α-particles, β-particles and γ-rays upon Atomic Nuclei.

Transcription

1 Etoant thod fo bokn th aton of uton, α-pat, β-pat and γ-ay upon Ato u. Fan D Aquno Copyht 01 by Fan D Aquno. A Rht Rvd. H w how an toant thod fo bokn th aton of xtna nuton, α- pat, β-pat and γ-ay upon ato nu. Th thod an b vy ufu fo toppn nua fon, a th han aton that ou nd a nua fon ato, and ao tho nua fon that ontnu oun, and natn hat (day hat), vn aft th hut down of th ato. y wod: uantu Gavty, Gavtatona a, ua hy, ua Chan Raton, Day hat. 1. Intoduton ua fon th pttn of an ato nuu nto a pat (ht nu). Th fon po oftn podu f nuton and aa ay, and a a vy a aount of ny. ua fon han aton podu ny n th nua fon ato of th nua pow pant, and dv th xpoon of nua wapon. Th han aton ou du to th ntaton btwn nuton and fonab otop (uuay uanu- and putonu-9.). Whn an ato undo nua fon, a fw nuton a jtd fo th aton. Th nuton w thn ntat wth th uoundn du, and f o fonab fu pnt, o ay b abobd and au o fon. Th ak pob a f-utann nua han aton that a ny at a ontod at n a nua ato o at a vy apd unontod at n a nua wapon. Th tha ny natd by a nua fon ato o fo th han aton podud nd th ato. An potant fat that th nua ato ontnu natn hat vn aft th toppn of th nua han aton (day hat [1]). Th hat ad a a ut of adoatv day podud a an fft of adaton on ata: th ny of th apha, bta o aa adaton onvtd nto th tha ovnt of ato. Th hat qu th oon of th ato dun on t. It bvd that pob quky top th phnonon * []. H w how an toant thod fo bokn th aton of xtna nuton, α-pat, β-pat and γ-ay upon ato nu. It wa dvopd tatn fo a po patntd n Juy, (BR atnt ub: I08006-) []. Th non nvav thod an b vy ufu fo toppn nua fon, a th han aton that ou nd a nua fon ato, and ao tho nua fon that ontnu oun vn aft th hut down of th ato. Th nua aton podu a nfant day hat, whh qu th pannt oon of th ato, and hav bn th au of o nua dat, a th oud n th ua ow ant of Fukuha [].. Thoy Th ontpoay att han of th Thota hy wa to pov that, Gavty a quantu phnonon. Th quantzaton of avty how that th avtatona a and nta a a oatd by an of th foown fato []: 1 Δp 1 () * Aft on ya offn, ud fu t t about kowatt of day hat ny p ton. Aft ya, t t 1 kw of hat p ton.

2 wh 0 th t nta a of th pat and Δp th vaaton n th pat knt ontu; th pd of ht. In na, th ontu vaaton Δ p xpd by Δ p FΔt wh F th appd fo dun a t ntva Δ t. ot that th no tton onnn th natu of th fo F,.., t an b hana, toant, t. Fo xap, w an ook on th ontu vaaton Δ p a du to abopton o on of toant ny. In th a, by ubttuton of Δ p ΔE v ΔE v ( )( v v) ΔEn nto Eq. (1), w t 1 ΔE 1 0 n 0 By dvdn Δ E and 0 n Eq. () by th vou of th pat, and bn that, Δ E W, w obtan 1 W 1 0 n ρ k. Anoth potant quaton obtand n th quantzaton thoy of avty th nw xpon fo th ontu q and ny of a pat wth avtatona a and voty v, whh vn by [ 6] wh ρ th att dnty ( ) wh Eq.(1),.., ( ) () q v ( ) ( ) E 1v ; vn by 1 v. Thu, w an wt ( 6) Subttuton of Eq. (6) nto Eq. () and Eq. () v q E v h v λ ( 7) () 8 Fo v, th ontu and th ny of th pat bo nfnt. Th an that a pat wth non-nu a annot tav wth th ht pd. Howv, n Ratvt han th a pat wth nu a that tav wth th ht pd. Fo th pat, Eq. (8) v q h λ () 9 ot that ony fo 1 th Eq. (9) dud to th wknown xpon of DBo ( q h λ). Sn th fato an b tony dud und tan utan (S Eq.(1)), thn aodn to th Eq. (7) and (9), th ny and ontu of a pat an ao b tony dud. Bad on th pobty, w hav dvopd an toant thod fo bokn th aton of xtna nuton, α-pat, β- pat and γ-ay upon ato nu. In od to db th thod w tat ondn an ato ubjtd to a tat ant fd B, and an oatn ant wth fquny f Bo (F.1). If th fquny qua to th ton pon fquny f p( ), thy abob ny fo th ant fd B (Eton ant Ronan). Th fquny f p ( ), vn by [ 6, 7] S z γ μ f p( ) B B B π π π ( nh ) h B B.798 B ( n ) π h π ( ) wh. 00 th ton -fato.

3 B B o F.1 In th thod, an oatn ant fd B o, wth a ntnty, appd ppnduay to a tat ant fd B. Thu, und th ondton, th ny abobd by on ton, vn by [8] ΔE γ hb ( 11) Th ton a oftn dbd a ovn aound th nuu a th pant ov aound th un. Th ptu, howv, adn. Th quantu thoy ha hown that du to th z of th ton, thy annot b ptud n an ato a oazd n pa, but ath houd b vwd a ad out ov th nt obt o that thy fo a oud of ha. Thu, th on aound th nuu pnt a oud of ha, n whh th ton a ot ky to b found. Howv, th oud ub-dvdd nto h. Eah h an ontan ony a fxd nub of ton: Th ot h to th nuu ad th " h" (ao ad "1 h"). Havy ato a Uanu, ha 7 h (,,,,,, ). Th h an hod up to two ton. Th nub of ton that an oupy ah h a: 8, 18,, 1, 9, [9, ]. Aodn to Eq. (11), th ny abobd by ah on of th h a ptvy, vn by ( 1 ) ΔE γ hb wh th nub of ton n th h. Dvdn th Eq. (1) by th opondnt vou of th h, w t γ hb W Subttuton of Eq. (1) nto Eq. () v ( 1) γ hbn + 1 ρ Subttuton of γ 0 (S Eq. ()) nto Eq. (1) v 1 1 hbn ρ In od to auat ρ w tat ondn th ( 1) ( 1) hydon a. If w ov th hydon nu what an an ton a wth dnty qua to ρ. Thu, w an auat th dnty by utpyn th dnty of th Hydon a by th fato ( 0 0 p + 0 ). Howv, n th a of havy ato th fato ut b, obvouy, ( Z 0 Z 0p + Z 0n + Z 0 0 0p). Thu, n th a, w an wt that 0 ρ ρ H 8.99 (.7 ) 0 p. k. Th vau of th ( 16), an b ay auatd tatn fo th thkn,, and th nn ad,, of th h. Th thkn, a vn by ( R ) R ( R ) 16R ( R ) 6R ( R ) 6R ( R ) R ( R ) 18R ( R ) R wh R th ton adu. It an b auatd tatn fo th Copton zd ton, whh v R.86 1, and fo th tandadzd ut nty obtand of R 1.16 [ 11]. Bad on th vau, th ava vau 1 R.09. Th nn ad of th h, a vn by

4 1. ( 1 + ).8 ( ) 6.0 ( ) 7.8 ( ) 1.07 ( ) 1.6 ( ) 1. 1 ot that ( ) Howv, n th a of th Uanu, outnn Thu, th a dffn of Th vau ut b addd n th vau of,...,, n od to obtan th otd vau of ut Fnay, w obtan π π π π π π π ( ) ( ) ( ) ( ) ( ) ( ) ,...,. Th 1 ( ).1 ( 17) F. Th 7 Ato Gavtatona Shdn uu Th obty of th obta ton onf an ta ondutvty fo ah h,.., ρ μ ( 18) wh ρ xp th onntaton of ton ( ) C and μ th obty of th ton. Th xpon of ρ ρ ( 19) n th oth hand, n by dfnton μ v d E and vd v πε 0 [1] and E Z, w obtan πε 0 1 πε 0 μ ( 0) Z Subttuton of Eq. (19) and (0) nto Eq. (18),v πε 0 ( 1) Z Th vau of, n th a of th Uanu, a vn by ( 1 + ).9 ( + ) 8.0 ( + ) 9.1 ( + ) 1.1 ( + ) ( + ) 1.6 Thfo, aodn to Eq. (1), th vau of th a th foown S / S / S / S / S / S / S / ( ) Fo Etodyna w know that th ndx of faton, n, of a ata wth atv pttvty ε, atv ant pabty μ and ta ondutvty vn by [1]

5 ε μ n ωε + v If >> ωε, ω πf, Eq. () du to n ( ) 1 ( ) μ πε 0 f ( ) Subttuton of f f Bo vn by, Eq. () nto Eq. () yd n 0.66 B ( ) Subttuton of th vn by Eq. () nto Eq. () yd n B 7.6 B n B 6.6 B n B 6.78 B n B 6.9 B n B.8 B n B.6 B n B. B ( 6) Subttuton of th vau of th ρ vn by Eq. (16) nto Eq. (1) v n B 1 ow, by ondn th vau of, (Eq. 17) and n B (Eq. 6), w an auat th vau of fo ah h,.., ( 7) { 1 [ 0.7 1] } ( 8) B { 1.09 } ( 9) { 1 [ 1.9 } ( 0) { 1 7. } ( 1) { 1. } ( ) { } ( ) { 1 [ ] } ( ) B B B B B B In th patua a of Eq. (8) (), yd B T, th ( ) In a pvou pap [1] t wa hown that, f th wht of a pat n a d of a ana thn th wht of th a pat, n th oth d of th ana, wh 0 ( and 0 a ptvy, th avtatona a and th nta a of th ana). ny whn 1, th wht qua n both d of th ana. Th ana wok a a Gavtatona Shdn. Th th Gavtatona Shdn fft. Sn ( ) ( ), w an ond that o that. If w tak two paa avtatona hdn, wth 1 and ptvy, thn th avtatona a bo: 1 1, 1 1, and th avty w b vn by,. 1 1 (a) 1 1 (b) F. an and Spha Gavtatona Shdn. Whn th adu of th avtatona hdn (b) vy a, any pat nd th pha ut w hav t avtatona a vn by, wh t avtatona a out of th ut.

6 (a) (b) F. Th avty aaton n both d of th avtatona hdn. In th a of utp avtatona hdn, wth 1,,..., n, w an wt that, aft th n th avtatona hdn th avtatona a, n, and th avty, n, w b vn by n 1... n, n 1... n ( 6) Th an that, n uppod avtatona hdn wth dffnt 1,,,, n a quvant to a n avtatona hdn wth 1... n. Sn th ato h,,,,, and, wok a avtatona hdn, thn thy a quvant to a n avtatona hdn wth. Thu, n th a of Uanu, whh utanouy ubjtd to a ant fd wth ntnty B T, and an oatn ant fd wth fquny f Bo f p ( ).798 B 6. 8GHz, th vau vn by Eq. (), yd th foown vau fo : 1. ( 7) 6 Conqunty, aodn to Eq. (9), whn a γ ay o th ato h of Uanu, ubjtd to th abov ntond ondton, th ontu of th γ ay, aft t av th ato h vn by h hf q λ ( 8) wh 1.. Und th ondton, th fft of th γ ay upon th nuu bo quvant to th fft podud by and photon wth ny hf. Thu, f hf << 1 [1], th photon w not hav uffnt ny to xt th nuu. Th ny of a photon wth f Hz, aft on th ato h, bo jut jou << jou. Und th utan, w an ay that γ ay wth f Hz, aft on th ato h, do not a ab to xt th Uanu nuu. Th fft ao xtnd to pat of att a nuton, α-pat, β-pat, t. Fo xap, ond a fat nuton thouh a Uanu ato. Aft on th ato h t ontu, aodn to Eq. (8), bo q v and, aodn to Eq. () t tota atvt ny E. Th nta knt ny oatd wth th avtatona knt ny by an of th foown aton []: Du to th ato adu b vy a, any pat nd th ntdat on btwn th h and th nuu w hav t avtatona a vn by, wh t avtatona a out of th ut (S F.)). Say, f th ny of a photon, out of th ato thn, nd th ntdat on, t ny bo A havy nuu undo fon whn aqu ny >. So nuu a th 9U undo fon whn abob jut a nuton. th a th 8 nd to abob fat nuton wth knt 9U hf hf. ny >1. Howv, n a a f th tota ny of th ndnt pat <<1, th fon do not ou.

7 Fo and v 1 v 0 0 ( ) 0 1 v << ( ), w t 1 v v. Thu, Eq. (9) du to 0 ( 9) ( ) 1 v ( 0) 0 Th how that th knt ny of th pat w b tony dud n th a of a vy a vau of. Aodn to th quaton (7) and (0), th knt ny of a nuton, nd th ntdat on btwn th h and th nuu of Uanu, vn by 1.. Fo << 7. 1G w obtan << 1. Th an that, nuton wth knt ny << 7. 1G (and ao pat uh a α-pat, β-pat, poton, t.) a not ab to podu th fon of an ato nuu of Uanu, ubjtd to th pvouy ntond ondton. It ao nay ond th a of o nu, a th nu of U 9, whh undo fon by th p abopton of a nuton nhbon th nuu. Ao, w ut ond th a of ton aptu by th nu, ( p + n +ν ). In th a, f th Uanu ato ubjtd to th pvouy ntond ondton, both nuton and th ton w hav th tota ny, aodn to Eq. (), vn by 1 E n 0n.1 jou and 17 E jou Th n a vy a than 1 and thfo, th nuton annot 7 xtat th nu of 9U to podu fon, and th ton do not hav uffnt ny to ntat wth a nua poton to podu a nuton and a nutno. Th thod h dbd qu B T, and an oatn ant fd wth fquny f Bo 6. 8GHz. Th ptot ud n th ua ant onan ptoopy, ot oony known a R ptoopy, wok wth up to 1GHz,. T (AACE 00 Hz R ptot, aunhd by Buk BoSpn). Fu how a 0.9GHz, 1.1T R ptot. By opan th vau qud by th thod h dbd wth th vau, w an onud that th nay thnooy on oon. F. - A 0.9GHz, 1.1 T R ptot at HWB-R, Bnha, U.

8 Rfn 8 [1] Rahb,. (011). Day Hat Gnaton n Fon Rato. Unvty of Ino at Ubana-Chapan. Rtvd 6 Januay 01. [] DE fundanta handbook Day hat, ua phy and ato thoy, o., odu, p. 61. [] D Aquno, F. (008) o and Dv fo Conton th oay th Gavtatona a and th Gavty Aaton, BR atnt ub: I08006-, Juy 1, 008. [] py,, t a., (01) Th Fukuha Dat and Japan ua ant unabty n Copaatv ptv. Envonnta Sn and Thnooy 7 (ay), [] D Aquno, F. (0) athata Foundaton of th Ratvt Thoy of uantu Gavty, af Jouna of Sn and Thnooy, 11 (1), pp [6] vtt,. H. (001) Spn Dyna, Wy. [7] Hand,.. and Fnh, J. D. (1998). Anayta han. Cabd, Enand: Cabd Unvty, p.19. [8] G,..S. and Gad, C.F.G.C. (1987) Ronâna anéta ua: Fundanto, étodo Apaçõ, Fundação Caout Gubnkan, boa. [9] B, A. (1967) Conpt of odn hy, Gaw-H, otuu von (1969) Ed. oíono, S.auo, p [] Joy, W.. (1991). odn Inoan Chty (nd d.). w Yok: Gaw-H. [11] a Go.. H., (199) Th Enat Eton. Boton: u Aad, 199, pp. -. [1] B, A. (1967)Conpt of odn hy, Gaw-H, otuu von (1969) Ed. oíono, S.auo, p.1. [1] uvdo, C.. (1977) Etoanto, Gaw- H, p. 70. [1] D Aquno, F. (0) Gavty Conto by an of Etoant Fd thouh Ga at Uta-ow u, af Jouna of Sn and Thnooy, 11() ovb 0, pp.178-7, hy/ [1] B, A. (1967)Conpt of odn hy, Gaw-H, otuu von (1969) Ed. oíono, S.auo, p.0.