Photodisintegration of light nuclei

Transcription

1 Photodsntegaton of lght nucle N Banea The Hebew Unvesty Jeusalem Guseppna Olandn Tento (Italy) Wnfed Ledemann Tento (Italy) Sona Bacca Damstadt (Gemany) Doon Gazt Jeusalem (Isael) Yael Ronen Jeusalem (Isael) Nuclea Stuctue and Astophyscs wth Radoactve Beams WIS Rehovot, June 4-6, 006

2 Photodsntegaton of lght nucle Neutno neutal eacton on 4 He Low enegy photodsntegaton of 16 O n an 4α-patcle model (A comment)

3 Some techncal emaks on ab-nto calculaton of nelastc eactons on lght nucle poectle photon electon neutno o anothe nucleon taget nucleus wth A=N+Z nucleons N neutons and Z potons

4 The coss-secton In geneal a eacton coss-secton can be wtten as whee the esponse functon s gven by σ R ( ω) = Const R( ω) ( ω) f Oˆ δ ( E E ω) = f f Due to the summaton ove the fnal states That ae usually contnuum states, Calculaton of eacton coss-sectons s much moe dffcult then calculatng bound states. Enegy levels of 4 He

5 The Loentz Integal tansfom (LIT) method In ode to avod contnuum wave functons we eplace the esponse functon wth ts tansfom, usng a Loentzan kenel, O n a dffeent fom, L ( ω,γ ) 0 = = dω R( ω) ( ω ω) Oˆ f ( ) f ω + E E 0 0 f Γ Γ L = f Oˆ ( ω + E E ) +Γ ( ω + E E ) 0 1 f f f 0 1 f Γ Oˆ = Oˆ 1 1 f f Oˆ Γ f ( ω + E H ) +Γ ( ω + E H ) 0 0 See mom no f!!! = Oˆ 1 ( ω + E H ) +Γ ( ω + E H ) Γ Oˆ = ~ ψ ~ ψ

6 Theefoe we have to solve the followng Schoednge lke equaton: Few Remaks ~ ψ ~ ( H E ω +Γ ) ˆ = ψ 0 O Thee s no soluton to the homogeneous equaton. Bounday condtons ae the same as fo bound state. The nveson s unque. Inveson of the tansfom s unstable and needs some egulaton. Efos, Ledemann & Olandn, PLB 408, 1 (1994).

7 Solvng the Schoednge equaton bound states We use the effectve nteacton hypesphecal hamoncs (EIHH) method Banea, Ledemann and Olandn, PRC 61, (000) Replacng only -body foces wth effectve ones ( )...,, ˆ = < < < k k eff K N m H ρ ρ ρ The effectve two-body potental s obtaned though the Applcaton of the Lee-Suzuk smlaty tansfomaton to the -body equaton ( ) ( ) N N K m H, 1 ˆ 1 + = ρ ρ

8 Benchmak test calculaton of a fou nucleon bound state Kamada et. al. Phys. Rev. C 64, (001)

9 4-body system wth the MT nucleon-nucleon potental EIHH BE bae Radus

10 4 He total photoabsopton coss-secton wth the ealstc foces A18+UIX. Beman et al. (g,n) 1980 Feldman et al. (g,p) 1990 Wells et al. 199 Nlsson et al. 005 Shma et al. 005 Gazt et. al., PRL 96, (006)

11 total photoabsopton coss-secton Fo A=6 nucle Soft dpole esonanace Gant dpole esonanace Bacca et. al., PRL (00)

12 6 He total photoabsopton coss-secton MN - Mnnesota potental MT - I-III Malflet-Ton Act only n the S=1,T=0 and S=0,T=1 channels. A4' - Agonne A4' Acts n all patal waves. Bacca et. al., PRC (004)

13 7 L total photoabsopton coss-secton wth A4 NN potental Bacca et. al., PLB 603, 159 (004)

14 Inelastc neutal neutno eacton on 4 He Neutno- 4 He (ν α) eactons ae mpotant n neutno dven supenova, and fo the nucleosyntess dung supenovae. Was fst calculated by Haxton (1988), usng shell model wth a Sussex model. Usng the LIT and EIHH methods we can now pefom abnto calculaton fo ths coss secton. Doon Gazt and N Banea, PRC, 70, (004)

15 Role n nucleosynthess The nucleosynthess of elements though neutno nduced nteactons (The ν pocess): Epsten, Colgate, and Haxton (1988). Woosley and Haxton (1988) Woosley, Hatmann, Hoffman, Haxton (1990) The poducton of 7 L n the 4 He ch laye s though the eacton sequences: 3 7 ( νν ) ( αγ) 4 He, 'p H, L ( νν ) ( αγ) ( ) 4 He, 'n He, Be n,p L

16 Inelastc neutal neutno eacton on 4 He ν " 4 He" Lepton cuent Nuclea cuent μ = ( k,k ) q μ = ( ω,q) k μ k = 1 1 ( k ),k 1 0 Z P μ f = P μ = ( ) E,P ( ) E,P ν 4 He

17 Inelastc neutal neutno eacton on 4 He The Impulse appoxmaton (consdeng only 1-body cuents) 90% of ou coss-secton s due to axal cuents. Axal -body cuents usually suppessed. ecto -body cuents ae potected n low enegy by the Seget Theoem.

18 Leadng tanston opeatos The closed shell chaacte of 4 He, suppesses the usually leadng opeatos: Gamow-Telle Fem Instead, the leadng opeatos ae popotonal to the momentum tansfe.

19 Coss-secton Whee the esponse functons, R ω = Ψ O ˆ Ψ Ψ O ˆ Ψ E E + ( ) ( ) f f δ f ω O,O ˆ ˆ f Ae needed to be calculated usng a model fo the 4 He nucleus we used the A8 NN potental.

20 Dffeent multpole contbutons to the coss-secton. Multpole Stength [10 4 cm/me] E 5 51% M % C 1, L 1, E 1 6% L 5.5% L % ω [Me]

21 Compason wth pevous esults equal 5% 15% 5% Woosley et. al, ApJ 356, 7 (1990) Haxton, PRL 60, 1999 (1988)

22 Conclusons A fst ealstc calculaton of the nelastc neutno neutal eacton on 4 He. Full Fnal state nteacton and ealstc nte-nucleon foce ae consdeed. The calculaton s done n the mpulse appoxmaton. The numecal accuacy s about 1%. The new esults facltate stonge neutno matte nteacton,.e. enhanced coss-secton. Stonge tempeatue dependence.

23 Low enegy photodsntegaton of 16 O n an 4α-patcle model 4 He Low enegy α 16 O Low enegy α α α α

24 The model Even-even nucle egaded as Nα systems The α s ae J=0 stuctueless patcles Non-elatvstc quantum mechancs Local nteactons H = 1 m α p + < c ( ) ( ) + α + K < Gudelne Use foce models that epoduce the 8 Be, 1 C gound states

25 Avalable foce models Fedotov, Katavtsev, Kochkn and Malykh, PRC. 70, (004). Fedoov and Jensen, Phys. Lett. B 389, 631 (1996). Intoduced a foce model of the fom = < Z + < α ( ) + ( ) 3 α,, k < < k () (a) μ a () μ α = 0 e 0 e (,, ) 3α k = (3) 0 e μ 3 ρ epoduce the 8 Be Resonance, and also the BE and the fst excted 0 + state of 1 C ρ 1 = + ( ) ( ) + ( 3 k k )

26 Pedctons fo the 4,5-body systems What do we expect to fnd? Gong fom 3-body nucle to 4-body one fnds the Ton-lne.e. potental models that epoduce,3-body data also epoduce the bndng enegy of the 4-body system!!! Same happens fo He atoms! What about α patcles?

27 Pedctons fo the 4,5-body systems Assumng that the 3-body foce acts only on S-waves 1 C 16 O 0 Ne FKKM FKKM FdJn Exp Concluson: the cuent models leads to a collapse of the N-boson system A epulsve 4-body foce must be added

28 Conclusons The foce models whch nclude only and 3 body tems tend to ovebnd the 16 O. Addng a 4-body foce, the gound state and 1 st excted state of 16 O can be epoduced faly well. The 4-body foce s not unque, thee exst many possble sets of paametes. We managed to calculate the low enegy 16 O(γ,α) 1 C coss-secton. Howeve the esults ae vey senstve to the foce model. Cuently we ty a new appoach, fttng a non-local -body foce.

29 Thats all...

30

31 Conclusons Contay to the common beleve, epoducng the two body data and 3-body gound state popetes ae not enough to make a nuclea foce model ealstc. Photoabsopton eactons ae a useful tool to dffeentate between foce models. The dffeences between models gow wth A (fo A=,3,4). The theoetcal tools and methods that we have developed allow an accuate descpton of nuclea stuctue and eactons (ncludng FSI) fo nucle wth A=,3,...7 patcles.

32 What ae the enegy scales? E [Me] N S_alpha BE BE/ N E* Exctaton enegy of the α patcle: E* ~ 0 Me

33 In compason Fo a system of N 4 He atoms BE mk = 10 7 e << 1e In nuclea physcs the ato between bndng enegy Pe nucleon and nucleon exctaton enegy BE / A 8 Me << 100 Me Fo N α patcles the ato between bndng enegy pe α and α exctaton enegy BE / A 3 Me < 0Me

34 The 16 O wth a fou-body foce The second excted level (J π = + ) expemental value Ths wok The fst excted level (J π =0 + ) expemental value Ths wok

35 Results fo A cm / Me cm d< > 0.0 T=10 Me ω [Me] 0.00

36 K E_0 E_ Exp C - FKKM1 Fedotov, Katavtsev, Kochkn and Malykh model 1 The convegence of the EIHH method s extemely fast Fo both, the GS and the excted state

37 The -body and 3- body Foces The full foce model ( ) ( ) ( ) < < < α < < α < α < = l k l k 4 k k 3,,,,, Z () a (a) 0 () 0 e e μ μ α = ( ) = ( ) 0 L e 0 L,, 3 (3) 0 3 k = = = ρ μ α ( ) k k 3 ) ( ) ( ) ( 3 1 v v v v v v + + = ρ The 4-body foce ( ) 4 4 e,,, (4) 0 l k 4 ρ μ α = < = ρ 4 ) ( 4 1 v v