Nuclear/Particle Physics. The Structure of Nuclei and Nucleons: Elastic electron scattering from a spin-less target (nucleus or nucleon):

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1 lastc electron scatterng rom a sn-less target (nucleus or nucleon): Puttng bac n the see o lght ( = v/c) an Plan constant, we get: Where Z F ( ) 0 F ( ) 0 Z Rutheror Cross-secton or nonrelatvstc scatterng rom a ont artcle. The rest o the ormula ( F ( ) ) s a earture rom Rutheror scatterng n that t now nclues relatvstc ynamcs encomasse by the amltue () an the ossblty that the artcle has a nte sze, arameterze by the orm actor F ( ) Phys 50 Intro Nuclear Physcs

2 0-0-6 Phys 50 Intro Nuclear Physcs What remans to be one s to n the wor out the relatvstc ynamcs. For scatterng o unolarze electrons one sums over the ntal electron olarzaton an averages over the nal electron olarzaton: Whch, ug the gamma-matrces gves: Trace 8 8 ) ( ) ( m m m m u u t 8 lastc electron scatterng rom a sn-less target (nucleus or nucleon):

3 0-0-6 Phys 50 Intro Nuclear Physcs 3 The ott Cross-Secton: ) ( F Z lastc electron scatterng rom a sn-less target (nucleus or nucleon):

4 The Structure o Nucleons (gong to hgher energes): lastc electron scatterng rom a nucleon wth sn: In the lab rame wth a statonary target: Phys 50 Intro Nuclear Physcs

5 0-0-6 Phys 50 Intro Nuclear Physcs 5 Proton recol: rom: lastc electron scatterng rom a nucleon wth sn:

6 0-0-6 Phys 50 Intro Nuclear Physcs 6 Cross-secton: cos e, s, s cos lastc electron scatterng rom a nucleon wth sn:

7 lastc electron scatterng rom a target nucleon wth sn: Cross-secton: cos m Rutheror: Non-relatvstc scatterng rom a statc ont charge. Aton ue to ott: Relatvstc scatterng rom a statc ont charge (electron sn). ott + roton sn contrbuton: Relatvstc scatterng rom a sn ½ (Drac) ont artcle. Proton recol: m Due to e -, snsn nteracton Phys 50 Intro Nuclear Physcs 7

8 lastc electron scatterng rom a nucleon wth sn: Wth the ntal beam energy xe, the cross-secton eens on a gle arameter: Scatterng angle. For a certan scatterng angle, both the nal electron energy an the momentum transer are xe by nematcs. xamle: e - e - = 59.5 ev, = 75o : m m cos cos75 cos cos GeV o 373 ev o Phys 50 Intro Nuclear Physcs 8

9 lastc electron scatterng rom an extene nucleon wth charge strbuton an sn: What was msg rom the ott cross-secton wth the sn-sn contrbuton were orm actors to allow or a ossble extene sze o the nucleon. But now a gle orm actor won t o anymore! We have exlctly allowe the roton to have a sn (ts total angular momentum ) whch means that we are not just ealng wth a statc charge strbuton, but wth a strbuton o movng charges! So we have two orm actors: lectrc Form Factor: G agnetc Form Factor: G Phys 50 Intro Nuclear Physcs 9

10 lastc electron scatterng rom an extene nucleon wth charge strbuton an sn: The magnetc moments o the neutron an roton are roton.79 neutron.9 An wth these we can wrte the cross-secton as: G G G tan ott Rosenbluth Cross-Secton wth ott cos m Phys 50 Intro Nuclear Physcs 0

11 lastc electron scatterng rom an extene nucleon wth charge strbuton an sn: Unle our revous scusson o orm actors, here the orm actors are a uncton o our-momentum transer, rather than three-momentum transer an cannot smly be consere n terms o the Fourer transorm o the charge an magnetc moment strbutons. However, ce We have m So as long as we have (the Bret conton) an Phys 50 Intro Nuclear Physcs an m m r G G e r r G G e r 3 3 r r

12 lastc electron scatterng rom an extene nucleon wth charge strbuton an sn: The electrc an magnetc orm actors can be etermne searately by measurng the cross-secton at secc scatterng angles. Ths s reerre to as the Rosenbluth searaton. Note that, or elastc scatterng, where the energy transerre to the roton s very small comare to the roton mass, the Bret conton s always satse Phys 50 Intro Nuclear Physcs

13 Note that, n the Rosenbluth ormula, t s assume that the roton s a sn-hal Drac artcle,.e. However, the exermentally measure value o the roton magnetc moment s larger than execte or a ont-le Drac artcle: So or the roton we exect: lastc electron scatterng rom an extene nucleon wth charge strbuton an sn: O course the anomalous magnetc moment o the roton s alreay evence that t s not ont-le! Phys 50 Intro Nuclear Physcs 3 e m.79 G G S e m S r 3 0 r r 3 0 r. 79

14 0-0-6 Phys 50 Intro Nuclear Physcs easurng the Form Factors: At very low momentum transer (small scatterng angle): So that At hgh momentum transer (large scatterng angle): So that 0 m ott G ott tan G tan ott G G G lastc electron scatterng rom an extene nucleon wth charge strbuton an sn:

15 lastc electron scatterng rom an extene nucleon wth charge strbuton an sn: easurng the Form Factors: In general we are senstve to both orm actors! These can be resolve rom the angular eenence o the cross secton at FIXD : Phys 50 Intro Nuclear Physcs 5

16 lastc electron scatterng rom an extene nucleon wth charge strbuton an sn: easurng the Form Factors: Rosenbluth searaton metho : A( ) B( ) tan ott Phys 50 Intro Nuclear Physcs 6

17 easurng the Form Factors: lastc electron scatterng rom an extene nucleon wth charge strbuton an sn: lectrc: agnetc: Q G Same shae!!! scalng relaton: Phys 50 Intro Nuclear Physcs 7 ( Q ) G ( Q ) / N ( Q / 0.7)

18 lastc electron scatterng rom an extene nucleon wth charge strbuton an sn: Phys 50 Intro Nuclear Physcs 8

19 Jeerson Lab Research Hghlghts: htt:// (new, hgh recson ata taen ug an alternatve technue, comlementary to the Rosenbluth metho.) Scalng law: µg /G = als or hgher momentum transer (Varous new theoretcal rectons, colore lnes.. 5) For more than 0 years t has been assume, base on the avalable ata, that the charge an magnetzaton strbutons n the roton were roortonal to one another (corresonng to µge/gm=). New ata rom Jeerson Lab shows ths s not true, an s leang to a re-examnaton o the ynamcs governng the roton s uar waveunctons.. K. Jones, et al., Phys. Rev. Lett. 8, 398 (000), O. Gayou, et. al., Phys. Rev. Lett. 88, 0930 (00) systematc error lmts Phys 50 Intro Nuclear Physcs 9

20 Inelastc electron scatterng: The G 0 exerment (/3 Canaan) Phys 50 Intro Nuclear Physcs 0