Tap chi KHOA HQC DHSP TPHCM Nguyen BAc Thanh Tuyen va tgk
I QUA TRINH ION HOA HAI DIEN TU* CUA NGUYEN TU*HELI BANG LASER CU'OfNG DO CAO XUNG ClTC N G A N
NGUYEN DCrC THANH T U Y ^ N " , N G U Y E N N G Q C T Y "
TOM TAT
Chung toi khdo sat qua trinh ion hoa hai dien tu bang phircmg phdp giai so phuang trinh Schrodinger phu thuoc thai gian cua ngityen tu heli trong truang laser. Kit qua cho thdy khi tang dan do dai xung, xdc sudt ion hoa hai dien tu cua nguyen tu heli tang dan vd tien tai gid tri bdo hoa. Han nUa. khi cucmg do cua laser cdng Ian thi xdc sudt ion hoavd toe do tang cua xdc sudt ion hoa hai dien tu cua nguyen tu heli cdng nhanh, diem bao hoa cua qud trinh ion hoa cdng liii dan ve cdc chu ki euoi eua xung.
Tir khda: nguyen tur heli, ion hoa hai dien tii, laser xung cue ngan.
ABSTRACT
Double ionization of helium in ultrashort intense laser fields
We investigate the double ionization by numerical solution of the time-dependent Schrodinger equation of helium in laser fields. Results show that when the laser duration increases, the double ionization probability goes up and reaches a saturation value. In addition, with more intense laser fields, this probability becomes higher and the saturation value occurs latter in the last cycles.
Keywords: helium, double ionization, ultrashort intense laser.
1. G i ^ thifu
Ngay nay vat li nguyen tu - phan tii la mot trong nhiing nganh duac nghien cmi rit soi dong vi day la ngu6n cung cap thong tin ve cau true cua nguyen tii, phan tu. Dae biet, cac qua trinh tuong tac giira nguyen tu, phSn tu vdi truang ben ngoai la mot trong nhung 6h tai nong bong va thu hut su quan tdm xk Ion cua nhiSu nha khoa hoc.
[3,4,12].
Khi nguyen tur, phan tu tucmg tac vai laser cuang do cao va xung cue ngan, c6 nhiSu hieu ung phi tuyen xay ra. Mot trong nhung hieu ung do la qua trinh ion hoa cua cac nguyen tii, p h ^ tu. Dot vai nguyen tii chi c6 mot dien tii nhu hidro, qua trinh ion hoa xay khi dien tii bi keo ra va mat lien ket vdi hat nhan. Doi vai cac nguyen tir c6 nhidu dien tii, thi su dong gop ciia cac dien tii con lai vao qua trinh nay phai duac ke d6n. Do do viec khao sat qua trinh ion hoa hai dien tu (double ionization) ciia cac nguyen tii c6 nhiSu ban mpt dien tii ciang !a mot v ^ dS dugc quan tam [5-8]. Heli la nguyen tur c6 hai dien tii, dugc cac nha khoa hoc lira chon de bat dau cho qua trinh nghien cuu cac qua trinh ion hoa hai dien tii.
Trong cong trinh [6], Panfili da su dung huong tiSp can c6 dien de khao sat qua trinh ion hoa hai dien tii ciia nguyen tii heli khi nguyen tu nay tuang tac vai laser ' GV, Tru'6'ng Trung hgc Thu-c h^nh, Tru-brg Dgi hoc Sir pham TPHCM
" TS, Tru-frng Dgii hoc Su pham TPHCM
Tap chi KHOA HOC BHSP TPHCM So 61 nam 2014
CLTong do cao, xung cue ngan. Trong cong trinh [7], cac tac gia da su dung cac phucmg piiap g£in dung TDHF, TDDFT ii Idiao sat cac qua trinh ion hoa mot va hai di?n tCr cua heli va da danh gia vai tro ciia tuong quan cua cac dien tir trong cac qua trinh ion hoa nay. Nam 2000 [5], Lein va cac cong su da sir dung phep bien doi Wigner, phan tich chuyen dong l<h6i tam ciia hai di$n tii de xac dinh co che cila qua trinh ion hoa hai dien til ciia nguyen tii heh. Tijp theo, den nam 2010, cong trinh [8] da cong b6 cac ket qua nghien curu ve qua trinh ion hoa hai dien tii ciia nguyen tii heli bdi cac tia hong ngoai va xung laser cue tim chan khong (vacuum ultraviolet - VUV). Cac tac gia sil dyng phuong phap Crank-Nicolson dS tinh xac suit ion hoa mpt dien til va ion hoa hai dien tu cila nguyen tii heli, dua ra cac so sanh xac suat ion hoa trong hai trucmg hop dCing tia h6ng ngoai va laser cue tim chan khong ling vdi cac do dai xung va cac cucmg do dinh khac nhau. Trong cac cong trinh tren, cac tac gia chi tinh toan xac suat ion hoa mot dien tii va ion hoa hai dien til cho timg truimg hop cuong do va do dai xung ctia laser mot each rieng biet, su khao sat qua trinh ion hoa hai dien tii ling vdi cac thong so laser khac nhau la cin thiSt. Trong bai bao nay, chiing toi se phan tich anh huong cu the cua tung thong so len qua trinh ion hoa hai dien tu ciia nguyen tii heli.
Nhim muc dich tren, de tinh xac suit ion hoa hai dien tii, chilng toi giai so phucmg trinh Schrodinger phu thuoc thai gian (phucmg phap TDSE). Hien nay, c6 nhieu nhom nghien ciiu theo huong nay va da thu dugc cac ket qua dang chii y [9-11].
Tuy nhien, do nguyen til, phan til la he nhieu hat phiic tap va tuong tac voi tnidmg laser nen viec giai chinh xac phuong trinh Schrodinger phu thuoc thdi gian doi hoi rat nhieu tai nguyen may tinh va thdi gian tinh toan, va nhu vay, vdi each tiep can nay, hau nhu cac nhom chi tap trung nghien cuu cho cac nguyen til, phan til don gian nhir H2, He [9- 11]. Cung trong khuon kho do, chiing toi se gidi han khao sat cho bai toan heli mot chieu.
Bang each thay doi cac thong so khac nhau ciia chiim laser nhu cudng do, dp dai xung va budc song, chiing toi khao sat su phu thuoc cila xac suat ion hoa hai dien tii ciia heli vao timg thong s6.
Bo cue bai bao dupe chia lam bon phan chinh. Sau phan gidi thieu, trong phin tiSp theo, chung toi gidi thi?u vS phucmg phap TDSE cho nguyen tit heli va tit do tinh xac suat ion hoa hai dien tu. Sau do, trong phin ba, chiing toi trinh bay cac ket qua thu dugc ve su phu thuoc cua xac suit ion hda hai dien tir vdi cac trudng laser khac nhau.
Cuoi ciing la phin ket luan noi chiing toi tdm tat lai cac kjt qua da dat dugc.
2. PhiroTig phap TDSE cho nguySn tir heli
Chung toi xet bai toan nguyen tit heli mot chieu, vdi cac tpa do cua hai dien tit doi vdi goe tpa dp d hat nhan la x,, x^. Toan tir Hamilton ciia nguyen tii heli trong he don vi nguyen tir(e = ,* = m,=7) dugc viSt
- _ 1 d' IB' Z Z 1 2 dx'. 2dxi X, x, I x , - x , |
Tap chi KHOA HOC DHSP TPHCM NguySn Dice Thanh Tuyen va tgk
trong do Z = 2 la di?d tich hat nhan.
Tu do ta CO phuang trinh Schrodinger phu thuoc thai gian cho nguyen tii heli khi tuong tac vai truang laser
••''^^^^-^-^4-^^^^c^^>(x„x..,0 (2)
dt \ 2dx] 21
De tranh diem ki dj trong the cac Coulomb mo ta tuang tac dien tii vai hat nhan va giGa cac dien tii voi nhau, cac h^ng so se dugc them vao, liic nay the dugc ggi la thi soft-Coulomb. Hang so them vao sao cho nang lugng cua he ung voi the soft-Coulomb gan bang vol nang lugng ciia he thuc. Doi vai nguyen tu heli, chung toi Ian lugt them cac hang s6 0.565 va 0.650 vao cac the mo ta tuong tac elctron-h^t nhan va dien tu- dien tii. Khi do thi tuong tac Coulomb dugc vilt lai nhu sau
Vc = - , ^ - , ^ + , ^ (3) yjx',+0.565 4x]+0.565 ^\x,-x,^+0.650
Khi the nang tuong tac K^ giua cac dien tu vai trucmg laser dugc bieu thi bdi
V,=(x,+K,)Eof(t)cos{m^), (4) vol EQ la cuong do a dinh cua dien truang (cuang do didn truong eye d^i) ciia truang
laser, / ( / ) la ham bao, (OQ \k tan s6 ciia xung laser va pha ban diu cua laser bing khong thi nghiem ciia (2) dugc viet dual dang
Id' Id'
^(x,,X2,t) = exp -^+Vr + V,\dt 2Sx'i 2dxl ^ '•I
W{x,.x„t = 0). (5) trong do f(xi,X2,t-0^ la ham song ban diu cua nguyen tir heli khi chua tuong tac vdi trudng laser dugc chiing toi giai phuong trinh Schrodinger dimg bSng phircmg phap thdi gian ao [2].
Tir ham song phu thuoc thdi gian c6 dugc, chiing toi tinh cac xac suat ion hda mot dien tit va ion hda hai dien tii. Cac mien khong gian irng vdi nguyen tu trung hoa, cac qua trinh ion hoa mot, hai dien tu dugc dinh nghia:
Mien A ||x,|,[x^l <a\, ling vdi nguySn tii trung hoa;
MienB {|x,|<a,|x^|>a}, hoac {|x,|>a,|xj|<a} irng vdi sir ion hda mot dien tit;
Mien C {|x,|, |x^| > a}, irng vdi sir ion hoa hai dien tit.
trong do a la khoang each tir hat nhan ciia nguyen tu den vi tri cd the dupe xem la bat dJiu xay ra sir ion hda, gia tri cua a dupe chpn la a = 20a.u. De c6 dupe gia tri a = 20au. chiing toi da tita hanh tinh toan vdi cac gia tri a khac nhau va nhan thay ring khi a Idn hon 20a.u. thi gia tri xac suit ion hoa thay doi khong dang kl. Xac suat ion hda mot va hai diSn til dugc tinh bdi cac cong thiic sau
Tap chi KHOA HOC BHSP TPHCM S6 61 nam 201^
B
P2{t)=^'P{x,.X2.tfdx,dX2.
(6) (1)
3. Ket qua , . Trong phin nay, chiing toi se trinh bay ket qua ve su phu thupc cua xac suat loti hda hai dien tu ciia nguyen tii heli vto cac thong s6: cudng dp, dp dai xung va budc song cua laser.
Sir dung cac cong thirc tinh toan xac suit ion hoa nhu da noi d tren, chiing toi tinh xac suit ion hda mot dien tit v4 ion hda hai di?n tit cua nguyen heli khi tuong tac vdi laser vdi ba thong s6 c6 dinh: cudng dp 6x10'* w/cm^, dp dai xung chiia 15 chuki (tuong duong 40fs), budc song 800nm.
- Hai (li^n li? t / - ' - ^ ^ ~
^htJ\ Kian (chu kl U s e r l
Hinb 1. Xdc suat ion hoa cua nguyen tir heli khi tucmg tac v&i laser cudng do 6x10 W/an , dodai xung 40fs va bircrc song SOOnm vai hai trucmg hop: ion hoa mot dien tic va ion hoa hai di^n tie
Trong hinh 1, ta thiy xac suit ion hda mot dien tit cd gia tri khong dang ke tit chu ki 1-5, nhung bit dau tit chu ki thir 5, xac suit ion hda mot dien tit tang gin nhu tuy6n tinh vdi toe dp nhanh. Khi dat gia tri cue dai, tit chu ki 10 dSn 15, xac suit ion hda mot dien tit gan nhu khong thay ddi, cd biSu hien giong nhu mot qua trinh bao hda. Qua trinh ion hoa hai di$n tir ciia nguyen tit heli trong truang hgp dang xet cd dudng bi6u diin giong qua trinh ion hda mot dijn tit nhung xac suit ion hda nhd hon khoang 4 Ian, dieu nay hoan toan phu hpp vdi cac ket qua ma mot s6 tac gia da cong b6 [1, 7]. Chiing ta cd the giai thich ket qua tren nhu sau: do laser bin vao lam lech rao thS Coulomb nen nguyen til hi ion hda, trude tien la ion hda mot dien tu. Khi trudng laser dat cirdng dp dinh, xac suit dien tii rdi khdi nguyen til djt cite dji, dien tit dupe gia tdc trong tmdng laser va thu dupe van tde Idn. Sau niia chu ki quang hoc, khi truong laser ddi chiSu dien tir cd dong nang Idn bi keo ngupe trd vh vdi hat nhan. Khi dien tii quay trd v6 vdi hat nhan me, cd the xay ra su tan xa khong dan hoi, trong dd dien tit trd lai va cham
Tap chi KHOA HOC BHSP TPHCIVI NguySn Birc Thanh Tuyin va tgk
them vao mot dien tit .tir nguyen tit lam nguyen tit mat bdt them mot dien tit dd la su ion hda hai dien tir. Qua trinh nay gpi la su ion hda lien tiep. Khi qua trinh dien tii bi biit ra khdi nguyen tir can bang vdi qua trinh dien til bi keo ngupe trd ve vdi hat nhan thi xac suit ion hda djt gia tri bao hoa.
Tiep theo, chiing toi s6 khao sat su phu thuoc cua xac suat ion hda hai dien tir vao cudng dp cua laser ling vdi budc sdng 800 nm va dp dai xung 15 chu ki. Hinh 2 the hien ket qua cho cac cudng dp 2 x l 0 " W / c m ^ 4 x l 0 " ' W / c m \ a 6 x l 0 " w / c m ^ Chiing ta thiy ring trong cac chu ki diu (tit 1 dSn 5), xac suit ion hoa khong dang ke.
Tit chu ki thii 6, gia tri nay tang dan, cudng dp cua laser cang Idn thi toe dp tang cua xac suat ion hda hai dien tii ciia nguyen tii heli cang nhanh. Khi cudng dp cua laser tang thi xac suat ion hda hai dien tic ciia nguyen tu heli ciing tang dan va mien bao hoa ciia qua trinh ion hda cang liii dan ve cac chu ki cuoi cua xung. Cu the khi cudng dp tang tir 1X10 W/cm len 6 x lo''* W/cm^ ta thay xac suat ion tang gan 2000 Ian. Dieu nay cd thS giai thich nhu sau: cudng dd ciia laser tang din dSn tde dp ion hda xuyen him cua dien tit tang, lam cho xac suit dien tit dupe tang tde ra viing lien tuc Idn, vk qua trinh tai ket hgp vdi ion me ciing manh hon, dan den xac suat ion hda hai dien tii ciing tang.
Thiri gian (i:liu ki la.er)
Hinh 2. Sttphu thuoc cua xdc sudt ion hoa hai dien tir cua nguyen tir Heli vao cuong dg cua laser khi tuang tac vai laser c6 cuong do thay doi tir 1^ lo'^ wjcm' den 6x10" WJcm', do dai xung 40fs tuong irng 15 chu kl. buac song SOOnm
TiSp theo chiing toi khao sat su phu thupc cua xac suit ion hda hai dien tit vao dp dai xtmg cua chiim laser khi thay ddi xung chiia tit 1 dSn 15 chu ki irng vdi budc sdng SOOnm va cudng do 6 x 10'" W/cm^
Chiing toi nhan thiy trong cac trudng hpp dp dai xung ngin (3fs, 5fs, 8fs tuong irng tit 1 dSn 3 chu ki), xac xuit ion hda hai dien tit gin nhu bang khong trong phan dau cua xung, sau dd bit dau tSng dan d phan cuoi xung nhimg gia tri khong dang ke, xdc suit Idn nhit cd thS dat dupe trong trucmg hpp 8fs la 0,40%. Khi tang din dp dai xtmg.
Tap chi KHOA HOC DHSP TPHCM Sd 61 nam 20U
xac suit ion hoa hai dien tit tang din va bit diu xuit hi|n qua trinh bao hoa. Hinh 3 the hien xac suit ion hda hai dien tit vdi cac dp dai xung 7 dSn 15 chu ki. Ta thay khi do dai xung tang tit 4 chu ki 16n 15 chu ki, xac suit ion hda hai dien tir tang tii 1% Kn 16%.
Thcri gian (chu ki laser)
Hinh 3. Xdc sudt ion hoa hai dien tir ciia nguyen tir heli khi tuang tac voi laser cuong
^p 6x10 W/cm , buac song SOOnm, vd cdc do ddi xung 4 chuki den 15 chu Id De khao sat su phu thupc cua qua trinh ion hda hai dien tit cua nguyen til heli vao budc sdng cua laser, trudc tien chiing toi chpn laser tuong tac cd cac thong sd: cudng dp3xlo'*w/cm^, dp dai xung 40fs (15 chu ki), va budc sdng thay ddi tit 400nm din 1200nm.
Khi thay ddi cac gia tri khac nhau ciia budc sdng laser tir 400nm djn 1200nm, chung toi nhjn thay dang dd thi cua xac suit ion hda hai dien tir cua nguyen tir heli theo thdi gian van khong thay ddi. Xac suit ion hda hai dien tit thay ddi tang giam mot each nglu nhien khi tang din gia tri cua budc sdng cua laser. Trong trudng hgp laser c6 cudng dp 3 x l 0 " ' w / c m \ dp dai xung 40fs (15 chu ki), va budc sdng 600nm, xac suit ion hda hai dien tit dat gia tri bao hda Idn nhit la 1,67% va khi laser cd cudng dp 3x10'" w/cm^, dp dai xung 40fs (15 chuki), budc sdng 600nm thi xac suit ion hda hai dien tii dat gia tri bao hda nhd nhit la 0,77%.
4. Ket lu|n
Chiing toi da sir dung phucmg phap giai sd TDSE de khao sat sir phu thuoc cua xac suat ion hda hai dien tu cua nguyen tir heli vao cac thdng sd cua laser cudng dp cao, xung cue ngan. Qua trinh ion hda mot dien tir va ion hda hai dien tir cua nguyen tii heli cd bieu hien gidng nhau: tang gan nhu tuySn tinh trong cac chu ki diu ciia xung laser va cd su bao hda d phan cuoi xung. Khi cudng dd cua laser cang Idn, xac suit ion hda va tde do tang cua xac suit ion hda hai dien tu ciia nguyen tit heli cang Idn mijn bao hda cua qua trinh ion hda cang liii din ve cac chu ki cudi cua xung. Khi tang din
Tap chi KHOA HOC DHSP TPHCM Nguyen Dice Thanh Tuyin vdtgk
do dai xung, xac suat ;on hoa hai dien tii cua nguyen tii heli tang ddn, tuy nhien khong phai tang tuyen tinh. Xac suat ion hoa hai dien tii cua nguyen tii hell thay dot tang giam mot each ngau nhien khi tang dan gia tn ciia buac song ciia laser. Trong cac cong trinh tiep theo, chiing toi tiep tuc khao sat qua trinh ion hoa hai dien tii cua cac phan tii c6 cau true nhu Ho.
Ghi chu: Cong trinh nay diroc thiec hien trong khuon kho de tai nghien curu khoa hoc cap ca sa nam 2014 cua Trucmg Dai hoc Sit pham TPHCM, md so CS20I4.19.63.
TAI LIEU THAM KHAO
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(Ngdy T6a soan nhSn dum: b^l- 26-5-2014, ngay phan bien d^nh gi^: 12-8-2014;
ngdy chip nh$n dSng: 20-8-2014)
