(most) due to long range e m forces i.e. via atomic collisions or due to short range nuclear collisions or through decay ( = weak interactions)

Transcription

1 Spring 01, P67, YK Monday January 30, 01 8 Obsrvabl particl dtction ffcts ar : (most) du to long rang m forcs i.. via atomic collisions or du to short rang nuclar collisions or through dcay ( = wak intractions) Lt s first considr (1) intractions of chargd particls with mattr via m. Litratur: B. Rossi High Enrgy Particls, Prntic Hall, Inc., Englwood Cliffs, NJ, 195 J.D. Jackson, Classical Elctrodynamics, Chaptr 13 Print: rv passag particls mattr.pdf

2 Gnral Disposition Swift particl with charg z and mass M (. g. m, p, d, a...) with E = gmc and p = gbmc collids with atomic lctron of mass m = m and charg (-). Elctrons ar in atoms with Z, and A. Enrgy losss of particl with mass M ar from th collisions with atomic lctrons. In many cass binding nrgy of lctrons in atoms can b nglctd for nrgtic collisions "scattring on fr lctrons" Enrgy losss of all particls with M m ( mp,, K, p, d, a...) can b dscribd by gnral law (from Ruthrford scattring) with M as a paramtr (+spin) + - Enrgy losss by or particls ar tratd diffrntly di to M = m Elctromagntic intractions of nutal particls ar not zro, but vry small (.g. nutrons). Elastic M on m via Coulomb scattring Ruthrford scattring f-la

3 Enrgy loss X-sction for scattring particls m 1 and m T = mv nrgy transfrrd in Lab from particl 1 to particl = nrgy lost by particl 1 in Lab v 1 = v sin LL1 (17.5) m1 + m Q d =, Î é0, E ù ë max û mv ds p E = m 3 ø 4mm c æ Q ö cos c ds = p ç dc çèmv sin c 1 max E 1 Lab ( m1 + m) m = v m Ruthrford scattring for Ur () ds µ d c sin Q = r 1 is for Coulomb (= atomic) fild. Compar with ds d = const for.g. na low-nrgy scattring 1

4 Scattring of particl with mass m and charg z on lctrons in mattr (lctrons ar in atoms with Z and A) [4] B. Rossi High Enrgy Particls, Prntic Hall, Inc., Englwood Cliffs, NJ, 195!

5 Enrgtic knock out of lctrons ( rays)

6 T Enrgy loss X-sction for scattring particls m 1 and m v = = mv nrgy transfrrd in Lab from particl 1 to particl = nrgy lost by particl 1 in Lab 1 = v sin LL1 (17.5) m1 + m Q d =, Î é0, E ù ë max û mv ds p E = m 3 ø 4mm c æ Q ö cos c ds = p ç dc çèmv sin c 1 max E 1 Lab ( m1 + m) m = v m Ruthrford scattring Ur () c sin Q = r ds 1 ds 1 µ or µ d dt T this is non - rlativistic tratmnt, T kintic nrgy transfrrd to lctron = nrgy loss by incidnt particl [Rmmbr t =- mt is invariant]

7 dn - probabilty distribution function (pdf) for charg particl with vlocity dtdx passing th layr of thicknss dx [ dx] usually xprssd in units g cm ( dx = r dl) b A K 4p whr Nrmc MV = = A A gcm é T ù FT ( ) = 1 -b for incidnt spin 0 particl (Bhabha) ê T ú ë max û é 1 for spin incidnt T 1æ T ö ù FT ( ) = 1 b - + T (Bhabha+Massy+Corbr) max ê ç è Mc ø ë E + ú û é æ T öæ 1 T ö ù 1 T FT ( ) = 1 b 1 æ ö æ 1 T ö ç çè T 1 ç max øè 3T C ø 3 + ê ç èe + Mc ø çè T C ø ë ú û for incidnt spin 1 particl (Massy+Corbr+Oppnhimr+...) rlativistic formula FT ( ) includs QFT spin tratmnt of colliding particls T C for A= 1g mol b r Mc m v = ; c = = 4p mc 0.8fm classical lctron radius; z - charg of particl

8 rlativistic formula from your HW sinc mm 1 and whn g is not vry larg th Tmax mcb g dn and ar ~"indpndnt" on mass M (but function of b= pc E or g= E M) dtdx - For incidnt (Møllr) for dn 1 Zé é 1 1 T ( T ) ù E ù KZê - E + E ú = K - = ë û E dtdx A êt( T) A ë E - E ú û ( E -T) T + For incidnt (Bhabha) for E mc é 1 T ( T ) ù dn KZê - E + E ú = ë û é1 T ( T ) ù dtdx A ê - E + E ú E ( E -T) T ë û E mc additional trm du to possibl positron and lctron rcoils

9 Exrcis: What is Tmax if incidnt particl is -? T max mc bg mc bg Ebg æ 1ö = = = = E 1 - = 1 g m ( m) 1+ g 1+ g ç è g + + ø M M T kin _ inc - - Howvr, in scattring lctrons ar not distinguishabl T max = E F-la for positrons is tratd as T = E as wll!!! max Mc If T T max and T T C = all abov f-las ar transform m dn K Z 1 1 to Ruthrford's formula: = z dtdx A b T 1 not whn T 0 T du to long-rang of -m forc

10 T max de æ d N ö - ( T > ) = T dt ; I (avrag ionozation potntial dx ò ç çèdtdx ø as minimum transfr nrgy) Bth Bloch formula: calld lctronic stopping powr for M>m particls K MV éde ù MV ê ú = A g cm ëdx û g cm accuracy of B-B f-la is about 1% hr 0.3 ê ú in th "usful" nrgy rang de For practical purposs in a givn matrial is function of only bg; dx de p for all havy particls sam ( bg) can b usd; bg = dx Mc

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13 Stopping powr and Rang DE= x ò x1 de dx dx E E dx de D x= ò de = ò de æ de ö E1 E1 ç èdx ø E1 x1 x = E E = E -DE dx Rrang ( )( E) 0 de = ò æ de ö E ç èdx ø

14 Stopping powr Rangs

15 Stopping Powr and Rang Tabls for Elctrons, Protons, and Hlium Ions: (a) (b)

16 Avrag ionization potntial I = man xcitation nrgy is an important non-trivial paramtr that is dtmind xprimntally compar with known I=13.6 V for hydrogn