Hadron-Nucleus Interactions. Beginners FLUKA Course

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Candice Miles
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1 Hadron-Nucleu Interaction Beginner FLUKA Coure

The FLUKA hadronic Model Hadron-nucleu: PEANUT Elatic,exchange Phae hift data, eikonal hadron hadron P<3-5GeV/c Reonance prod and decay Sophiticated G-Intranuclear Cacade

2 The FLUKA hadronic Model Hadron-nucleu: PEANUT Elatic,exchange Phae hift data, eikonal hadron hadron P<3-5GeV/c Reonance prod and decay Sophiticated G-Intranuclear Cacade Gradual onet of Glauber-Gribov multiple interaction low E π,k Special High Energy DPM hadronization Preequilibrium Coalecence Evaporation/Fiion/Fermi break-up deexcitation

3 Hadron-nucleon interaction model p-p and p-n cro ection FLUKA and data total Particle production interaction: two kind of model Thoe baed on reonance production and decay, cover the energy range up to 3 5 GeV elatic Thoe baed on quark/parton tring model, which provide reliable reult up to everal ten of TeV Elatic, charge exchange and trangene exchange reaction: Available phae-hift analyi and/or fit of experimental differential data At high energie, tandard eikonal approximation are ued 3

Dominance of the Δ reonance and of the N reonance π-nucleon cro ection iobar model all reaction proceed through an Iopin intermediate tate containing at

4 Nonelatic hn interaction at intermediate energie N 1 + N N 1 + N + π threhold at 90 MeV, important above 700 MeV, π + N π + π + N open at 170 MeV. Anti-nucleon -nucleon open at ret! Dominance of the Δ reonance and of the N reonance π-nucleon cro ection iobar model all reaction proceed through an Iopin intermediate tate containing at decompoition leat one reonance. Reonance energie, width, cro ection, branching ratio from data and conervation law, whenever poible. Inferred from incluive cro ection when needed N 1 + N N 1 + Δ(13) N 1 + N + π π + N Δ(1600) π + Δ(13) π + π + N N 1+ N Δ 1 (13) + Δ (13) N 1 + π 1 + N + 4π

5 Inelatic hn at high energie: (DPM, QGSM,...) Problem: oft interaction QCD perturbation theory cannot be applied. Interacting tring (quark held together by the gluon-gluon interaction into the form of a tring) Interaction treated in the Reggeon-Pomeron framework each of the two hadron plit into colored parton combination into colourle chain back-to-back jet each jet i then hadronized into phyical hadron 5

6 Hadron-hadron colliion: chain example Leading two-chain diagram in DPM for p-p cattering. The color (red, blue, and green) and quark combination hown in the figure i jut one of the allowed poibilitie Leading two-chain diagram in DPM for + -p cattering. The color (red, blue, and green) and quark combination hown in the figure i jut one of the allowed poibilitie 6

7 DPM and hadronization from DPM: Number of chain Chain compoition Chain energie and momenta Diffractive event Almot No Freedom Chain hadronization Aume chain univerality Fragmentation function from hard procee and e+e cattering Tranvere momentum from uncertainty conideration Ma effect at low energie The ame function and (few) parameter for all reaction and energie 7

8 Inelatic hn interaction: example + + p + + X (6 & GeV/c) + + p Ch + /Ch - + X (50 GeV/c) Poitive hadron X Negative hadron Connected point: FLUKA Symbol w. error : DATA 6 GeV M.E. Law et. Al, LBL80 (197) GeV Dot: Exp. Data Hito : FLUKA 8

9 Nuclear interaction in PEANUT: Target nucleu decription (denity, Fermi motion, etc) t () Glauber-Gribov cacade with formation zone 10-3 Generalized IntraNuclear cacade 10 - Preequilibrium tage with current exciton configuration and excitation energy (all non-nucleon emitted/decayed + all nucleon below MeV) Evaporation/Fragmentation/Fiion model 10-0 γ deexcitation

10 Nucleon Fermi Motion Fermi ga model: Nucleon = Non-interacting Contrained Fermion dn k Momentum ditribution dk for k up to a (local) Fermi momentum k F (r) given by k F 1 3 ( ) 3 ( r) r N The Fermi energy (k F 1.36 fm, P F 60 MeV/c, E F 35 MeV, at nuclear max. denity) i cutomarily ued in building a elf-conitent Nuclear Potential Depth of the potential well Fermi Energy + Nuclear Binding Energy 10

11 Poitive kaon a a probe of Fermi motion 11

12 (Generalized) IntraNuclear Cacade Primary and econdary particle moving in the nuclear medium Target nucleon motion and nuclear well according to the Fermi ga model Interaction probability free + Fermi motion (r) + exception (ex. ) Glauber cacade at higher energie Claical trajectorie (+) nuclear mean potential (reonant for ) Curvature from nuclear potential refraction and reflection Interaction are incoherent and uncorrelated Interaction in projectile-target nucleon CMS Lorentz boot Multibody aborption for, m -, K - Quantum effect (Pauli, formation zone, correlation ) Exact conervation of energy, momenta and all addititive quantum number, including nuclear recoil 1

13 ha at high energie: Glauber-Gribov cacade with formation zone Glauber cacade Quantum mechanical method to compute Elatic, Quaielatic and Aborption ha cro ection from Free hadronnucleon cattering + nuclear ground tate Multiple Colliion expanion of the cattering amplitude Glauber-Gribov Field theory formulation of Glauber model Multiple colliion Feynman diagram High energie: exchange of one or more Pomeron with one or more target nucleon (a cloed tring exchange) Formation zone (=materialization time) 13

14 14 Glauber Cacade ), ( ), ( ), ( ), ( b i hn b i hn hn hn e b e b S Quantum mechanical method to compute all relevant hadron-nucleu cro ection from hadron-nucleon cattering: and nuclear ground tate wave function i 1 3, 1 A j j hn i f fi ha f ha r b S u u d b d Scattering 1 3, 1 A j j hn i el ha r b S u u d b d Elatic A j j hn i T ha r b S u u d b d 1 3, Re 1 Total A j j hn i f ha hat ha ab r b S u u d b d 1 3, Aborption probability over a given b and nucleon configuration Aborption (particle prod.)

15 Gribov interpretation of Glauber multiple colliion Therefore the aborption cro ection i jut the integral in the impact parameter plane of the probability of getting at leat one non-elatic hadron-nucleon colliion and the overall average number of colliion i given by Z hp r N haab hnr Glauber-Gribov model = Field theory formulation of Glauber model Multiple colliion term Feynman graph At high energie : exchange of one or more pomeron with one or more target nucleon In the Dual Parton Model language: (neglecting higher order diagram): Interaction with n target nucleon n chain Two chain from projectile valence quark + valence quark of one target nucleon valence-valence chain (n-1) chain from ea quark of the projectile + valence quark of target nucleon (n-1) ea-valence chain 15

16 Formation zone Naively: materialization" time (originally propoed by Stodolki). Qualitative etimate: In the frame where p =0 t t E T p T M Particle proper time M E T t p T M M Going to the nucleu ytem x for c t lab p E lab T t p M lab k for p p T lab M Condition for poible reinteraction inide a nucleu: x for R A 1 3 r 0 A 16

17 Effect of Glauber and Formation Zone No Glau No FZ Rapidity ditribution of charged particle produced in 50 GeV + colliion on Gold Point: exp. data (Agababyan et al., ZPC50, 361 (1991)). No Glau Ye FZ Ye Glau No FZ Ye Glau Ye FZ 17

18 WARNING PEANUT ha been extended to cover the whole energy range in late 006 A le refined GINC model i available for projectile momenta above about 5 GeV/c, and wa the only choice until recently However: the extended peanut i NOT yet the default, mainly becaue of ome ambiguity in the definition of quai-elatic cro ection. To activate PEANUT at all energie: PHYSICS PEATHRESH 18

19 Nonelatic ha interaction at high energie: example Recent reult from the HARP experiment 1.9 GeV/c p on Al + production at different angle Double differential + production for p C interaction at 158 GeV/c, a meaured by NA49 (ymbol) and predicted by FLUKA (hitogram) 19

20 Pion in nuclear medium 0

21 Pion aborption Pion aborption cro ection on Gold and Bimuth in the reonance region (multibody aborption in PEANUT) Emitted proton pectra at different angle, 160 MeV + on 58 Ni Phy. Rev. C41,15 (1990) Phy. Rev. C4,11 (1981) Proton pectra extend up to 300 MeV 1

22 Preequilibrium emiion For E > production threhold only (G)INC model At lower energie a variety of preequilibrium model Two leading approache The quantum-mechanical multitep model: Very good theoretical background Complex, difficultie for multiple emiion The emiclaical exciton model Statitical aumption Simple and fat Suitable for MC Statitical aumption: any partition of the excitation energy E * among N, N = N h +N p, exciton ha the ame probability to occur Step: nucleon-nucleon colliion with N n+1 =N n + ( never come back approximation) Chain end = equilibrium = N n ufficiently high or excitation energy below threhold N 1 depend on the reaction type and cacade hitory

23 Thin target example Angle-integrated 90 Zr(p,xn) at 80.5 MeV The variou line how the total, INC, preequilibrium and evaporation contribution Experimental data from M. Trabandt et al., Phy. Rev. C39, 45 (1989) 3

24 Thin target example p + 90 Zr p + X (80 MeV) p + Al - + X (4 GeV/c) 4

25 Coalecence High energy light fragment are emitted through the coalecence mechanim: put together emitted nucleon that are near in phae pace. Example : double differential t production from 54 MeV neutron on Copper Warning: coalecence i OFF by default Can be important, ex for. reidual nuclei. To activate it: PHYSICS 1. COALESCE If coalecence i on, witch on Heavy ion tranport and interaction (ee later) 5

26 Equilibrium particle emiion (evaporation, fiion and nuclear break-up) From tatitical conideration and the detailed balance principle, the probabilitie for emitting a particle of ma m j, pin S j, ħ and energy E, or of fiioning are given by: (i, f for initial/final tate, Fi for fiion addle point) Probability per unit time of emitting a particle j with energy E Probability per unit time of fiioning ρ : nuclear level denitie U : excitation energie V j : poible Coulomb barrier for emitting a particle type j B Fi : fiion barrier P J S j 1 mjc Ui Q j f f U f 3 V j U 1 U i B Fi Fi Ui BFi E PFi 0 U i i i i inv E EdE Q j : reaction Q for emitting a particle type j σ inv : cro ection for the invere proce Δ : pairing energie Neutron emiion i trongly favoured becaue of the lack of any barrier Heavy nuclei generally reach higher excitation becaue of more intene cacading 6 de

27 Equilibrium particle emiion Evaporation: Weikopf-Ewing approach ~600 poible emitted particle/tate (A<5) with an extended evaporation/fragmentation formalim Full level denity formula with level denity parameter A,Z and excitation dependent Invere cro ection with proper ub-barrier Analytic olution for the emiion width (neglecting the level denity dependence on U, taken into account by rejection Emiion energie from the width expreion with no. approx. Fiion: pat, improved verion of the Atchion algorithm, now fi baed of firt principle, full competition with evaporation Improved ma and charge width Myer and Swiatecki fiion barrier, with exc. en. Dependent level denity enhancement at addle point Fermi Break-up for A<18 nuclei ~ combination included with up to 6 ejectile de-excitation: tatitical + rotational + tabulated level 7

Reidual Nuclei The production of reidual i the reult of the lat tep of the nuclear reaction, thu it i influenced by all the previou tage Reidual ma ditribution are very well reproduced Reidual near

28 Reidual Nuclei The production of reidual i the reult of the lat tep of the nuclear reaction, thu it i influenced by all the previou tage Reidual ma ditribution are very well reproduced Reidual near to the compound ma are uually well reproduced However, the production of pecific iotope may be influenced by additional problem which have little or no impact on the emitted particle pectra (Senitive to detail of evaporation, Nuclear tructure effect, Lack of pin-parity dependent calculation in mot MC model) 8

29 Example of fiion/evaporation 1 A GeV 08 Pb + p reaction Nucl. Phy. A 686 (001) Data FLUKA FLUKA after cacade FLUKA after preeq Quai-elatic Spallation Evaporation Fiion Deep pallation Fragmentation 9

30 Reidual nuclei Experimental and computed reidual nuclei ma ditribution for Ag(p,x)X at 300 GeV Data from Phy. Rev. C (1979) and Nucl. Phy. A543, 703 (199) The fragmentation model ha much improved the FLUKA prediction Alo for A-A interaction Warning: fragmentation i OFF by default, becaue it i a cpu-eater. It i NECESSARY to activate it for activation tudie: PHYSICS 3. EVAPORAT If fragmentation i on, witch on Heavy ion tranport and interaction (ee later) 30

Hadron-Nucleus Interactions. Beginners FLUKA Course

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