Nuclear Physics (7 th lecture)

Transcription

1 Gaa ecay (cont.) Su ues Nucea Physcs (7 th ectue) Content Measung ethos o the gaa ecay constant Gaa-gaa angua coeaton (utoaty eas.) Nucea oes #: qu o oe Nucea oes #: The Fe-gas oe Gaa-ecay Suay o evous ectue: ) Mutoe exanson o eectoagnetc waves ( ) ( ) ( ) B, b, kly, an, B, eectc k ( M ) ( M ) ( M ), a, kly, an B,, agnetc k These waves have goo angua oentu an aty! ectc tanstons aty change: Magnetc tanstons aty change: ) Seecton ues ngua oentu: I I I I Paty: Note: snce the ntnsc angua oentu o a hoton s, tanstons ae stcty oben. The gaa-ecay (cont.) Decay constant (tanston obabty) Cocate quantu-eectoynac cacuaton. oxaton: ony one unt chage changes ts state. Resut: nteacton oeato 8, M, o eectc tanstons!! c na an nta wave unctons Sa o agnetc tanstons Futhe aoxatons: - The an wave unctons contan Y, sheca haoncs, these can be ntegate wth the M, oeato S(I, I, ) statstca acto - The quantu nubes aveage (no ect obsevaton) - The aa at o the wave unctons = constant (!) The gaa-ecay (cont.) Fnay we get the Wessko unts: 4,4 R SI, I,!! 97 M,9 R SI, I,!! 97 Snce ths s eenent on unts, R shou be n, n MeV. The esuts ae n /s. How o the tanston obabty change wth utoaty? R R R hc Take = 5 nuceus, an =,5 MeV R 4 R, 5 6 4,5 In atoc hyscs R 4 8 R an 8 Ony tanstons occu o the atos! Roe o cosons! 4

2 The ten o the Wessko unts The gaa-ecay (cont.) 4) Moe cocate tanstons B I, I I M, Reuce tanston obabty Gaa-ecay (cont.),, Inta an na state ectons Snge atce atx eeents The B() vaues ae usuay gven n Wessko unts (W.u.). I B(L) ~ W.u. snge atce exctatons I B() >> W.u. coectve exctaton (nvovng any atces) 5 6 xctaton o the nuceus Su ues The quauoe oeato: ˆ ˆ Yˆ Ω Q The ossbe quauoe exctatons: q ˆQ Usuay q > s not an egenuncton o the Hatonan, an even not noaze! q? Howeve, t can be exane! I > s a coete noaze set o egenunctons then q c q c c, Muty ths by < c q > can be noaze c q S 7 Fnay we have: Su ues (cont.) ˆQ S Ths s the Thoas-Kuhn su ue. Hee Qˆ can eesent any utoe oeato (not ony quauoe) It can be cacuate theoetcay usng se assutons! Fo exae o the oe oeato: e D D c What oes the su ue ean hyscay? 6 q ˆQ ~ how stongy the < nucea state can be excte o the goun state wth the Qˆ oeato NZ NZ [MeV b] 8

3 Thee can be any exctatons wth the sae utoaty! The su ue escbes the tota ossbe stength o exctaton (wth any enegy) o a utoe oeato Su ues (cont.) I ony one < contbute to S, then ths atcua state wou exhaust % o the su ue. Snge atce tanstons Few Wessko unts B() vaues Gant utoe vbatons Su ues (cont.) coectve tanstons Gant esonances Su ue Gant oe esonance exctaton stength ˆ Q escbes the contbuton o one atcua S exctaton to the su ue (e.g. n %) 9 beathng oe htts://nsehe.net/eco/45/es/dcs_tst.ng Measung the gaa-ecay constant The exonenta ecay aw t t ) Dect easueent o e te The etho o eaye concences t e e s Measung the gaa-ecay constant ) Usng the Doe sht 9 s ojecte bea taget stoe o Dung the ght: Doe sht te the sto: No Doe sht Fght te: t v TC = te to atue convete (aso te to gta convete TDC cou be use)

4 etecto # Detecto Measung the gaa-ecay constant ) Doe sht n the taget 5 s taget Doe sht &boaenng ojecte bea Detecto Doe boaenng ony 4) Fo ne-wth The echans o the stong n the taget ust be we known (usuay suaton) ( > etecto esouton) Gaa-gaa angua coeaton etho o etenng the utoaty The ea: The angua stbuton o eent utoates ae eent (e.g. oe antenna) The obe: The nuce n a sae ae not agne obsevaton o snge gaa-ays s sotoc The souton: Detect two consecutve gaa-ays! The etecton o the st gaa-ay xes a ecton obsevaton o the secon gaa-ay w not be sotoc esectve to the ecton o the st one! The ange between the two -ays eens on the utoaty! 4 Gaa-gaa angua coeaton (cont.) W a cos Concence exeent souce ovabe etecto & The nube an the vaues o the a coecents ae chaactestc o the utoates nvove xae: angua coeaton esut The obe: Unke the ato, the nuceus cannot be escbe exacty, because a) the nuceus s he togethe by the two-boy nteactons between ts consttuents; thee s no centa souce o the nucea otenta; b) we on't know exacty the nuceon-nuceon nteacton. The souton: Nucea oes We use se oes. The ay-o s that these oes escbe the behavou ony aty. htts://wk.un.eu/ub/mxp/nguacoeatonogaaraysocobat6/gah.jg 5 6 4

5 ) The qu o oe We have teate t aeay. That e to the Wezsäcke-oua. It escbes we the bnng enegy. But ony that! ssutons: - Nucea oces ae attactve an shot-ange the ensty s constant (ke n a qu) - The nuceus s shee-shae (because o the suace tenson) the suace enegy s ootona to the suace - The nuceus s hoogeneousy chage Couob te - The consttuents ae eons (Pau nce) asyety enegy te - Pang enegy can be ecay taken nto account B b V b F Z N Z bc b bp 7 ) The Fe-gas oe Snce the nuceons ae eons, we can ty to set u a oe o eon gas. ssuton: the eons ae cose n a sheca otenta we, but they ove eey nse. What can be execte o ths oe? - Descbe ony the knetc enegy contbuton o the nuceons - Snce quantu echancs s use, the asyety te ght be escbe - Soe suace eects can aso be execte The goun state: - Snce they ae eons, ony one atce n a state (Pau excuson nce) - Snce goun state the owest enegy states ae e - =ħk n,, 8 N The nube o states n the hase-sace: N Because o the sn n N n 4 V V 4 Fo the nube o otons an o neutons we have V 4 Z V 4 n N 4 Usng an 4 R V R we get : Z Z N, an 4 n 9 To get soe nueca estaton we aoxate: Snce the aveage bnng enegy o a nuceon s ~ 7 MeV, we get the oowng ctue o the nucea otenta: -4 7 R Z N we get n Contans ony known constants!, The hghest knetc enegy at the Fe-eve: MeV M 5