Modern Physics. Unit 15: Nuclear Structure and Decay Lecture 15.2: The Strong Force. Ron Reifenberger Professor of Physics Purdue University

Transcription

1 Mder Physics Uit 15: Nuclear Structure ad Decay Lecture 15.: The Strg Frce R Reifeberger Prfessr f Physics Purdue Uiversity 1

2 Bidig eergy er ucle - the deuter Eergy (MeV) ~0.4fm B.E. A =.MeV/ = 1.1 MeV/ucle. MeV radial searati, r ~0 MeV R~1.4 fm R I 3-d, ALL the ucles are acked it a shere f radius R.

3 Emirical study f bidig eergy (B.E.) vs. mass umber (A) B.E. (i MeV) A fusi fissi Fe is mst stable ucleus lcal eak verall shae fit reasably well by the Bethe-Weizsäcker mass frmula Deuter 3

4 Culmb Reulsive Frce is Large v ucle ~ 0.3 c Searati ~ x10-15 m F electrstatic qq = k = 9 10 r ( ) 1 9 ( ) 0. lbs = 58N 1.6 lbs f frce (reulsive) 1 N 4

5 Nuclear Bidig The strg frce eutr II. Large mass umber: schematic ucleus mes exchage He electrstatic reulsi rt I. Small mass umber: 4 electrstatic reulsi (A-Z)=Z attractive very shrt rage (~ fm) uclear frce. (A-Z)>Z exterir ucles iterir ucles As size f ucleus icreases, mre eutrs are required t hld ucleus tgether. Neutrs i) icrease distace betwee rts ad ii) act as a glue t hld ucleus tgether. 5

6 Nuclear frce betwee rts (schematic) Imrtat Features 1. Strg Culmb reulsi as r 0. Eve strger attractive frce betwee ucles vercmes Culmb reulsi 3. Net frce must be reulsive as r 0, therwise ucles wuld ctiue t ile u t each ther Frce Reulsive Attractive 0 Culmb electrstatic reulsi et frce 1 e F= 4πε r Strg uclear attracti - searati I ctrast t the frce betwee charged articles, the equati fr frce betwee ucles is t well-kw. 6

7 Frce Reiterreted Whe e article iteracts with ather, there are tw ways t thik abut the rcess. Field Reresetati Imagie a field geerated by e bject that causes a frce ather bject. Acti at a distace! e - Virtual Particle Reresetati Imagie e bject emittig a virtual article which is absrbed by the ther bject. The virtual article trasfers mmetum betwee the tw bjects. e - e - E γ (virtual ht) e - qq 1 F = k rˆ r e - e - (ht mass =0 ifiite rage) 7

8 Examles electr-electr iteracti eutr-rt iteracti m e =0.511 MeV/c m γ = 0 ifiite rage e - e - γ m =938.3 MeV/c m =939.6 MeV/c m π =135 MeV/c e - e - Yukawa s thery f mess 1935 (1949 Nble Prize i Physics) Pis discvered i high altitude csmic ray exerimets

9 What is the ature f the ucle-ucle iteracti? The birth f high eergy article acceleratrs Measure: sub-atmic articles agular distributi elastic vs. ielastic eergy deedece Examle: - cllisi; 930 MeV icidet eergy Dwell et al., Prc. Phys. Sc (1959) 9

10 Rage (R) f Nuclear Frce? Estimated frm Heiseberg s Ucertaity Pricile E t If yu wat t measure the eergy f a quatum system with a accuracy ΔE, yu require a time greater tha Δt where. mc π 1 c > > Frce Rage = R c t E mc m c 34 8 ( )( ) c = Js m / s = MeV fm R = = 0.73 fm = m ( 5MeV c ) 13 π π MeV fm c E t > rage f frce (i m) 1 mass f mediatig article 10

11 Frm scatterig data ifer a uclear tetial well U(r) (values arriate fr middle mass ucleus: A~10) ~ +0MeV Culmb Reulsi : Z e Ucul =+ ; r > R 4πε r ~ -50 MeV ΔU (see Aedix) 1 3 R = = Rfrce A rage ( frce rage) R meters = fm The STRONG NUCLEAR FORCE that bids uclei is always attractive ad therefre rduces a POTENTIAL ENERGY "WELL. The ucles "fall it this well whe they are sufficietly clse t each ther. 11

12 U Next Nuclear Shell Structure 1

13 Aedix: Aalytical shae f uclear tetial well U(r) (Wds-Sax Mdel, emirical) U ( r) U = + crrectis 1+ e ( ) U 57 MeV ; R 1.17 A (i fm); a 0.65 fm Crrectis : r R 1 3 N Z U = ± 7 MeV chse + fr a rt; chse A 1 Ze U ( r) = fr r > R 4πε r c a Symmetry Eergy: uclear well is deeer fr tha fr Culmb Ptetial: ly fr rts 1 Ze 1 r U () r = 1+ 1 < fr r R 4πε Rc Rc c c fr a eutr Culmb reulsi crrecti fr rts R is charge radius, differet tha R which is uclear tetial radius htt://hyerhysics.hy-astr.gsu.edu/hbase/uclear/shell.html#c3 13