CTv149V18ST12015092.pdf

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Scieice ( TecmolOH Developieol, Vei I I , No.TI- ZOIS

U'ng dung m i u dan hat trong viec xac djnh spin va do chin le a cac mipc cua hat nhan ^^Fe ,

• Nguydn An Sen ^ ^

• O^ng Lanh Trifd-ng Dgi hoc Da Lat

(Bill nhQn ngay 03 Ihdng 02 nam 2015. nhgn dang ngay IS ihdng 06 nam 201S)

TOM T A T

Spin vd dd chin Id d cdc mdc kich thich vd mdc CO bdn cua hat nhdn Id hai dai lugng quan trgng trong cdc tinh chit luong td cua hat nhdn. Tuy nhidn. hidn nay d Vidt Nam chua cd h$ do ndo cd thi xdc dmh true tiip hai dai luong ndy. Bdi bdo trinh bay phuong phdp dung miu Idp di xdc dmh spin vd dd

Td khda: Spin hat nhdn. dd chin Id. muc kich thich. miu ldp. miu don hat.

chdn Id ciia muc tmng gian cDng nhu tr$ng thdi CO bdn cua hat nhdn ^'Fe. Kit qua dugc so sdnh vdi nhi/ng thuc nghidm trudc ddy.

Kit qud cOa bdi bdo ndy cQng cho thiy si/

phu hgp trong ung dung miu don hat cua hat nhdn A ldo vung h^t nhdn trung binh.

M O DAU

Cdc d$c trung lugng tfi ciia hat nhdn Id van dfi cdn quan tam trong nghien ciiu cau tnic hat nhan ngay ca trong ly thuyet cQng nhu thgc nghifim. Tuy nhifin, mdt sd ddc trung lugng tu rdt khd xdc djnh bdng thuc nghifim, chdng han spin vd dd chdn le cua cdc mfic trung gian. Thdng thudng, he do tuong quan gdc thudng dugc dung trong vific xdc dinh spin va dg chdn le cua cdc mfic kinh thich trung gian.

Cho den nay, Viet Nam chua cd he pho kfi do dac spin cung nhu ndng lugng kich thich mfic trung gian. Tai Ld phdn fing Dd Lat cd hfi trimg phfing gamma - gamma, nhung he nay cung khdng thfi xdc dinh tit cd spin ciia cdc mfic trung gian mgt cdch true tifip, md chi giai doan gid trj ndng lugng mfic Uung gian cung nhu spin vd dg chdn le cua mfic qua ndng luong cdc cdp chuyin

nhu cdc tinh chit cln quan tdm ma sfi dung cdc mdu lj- Ihuyfit khac nhau. Ci hat nhan nhe, mau gigt chdt Idng kha phu hgp khi gidi thfch mdt sd tfnh chdt vh ndng lugng lifin kit; d cdc hat nhdn trung binh khdng bi suy bifin thi mau ldp Id phii hgp hon cd; trong khi d hat nhdn n^ng suy blln thi miu suy rdng dugc fing dyng nhifiu hem. Tuy nhien, khi tfnh todn den spin vd dg chdn Ie ciia hat nhan d trang thai c a ban ciing nhu cdc mfic kich thfch thi mau ldp la khd phu hgp cho nhfing hat nhan trong ddi sd khdi 20 < A < 120.

Sdt la kim loai dugc su d\ing trong thifit ke mdt sd thifit bi trong cdu true Ld phan fing hat nhan. Do vay, dfi tifip can vdi cdng nghfi Ld phdn ling, thi vific nghien cuu tinh chat cua cdc v§t lifiu la cdn thifit vd thifit thgc. " F e Id hat nhdn trung binh, cd A le, do vay ly Ihuyfit mdu dan h^t cd

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T9P e i i PIAT TIIEM KlftCN, Ti|P 18, S() 11 - 201§

sd cdng trinh da xdc djnh cdc mfic spin thuc nghifim [3, 4 ] . Tuy nhifin cdc tac gia ndy chi xac dinh dugc spin thuc nghifim d mfic ndng Iugng thip < 2 MeV. Vific khd khdn khi xdc djnh bdng thgc nghifim cfia cdc tia gamma cua " F e Id vi chinh " F e cdng tifip tuc phdn rd beta dfi vfi " C o , vd thdi gian bdn ra cua " M n rit ngdn, chi khoang 4,59 s [5].

Cdng trinh nghifin cim thuc nghiem d l y dfi nhdt cho dfin nay Id cdng trinh cfia Coral M.

Baglin [5]. CJ nghifin cfin ndy, tdc gia da do va tfnh dugc cdc ndng lugng, cudng dg chuyfin ddi, hfi sd rg nhdnh cua cdc tia gamma phdt ra cua

" F e khi gidl kich thich tfi qud trinh phan rd beta cfia " M n .

Cdc cdng bd trudc cung chua Ihly cd cdng Uinh cdng bd vfi dp dung mdu cau trfic hat nhdn cho vific tfnh toan cdc d$c trung lugng tu cfia cdc mfic ndng Iugng kich thfch.

CO S 6 Li T H U Y E T

M I U Idp hat nhdn dugc xdy dgng theo md hinh miu nguyfin tu, bdng cdch chuyin bdi toan h^ nhilu nucleon (bdi todn nhilu li^t) v l bai todn mfit hat chuyfin ddng trong trudng the xuyfin tam tg hgp. Gidi bdi todn Schodinger ddi vdi chuyfin ddng cua nucleon trong trudng thl tg hgp sfi nhan Bdng 1. Cdc trang thdi nh^n dugc tu viec giai

dugc mgt he cdc trang thai img vdi mdl mfic ndng lugng xac dinh. Theo nguyen ly loai trii Pauli, mdi nucleon trong hat nhan chiem mot mfic ndng Iugng, vd b i t diu tfi mfic thap nhat.

Phuang phdp don gian nhat cita mdu ldp Id mdu dan hat ddi vdi hat nhdn cd sd khdi A le.

Trong mau nay, ngoai trfi nucleon le cudi ciing thi cdc nucleon cdn Iai tao nfin mgt cdi ldi ddi xfing cau vdi moment ddng lugng vd moment tfi bdng khdng. Nhu vdy, cdc Ifnh chat ciia hat nhdn dugc quyet djnh bdi tfnh chdt cfia nucleon Ifi khdng lifin kfit cdp.

Trong hat nhan, trang thdi cua nucleon trong trudng the tu hgp dugc ddc trung bdi 4 sd Iugng tfi n, /, j vd mj. Vdi n Id sd lugng Ifi chinh nhan cdc gid tri nguyen 1, 2. 3, ... xdc djnh phan bd cdc mfic ndng lugng tdng din; / Id sd lugng t u quy dao n h | n cac gid trj 0, 1, 2, 3, ... va dugc ky hifiu Id s, p, d, f,...; j Id moment todn phin (spin) cua nucleon, j = / + 1/2; mj la hinh chifiu cfia j , nij = -j,-j-l. . . . , j - l , j n h § n 2 j + 1 gid tri.

Cdc mfic sdp xep theo thfi tg tdng din vd dugc ddc trung bdng 2 sfi Iugng bJ n vd /. Theo nguyfin ly loai trii Pauli dugc Irinh bay d Bdng 1, moi muc chira tdi da N = 2(2/ + I) nucleon mdi loai proton hay neutron.

phuong trinh Schodinger vdi thfi chQ nhdt [6, 7].

Tr^g thi!

/

N-2(2/+l) Is 0 2

lp 1 6

2s 0 2

Id 2 10

If 2P 3 1

14 6 lg 2d 3s 4 2 0 18 10 2

Ih 2f 3p 5 3 1 22 14 6

Thdng thudng mdt mfic ndng lugng nucleon trong h^l nhdn dugc ky hifiu bdi 3 sd Iugng tfi la

ll, /, j . Bdng 2 vd Hinh I md ta sg phdn bd cdc mfic ddi vdi mau Idp.

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Scieoce tltcloeloH l,Voll8,IIO.TI'20IS

Bang 2. Cac trang thii iJng vdi cdc ldp v6 c6 tinh dgn spin quy dao [6,7],

L&pvo

I 11 III IV V VI

Trang thai Isin lP3/2lPl/2 lds/22Si,2ld3/2 lf7/!lf5n2pM2piolg,n lg7/22d5a2d3/23si/2lh,,/2 lh9/22f7/22fs/33p3/23Pl/2lil3/2

nij

2 4 + 2 6 + 2 + 4 8 + 6 + 4 + 2+10 8 + 6 + 4 + 2 + 12 10 + 8 + 6 + 4 + 2 + 14

N 2 8 20 50 82 126

13/3 ^^—

3pi/:

3P3/:

-WT

Hinh 1. So do cdc mfic nucleon Spin cfia hat nhan dugc xdc djnh theo nguyen tdc sau:

NIU hat nhdn cd A Ie thl spin cfia hat nhdn chinh Id spin cfia nucleon rifing Ifi khdng lifin kit c$p:

Cdc trudng hgp khac thi spin cua hat nhdn dugc xdc dinh Iheo quy tie Brennan - Bernstein [7] (dp dgng 20 < A < 120) nhu sau:

trong hat nhdn theo mdu Idp.

NIU / Idp cudi ciia proton vd neutron Id lfi - le thi spin cua hat nhdn dugc xdc djnh Iheo ting spin cua Idp cudi, J = I Jp + Jn I;

Nlu / ldp cudi eua proton vd neutron Id chin - chin thi spin cfia hat nhdn J = | Jp + Jn - 11.

DO chin Ie dugc xdc djnh theo nguyfin tdc

TTy = ( - ! ) ' . Trudng hffp hat nhdn A le lhi /

dugc xdc djnh Id / d ldp cfia nucleon khdng lifin

kit cjp. Cdc trudng hgp khde dugc xdc djnh theo

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TAP Cil P I A T T H E N KlftCN, TAP 18, SO Tl • 2815

neucleon. Qud trinh phdt gamma Id dang dich

chuyfin difin tu. Gia su hat nhdn cd ndng Iugng, spin vd dg chdn lfi d trang Ihdi ddu tuong fing Id H„ Ji, ir, vd trang thdi kl sau Id Ef, Jf, Ttf, thi ndng Iugng cua lia gamma phdt ra dugc xdc djnh tu dg lech gitta hai mfic ndng Iugng:

Er = E,-Ef (1) Gamma Id nhfing photon, tuc Id hat boson, cd

spin bdng 1, vl spin Jy cfia photon phdi Id nguyfin duong. Trong dich chuyfin difin tu glQa hai trang thdi hat nhdn J / ) — > L / ^ ) thi spin J^ cua photon dugc xdc dinri tu hfi thuc tam gidc sau:

\j,~J^\<J^<J,+Jj. (2)

Do chdn lfi cung dugc bdo todn trong qud trinh djch chuyfin difin Ifi.

n.jtjTif = 1 (3)

Nhu vay dd chdn Ifi cfia photon n^ Id duong

nfiu n, = Ttf va 71^ phai Id dm neu Hj = -nf.

Trong djch chuyfin difin thi:

-V =(-!)•'• W vd djch chuyen tfi thi:

^ , = ( - ! / ' * ' (5) Bfic xa gamma vdi Jy = 1 gpi Id bfic xa lu&ng

cgc, J^ = 2 ggi la buc xa Ifi cue, Jy = 3 ggi Id bfic xa bat cue,...

KET QUA TINH TOAN VA SO SANH

T H V C N G H I $ M

Sdp xip cdc nucleon theo mau Idp Hat nhan ^^Fe cd 26 proton vd 33 neutron.

Hinh 2 binh bdy su sdp xfip cdc nucleon cua *^Fe theo mau Idp. 0 trang thdi co bdn, sg slp xip cdc nucleon trong hat nhan nhu sau:

Proton: l s f „ l p ; „ l p ; „ l d f „ 2 s ; „ l d ; „ l 4 . Neutron:

itm

Idsn 2si/2

lpi/2 lP3Q

2.A) sap xif

3K>ton

Ipit lP3I Isin

-O—O-

2,B) sap xSp neutron Hlnh 2. Stt sip xip c^ nucleon dia ^^e o tr^g thii co ban.

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Scieice & Tedmology 8evelopiiienl, Vol 18, No.TI- 2015

Nhu vay vdi cdc sdp xep ndy, Fe d trang thai ca ban cd spin dugc quyfit djnh bdi nucleon rifing le, dd Id neutron n i m d mfic 2p3/2, tuc spin hat nhdn 1 = 3/2, dfi chin le

TT = (—1) = (—1) = — 1 . Nhu vdy, d mfic ca bdn I = 3/2-. Kfit qud ndy phu hgp vdi cdc kfit qua thuc nghifim dd xac djnh [5, 8].

Bdy gid xem hat nhan " F e gdm mdt ldi hat nhdn vdi sg lifin kit cdp bfin ciia 26 proton vd 26 neutron. Cdc mfic kich thfch tifip theo neu cd Id su Ihay ddi muc ciia 8 neutron thfia d muc trfin.

Vdy xem xet cac trudng hgp eg thfi sau:

M^c kich thfch thU- nh&t: 1 neuUon d ldp 2p3/2 nhdy len muc cao hon liln kfi (Hinh 3), tuc Id mfic 2pi/2. Nhu vdy d mfic kfch thfch ndy dd chdn le TT = ( — 1 ) = ( — 1 ) = — 1 , vd spin cua

hat nhan d mfic kfch thich ndy Id 1 = 1/2-. Mdt khde, d mfic 2pj/2 khdng cdn nucleon, do dd theo quy tdc, spin cua hat nhan ciing cd thfi quylt dinh bdi spin cua muc ndy va dd chin le ngugc vdi dd chdn le d mfic ndy, tuc day Id mfic kep, cd thfim 1

= 3/2+.

MAc kich thich thu hai: I neutron tfi mfic

\fsa dich chuyin Ifin mfic 2pi/2 (Hinh 4), nen spin cua hat nhan quyfit dinh bdi muc le, tfie mfic Ifj/j (cdn 5 neutron). Nhu vdy d mfic kfch thich nay dg chdn le ?r^ = ( - 1 ) ' = ( - 1 ) ^ = - 1 , vd hat nhan d mfic nay cd spin Id I = 5/2-. Tuong tg nhu giai thich d muc kich thich thfi nhdt, spin cua hat nhan cdn anh hudng bdi mfic 2p3/2 khdng cdn nucleon, do dd cd thfim I = 3/2+.

lS|/2 •

-o—O- O—O-

Hinh 3. Mfic kich thich thfi nhit. Hinh 4. Mfic kich thich thfi hai.

Mdx kich thich th^ ba: 2 neutron d mfic Uia chuyin Ifin mfic 2p3/a (Hlnh 5), nfin spin cua hat nhdn quylt djnh bdi muc lfi, tuc mfic \fsa (cdn 3 neutron). Nhu vay d mfic kich thich ndy hat nhdn cung cd spin Id I = 5/2-.

Mirc kich thick thUr tu: 1 neutron d mfic 1 fs/j tiep bic chuyfin Ifin mfic 2p3/2 (Hlnh 6). Do dd

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Tlir cil NAT TIIEU lUCN, TAP I I , SI Tl - 2115

2pt/2 — 2p3/2

lfs/2 0 -

lPl/2 . lP3(

- O — O -

-o-o

- o - o - o—o

Hinh 5. Mirc kich thich thu ba

2pu.

2p3/2

lf5/2 0 - -o-o—o-

Iptc lP3I

-o—o-

Hinh 6. Miic kich thich thu ni.

Tuong ttr nhu vgy, spin vk do chan le o cAc miic kich thfch thii nam I = 7/2+, muc thii sau 1 = 3/2-, miic thli bay I = 5/2-, miic thir tim la mirc k^p voi I = 3/2- va i = 5/2+, miic thii chin la miic kep vol 1=

7/2- vi 1 = 5/2+, muc thii mudi la miic Up vSi 1 - 3/2- va 1 - 5/2+. Hlnh 7, 8, 9, 10, 11, 12 trinh bay su s3p xep cac neutron trong cac i6p.

lpi/

lP3/2

-o—o- -o—o-

Ipl/

lp3/2

- o - o - - o - o -

Hinh 7. Muc kich thich thu ndm. Hinh 8. Mirc kich thich thfi sau.

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Sclnce t Tickioloi) l e i e l m i u l , Vol 18, ND.T1- 2011

l g 7 / 2 - 2pii 2pin-

Usa-

ld3/2 2su l d 5 / 2 ' I p l I 1P3/

Ipi/

lP3/:

Hinh 9. Muc kich thich thir b

o - o o

Hlnh 10. Miic kich thich thir tam

-o-o-

Ipl/

lP3/!

- o - o -

Hinh 11. Muc kich thich thfi chin.

So sdnh k i t qua thgx! nghidm

Ket qud tinh todn spin vd do chdn Ifi d cdc muc kich thich cua " F e dugc so sdnh vdi thuc nghifim do dac [5]. Hinh 13 Id cac mfic kich thich

Hinh 12 Mfic kich thich thfi mudi.

cfia Fe do dugc tfi phdn rd beta cua hat nhdn

" M n .

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T$P CIJ PHAT TIIEN KI&CN, TAP 18, Sil Tl - 2815

Q(^)=518S keV 29 ^ 1%) L^^

P-:100%

Hinh 13. Cac mfic kich thich ciia • Fe Cd thl fing dgng each tinh todn ndy cho nhihig hat nhdn khac vdi sd khdi A le vd trung binh. Lay thf dy vdi hat nhan 145/15 cho viec fing dyng mdu ldp trong vfing sd khdi hat nhdn dd nfiu.

6 mfic CO bdn, " S i , , cd cdu trfic nucleon theo mau Idp theo quy Idc d Bdng 1, Bdng 2 vd Hinh 1 Id:

Proton: I s ^ ^ l p j ^ l p f / j l d * ^ . Neutron: I s ^ ^ l p 3 / j l p ^ ^ l d 5 / j 2 s ^ / j l d 3 ^ . Nhu v§y theo cdch gidi thich miu Idp thi spin d trang thdi eg bdn cua " 5 / , ^ quylt djnh bdi

do dugc tfi phat beta cua dong vj ^^Mn [8].

nucleon khdng lifin kit cdp, tfie nucleon d ldp 1 d^'^, vd do chdn Ifi dugc xdc djnh

^ j . = (—1) = ( ~ 1 ) = + 1 , tfie spin vd dp chin lfi d mfic CO ban cua i^^S/,, Id 3/2+.

Khi bi kfch thfch, nhfing nucleon d cdc mfic ngoai cung bi day len muc ndng lugng cao hon.

Cdc mfic cao hon cd thfi cd Iheo mau vd (Hinh 1) Id muc IfjQ, If;;; SpjQ, 2pi,2, lg9,2, -•-- Do dd, spin vd dg chdn Ie khd dT cfia cdc mfic trung gian Id 7/2-, 3/2+, I/2+, 9/2-, ... Kfit qud ndy Id phu hgp vdi thgc nghifim [9] khi xdc djnh spin va do chdn le cua cac nghifin cfiu khde.

T r a n g 9 9

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Science S TechBology Bevelopaieit, Vol 18, No.TI- 2815 Nhu vay, trong nghien cuu nay, kfit qua Ifnh toan bdng mdu idp cho thay khd phfi hgp vdi kfit qud thuc nghifim do dugc cfia ^^Fe vd " S l . d

" F e , trong 10 muc tfnh todn ly thuylt theo mdu dan hat, thi cdc mfic dan phu hgp hoan todn gifia tfnh todn spin vd dp chdn le cua cac mfic trung gian. 6 cac mfic kep, thuc nghifim do dac trCing hgp vdi ly thuyfit d mfic kich thich thfi tam. Tuy nhifin cac mfic thfi nhdt, thfi hai, thfi chin vd thfi mudi thuc nghifim chi xac dinh dugc mfic dan.

Difiu nay Id hodn todn cd thl, bdi chua cd mau Iy thuylt ndo phu hgp hodn todn, va do vdy khdng thl thay thfi thuc nghifim bdng vific ifnh todn todn bg qua ly ihuyfit trong nghifin cuu clu true hat nhdn.

KET LU^iN

Bdng vific fing dung m i u ldp dd xdc djnh dugc spin va do chdn le cua 10 muc kich thich vd Uang thdi c a ban cua " F e . Kfit qud cho thay vific tinh todn theo mdu don hat Id phu hop vdi kfit qua thuc nghifim cho bdi todn xac djnh spin vd do chdn lfi cfia cac trang thdi hat nhan d hat nhan cd A le vd khdi lugng trung binh. Nhu v§y, kfit qud nghifin cfiu ndy gifip xdc djnh dugc spin vd do chdn lfi ciia cdc mfic cfia hat nhan trung binh bdng ly thuyfit kha chfnh xac, difiu nay dd khic phuc dugc han c h l thifit bi nghifin cfiu cdc d^c nimg lugng tfi d cac muc trung gian cua hat nhan trong dilu kifin thuc hifin nghifin cfiu hat nhdn d Vifit Nam cdn han che.

Application of single particle model to determine the spin and parity of levels of Fe nucleus 59

• Nguyen An Son

• Dang Lanh Dalat University

ABSTRACT

The spin and parity of the excited state and the ground state of nuclei are two of important pn^periies of the nuclei quantum.

However, up to now we do not have appropnate equipments to directly detetmine the spin and parity of nuclei. This paper shows the application of nuclear shell Keywords: Spin nuclei. Parity nuclei, excited particle model.

TAI LIEU THAM K H A O

[1]. V.H. Tdn vd cdc cdng sg, Bao cdo tdng kfit

model to study the spin and parity of intermediate levels and ground state of ^Fe nucleus. Comparing to previously experimental data, this nucleus single- particle model is suitable of the average mass and odd A nuclei

nuclear level, nuclear shell model, nuclear single

U bdng phuong phdp cdng bifin dp cdc

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TAP CHl P I A T TIIEN KI&CN, TAP 18, SQ Tl - 2815

Ihdng phd kfi hat nhan do trfin chiim notron

phyc vu nghifin cfiu chuyfin ddi gamma ndi tang, do dac sd lifiu hat nhan va cdc fing dyng lifin quan, Vifin NCHN, Dd Lat (2010).

[3]. http://www.lnl.lnfn.it/~annrep/read_ar/2007/

contributions/pdfs/013__A_125_A 120.pdf [4]. V. Subrahmanyam, Spins and y-

multipolarilies in the decay of"Fe, Journal

of Inorganic and Nuclear Chemistry, 3319-

3322, 34, 11 (1972).

[5]. CM. Baglin, Nuclear Data Sheets for A = 59, Science Direct, 95, 2, 215-541 (2002).

[6]. N.Q. Huy, Ca sd vat ly hat nhan, Nhd xuit ban khoa hoc vd ky thuat, (2006).

[7]. J.M. Blatt, V.F. Weisskopf, Theoretical Nuclear Physics, John Wiley and Sons, Newyork(1972).

[8]. http://www.nndc.bnl.gov/nudat2/geldecaysc heme.jsp?nucleus-59FE&dsid=59mn%20b M%20decay&unc=nds

[9], http://www.nndc.bnl.gov/nudat2/getbandplot .jsp?unc=nds

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