In the name of Allah Proton Electromagnetic Form Factors

Transcription

1 I th a of Allah Poto Elctoagtc o actos By : Maj Hazav Pof A.A.Rajab Shahoo Uvsty of Tchology

2 Atoc o acto: W cos th tactos of lcto bas wth atos assu to b th gou stats. Th ct lcto ay gt scatt lastcally wth fal atos uct; ato ato To th tt that th ato ca b ga as ftly havy, th tc gy of th lcto os ot chag. It s also ossbl fo th tagt ato to gt ct; ato ato I ths cas w tal about lastc scattg bcaus th tc gy of th fal outgog lcto s ow lss tha that of th tal cog lcto, th ffc bg us to ct th tagt ato. Th tal t of th lcto lus th atoc syst s wtt as;. ψ,,...,, z L,

3 Wh w us th bo oalzato fo th la wav. Th fal-stat t cosog wav fucto s; Assug that t-t tubato thoy s alcabl, w ca atly wt th fftal coss scto; I gal,fo lastc scattg;,.,,...,,. z L ψ h h h L V L Ω π π σ 6,, V L h π

4 Th ct lcto ca tact wth uclus, assu to b stuat at th og; t ca also tact wth ach of atoc lctos. So V s to b wtt as z V z L V,. z z z z L,.., ] [,.., *. ψ ψ... π π δ Sco t Sco t st t st t

5 z. W custoaly f th fo facto fo ctato to as follows If :. z o ; hc th fo facto aoachs uty th lastc Scattg.

6 ] [ z Ω δ π π σ h z h δ a a a z, h Ω σ

7 Nucla fo facto: At tly hgh,, wh s ow of o, th z Wh z ρ ρ c R ucl stuctu of th uclus bcos otat. Th Coulob ottals u to th ot uclus ust ow b lac by a Coulob ottals u to a t objct, s a ucla chag stbuto, oalz so that ρ z. ρ z π ucl ucl. ρ

8 σ Ω R σ Ω σ Ω R s th fftal coss scto fo th lctc scattg of lctos by a ot l uclus of chag Z. o sall w hav; ucl. ˆ.ˆ... 6 ucl... ρ th uatty s ow th a sua aus of th uclus. I ucl ths way t s ossbl to asu th sz of th uclus a also of th oto. 6 I th oto cas th s agtc ot ffct s also otat.

9 Poto o acto: If oto was as ot l chag wth agtc otu /M,, w hav; Th ocss th Laboatoy fa σ Ω lab E α s θ E {cos E θ M s θ } E E E s M θ

10 o lcto-oto scattg, w hav; j J T f Lowst-o lcto oto lastc scattg

11 j J γ u γ u u. []. u Sc th oto s a t stuctu, w caot lac bacts by, as fo s-/ atcls. But w ow that J ust b a Lotz fou-vcto, a so ust us th ost gal fou-vcto fo that ca b costuct fo,, a th Dac γ -atcs sawch btw u a u. Th a two ν t ts, a σ,a ν th coffct a fuctos of s 5 oly t scala vaabl at th oto vt. Ts volvg γ a ul out by th cosvato of aty. Thfo w ay wt th sua bat th fo ν [] [ γ M σ ν ] J γ σ Ω lab E α s θ E { E M cos θ M s θ }

12 I actc, t s btt to us la cobatos of I actc, t s btt to us la cobatos of,, ;, s cos s M G G G E E E G M G M M E lab M E Ω τ θ τ θ τ τ θ α σ W ca wt oto tasto cut th fo W ca wt oto tasto cut th fo u M u J γ P P That s, th Bt fa wh. That s, th Bt fa wh.

13 J ρ, J o, w hav, ρ J ± MG E J G M G M G E Hc, fo factos a a closly lat to th oto chag a agtc ot stbuto, sctvly.

14 Elctoagtc fo factos a lato wth wav fucto;. ρ G E. ρ cos θ A fo, w hav; G E ρ cosθ ϕ s [ g f ] j [ g f ] ψ ψ

15 ψγψ M j j G. cos cos j j θ θ g f j M G M g f G M j M

16 c b a Calculatg oto wav fucto ottal ψ χ φ εχ χ φ σ εφ φ χ σ.. V U V U U V f φ ε σ χ.

17 φ ε φ ε φ 6 9 V Wh;. σ Wth us Jacob cooat,, 6, R ρ λ Wh w hav lft th oto of ct ass, w obta; [ ] φ ε φ ε φ λ ρ V, λ λ ρ ρ

18 ρ λ [ ]φ ε ε φ 5 V L W suggst ; ξ φ 5 W touc ; ξ ζ ξ ξ c b a 5

19 L h h δ β α ξ, α β λ δ α 5 9,,, a c b a V A g g a c b c a ε

20 ,. λ ρ ε σ π ψ Ω Ω Y c a N c a a f } { g g V A φ χ χ.6

21 wh w obta; a c f f f b. 6 f At th, oto wav fucto s; ψ N σ.ˆ π ε wh N.788

22 calculato of oto lctoagtc fo factos: fst, lctc fo facto; G E j [ χ φ ]..

23 .95.9 GE GE Coa wth JLAB [6]

24 A th agtc fo facto; G M M j χ φ A w hav; G E f GM χ.89 M E.

25 Coclusos: U c R.Tg.6 f U U a a b b c c Etal valu O atcl Th atcl...9 f f f.79.

26 Suggstos:.Ct ass cocto.mso clou coctos.atoal ts to ottals such as ±5 ± f و و ±

27 Rfcs:..E. Clos;" A Itoucto to Quas a Patos" Halz, Al D.Mat;"Quaa a Ltos: A Itouctoy cous o atcl hyscs.". Ry;" Quatu l thoy" Saul S.M. Wog;" Itoucto Nucla Physcs" Goss;"Rlatvstc to Quatu Mchac" Tg,R., Boca,R. Ws,W : Z.Phys.A 7, A.A. Rajab ; w-boy Systs 7, A.A.Rajab, Iaa Joual of Scc & Tchology, Tasacto A, Vol, 8. No.A. 9. A.A Rajab., Ia Joual of u a al hys vol, 89-9 b..t.va N CAUTEREN, T. COTHALS, S. JANSSEN AND J. RYCKEBUSCH Ght Uvsty, B-9 Gt, Blgu.Doal Day, Datt of Physcs, Uvsty of Vga, Chalottsvll, Vga 9.H.W.Ha a M.J.Rasy-Musolf TRI-PP- Dc 998.Gl Wa, Battll & Jffso Lab, Dvso of Nucla Physcs, Octob,.Mac Vahagh Collg of Wlla & May / JLab, ay th 5.J.J.SAKURAI,"MODERN QUANTUM MECHANIC" 6.G.G. So t al., Nucl. Phys. A,

28 Thas.