tch nucleon vo khong 8 MeV, ta tnh c:034nV MeV v 031 .pV MeV Nhn xt : Chiu su h th ca neutron su hn h th ca proton. iu ny gp phn gii thch cc ht nhn nng th s neutron nhiu hn s proton.-15-HVTH: Quyn GVHD: TS. V Xun nIII. NG DNG CA MU KH FERMI Nu vn Ta bit, nng lng lin kt l thnh phn nng lng gi cc nucleon lin kt li vi nhau trong ht nhn.Nng lng lin kt c ln : Elk = T + U Trong :T : tng ng nng ton phnU : tng th nng ton phnBi ton t ra y l tm cng thc tnh nng lng lin kt. Gii quyt vn Xc nh T, U gm nhng thnh phn g, c ln th no ? III.1 ng nng III.1.1 ng nng ca cc nucleon khi cha k n nng lng b mtChng ta c th gi thit rng cc nucleon chuyn ng mt cch t do trong ht nhn. Gi thit trn c th hp l i vi nhng ht nhn nng. Nh vy mt cch gn ng th t mi pha, mt cc nucleon gn nh bng nhau. Do , nh hng ca cc lc vi cc hng khc gy ra bi cc nucleon bn cnh trit tiu ln nhau. iu c ngha l lc trung bnh tc ng bi mt nucleon ang chuyn ng bn trong ht nhn l bng khng. R rng y chng ta cha cp ti cc nucleon chuyn ng gn b mt ht nhn. Vi s nghin cu gn ng, ta b qua nh hng ca cc nucleon chuyn ng gn b mt ca ht nhn. Hm sng m t trng thi ca cc nucleonTrong mu ny, chng ta m t cc nucleon bng hm sng ring c trng cho chuyn ng t do ca n, tc l bng hm exp(ir k).Nu k ti phn c trng cho spin ca cc nucleon th chng ta s nhn phn ph thuc vo ta vi cc hm s c trng cho trng thi spin. l (s) nucleon c hng ln trn v (s) ng vi cc nucleon c hng xung di. Vy hm s trng thi ton phn ca mt nucleon s c dng:) exp( ) ( ) , ( r k i s s r hoc ) exp( ) ( ) , ( r k i s s r -16-HVTH: Quyn GVHD: TS. V Xun ni vi neutron cng nh i vi proton hoc i vi cc ht Fermi, theo nguyn l Pauli, chng ta thy trong ht nhn hai ht (hoc proton hoc neutron) cng loi khng c cng mt trng thi, nh vy r rngphn ph thuc vo spin ca trng thi s c gi tr ngc nhau. Th d i vi neutron s c , tng t, i vi proton th .Trong phn hm sng ph thuc vo ta , chng ta s lp gi trknh th no?Ta c cng thc tnh ng nng l: m mp2 222 Gii bi ton hm ring- tr ring nh sau:) ( ) (2) (22 2 EddmTTrong ) ( l hm ring v E l tr ring ca Tt 222mEk , ta c:0 ) () (222 +kdd Nghim ) ( c dng:

ikAe ) (T iu kin n gi ) 2 ( ) ( + , ta c:21 0, 1, 2, 3,...ike hay k t t tVy: 2 2( ) ,2ikkAe Em hvi,... 3 , 2 , 1 , 0 t t t kVy ta c tr ring ca n l mk22 2nu ta ly hm s trng thi ph thuc vo ta l hm sng phng. -17-HVTH: Quyn GVHD: TS. V Xun nTa c th biu th k di dng L 2 bng cch phn tch nh sau: 3 2 1k k k k + + nLmLlL L 2 2 2 2+ + trong :l vector c ba thnh phn l l, m, n v nhn cc gi tr , , 0, 1, 2,... l m n t tTa li c cng thc tnh xc sut:dV z y xV20) , , ( =dxdydz r k i r k ijLLLi) exp( )) (exp(0 0 0* ( ) ( ) ( ) [ ]dxdydz z n n y m m x l lLii j i j i jLLL + + 0 0 02exp ( ) ( ) ( )i j i j i jn n m m l l L , , ,3 Theo c lng t: Nu tch phn ca 2 theo tt c cc gi tr kh dca ta hi t:A dV t z y x 2) , , , (th tacthchnhmsngmi sai khchmsngcbngmt hngs: 12A sao cho ng thc sau tha mn:12dV Vy, ta chn hm sng l:( ) ) exp(123r k iLri l hm sng c chun ha trn ton th tch L3, tc l:( ) ( ) ( )i j jLiL L dV r r , *3 -18-HVTH: Quyn GVHD: TS. V Xun n( ) ( ) ( )i j i j i j i jn n m m l l L L , , , ) , ( Nu chng ta ly hnh cu bn knh 2KL cha tt c cc ta ca cc nucleon chuyn ng trong ht nhn th th tch ca qu cu l:33 3) 2 ( 34 L KV Vi hm sng c m t trn, th trong mi mt lp phng c cnh l L trong qu cu c yu t th tch L3s c xc sut tm thy ht bng 1. Tng t nh vy, trong mt th tch ht nhn l v, chc chn chng ta cng s tm thy mt xc sut nucleon nht nh. Vy, nu ta chn L3=v v ta c:) () () () , ( rsss r ;'s tha mn K k ca cc nucleon. S trng thi nucleon nm trong vng (k, k+dk)Ta gi ( ) n k l s trng thi vi hm s sng trn v hm s spin ly c v 2 pha trong ton b th tch v th n c dng sau :3 33 24( ) 23 (2 ) 3Kv Kvn k Vy s trng thi proton hay neutron nm trong vng (k,k+dk) s l: 22( ) ( )vkdkdn n k dk n k + Chng minh-19-HVTH: Quyn GVHD: TS. V Xun n[ ]( )( )22223 23 3 2 2 323 322323331 , 13 33) (33 3) () ( ) ( dk vkdk kvdk dk dok dk kdk dk k kvk dk kvv k v dk kk n dk k n dn