1 Breakup of weakly bound nuclei and its influence on fusion Paulo R. S. Gomes Univ. Fed. Fluminense (UFF), Niteroi, Brazil Forum Brasil-JINR Dubna, June, 2015
2 For a comprehensive review of this subject up to 2006: Phys. Rep. 424 (2006), An update will come out later in 2015 or 2016
3 Reactions with weakly bound nuclei example with 9 Be
4 However, nature is even more complicated than that simple picture: Breakup following transfer RESULTS n p after before measured measured calculated by p conservation known Courtesy of Luong
5 Questions that we investigate and try to answer -Does the BU channel enhance or suppress the fusion cross section? Is the effect on σ CF or σ TF= CF + ICF? -What are the effects on different energy regimes and on different target mass regions? - What is the relative importance between nuclear and Coulomb breakups? Do they interfer? - How large is the NCBU compared with CF? How does it depend on the energy region and target mass?
6 Different answers, depending on several things
7 NCBU - Recent results at ANU D. H. Luong, M. Dasgupta, D.J. Hinde et al. Physics Letters B 695 (2011) 105 PRC 88 (2013) Sub-barrier breakup dominated by transfer Slides by Luong and Dasgupta
8 EXPERIMENT Detector system E res ΔE 512 pixels 400μm, 150 kev Solid angle 0.6π (sr) Isotopic identification for hydrogen
9 Breakup mechanism: Q-values after before measured measured calculated by p conservation known
10 Breakup mechanism: Q-values RESULTS n p after before measured measured calculated by p conservation known
11 Breakup mechanism: Q-values RESULTS n d
12 Breakup time scale: Relative energy Only prompt breakup may affect fusion
15 Very important question When one talks about enhancement or suppression, is that in relation to what?
16 Frequently used procedures to answer Enhancement or suppression in relation to what? a) Comparison of data with theoretical predictions. b) Comparison of data for weakly and tightly bound systems.
17 Effects to be considered Static effects longer tail of the optical potential arising from the weakly bound nucleons. Dynamical effects: strong coupling between the elastic channel and the continuum states representing the break-up channel.
18 1. E x p e rim e n t v s. th e o ry F e x p F - th e o F 'in g re d ie n ts' m issin g in th e th e o ry T h e o re tic a l p o ssib ilitie s: a ) S in g le c h a n n e l - s ta n d a rd d e n s itie s F a ris e s fro m a ll s ta tic a n d d y n a m ic e ffe c ts b ) S in g le c h a n n e l - re a lis tic d e n s itie s F a ris e s fro m c o u p lin g s to a ll c h a n n e ls c ) C C c a lc u la tio n w ith a ll re le v a n t b o u n d c h a n n e ls F a ris e s fro m c o n tin u u m c o u p lin g s d ) C D C C n o d e v ia tio n e x p e c te d
19 Example: 6 He Bi Single channel - no halo Single channel with halo CC with bound channels (schematic calculation) Shortcomings of the procedure: Choice of interaction plays fundamental role Does not allow comparisons of different systems Difficult to include continuum no separate CF and ICF
20 Example of Model Dependent Conclusions Kolata et al., PRL 81, 4580 (1998) Gomes et al., PLB 695, 320 (2011)
21 Old controversy between Kolata`s and Raabe`s data (6He + 209Bi and 238U) Important: Bare Potential deduced from double-folding procedure Gomes et al., PLB 695, 320 (2011)
22 2. C o m p a re w ith F o f a sim ila r tig h tly b o u n d sy ste m ( e x a m p le : 6 H e U v s. 4 H e U ) Differences due to static effects: 1. G ro s s d e p e n d e n c e o n s iz e a n d c h a rg e : Z P, Z T, A P, A T a ffe c ts V B a n d R B V B : Z P Z T e 2 2 / R B ; g e o : R B, R B A 1 / 3 P A 1 / 3 T ) 2. D iffe re n t b a rrie r p a ra m e te rs d u e to d iffu s e d e n s itie s (lo w e r a n d th ic k e r b a rrie rs )
23 Differences due to dynamic effects: 3. C o u p lin g s to b o u n d c h a n n e ls (la rg e r F a t E V B ) 4. C o n tin u u m c o u p lin g s (b re a k u p ) T o in v e s tig a te 4, it is n e c e s s a ry to e lim in a te e ffe c ts 1, 2 a n d 3! F u s io n d a ta re d u c tio n re q u ire d!
24 E x E V B Fusion functions F(x) (our reduction method) h a n d F e x p F e x p ( x ) 2 E h R B 2 F e x p Inspired in Wong s approximation F W R B 2 h 2 E ln 1 e x p 2 E V B h If F e x p F W F ( x ) F 0 ( x ) ln 1 e x p 2 x F 0 (x) = Universal Fusion Function (UFF) system independent!
25 Shortcomings: a) Wong approximation may not work O.K. for light systems only above V B O.K. for heavy systems (Z P Z T > 500), even below V B
26 b) Channel coupling channel effects (a) CC: 2 +,3 - (T); 3 - (P) (a) Wong is bad (a) CC Rot. band (T); 3 - (P) (a) CC 3 -,5 - (T)
27 Direct use of the reduction method C o m p a re F e x p ( x ) w ith U F F fo r x v a lu e s w h e re F o p t F W D e v ia tio n s a re d u e to c o u p lin g s w ith b o u n d c h a n n e ls a n d b re a k u p Refining the method E lim in a te in flu e n c e o f c o u p lin g s w ith b o u n d c h a n n e ls R e n o rm a liz e d fu s io n fu n c tio n F e x p ( x ) F e x p ( x ) F e x p ( x ) R ( x ), w ith R ( x ) F C C F W F C C F o p t If C C c a lc u la tio n d e s c rib e s d a ta F e x p U F F
28 Illustration: If C C c a lc u la tio n s a re a c c u ra te : fo r tig h tly b o u n d s y s te m s F e x p ( x ) = U F F fo r w e a k ly b o u n d s y s te m s d iffe re n c e is d u e to b re a k u p
30 Systematics reached from the investigation of he role of BU dynamical effects on the complete and total fusion of stable weakly bound heavy systems, para cada um destes físicos, We did not include any resonance of the projectiles in CCC. Suppression above the barrier- enhancement below the barrier
31 Systematics reached from investigation of the role of BU dynamical effects on fusion of neutron halo 6 He, 11 Be weakly bound systems Suppression above the barrier- enhancement below the barrier
32 Conclusion from the systematics (several systems): CF enhancement at sub-barrier energies and suppression above the barrier, when compared with what it should be without any dynamical effect due to breakup and transfer channels.
33 Do all the systems follow the systematics? Almost all of the tens of systems follow the systematics. For those which do not follow, either a) There is something very special with those systems. b) There is something wrong with the data. c) Wrong CC calculations.
34 What about proton-halo systems? Up to recently, there was only one system measured Fusion of proton-halo 8 B + 58 Ni Aguilera PRL 107, (2011)
35 Fusion of proton-halo 8 B + 58 Ni New dynamic effect for proton-halo fusion? Or Something wrong with the data? Rangel et al., EPJA 49, 57 (2013)
36 Other recent result: Fusion of 8 B + 28 Si Pakou et al. PRC 87, (2013) Measurements at Legnaro. Fusion cross sections derived from alpha measurements (there is no alpha from BU) Normal behavior, within our systematic!!!
37 We believe that there is nothing special with fusion of proton-halo nuclei We believe it is very important to measure fusion of 8B with other (or the same) targets.
38 So, the next question is: How does the BU vary with target mass (or charge)? Coulomb and nuclear breakups: Is there interference between them? One believes that the BU depends on the target mass (charge).
39 CF Suppression for stable weakly bound nuclei on different targets 9Be The BU effect on fusion does not seem to depend on the target charge!!!! Wang et al. PRC 90, (2014)
40 CF suppression factor as a function of the BU threshold energy ee Wang PRC 90, (2014)
41 Calculations of NCBU by means of CDCC: D. R. Otomar, P.R.S. Gomes, J. Lubian, L.F. Canto, M. S. Hussein PRC 87, (2013) M.S. Hussein, P.R.S. Gomes, J. Lubian, D.R. Otomar, L. F. Canto PRC 88, (2013)
42 Our first theoretical step was to perform reliable CDCC calculations. What do we mean by reliable? No free parameters, only predictions. The predictions have to agree with some data. Which data are available? Elastic scattering angular distributions.
43 Examples of calculations for elastic scattering 6 Li + 59 Co 6 Li Sm 6 Li Pb
44 Relative importance between Coulomb and nuclear breakups Total BU black Coulomb BU red Nuclear BU - blue For higher energies and light targets, nuclear BU may predominate Small angles (large distances) Coulomb BU always predominates For larger angles, nuclear BU may predominate crossing angle.
45 Interference between Coulomb and nuclear breakups If there were were no interference, the last column should be unity.
46 What is the relative importance between breakup and fusion cross sections?
47 How does the BU vary with target mass (or charge)? Coulomb and nuclear breakups? The nuclear BU increases linearly with A T 1/3 for the same E c.m. /V B The Coulomb BU increases linearly with Z T for the same E c.m. /V B
48 Conclusions from direct BU calculations Both, the nuclear and Coulomb BU components increase with target mass and charge. The relative importance between nuclear and Coulomb breakups is not so simple as it is usually thought. There is a strong destructive interference between nuclear and Coulomb breakup. Otomar et al PRC 87, (2013), Hus
49 It seems that we have a contradiction!!!
50 Possible explanation for the contradiction When one calculates BU cross sections with CDCC, one does not distinguish prompt and delayed BU. Most of the BU seems to be delayed and only the prompt BU affects fusion.
51 Possible explanation for the contradiction When one calculates BU cross sections with CDCC, one does not distinguish prompt and delayed BU. Most of the BU seems to be delayed and only the prompt BU affects fusion.
52 Or... Very recent results for 6Li + 96Zr S.P. Hu et al. PRC (2015) Only 25% suppression!! One needs to measure CF for light systems How?
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