Description of (p, pn) reactions induced by Borromean nuclei

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/FBK, Trento, Italy Mario Gómez-Ramos Antonio M.

1 Fiera di Primiero. October 6, 2017 Selected Topics in Nuclear and Atomic Physics Description of (p, pn) reactions induced by Borromean nuclei Jesús Casal ECT /FBK, Trento, Italy Mario Gómez-Ramos Antonio M. Moro Dpto. de Física Atómica, Molecular y Nuclear Universidad de Sevilla, Spain

2 J. Casal, Fiera di Primiero 2017

3 J. Casal, Fiera di Primiero 2017

4 (p, pn) reactions A nucleus and a proton collide One nucleon is removed leaving a residual fragment High energies to increase mean free path of nucleon inside nucleus Proton-target knockout (p, pn) or (p, 2p) The interaction happens between the proton and a single nucleon Used to extract spectroscopic information of nuclei J. Casal, Fiera di Primiero 2017 p. 1

16 Ne 17 Ne 18 Ne 19 Ne 20 Ne 21 Ne 22 Ne 23 Ne 24 Ne 25 Ne 26 Ne 10 Borromean nuclei 14 F Z 15 F 16 F 17 F 18 F 19 F 20 F 21 F 22 F 23 F 24 F 25 F 3b systems with no bound 2b pairs 12 O 13 O 14 O 15

5 16 Ne 17 Ne 18 Ne 19 Ne 20 Ne 21 Ne 22 Ne 23 Ne 24 Ne 25 Ne 26 Ne 10 Borromean nuclei 14 F Z 15 F 16 F 17 F 18 F 19 F 20 F 21 F 22 F 23 F 24 F 25 F 3b systems with no bound 2b pairs 12 O 13 O 14 O 15 O 16 O 17 O 18 O 19 O 20 O 21 O 22 O 23 O 24 O 10 N 11 N 12 N 13 N 14 N 15 N 16 N 17 N 18 N 19 N 20 N 21 N 22 N 23 N 8C 9C 10 C 11 C 12 C 13 C 14 C 15 C 16 C 17 C 18 C 19 C 20 C 21 C 22 C 6B 7B 8B 9B 10 B 11 B 12 B 13 B 14 B 15 B 16 B 17 B 18 B 19 B 20 B 5 Be 6 Be 7 Be 8 Be 9 Be 4 Li 5 Li 6 Li 7 Li 8 Li 9 Li 10 Li 11 Li 3 He 4 He 5 He 6 He 7 He 8 He 9 He 10 He 2H 3H 4H 5H 6H 7H Li 2 1H 10 Be 11 Be 12 Be 13 Be 14 Be 15 Be 16 Be 12 Li 13 Li p-rich n-rich 2n halo stable unbound N n J. Casal, Fiera di Primiero p. 2

6 (C + N 1 + N 2 ) + p }{{} (C + N 2 ) +N }{{} 1 + p A B If A is Borromean, the unbound fragment B will eventually decay Spectroscopic information on the projectile by probing the continuum wave function of the unbound fragment J. Casal, Fiera di Primiero 2017 p. 3

7 Linking structure and dynamics in (p, pn) reactions with Borromean nuclei: The 11 Li(p, pn) 10 Li case M. Gómez-Ramos, J. Casal, A. M. Moro PLB 772 (2017) 115 arxiv: B 11 B 12 B 13 B 14 B 15 B 16 B 17 B 9 Be 10 Be 11 Be 12 Be 13 Be 14 Be 15 Be 16 Be 8 Li 9 Li 10 Li 11 Li 12 Li 13 Li 7 He 8 He 9 He 10 He Data on 8 He, 11 Li, 14 Be from GSI available 6 H 7 H New exp. on 11 Li, 14 Be, 17 B from RIKEN under analysis J. Casal, Fiera di Primiero 2017 p. 4

8 Transfer to the Continuum (TC) Overlaps J. Casal, Fiera di Primiero 2017

9 Transfer to the Continuum (TC) Overlaps Transfer to the Continuum (TC) No IA assumed No factorization approximation Participant/spectator approach N 2 C x y N 1 A R p N 2 B x C R p N 1 r J. Casal, Fiera di Primiero 2017 p. 5

10 Transfer to the Continuum (TC) Overlaps Transfer to the Continuum (TC) No IA assumed No factorization approximation Participant/spectator approach N 2 C x y N 1 A R p N 2 B x C R p N 1 r Prior representaton of the T-matrix T if = ( x)ψ ( ) f ( r, R ΦA ) V pn1 + U pb U pa ( x, y)χ (+) pa ( R), where ϕ ( ) q ϕ q continuum wave function of the binary fragment B Ψ f final (pn)-b wave function Φ A g.s. wave function of the initial 3b composite A χ pa distorted p-a wave [M. Gómez-Ramos, J.C., A.M. Moro, PLB 772 (2017) 115] J. Casal, Fiera di Primiero 2017 p. 5

11 Transfer to the Continuum (TC) Overlaps Final wave function Expanded in proton-nucleon states (CDCC) Ψ f ( r, R ) nj Π φ J n Π (k n, r )χ J n Π ( K, R ) R N 1 r B p J. Casal, Fiera di Primiero 2017 p. 6

12 Transfer to the Continuum (TC) Overlaps Final wave function Expanded in proton-nucleon states (CDCC) Ψ f ( r, R ) nj Π Basis of N discretized bins φ J n Π (k n, r )χ J n Π ( K, R ) φ J Π n (k n, r ) = 2 kn φ J Π pn πn 1 (k, r )dk. k n 1 R N 1 r B p A + p B + pn 1 J. Casal, Fiera di Primiero 2017 p. 6

13 Transfer to the Continuum (TC) Overlaps Final wave function Expanded in proton-nucleon states (CDCC) Ψ f ( r, R ) nj Π Basis of N discretized bins φ J n Π (k n, r )χ J n Π ( K, R ) φ J Π n (k n, r ) = 2 kn φ J Π pn πn 1 (k, r )dk. k n 1 R N 1 r B p If we select the (p, d) channel TC reduces to DWBA A + p B + pn 1 Ψ f ( r, R ) φ d ( r )χ d-b ( R ) J. Casal, Fiera di Primiero 2017 p. 6

14 Transfer to the Continuum (TC) Overlaps 2b continuum state of fragment B s 2 N 2 x L, J C I ϕ (+) 4π q,σ 2,ι ( x) = qx LJJ T M T i L Y LM ( q) LMs 2 σ 2 JM J JM J Iι J T M T f J T LJ (qx)[y Ls 2J( x) κ I ] JT M T Coupling order: L + s 2 = J, J + I = JT Obtain solution for each (L, J)J T : f J T LJ (qx) i [ 2 eiσ L H ( ) L (qx) SJ T LJ H(+) L (qx) ] J. Casal, Fiera di Primiero 2017 p. 7

15 Transfer to the Continuum (TC) Overlaps 3b g.s. wave function of A N 2 s 2 l x, j x x y l y C I N 1 s 1 β {K, l x, j x, j 1, l y, j 2 } lx + s 2 = j x, j x + I = j 1 ly + s 1 = j 2, Analytical THO method j 1 + j 2 = j Diagonalize H 3b using: [PRC 88 (2013) ] Binary interactions C-N i, N 1 -N 2 Three-body force to fine-tune g.s. energy Φ jµ A ( x, y) = β w j β (x, y) { [Y lxs 2j x ( x) κ I ] j1 [ Y ly (ŷ) κ s1 ] j 2 }jµ Consistent with 2b wave function: same potential and couplings J. Casal, Fiera di Primiero 2017 p. 8

16 Transfer to the Continuum (TC) Overlaps Assume (V pn1 + U pb U pa ) does not change the state of B Define overlaps 2b 3b : ψ LJJT M T (q, y) = f J T LJ (qx) x [Y Ls2 J( x) ψ I ] JT M T Φ jµ A ( x, y)d x J. Casal, Fiera di Primiero 2017 p. 9

17 Transfer to the Continuum (TC) Overlaps Assume (V pn1 + U pb U pa ) does not change the state of B Define overlaps 2b 3b : ψ LJJT M T (q, y) = f J T LJ (qx) x [Y Ls2 J( x) ψ I ] JT M T Φ jµ A ( x, y)d x Auxiliary amplitudes for each 2b configuration {(L, s 2 )J, I}J T : T LJJ T M T if Ψ ( ) f ( r, R ) V pn1 +U pb U pa ψ LJJT M T (q, y)χ (+) pa Cross sections dσn 2 T LJJ T M T dω B dε if x 2 J. Casal, Fiera di Primiero 2017 p. 9

18 GSI data TC calculations Transfer reaction J. Casal, Fiera di Primiero 2017

19 GSI data TC calculations Transfer reaction 11 Li(p, pn) 10 Li in inverse kinematics ALADIN-LAND setup at GSI [Aksyutina et al., PLB 666 (2008) 430] 280 AMeV spectroscopic information extracted through fitting reaction dynamics not considered More recent data from RIKEN is coming J. Casal, Fiera di Primiero 2017 p. 10

20 GSI data TC calculations Transfer reaction TC calculations [spin of 9 Li ignored, I π = 0 + ] 10 Li ( 9 Li + n) 11 Li ( 9 Li + n + n) 2s 1/2 virtual state: a = 20.9 fm 1p 1/2 resonance at 0.5 MeV 1d 5/2 state around 4.5 MeV 0 + g.s. at MeV r mat = 3.55 fm, r ch = 2.48 fm 64% s 1/2, 30% p 1/2, 3% d 5/2 J. Casal, Fiera di Primiero 2017 p. 11

21 GSI data TC calculations Transfer reaction TC calculations [spin of 9 Li ignored, I π = 0 + ] 10 Li ( 9 Li + n) 11 Li ( 9 Li + n + n) 2s 1/2 virtual state: a = 20.9 fm 1p 1/2 resonance at 0.5 MeV 1d 5/2 state around 4.5 MeV 0 + g.s. at MeV r mat = 3.55 fm, r ch = 2.48 fm 64% s 1/2, 30% p 1/2, 3% d 5/2 dσ/dε n- 9 Li (mb/mev) TC, p 1/2 TC, s 1/2 TC, total; σ = 32.0 mb experimental resolution ε 9 n- Li (MeV) ε n- 9 Li (MeV) J. Casal, Fiera di Primiero 2017 p. 11

22 GSI data TC calculations Transfer reaction TC calculations [spin of 9 Li ignored, I π = 0 + ] 10 Li ( 9 Li + n) 11 Li ( 9 Li + n + n) 2s 1/2 virtual state: a = 20.9 fm 1p 1/2 resonance at 0.5 MeV 1d 5/2 state around 4.5 MeV 0 + g.s. at MeV r mat = 3.55 fm, r ch = 2.48 fm 64% s 1/2, 30% p 1/2, 3% d 5/2 dσ/dε n- 9 Li (mb/mev) Exp data, σ = 30.3 mb TC ε 9 n- Li (MeV) J. Casal, Fiera di Primiero 2017 p. 11

23 dσ/de n 9 Li (mb/mev) s-wave p-wave total s-wave p-wave total s-wave p-wave d-wave total P3 P4 P E 9 n Li (MeV) GSI data TC calculations Transfer reaction w/o energy resolution with energy resolution Sensitivity to the structrure model P3: reference model Not sufficient to confirm d 5/2 resonance P4: virtual state at higher E p resonance at lower E P5: with d resonance 1.5 MeV a E r[p 1/2 ] E r[d 5/2 ] P P P (fm) (MeV) (MeV) %s 1/2 %p 1/2 %d 5/2 P P P J. Casal, Fiera di Primiero 2017 p. 12

24 GSI data TC calculations Transfer reaction spin-spin splitting: s 1/2 1, 2 p 1/2 1 +, 2 + Include spin of 9 Li; I π = 3/2 Model P1I: 10 Li: a = 37.9 fm (2 ) res. at 0.37, 0.61 MeV 11 Li: 3/2 g.s. at MeV r mat = 3.2 fm r ch = 2.41 fm 67% s, 31% p J. Casal, Fiera di Primiero 2017 p. 13

25 GSI data TC calculations Transfer reaction spin-spin splitting: s 1/2 1, 2 p 1/2 1 +, 2 + Model P1I: 10 Li: a = 37.9 fm (2 ) res. at 0.37, 0.61 MeV 11 Li: 3/2 g.s. at MeV r mat = 3.2 fm r ch = 2.41 fm 67% s, 31% p dσ/dε n- 9 Li (mb/mev) Include spin of 9 Li; I π = 3/2 Exp. data 1-, 27% 2-, 40% 1+, 12% 2+, 19% total P1I P3 P ε 9 n- Li (MeV) d 5/2 resonance not required to explain the data Data from Aksyutina et al. [PLB 666 (2008) 430] J. Casal, Fiera di Primiero 2017 p. 13

26 GSI data TC calculations Transfer reaction Transfer reaction 11 Li(p, d) 10 Li IRIS at TRIUMF, 5.7 AMeV Sanetullaev et al. [PLB 755 (2016) 481] weight p 1/2 : 33% J. Casal, Fiera di Primiero 2017 p. 14

27 GSI data TC calculations Transfer reaction DWBA calculations for 11 Li(p, d) 10 Li 10 3 dσ/dω (mb/sr) [PLB 767 (2017) 307] 31% p 1/2 content in 11 Li Model P1I Exp. data p 1/2 (1 +,2 + ) s 1/2 (1 -, 2 - ) θ c.m. (deg) Same model gives good agreement on (p, pn) and (p, d) reactions J. Casal, Fiera di Primiero 2017 p. 15

28 Experimental data Structure considerations Preliminary calculations J. Casal, Fiera di Primiero 2017

29 Experimental data Structure considerations Preliminary calculations 14 Be ( 12 Be + n + n) Ground state j π = 0 +, separation energy S 2n 1.3 MeV 11 Be + n Excited 12 Be components in the ground-state wave function of 14 Be are essential Inclusion of core excitations needed!! 0 + g.s. 12 Be e.g.: rotational model in NPA 733 (2004) 53 by Tarutina et al. to couple 0 + 1, 2+ 1 states J. Casal, Fiera di Primiero 2017 p. 16

30 Experimental data Structure considerations Preliminary calculations 14 Be(p, pn) 13 Be a) Kondo et al. 69 MeV/u PLB 690 (2010) 245 b) Aksyutina et al. 304 MeV/u PRC 87 (2013) ) l = 0, 1/2 + 2) l = 1, 1/2 3) l = 2, 5/2 + 4) l = 1, 1/2 5) l = 2,? a) decay 5/ Be(2 + ) b) decay into 12 Be(1 ) J. Casal, Fiera di Primiero 2017 p. 17

31 Experimental data Structure considerations Preliminary calculations 14 Be(p, pn) 13 Be a) Kondo et al. 69 MeV/u PLB 690 (2010) 245 b) Aksyutina et al. 304 MeV/u PRC 87 (2013) P (E fn ) = (p x fn )2 p x fn 2 1) l = 0, 1/2 + 2) l = 1, 1/2 3) l = 2, 5/2 + 4) l = 1, 1/2 5) l = 2,? a) decay 5/ Be(2 + ) b) decay into 12 Be(1 ) J. Casal, Fiera di Primiero 2017 p. 17

32 Experimental data Structure considerations Preliminary calculations Aksyutina et al. PRC 87 (2013) ) using two 1/2 + states No low-energy 1/2 resonance required Momentum profile gives an average: mostly l = 0, l = 2 13 Be structure not clear New data from RIKEN, 250 MeV/u. Anna Corsi et al. J. Casal, Fiera di Primiero 2017 p. 18

33 Experimental data Structure considerations Preliminary calculations Structure model Deformed 12 Be + n potential with core couplings in a rotational model Only 0 + (g.s.) and 2 + (2.1 MeV) of 12 Be included. Deformation parameter β 2 = 0.8 [Tarutina et al. NPA 733 (2004) 53] V (l = 0, 2) and V ls adjusted to give: - near-threshold 1/2 + state - 5/2 + resonance at 2 MeV Shallow V (l = 1) for simplicity l x, j x x N 2 s 2 y l y C I N 1 s 1 J. Casal, Fiera di Primiero 2017 p. 19

34 Experimental data Structure considerations Preliminary calculations Structure model Deformed 12 Be + n potential with core couplings in a rotational model Only 0 + (g.s.) and 2 + (2.1 MeV) of 12 Be included. Deformation parameter β 2 = 0.8 [Tarutina et al. NPA 733 (2004) 53] V (l = 0, 2) and V ls adjusted to give: - near-threshold 1/2 + state - 5/2 + resonance at 2 MeV Shallow V (l = 1) for simplicity l x, j x x N 2 s 2 y l y C I N 1 s 1 Three-body calculations: 14 Be ( 12 Be + n + n) 0 + g.s. fixed at S 2n (exp) 1.3 MeV About 60% of l x = 0 and 35% of I = 2 + J. Casal, Fiera di Primiero 2017 p. 19

35 Experimental data Structure considerations Preliminary calculations Multichannel problem Two-body coupling order: {(L, s 2 )J, I}J T {L J I}J T }{{} s.p. x I N 2 s C Example: 2 L, J 13 Be(5/2 + ): {d 5/2 0 + }, {s 1/2 2 + }, {d 3/2 2 + }, {d 5/2 2 + } So (up to L max = 2) we have 4 asymptotic channels The w.f. for each channel comprises 4 components 2b 3b overlaps mix them One contribution to the cross section for each asymptotic channel Similar for other J T configurations J. Casal, Fiera di Primiero 2017 p. 20

36 Experimental data Structure considerations Preliminary calculations 14 Be(p, pn) MeV/u data from RIKEN (A. Corsi) dσ/dε n- 12 Be (mb/mev) /2 + [s1/2 0 + ] 5/2 + [d5/2 0 + ] 5/2 + [s1/2 2 + ] 3/2 + [s1/2 2 + ] PRELIMINARY total new data folded with σ = 0.25 ε fn ε 12 n- Be (MeV) Virtual state does not fit - too large scattering length Missing cross section at high ε J. Casal, Fiera di Primiero 2017 p. 21

37 Experimental data Structure considerations Preliminary calculations 14 Be(p, pn) MeV/u data from RIKEN (A. Corsi) 40 dσ/dε n- 12 Be (mb/mev) PRELIMINARY new data P1 P2 P3 P ε 12 n- Be (MeV) The 1/2 + state cannot account for the low-energy peak J. Casal, Fiera di Primiero 2017 p. 22

38 Experimental data Structure considerations Preliminary calculations 14 Be(p, pn) MeV/u data from RIKEN (A. Corsi) dσ/dε n- 12 Be (mb/mev) PRELIMINARY new data 1/2 + [s1/2 0 + ] 1/2 - [p1/2 0 + ] 5/2 + [d5/2 0 + ] 5/2 + [s1/2 2 + ] 3/2 - [p3/2 0 + ] 3/2 - [p1/2 2 + ] total ε 12 n- Be (MeV) A low-energy 1/2 resonance improves agreement J. Casal, Fiera di Primiero 2017 p. 23

39 J. Casal, Fiera di Primiero 2017

40 Transfer to Continuum (TC) framework to describe (p, pn) reactions induced by 3b projectiles; reduces to DWBA for (p, d) transfer. Structure information contained in ϕ q 2b Φg.s. 3b overlaps. Provides absolute cross sections. 11 Li(p, pn) 10 Li: including the spin of 9 Li improves agreement in the relative energy spectrum. Same model gives also a good agreement for (p, d) reaction. Our model is consistent with 31% of p-waves in 11 Li, in agreement with recent experimental estimations. No need for a d resonance in 10 Li at low energies. 14 Be(p, pn) 13 Be: contribution from excited-core components can be included in a rotational model. The analysis is ongoing. J. Casal, Fiera di Primiero 2017 p. 24

41 Transfer to Continuum (TC) framework to describe (p, pn) reactions induced by 3b projectiles; reduces to DWBA for (p, d) transfer. Structure information contained in ϕ q 2b Φg.s. 3b overlaps. Provides absolute cross sections. 11 Li(p, pn) 10 Li: including the spin of 9 Li improves agreement in the relative energy spectrum. Same model gives also a good agreement for (p, d) reaction. Our model is consistent with 31% of p-waves in 11 Li, in agreement with recent experimental estimations. No need for a d resonance in 10 Li at low energies. 14 Be(p, pn) 13 Be: contribution from excited-core components can be included in a rotational model. The analysis is ongoing. This is a lot of work! 14 Be; also 8 He, 17 B, 17 Ne... Momentum profile, missing momentum, opening angle... J. Casal, Fiera di Primiero 2017 p. 24

5-9 March 2018 Trento, Italy Pierre Capel Jose A.

42 Recent advances and challenges in the description of nuclear reactions at the limit of stability ECT* Workshop 5-9 March 2018 Trento, Italy Pierre Capel Jose A. Lay Antonio M. Moro Jesu s Casal J. Casal, Fiera di Primiero 2017 p. 25

43 J. Casal, Fiera di Primiero 2017

44 Appendix A HH expansion EXTRA: Dipole response 11 Li Halo nuclei Small separation energy of valence nucleons Large interaction cross sections Extended radius due to diffuse tail of the w.f. Discovered in the 80s [ 11 Li; Tanihata et al.] Available in Radioactive Ion Beam facilities Assess structure knowledge gained from stable nuclei Explore the edges of the nuclear landscape Study the extremes of stability Two-nucleon halo systems are Borromean, which can be naturally described within three-body models. J. Casal, Fiera di Primiero 2017

45 Appendix A HH expansion EXTRA: Dipole response 11 Li Basis states: ψ iβjµ (ρ, Ω) = ρ 5/2 U iβ (ρ)y βjµ (Ω) β {K, l x, l y, l, S x, j ab } defines a channel Y βjµ (Ω) are states of good total angular momentum j Expanded in hyperspherical harmonics (HH) Υ lxly Klm (Ω) { [ } Y βjµ (Ω) = Υ lxly Klm (Ω) χ S x κ I ]j ab Eigenfunctions of the hypermomentum operator K 2 Υ lxly Klm l (Ω) = ϕ lxly K (α) [ Y lx ( x) Y ly (ŷ) ] l, ϕ lxly lxly K (α) = NK (sin α)lx (cos α) ly P lx+ 1 2,ly+ 1 2 n (cos 2α) where P a,b n is a Jacobi polynomial of order n = (K l x l y )/2 jµ J. Casal, Fiera di Primiero 2017

46 Appendix A HH expansion EXTRA: Dipole response 11 Li K is the hypermomentum, K2 Υ lxly Klm = K(K + 4)Υlxly Klm l = l x + l y is the total orbital angular momentum S x the spin of the particles in subsystem x j ab = l + S x I the spin of the third particle j = j ab + I the total angular momentum χ σ S x the spin wave function of the particles related by x κ ι I the spin wave function of the third particle J. Casal, Fiera di Primiero 2017

47 Appendix A HH expansion EXTRA: Dipole response 11 Li Electromagnetic transition probabilities (O = E, M) ( ) 2λ + 1 B(Oλ)(ε n ) = B(Oλ; n 0 j 0 nj) = n 0 j 0 Ôλ nj 2 4π J. Casal, Fiera di Primiero 2017

48 Appendix A HH expansion EXTRA: Dipole response 11 Li Electromagnetic transition probabilities (O = E, M) ( ) 2λ + 1 B(Oλ)(ε n ) = B(Oλ; n 0 j 0 nj) = n 0 j 0 Ôλ nj 2 4π Electric transitions Q λmλ (x k, y k ) = ( ) 4π 1/2 3 Z q e rq λ Y λmλ ( r q ) 2λ + 1 q=1 J. Casal, Fiera di Primiero 2017

49 Appendix A HH expansion EXTRA: Dipole response 11 Li Electromagnetic transition probabilities (O = E, M) ( ) 2λ + 1 B(Oλ)(ε n ) = B(Oλ; n 0 j 0 nj) = n 0 j 0 Ôλ nj 2 4π Electric transitions Q λmλ (x k, y k ) = Energy distribution ( ) 4π 1/2 3 Z q e rq λ Y λmλ ( r q ) 2λ + 1 q=1 db(oλ) (ε, w) = dε n D(ε, ε n, w)b(oλ)(ε n ) D(ε, ε n, w) are Poisson distributions with w width parameter J. Casal, Fiera di Primiero 2017

50 Appendix A HH expansion EXTRA: Dipole response 11 Li Factorization of the cross section dσ LJJ T dε x C LJJ T K(E)η LJJ T (E) Structure form factors (SF): η LJJ T (E) d y ψ LJJT M T (E, y) 2 J. Casal, Fiera di Primiero 2017

51 Appendix A HH expansion EXTRA: Dipole response 11 Li Factorization of the cross section dσ LJJ T dε x C LJJ T K(E)η LJJ T (E) dσ/de n 9 Li (mb/mev) P3 model solid: full TC s 1/2 C = p 1/2 C = Structure form factors (SF): dashed: scaled SF η LJJ T (E) d y ψ LJJT M T (E, y) 2 dσ/de n 9 Li (mb/mev) P1I model 1 - C = C = C = C = E 9 n Li (MeV) J. Casal, Fiera di Primiero 2017

52 Appendix A HH expansion EXTRA: Dipole response 11 Li Factorization of the cross section dσ LJJ T dε x C LJJ T K(E)η LJJ T (E) dσ/de n 9 Li (mb/mev) P3 model solid: full TC s 1/2 C = p 1/2 C = Structure form factors (SF): dashed: scaled SF η LJJ T (E) Correct up to certain extent BUT!! ratio depends on L, J, J T d y ψ LJJT M T (E, y) 2 dσ/de n 9 Li (mb/mev) P1I model 1 - C = C = C = C = reaction calc. to obtain relative weights less ambiguous than fitting E 9 n Li (MeV) J. Casal, Fiera di Primiero 2017

53 Appendix A HH expansion EXTRA: Dipole response 11 Li 9 Be photodissociation cross section σ γ (mb) /2 + E1 3/2 + E1 5/2 + E1 5/2 - M1 1/2 - M1 Total ε (MeV) J. Casal, Fiera di Primiero 2017 PRC 90 (044304) 2014

54 Appendix A HH expansion EXTRA: Dipole response 11 Li 9 Be photodissociation cross section σ γ (mb) Arnold (2012) Sumiyoshi (2002) THO de Diego (2014) Garrido (2011) ε (MeV) J. Casal, Fiera di Primiero 2017 PRC 90 (044304) 2014

55 Appendix A HH expansion EXTRA: Dipole response 11 Li Continuum of 11 Li: Dipole response 4.0 db(e1)/dε (e 2 fm 2 MeV -1 ) exclusive RIKEN data inclusive TRIUMF data 3b model res. at 0.69 MeV PRL 110 (2013) b model with 9 Li correlations PRC 87 (2013) ε (MeV) Large discrepancies between experiments and theory J. Casal, Fiera di Primiero 2017

56 Appendix A HH expansion EXTRA: Dipole response 11 Li 2.0 db(e1)/dε (e 2 fm 2 MeV -1 ) PRELIMINARY 1/2 + 3/2 + 5/2 + total no 9 Li spin ε (MeV) Again same model P1I seems reasonable J. Casal, Fiera di Primiero 2017

57 Appendix A HH expansion EXTRA: Dipole response 11 Li 2.0 db(e1)/dε (e 2 fm 2 MeV -1 ) PRELIMINARY RIKEN data total no 9 Li spin folded with resolution 0.17 ε ε (MeV) Again same model P1I seems reasonable J. Casal, Fiera di Primiero 2017

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