Weak and Electromagnetic Interactions in Nuclei

Transcription

1 Wak and Elctromagntic Intractions in Nucli Toshio Suzuki Nihon Univrsity/CNS CSN Summr School Aug. 8, 7

2 Intractions Situation Strngth Handling (Cross sctions) EM (lctro- Known modrat (nough) clar magntic) 36 6 (1 1 cm / sr ) Wak (W) Known within wak (small) clar th standard modl 4 38 (1 1 cm ) Not wll dtrmind part rmains at hadron lvl Strong (S) Not compltly strong (larg) non-asy known at hadron lvl (7 ) (1 cm )(distortion (nd phnomnology) + absorption)

3 EM and Wak Intractions in Nucli 1. Prob of nuclar structur γ γ ν W ± Z Z ν ν. Prob of wak nutral currnt.g. sγ s, sγγs 5

4 EM γ fi 4πα T = i γ γ J q γ γ 1 1 J = i < N uγ u dγ d sγ s N > = i < N ( uγ u + dγ d sγ s) + ( uγ u dγ d) N > 6 isoscalar ( j 8 ) isovctor (j 3 ) 1 = iu ( p ')[ F ( q ) γ + F ( q ) σ q ] u( p) 1 ν ν m 1 S V 1 S V = iu ( p ') [( F + F τ ) γ + ( F + F τ ) σ q ] u( p) ν ν m S V S V F () = F () = 1, F () =.1 F () = r γ 1 r r 1 r r J = F ( p + p ') + ( F + F ) ( iσ q) 1 1 m m γ q i r r r J = F ( F + F )( q ( σ q)) 1 1 8m 4m

5 Wak ± W, Z ν ν ν G L i J ( ± ) = {[ γ (1 + γ ) ν + ( )] ( + ) ff 5 5 ( ν ) () ( ) + [ νγ (1 + γ ) + ( )] J } G L = i [ νγ (1 + γ ) ν + ( ) +..] J ff 5 G L = i [ γ (1 + γ ) 4sin θ γ ] J ff ( ) () 5 W

6 Chargd Currnt ( + ) J = i < N u + d + s 5 C γ (1 γ )[ cosθ sin θ ] + cγ (1 + γ )[ d sin θ + s cos θ ] N > 5 ( + ) J i θ N γ τ N N γ γ τ N C ± 5 ± = cos { < >+< > } 1 < N γ τ N >= u ( p ')[ Fγ + F σ q ] τ ] u( p) ± 1 ν ν ± m < N γ γ τ N >= u ( p ')[ F γ γ if γ q ] τ ] u( p) 5 ± A 5 P 5 ν ± mfa F () = 1.6 F = A P q + m π r r V V 1 r r V 1 r r J = F σ ( F + F ) iσ q + F ( p + p ') A 1 1 m m V 1 r r r J = F + F σ ( p + p ') 1 A m C V(vctor) AV(axial-vctor) C C CVC

7 Nutral Currnt i i = < N [( uγu dγd) + ( uγγu dγγd) sγs sγγs N > () γ J = < N [ uγ (1 + γ ) u dγ (1 + γ ) d sγ (1 + γ ) s N > sin θ J W isovctor-v isovctor-av strang-v strang-av = S S γ V A V A sin θ J W 3 i i V 1 V V = < N ( uγ u dγ d) N >= u( p')[ F γ + F σ q] τ u( p) 1 ν 3 m 3 i i A = < N ( uγγu dγγd) N >= u( p')[ F γγ if γq ] τu( p) 5 5 A 5 P 5 ν 3 S i i S 1 S V = < N sγ s N >= u( p')[ F γ + F σ q] u( p) 1 ν m S i i S A = < N sγγs N >= G u( p') γγu( p) S S S S F () = F ( q ), F, G not wll dt r min d 1 1 1

8 Not 1 ( ) 1 ( 3 ) 1 ( 3 ) 3 j = u Γu d Γd 8 j = u Γ u + d Γd s Γs j = u Γ u + d Γ d + s Γs j not wll dtr min d Asumption A Not: vctor part S S = V = = + sin () 3 3 γ J A V θ J W () 3 V = V sin θ J γ W IV () C ( G sin θ G ) < j ( qr) Y > E W E 1.8 proton G θ ρ r G ρ r 1 p n 1 p nutron : ( G sin θ G ) ρ ( r) G ρ ( r) E W E n E n p p : (1 4sin ) ( ) = ( ) E W p E p

9 + Cross sctions for ( ν, ),( ν, ),( ν, ν),( ν, ν ) 3 W h ( f i ) ( ) 3 π d σ = π < f H i > δ W W 3 d G d k = d Ω m π ( k p ) ε η = Tr[ γ (1 + γ ) k/ γ (1 + γ ) k/ ] ν 5 1 ν 5 4 = ( k k + k k ( k k ) δ ± ε k k ) 1 ν 1ν 1 ν ν ρ σ 1 ρ σ W = W + W + W VV VA AA VV W p q p q W = W δ + ( p q )( p q ) ν 1 ν ν ν M q q W σ ν ν ν ν T η W ν ν W W = W δ + p p + q q M M AA 4 5 ν 3 ν ν ν W W ( p q + p q ) + ( p q p q ) ν ν ν ν M M T W W = ε p q M VA 8 ν νρσ ρ σ T T T T d k

10 VV VV VV VV qw = W q =, qη = η q = ν ν ν ν ν ν d σ G ε 1 θ θ {( )cos ( )sin dωd M J = 1 m = W + W + W + W ε π m T W M θ θ r θ 1/ 8 sin ( q cos + q sin ) } T Multipol xpansions d σ G ε 4π θ q d J q = {cos < J M ( q) L ( q) J > f J J i Ω m π + 1 i q θ θ + [ cos + sin ] [ < ( ) > mag J T q J f J i q J = 1 θ sin θ r θ + < > + q Currnt Consrvation 1/ l J T ( q) J ] m ( q cos q sin ) f J i mag l R [ < J T ( q) J >< J T ( q) J f J i f J i > * ]}

11 3 r M ( q) = ( ) ( ˆ ) ( ) JM d x j qx Y x ρ x J JM i r r 3 r L ( q) = [ ( ) ( ˆ )] ( ) JM d x j qx Y x J x J JM q r r mag 3 M r T ( q) = d x[ j ( qx) Y ( x)] ( ) JM J JJ 1 ˆ J x 1 r r r r T q = d x j qx Y x J x q q l 3 M ( ) [ ( ) ( )] ( ) JM J JJ 1 ˆ q = (J + 1)!! J 3 M d xy J JM JM 1 q i (J + 1)!! r r r ( ) J 1 3 L = d xy JM JM J x 1 q J i (J + 1)!! J J + 1 J mag 3 J T = d x [ x J ( x )] x Y J M JM q J i (J + 1)!! J r r r ( ) J 1 l J T = d xx Y J x JM JM Rf: J. D. Walcka, Thortical Nuclar and Subnuclar Physics, Oxford (1995) r r r r

12 Vctor: T mag i hq 3 r r = ( l + σ ) 3 mc 4π 1M i i i i E E l f i J + 1 < f T ( q) i> f M ( q) i JM < > JM q q J l 5 AV: T = L = F 1M 1M A στ GT i ± i i 1 6π 5 M = F 1 τ Frmi ± i i 4π Spin-dpndnt xcitations Gamow-Tllr (1 + ): Spin-diol ( -, 1 -, - ): Multipols 1 + : E 5 1, M1, C 5 1, L : E 5, M, C 5, L : M 5 1, E1, C1 - : C 5, L 5 i r [ σ r τ r r± σ r ] J τ ±

13 Prob of nuclar structur (,) Frois & Papanicolas, Ann. Rv. Nucl. Part. 37 (1987) Charg dnsity Charg dnsity of s 1/ orbit

14 M1 s 1/ p 1/ M7 f 7/ <r n (f 7/ )> Cor-Polarization

15 MV fm Shll-modl intractions V = VC + VTnsor + VLS r r r r r r VT = τ1 τ1{3( σ1 rˆ)( σ rˆ) σ1 σ } Y( r) Monopol trms in p-shll = + < > + T jj ( 1) 1 1 : 1 : / ( 1) J J Monopol matrix lmnts V J j j JT V j j JT J TE π+ρ M3Y(Rid) Tamagaki OPEP AV fm (MV) T= C T ls S C T ls S C T ls S (j (1,1) (,1) (,) 1,j ) C=cntral T=tnsor ls=ls S=Sum 1=p =p 1/ 3/ CK SFO

16 Effcts of Tnsor Forc on Shll Evolution Otsuka, Suzuki, Fujimoto, Graw, Akaishi, PRL 69 (5) (MV) Monopol matrix lmnts tnsor T= SFO M3Y π+ρ CK j j =p 1/ =p 3/ 3=d 3/ 4=d 5/ ε ff (MV) 1 5 Effctiv Singl-Particl Enrgy for N=8 Nucli 11 Li SFO PSDMK 1 B 1s 1/ p p 1/ 3/ 13 B

17 B(GT) valus for 1 C -> 1 N B(GT) B(GT) EXP C N -> C x1/3 hw hw SFO PSDMK OFU* prsnt PSDWBP B(GT) valus for 14 N -> 14 C SFO x E (MV) m.m.(cal.)-m.m.(xp.) m.m.(cal.)-m.m.(xp.) Magntic momnts of p-shll nucli CK (hw) OFU* (hw) PSDWBP (hw) PSDMK (-3hw) prsnt (-3hw) 7 Li 8 Li 8 B 9 Li 9 B 9 C 1 B 11 Li 11 B 11 B 11 C CK (hw) OFU* (hw) PSDWBP (hw) PSDMK (-3hw) prsnt (-3hw) 1 B 1 N 13 B 13 C 13 N 13 O 14 B 14 N 15 B 15 C 15 N 15 O prsnt = SFO Suzuki, Fujimoto, Otsuka, PR C67 (3) Ngrt t al., PRL 97 (6) KVI RCNP SFO*: g A ff /g A =.95 B(GT: 1 C) fittd to xprimnt

18 Suprnova ν Spctra σ E <E> & tail part f ( E ) = N 1+ E / xp[ E 3 T / T α] T=8 T=6.6 T=5 T= MV ν, ν τ ν ν : < E >= 5 ( T, α) = ( 8MV, ) : < ( 6. 6MV, 3) E >= 11 MV MV ( T, α ) = ( 3. 5MV, ) : < E >= 16 MV ( T, α ) = ( 5MV, )

19 σ (1 cm ) -4 RATIO Cross sctions for Suprnova Nutrinos with tmpratur T (a) 1 C SFO PSDMK Woosly t al. (ν, - ) _ (ν, + ) T (MV) 1 - C (ν, ) Suzuki, Chiba, Yoshida, Kajino, Otsuka, PR C74 (6) SFO/PSDMK SFO/Woosly σ(1 cm ) -4 Nutral-Currnt (b) σ (1 cm ) (b) 1 C T (MV) 1 C SFO PSDMK SFO PSDMK Woosly t al. {(ν, ν ) + (ν, ν )}/ Proton and nutron missions BR: Hausr-Fshbach modl Nutral-Currnt _ T (MV) 1-1 {(ν, ν p) + (ν, _ - _ {(ν, ν n) + (ν, ν n)} T (MV)

20 Light Elmnt Abundancs and Nuclosynthsis Procsss T. Yoshida

21 -4 ν- 4 H raction cross sctions σ (1 cm ) σ (1 cm ) (a) T (MV) 4 4 H H SPSDMK WBP Woosly t al. (ν, - ) _ + (ν, ) SPSDMK WBP Woosly t al. Gazit t al. Nutral-Currnt {(ν, ν ) + (ν, ν )}/ T (MV) -6 1 Msun Abundancs of 7 Li and 11 B producd in suprnova xplosion procsss M=16. M (SN 1987A) cf. Woosly-Haxton: Sussx potntial by Elliott t al. T = 3. MV, T = 5. MV T ν ν, ν τ = 6. MV ( ν, ν' p),( ν, ν' n) ν = ν, ν 7 Abundancs of Li and 11 B HW9 PSDMK/SPSDMK SFO/WBP M( Li) M( B) M( Li)/M( B) ν, τ, τ

22 Nuclosynthsis through nutrino-inducd ractions Production of rar lmnts by ν- ractions Ba( ν, ) La Hf ( ν, ) Ta Calculation by Hgr t al. Rol of νin r-procss nuclosynthsis N=8, 16 rgions With ν-inducd n mission solar abundancs GT xp. RCNP ( 3 H, t) Mor GT strngth than RPA (Hgr t al.) Bylikov t al., PRL 98 (7) Qian, Haxton, Langank, Vogl,PR C55 (1997)

23 Prob of Wak Nutral Currnt S G ( < N sγ γ s N > ) via A( ν, ν ') A( T = ) 1 5 dσ V + A sin θ J A ( G ) W 1 d Ω S S γ S S G 1 S G 1 S Suzuki, Kohyama, Yazaki

24 Polarizd lctron scattring r A(, ) A dσ dσ A = d σ + d σ R{ 1 1 R L= (1 γ ) (1 + γ ) = γ A Tr k/ k/ + J J * R{ [ γγ γ(1 4sin θ γ γ W ) } 5 1 ν W 5 ν + * * R{(1 4sin θ γ A γ V ) JJ JJ } W γ J {.8 < N sγγs N >+< N sγs N > } 5 F S }

25 1 C M F S =-.3 M1+C+C1 SAMPLE tc Ent, in EM Int. and Hadron Structur (7)

26 r A(, ) A Isoscalar Coulom b scatt. A 4πα n p ( q ) ( q ) q S S S S ( G = F F ( F ( ) = )) E m S Gq A πα A G q ρ ρ /( sin θ ) W 1 N q < > < > {1 ( r r )} n p 4sin θ Z 6 W + + Ca isotops

27 Byond standard modl Nutrino oscillations U c ij α= μ τ ν = U ν = ν a=1,,3 1 c s α α a a c s 1 1 ij 3 3 s c = cosθ, 1 1 s c s ij c s = sin θ ij iδ 13 1 s c iδ 13 a Prsnt status of paramtrization < m < V o θ = 45± 8 (9%) (KK) m = 8. 1 V θ = 3.3 (1 σ) (KamLAND,SN) oscilltions in sup rnova xp losion o o sin θ 13 <.1 (Chooz) Possibl constra int on lowr lim it of θ 13