A new approach to detect hypernuclei and isotopes in the QMD phase space distribution at relativistic energies

A new approach to detect hypernuclei and isotopes in the QMD phase space distribution at relativistic energies A. Le Fèvre 1, J. Aichelin 2, Ch. Hartnack 2 and Y. Leifels 1 1 GSI Darmstadt, Germany 2 Subatech Nantes, France

A new approach to detect hypernuclei and isotopes in the QMD phase space distribution at relativistic energies Motivations A. Le Fèvre 1, J. Aichelin 2, Ch. Hartnack 2 and Y. Leifels 1 1 GSI Darmstadt, Germany 2 Subatech Nantes, France

A new approach to detect hypernuclei and isotopes in the QMD phase space distribution at relativistic energies A. Le Fèvre 1, J. Aichelin 2, Ch. Hartnack 2 and Y. Leifels 1 1 GSI Darmstadt, Germany 2 Subatech Nantes, France Motivations The major difficulty that are facing transport models is the formation of clusters. For this reason, this aspect is often oversimplified, when not omitted.

A new approach to detect hypernuclei and isotopes in the QMD phase space distribution at relativistic energies A. Le Fèvre 1, J. Aichelin 2, Ch. Hartnack 2 and Y. Leifels 1 1 GSI Darmstadt, Germany 2 Subatech Nantes, France Motivations The major difficulty that are facing transport models is the formation of clusters. For this reason, this aspect is often oversimplified, when not omitted. Having the clusters correctly formed is as important as the transport and creation of their constituents in the curse of the collisions.

A new approach to detect hypernuclei and isotopes in the QMD phase space distribution at relativistic energies A. Le Fèvre 1, J. Aichelin 2, Ch. Hartnack 2 and Y. Leifels 1 1 GSI Darmstadt, Germany 2 Subatech Nantes, France Motivations The major difficulty that are facing transport models is the formation of clusters. For this reason, this aspect is often oversimplified, when not omitted. Having the clusters correctly formed is as important as the transport and creation of their constituents in the curse of the collisions. Because, apart from emitted elementary particles, they carry the only information that the experimental instruments can measure.

A new approach to detect hypernuclei and isotopes in the QMD phase space distribution at relativistic energies A. Le Fèvre 1, J. Aichelin 2, Ch. Hartnack 2 and Y. Leifels 1 1 GSI Darmstadt, Germany 2 Subatech Nantes, France Motivations The major difficulty that are facing transport models is the formation of clusters. For this reason, this aspect is often oversimplified, when not omitted. Having the clusters correctly formed is as important as the transport and creation of their constituents in the curse of the collisions. Because, apart from emitted elementary particles, they carry the only information that the experimental instruments can measure. Making clusters is not an easy task, because it involves, in a complex environment: the fundamental nuclear properties, quantum effects, and variable timescales.

Simulated Annealing Clusterization Algorithm (SACA): The principles

Simulated Annealing Clusterization Algorithm (SACA): The principles If we want to identify fragments early, one has to use momentum space info as well as coordinate space info.

Simulated Annealing Clusterization Algorithm (SACA): The principles If we want to identify fragments early, one has to use momentum space info as well as coordinate space info. Idea by Dorso et al. (Phys.Lett.B301:328,1993) :

Simulated Annealing Clusterization Algorithm (SACA): The principles If we want to identify fragments early, one has to use momentum space info as well as coordinate space info. Idea by Dorso et al. (Phys.Lett.B301:328,1993) : a) Take the positions and momenta of all nucleons at time t.

Simulated Annealing Clusterization Algorithm (SACA): The principles If we want to identify fragments early, one has to use momentum space info as well as coordinate space info. Idea by Dorso et al. (Phys.Lett.B301:328,1993) : a) Take the positions and momenta of all nucleons at time t. b) Combine them in all possible ways into fragments or leave them as single nucleons.

Simulated Annealing Clusterization Algorithm (SACA): The principles If we want to identify fragments early, one has to use momentum space info as well as coordinate space info. Idea by Dorso et al. (Phys.Lett.B301:328,1993) : a) Take the positions and momenta of all nucleons at time t. b) Combine them in all possible ways into fragments or leave them as single nucleons. c) Neglect the interaction among clusters.

Simulated Annealing Clusterization Algorithm (SACA): The principles If we want to identify fragments early, one has to use momentum space info as well as coordinate space info. Idea by Dorso et al. (Phys.Lett.B301:328,1993) : a) Take the positions and momenta of all nucleons at time t. b) Combine them in all possible ways into fragments or leave them as single nucleons. c) Neglect the interaction among clusters. d) Choose that configuration which has the highest binding energy.

Simulated Annealing Clusterization Algorithm (SACA): The principles If we want to identify fragments early, one has to use momentum space info as well as coordinate space info. Idea by Dorso et al. (Phys.Lett.B301:328,1993) : a) Take the positions and momenta of all nucleons at time t. b) Combine them in all possible ways into fragments or leave them as single nucleons. c) Neglect the interaction among clusters. d) Choose that configuration which has the highest binding energy. Simulations show: Clusters chosen that way at early times are the prefragments of the final state clusters, because fragments are not a random collection of nucleons at the end but initial-final state correlations.

SACA: How does this work? Simulated Annealing Procedure: PLB301:328,1993; later called SACA. 2 steps: 1) Pre-select good «candidates» for fragments according to proximity criteria: real space coalescence = Minimum Spanning Tree (MST) procedure. E=E 1 kin +E2 kin +V1 +V 2

SACA: How does this work? Simulated Annealing Procedure: PLB301:328,1993; later called SACA. 2 steps: 1) Pre-select good «candidates» for fragments according to proximity criteria: real space coalescence = Minimum Spanning Tree (MST) procedure. 2) Take randomly 1 nucleon out of one fragment E=E 1 kin +E2 kin +V1 +V 2

SACA: How does this work? Simulated Annealing Procedure: PLB301:328,1993; later called SACA. 2 steps: 1) Pre-select good «candidates» for fragments according to proximity criteria: real space coalescence = Minimum Spanning Tree (MST) procedure. 2) Take randomly 1 nucleon out of one fragment 3) Add it randomly to another fragment E=E 1 kin +E2 kin +V1 +V 2 E =E 1 kin +E2 kin +V1 +V 2

SACA: How does this work? Simulated Annealing Procedure: PLB301:328,1993; later called SACA. 2 steps: 1) Pre-select good «candidates» for fragments according to proximity criteria: real space coalescence = Minimum Spanning Tree (MST) procedure. 2) Take randomly 1 nucleon out of one fragment 3) Add it randomly to another fragment E=E 1 kin +E2 kin +V1 +V 2 If E < E take the new configuration E =E 1 kin +E2 kin +V1 +V 2

SACA: How does this work? Simulated Annealing Procedure: PLB301:328,1993; later called SACA. 2 steps: 1) Pre-select good «candidates» for fragments according to proximity criteria: real space coalescence = Minimum Spanning Tree (MST) procedure. 2) Take randomly 1 nucleon out of one fragment 3) Add it randomly to another fragment E=E 1 kin +E2 kin +V1 +V 2 E =E 1 kin +E2 kin +V1 +V 2 If E < E take the new configuration If E > E take the old with a probability depending on E -E

SACA: How does this work? Simulated Annealing Procedure: PLB301:328,1993; later called SACA. 2 steps: 1) Pre-select good «candidates» for fragments according to proximity criteria: real space coalescence = Minimum Spanning Tree (MST) procedure. 2) Take randomly 1 nucleon out of one fragment 3) Add it randomly to another fragment E=E 1 kin +E2 kin +V1 +V 2 E =E 1 kin +E2 kin +V1 +V 2 If E < E take the new configuration If E > E take the old with a probability depending on E -E Repeat this procedure very many times...

SACA: How does this work? Simulated Annealing Procedure: PLB301:328,1993; later called SACA. 2 steps: 1) Pre-select good «candidates» for fragments according to proximity criteria: real space coalescence = Minimum Spanning Tree (MST) procedure. 2) Take randomly 1 nucleon out of one fragment 3) Add it randomly to another fragment E=E 1 kin +E2 kin +V1 +V 2 E =E 1 kin +E2 kin +V1 +V 2 If E < E take the new configuration If E > E take the old with a probability depending on E -E Repeat this procedure very many times... It leads automatically to the most bound configuration.

SACA versus coalescence (Minimum Spanning Tree) BQMD* * P.B. Gossiaux, R. Puri, Ch. Hartnack, J. Aichelin, Nuclear Physics A 619 (1997) 379-390 0 0 200 300 400 500 600 700 800 900 time (fm/c)

SACA versus coalescence (Minimum Spanning Tree) BQMD* * P.B. Gossiaux, R. Puri, Ch. Hartnack, J. Aichelin, Nuclear Physics A 619 (1997) 379-390 0 0 200 300 400 500 600 700 800 900 time (fm/c)

SACA versus coalescence (Minimum Spanning Tree) BQMD* * P.B. Gossiaux, R. Puri, Ch. Hartnack, J. Aichelin, Nuclear Physics A 619 (1997) 379-390 0 0 200 300 400 500 600 700 800 900 time (fm/c)

SACA versus coalescence (Minimum Spanning Tree) BQMD* Unlike SACA, MST is not able to describe the early formation of fragments. * P.B. Gossiaux, R. Puri, Ch. Hartnack, J. Aichelin, Nuclear Physics A 619 (1997) 379-390 0 0 200 300 400 500 600 700 800 900 time (fm/c)

SACA versus coalescence (Minimum Spanning Tree) BQMD* Unlike SACA, MST is not able to describe the early formation of fragments. With MST, one has to consider necessarily later times (typically 200-400 fm/c), where the dynamical conditions are no longer the same. * P.B. Gossiaux, R. Puri, Ch. Hartnack, J. Aichelin, Nuclear Physics A 619 (1997) 379-390 0 0 200 300 400 500 600 700 800 900 time (fm/c)

SACA versus coalescence (Minimum Spanning Tree) BQMD* Unlike SACA, MST is not able to describe the early formation of fragments. With MST, one has to consider necessarily later times (typically 200-400 fm/c), where the dynamical conditions are no longer the same. Advantage of SACA : the fragment partitions can reflect the early dynamical conditions (Coulomb, density, flow details, strangeness...). * P.B. Gossiaux, R. Puri, Ch. Hartnack, J. Aichelin, Nuclear Physics A 619 (1997) 379-390 0 0 200 300 400 500 600 700 800 900 time (fm/c)

Toward the isotope yields... IQMD + new SACA SACA is applied here on the IQMD transport model* calculations *C. Hartnack et al., Eur. Phys. J. A1, 151(1998). Au+Au at 0 A.MeV - b=7 fm

Toward the isotope yields... IQMD + new SACA SACA is applied here on the IQMD transport model* calculations *C. Hartnack et al., Eur. Phys. J. A1, 151(1998). Au+Au at 0 A.MeV - b=7 fm

An example of complex system accurately measured Large Z range of measured isotopes, large flow, high excitation energy.

An example of complex system accurately measured Large Z range of measured isotopes, large flow, high excitation energy. ALADiN - INDRA collaboration Si (mv) 140 Be 2 120 0 Li 80 60 H He 1 40 0 500 00 1500 2000 2500 CsI total light

An example of complex system accurately measured Large Z range of measured isotopes, large flow, high excitation energy. Si (mv) 140 ALADiN - INDRA collaboration Be 2 H He 120 0 Li 80 60 H He 1 Li Be 40 0 500 00 1500 2000 2500 CsI total light

An example of complex system accurately measured Large Z range of measured isotopes, large flow, high excitation energy. Si (mv) 140 120 0 80 60 H He Li ALADiN - INDRA collaboration Be 2 Our goals: not only predict the isotope yield ratios, but the absolute yields, and the isotopic dynamical features (in relation with the EOS : asymmetry energy,...), Li 1 in such complex collisions. H He Be 40 0 500 00 1500 2000 2500 CsI total light

SACA versus coalescence (Minimum Spanning Tree) SACA version: IQMD 136 Xe+ 112 Sn at 0 A.MeV, b=1 fm, t Multiplicity 2 1 =60 fm/c SACA MST only (200 fm/c) E asy =0, no pairing -1-2 -3-4 0 5 15 20 25 30 Z Multiplicity (Z=1) 2 1-1 H Multiplicity (Z=2) 1-1 He -2-2 -3-3 -4 0 2 4 6 8 A -4 0 2 4 6 8 12 14 A Multiplicity (Z=3) 1-1 -2 Li Multiplicity (Z=4) 1-1 -2 Be -3-3 -4 0 2 4 6 8 12 14 A -4 0 2 4 6 8 12 14 16 18 A

SACA versus coalescence (Minimum Spanning Tree) SACA version: IQMD 136 Xe+ 112 Sn at 0 A.MeV, b=1 fm, t Multiplicity 2 1 =60 fm/c SACA MST only (200 fm/c) E asy =0, no pairing -1-2 -3-4 0 5 15 20 25 30 Z At this stage, SACA contains as ingredients of the potential making the binding energy of the clusters : ➀ volume component: mean field (Skyrme, dominant) ➁ correction of surface effects: Yukawa Multiplicity (Z=1) Multiplicity (Z=3) 2 1-1 -2-3 -4 1-1 -2 H 0 2 4 6 8 A Li Multiplicity (Z=2) Multiplicity (Z=4) 1-1 -2-3 -4 1-1 -2 He 0 2 4 6 8 12 14 A Be -3-3 -4 0 2 4 6 8 12 14 A -4 0 2 4 6 8 12 14 16 18 A

SACA version: SACA with asymmetry energy IQMD 136 Xe+ 112 Sn at 0 A.MeV, b=1 fm, t Multiplicity 2 1 =60 fm/c SACA E asy =0, no pairing -1-2 E asy =32 MeV ( =1), no pairing -3-4 0 5 15 20 25 30 Z Multiplicity (Z=1) 2 1-1 H Multiplicity (Z=2) 1-1 He -2-2 -3-3 -4 0 2 4 6 8 A -4 0 2 4 6 8 12 14 A Multiplicity (Z=3) 1-1 -2 Li Multiplicity (Z=4) 1-1 -2 Be -3-3 -4 0 2 4 6 8 12 14 A -4 0 2 4 6 8 12 14 16 18 A

SACA version: SACA with asymmetry energy IQMD 136 Xe+ 112 Sn at 0 A.MeV, b=1 fm, t Multiplicity 2 1 =60 fm/c SACA E asy =0, no pairing -1-2 E asy =32 MeV ( =1), no pairing -3-4 0 5 15 20 25 30 Z Here, in IQMD and SACA, we adopt the following asymmetry energy parametrisation: Easy=E0.(<ρB>/ρ0) (γ-1).(<ρn>-<ρp>)/<ρb> with E0=32 MeV, γ=1 («stiff») Z and A yields not strongly modified Isotope yields shrink onto the N=Z line Still not fully realistic: shell, odd-even effects (pairing) still absent. Multiplicity (Z=1) Multiplicity (Z=3) 2 1-1 -2-3 -4 1-1 -2 H 0 2 4 6 8 A Li Multiplicity (Z=2) Multiplicity (Z=4) 1-1 -2-3 -4 1-1 -2 He 0 2 4 6 8 12 14 A Be -3-3 -4 0 2 4 6 8 12 14 A -4 0 2 4 6 8 12 14 16 18 A

SACA with asymmetry energy and pairing INDRA@GSI - central 129 Xe+ 112 Sn at 0 A.MeV SACA version: E asy =0, no pairing E asy =32 MeV ( =1), no pairing Multiplicity 2 1-1 -2-3 E asy =32 MeV ( =1) + =0.25 pairing -4 0 5 15 20 25 30 Z Multiplicity (Z=1) 2 1-1 H Multiplicity (Z=2) 1-1 He -2-2 -3-3 -4 0 2 4 6 8 A -4 0 2 4 6 8 12 14 A Multiplicity (Z=3) 1-1 -2 Li Multiplicity (Z=4) 1-1 -2 Be -3-3 -4 0 2 4 6 8 12 14 A -4 0 2 4 6 8 12 14 16 18 A

How the dynamical patterns of isotopes are affected dn/dp // 4.5 4 3.5 IQMD 136 Xe+ 112 Sn at 0 A.MeV, b=1 fm protons SACA version MST only No E asy, no pairing E asy =32 A.MeV ( =1), no pairing idem + pairing ( =0.25) 3 2.5 2 1.5 1 0.5 0 0.6 0.4 0.2 0 0.2 0.4 0.6 p // (GeV/c)

How the dynamical patterns of isotopes are affected x dn/dp 4.5 4 3.5 IQMD 136 Xe+ 112 Sn at 0 A.MeV, b=1 fm protons SACA version MST only No E asy, no pairing E asy =32 A.MeV ( =1), no pairing idem + pairing ( =0.25) 3 2.5 2 1.5 1 0.5 0 0.6 0.4 0.2 0 0.2 0.4 0.6 p x reaction plane (GeV/c)

How the dynamical patterns of isotopes are affected dn/dp // 0.2 0.18 0.16 IQMD 136 Xe+ 112 Sn at 0 A.MeV, b=1 fm He SACA version MST only No E asy, no pairing E asy =32 A.MeV ( =1), no pairing idem + pairing ( =0.25) 3 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 1 0.5 0 0.5 1 p // (GeV/c)

How the dynamical patterns of isotopes are affected x dn/dp 0.2 0.18 0.16 IQMD 136 Xe+ 112 Sn at 0 A.MeV, b=1 fm He SACA version MST only No E asy, no pairing E asy =32 A.MeV ( =1), no pairing idem + pairing ( =0.25) 3 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 1 0.5 0 0.5 1 p x reaction plane (GeV/c)

How the dynamical patterns of isotopes are affected ) )/ (p // x (p 1 IQMD 136 112 Xe+ Sn at 0 A.MeV, b=1 fm SACA version MST only No E asy, no pairing E asy =32 A.MeV ( =1), no pairing idem + pairing ( =0.25) 0.95 0.9 He tritons protons deuterons neutrons 3 4 He 6 He

Excitation energy of the primary fragments E* = Eg.s. - Ebind

Excitation energy of the primary fragments E* = Eg.s. - Ebind /A primary fragments (MeV) * 8 6 4 2 0 IQMD+SACA 129 124 Xe+ Sn at 0 A.MeV - b < 0.2 b 0 fm (central) E -2-4 2 4 6 8 12 14 16 18 20 Z On Average, 2 A.MeV of excitation energy. Corresponds to findings of S. Hudan et al. (INDRA collaboration), PRC 67, 064613 (2003). => secondary decay (GEMINI) justified here.

Excitation energy of the primary fragments E* = Eg.s. - Ebind /A primary fragments (MeV) * E /A primary fragments (MeV) * 8 6 4 2 0 8 6 4 2 0 197 IQMD+SACA Au+ IQMD+SACA 197 129 Au 124 at 600 A.MeV - b < 0.2 b fm (central) 0 Xe+ Sn at 0 A.MeV - b < 0.2 b 0 fm (central) central Au+Au @ 600 A.MeV E -2-2 -4-4 2 4 6 8 12 14 16 18 20 2 4 6 8 12 14 16 18 Z 20 Z At relativistic energies, in the participant-spectator regime, heavy primary clusters are produced colder on average. On Average, 2 A.MeV of excitation energy. Corresponds to findings of S. Hudan et al. (INDRA collaboration), PRC 67, 064613 (2003). => secondary decay (GEMINI) justified here.

What can we learn from the isotope yields regarding the asymmetry energy? Mean radius of primary clusters IQMD+SACA

What can we learn from the isotope yields regarding the asymmetry energy? Mean radius of primary clusters (fm) r 0 3 2.5 IQMD+SACA 129 124 central Xe+ Sn at 0 A.MeV 2 1.5 1 normal density 197 197 central Au+ Au at 600 A.MeV 0.5 0 2 3 4 5 6 7 8 9 11 Z

What can we learn from the isotope yields regarding the asymmetry energy? Mean radius of primary clusters (fm) r 0 3 2.5 2 1.5 1 0.5 normal density IQMD+SACA 129 124 central Xe+ Sn at 0 A.MeV 197 197 central Au+ Au at 600 A.MeV Though the medium is dense at this early stage, the dense clusters are disfavoured, because they would correspond to nucleons flowing against each other, hence with too high relative momenta to make a cluster. 0 2 3 4 5 6 7 8 9 11 Z

What can we learn from the isotope yields regarding the asymmetry energy? Mean radius of primary clusters (fm) r 0 3 2.5 2 1.5 1 0.5 normal density IQMD+SACA 129 124 central Xe+ Sn at 0 A.MeV 197 197 central Au+ Au at 600 A.MeV Though the medium is dense at this early stage, the dense clusters are disfavoured, because they would correspond to nucleons flowing against each other, hence with too high relative momenta to make a cluster. 0 2 3 4 5 6 7 8 9 11 Z => The isotope yields can only inform on the low density dependence on the asymmetry energy.

Asymmetry energy influence versus system energy

Asymmetry energy influence versus system energy W. Reisdorf and the FOPI Collaboration Nuclear Physics A 848 (20) 366 427

Asymmetry energy influence versus system energy W. Reisdorf and the FOPI Collaboration Nuclear Physics A 848 (20) 366 427

Asymmetry energy influence versus system energy W. Reisdorf and the FOPI Collaboration Nuclear Physics A 848 (20) 366 427 INDRA@GSI

Asymmetry energy influence versus system energy W. Reisdorf and the FOPI Collaboration Nuclear Physics A 848 (20) 366 427 INDRA@GSI

Asymmetry energy influence versus system energy W. Reisdorf and the FOPI Collaboration Nuclear Physics A 848 (20) 366 427 INDRA@GSI => At high energy, the asymmetry energy effect on clusters seems to vanish. Timescale effect? Non-linear dependence on the density?

Another application of SACA : hypernuclei production n Λ p Λt

Another application of SACA : hypernuclei production A hypernucleus is a nucleus which contains at least one hyperon (Λ(uds),...) in addition to nucleons. n Λ p Λt

Another application of SACA : hypernuclei production A hypernucleus is a nucleus which contains at least one hyperon (Λ(uds),...) in addition to nucleons. n Λ p Λt Extending SACA for clusterising hadrons with hyperons (lambdas,...) for making hypernuclei is straightforward: one replaces Vn-p by VΛ-p and Vn-n by VΛ-n and applies with these modifications the SACA algorithm. If in a final fragment there is a lambda, a hypernucleus should be created. As a first approach, we have adopted VΛ-N = 2/3 Vn-N ; further refinements are possible.

Another application of SACA : hypernuclei production A hypernucleus is a nucleus which contains at least one hyperon (Λ(uds),...) in addition to nucleons. n Λ p Λt Extending SACA for clusterising hadrons with hyperons (lambdas,...) for making hypernuclei is straightforward: one replaces Vn-p by VΛ-p and Vn-n by VΛ-n and applies with these modifications the SACA algorithm. If in a final fragment there is a lambda, a hypernucleus should be created. As a first approach, we have adopted VΛ-N = 2/3 Vn-N ; further refinements are possible. Many ways of producing lambdas: K N Λ π, π + n Λ K +, π - p Λ K0, p p Λ X influence of the EOS, in medium-properties, etc.

Another application of SACA : hypernuclei production IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c A hypernuclei 6 5 58 IQMD+SACA 58 Ni+ Ni at 1.93 A.GeV (b < 6 fm, t cluster. Λ 6 He Λ 5 He = 20fm/c) - soft no mdi, kaon pot. -2-3 n Λ p Λt 4 3 Λ 4 H Λ 3 H Λ 4 He -4 Soft EOS no m.d.i. with Kaon pot. 2 n-λ p-λ -5 1 0 1 2 3 Z hypernuclei -6

Another application of SACA : hypernuclei production IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c A hypernuclei 6 5 58 58 58 IQMD+SACA Ni+ 58 Ni Ni at at 1.93 A.GeV (b (b < 6 < fm, 6 fm, t t = 20fm/c) = - soft - soft no no mdi, mdi, no kaon pot. cluster. Λ 6 He Λ 5 He -2-3 n Λ p Λt 4 3 Λ 4 H Λ 3 H Λ 4 He -4 Soft EOS no m.d.i. with no Kaon Kaon pot. pot. 2 n-λ p-λ -5 1 0 1 2 3 Z hypernuclei -6

Another application of SACA : hypernuclei production IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c A hypernuclei 6 5 58 58 58 IQMD+SACA Ni+ 58 Ni Ni at at 1.93 A.GeV (b (b < < 6 6 fm, fm, t t = 20fm/c) = = 20fm/c) - soft - soft no - soft+mdi, no no kaon pot. pot. cluster. cluster. Λ 6 He Λ 5 He -2-3 n Λ p Λt 4 3 Λ 4 H Λ 3 H Λ 4 He -4 Soft EOS no with m.d.i. no with Kaon pot. pot. 2 n-λ p-λ -5 1 0 1 2 3 Z hypernuclei -6

Another application of SACA : hypernuclei production IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c A hypernuclei 6 5 58 58 58 58 IQMD+SACA Ni+ Ni at 1.93 A.GeV (b (b < < 6 6 fm, fm, t t = = = 20fm/c) = 20fm/c) - - - soft+mdi, no - soft+mdi, no no no kaon kaon pot. pot. cluster. cluster. Λ 6 He Λ 5 He -2-3 n Λ p Λt 4 3 Λ 4 H Λ 3 H Λ 4 He -4 Soft EOS no with m.d.i. with no Kaon pot. pot. 2 n-λ p-λ -5 1 0 1 2 3 Z hypernuclei -6

Strong phase space constraints n Λ p Λt

Strong phase space constraints detected decay : 3 He + π - n Λ p Λt

Strong phase space constraints FOPI Coll. Y. Zhang, Heidelberg p t /m A B detected decay : 3 He + π - n Λ p Λt y Lab target projectile Ni+Ni @ 1.91 A.GeV Preliminary

Strong phase space constraints FOPI Coll. Y. Zhang, Heidelberg Excess over combinatorial background only in region A p t /m A B detected decay : 3 He + π - n Λ p Λt y Lab target projectile Ni+Ni @ 1.91 A.GeV Preliminary

Strong phase space constraints IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c n Λ p Λt

Strong phase space constraints IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c IQMD+SACA Soft Ni+ EOS, Ni at 1.93 no A.GeV m.d.i., (b < 6 fm, t with 58 58 = 20fm/c) Kaon - soft no pot. mdi, kaon pot. cluster. n Λ p Λt lab dn/dy -1 tritons -2 0 t -3-4 -5-0.5 0 0.5 1 1.5 2 2.5 y lab

Strong phase space constraints IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c IQMD+SACA Soft Ni+ EOS, Ni at 1.93 no A.GeV no (b m.d.i., (b < 66 fm, t t with no = 20fm/c) = Kaon - soft - soft no mdi, no pot. 58 58 mdi, no kaon pot. pot. cluster. cluster. n Λ p Λt lab dn/dy -1 tritons 0 t -2-3 -4-5 -0.5 0 0.5 1 1.5 2 y 2.5 lab

Strong phase space constraints IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c IQMD+SACA Soft (b 6 t = 20fm/c) = - soft - no no 58 Ni+ EOS, 58 Ni Ni at at 1.93 1.93 no A.GeV m.d.i., (b (b < 6 < fm, 6 fm, t twith no = 20fm/c) Kaon - soft+mdi, pot. 58 58 no kaon pot. cluster. cluster. n Λ p Λt lab dn/dy -1 tritons 0 t -2-3 -4-5 -0.5 0 0.5 1 1.5 2 y 2.5 lab

Strong phase space constraints IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c IQMD+SACA Soft t t = - soft no no 58 58 Ni+ Ni+ EOS, 58 Ni Ni at at 1.93 1.93 no A.GeV no (b m.d.i., (b < 6 < fm, 6 fm, t twith no = = 20fm/c) Kaon - soft+mdi, - pot. 58 58 mdi, no no kaon pot. cluster. cluster. n Λ p Λt lab dn/dy -1 tritons 0 t -2-3 -4-5 -0.5 0 0.5 1 1.5 2 y 2.5 lab

Strong phase space constraints IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c n Λ p Λt

Strong phase space constraints x (fm) 20 15 5 58 58 IQMD+SACA Ni+ Ni at 1.93 A.GeV (b < 6 fm, t cluster. IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c = 20fm/c) - soft no mdi, kaon pot. tritons (color plot) 0 (contour) t (points) 0.02 0.018 0.016 0.014 0.012 n Λ p Λt 0 0.01-5 0.008 - -15 0.006 0.004 0.002-20 -20-15 - -5 0 5 15 20 z (fm) 0

Strong phase space constraints x (fm) 20 15 5 IQMD+SACA 58 Ni+ 58 Ni at 1.93 A.GeV (b < 6 fm, tt IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c cluster. = = 20fm/c) - soft - soft no no mdi, mdi, no kaon pot. tritons (color plot) 00 (contour) t t (points) 0.02 0.018 0.016 0.014 0.012 n Λ p Λt 0 0.01-5 - -15-20 -20-15 - -5 0 5 15 20 20 z (fm) 0.008 0.006 0.004 0.002 00

Strong phase space constraints x (fm) 20 15 5 IQMD+SACA 58 58 Ni+ Ni at at 1.93 A.GeV (b (b < 6 < fm, 6 fm, tt t IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c cluster. cluster. = = 20fm/c) = 20fm/c) - soft - soft - no soft+mdi, no no kaon pot. tritons (color plot) 0 0 (contour) t t (points) 0.02 0.018 0.016 0.014 0.012 n Λ p Λt 0 0.01-5 - -15-20 -20-15 - -5 0 5 15 20 20 z (fm) 0.008 0.006 0.004 0.002 0 0

Strong phase space constraints x (fm) 20 15 5 IQMD+SACA 58 58 Ni+ Ni at 1.93 A.GeV (b (b < < 6 6 fm, fm, t t t IQMD+SACA 58 Ni+ 58 Ni at 1.91 A.GeV (b < 6 fm) - tcluster.=20 fm/c cluster. cluster. = = 20fm/c) = - soft - soft+mdi, - no no mdi, no kaon pot. tritons (color plot) 0 0 (contour) t t (points) 0.02 0.018 0.016 0.014 0.012 n Λ p Λt 0 0.01-5 - -15-20 -20-15 - -5 0 5 15 20 20 z (fm) 0.008 0.006 0.004 0.002 0 0

Summary and perspectives

Summary and perspectives Summary: Supplying SACA with a more precise description of nuclei binding energy at abnormal density allows promising, realistic predictions of absolute isotope yields, and hypernuclei. The asymmetry energy has a strong influence on the anisotropy (apparent stopping power) for some isotopes ( 3 He, 4 He,...). Within this model, isotope yields cannot inform on the high density dependence of the asymmetry energy. better look at n / p, K + / K -, π + / π - yields/flows for that purpose.

Summary and perspectives Summary: Supplying SACA with a more precise description of nuclei binding energy at abnormal density allows promising, realistic predictions of absolute isotope yields, and hypernuclei. The asymmetry energy has a strong influence on the anisotropy (apparent stopping power) for some isotopes ( 3 He, 4 He,...). Within this model, isotope yields cannot inform on the high density dependence of the asymmetry energy. better look at n / p, K + / K -, π + / π - yields/flows for that purpose. Further developments: After processing SACA, proceed: further decay of primary unstable isotopes like 8 Be, 5 He, etc., which lifetime do not allow to detect them still bound in the detectors, allow early 3 He + n 4 He according to its particularly high cross-section. secondary decay (evaporation code like GEMINI) of still excited clusters. Particularly relevant at intermediate energies (Ebeam 0 A.MeV down to the Fermi regime) for hypernuclei formation, refine lambda-n potential in SACA or EOS/Kaon potential in IQMD in order to predict reasonnably the measured cross-sections, and momentum distributions, which are very constraining.

Density dependant pairing in SACA Do the pairing and shell effect affect the primary fragments? Probably yes, because: according to E. Khan et al., NPA 789 (2007) 94, pairing vanishes above T 0.5Δpairing Δpairing(ρ0) = 12 MeV/ A; ΔBpairing( 4 He)=12 MeV, ΔBpairing( 3 He)=6.9 MeV. in SACA, primary fragments are quite cold (T < 1-2 MeV)

Density dependant pairing in SACA Do the pairing and shell effect affect the primary fragments? Probably yes, because: according to E. Khan et al., NPA 789 (2007) 94, pairing vanishes above T 0.5Δpairing Δpairing(ρ0) = 12 MeV/ A; ΔBpairing( 4 He)=12 MeV, ΔBpairing( 3 He)=6.9 MeV. in SACA, primary fragments are quite cold (T < 1-2 MeV) BUT, pairing effects have to vanish at high or low density. Need to apply a pairing correction factor depending on the cluster density. E. Khan, M. Grasso and J. Margueron, in PRC 80 (2009) 044328 have derived the following function from the pairing potential Vpair = V0{1- η[ρ(r)/ρ0]}δ(r1-r2) within the Hartree-Fock-Bogolioubov method:

Density dependant pairing in SACA Do the pairing and shell effect affect the primary fragments? Probably yes, because: according to E. Khan et al., NPA 789 (2007) 94, pairing vanishes above T 0.5Δpairing Δpairing(ρ0) = 12 MeV/ A; ΔBpairing( 4 He)=12 MeV, ΔBpairing( 3 He)=6.9 MeV. in SACA, primary fragments are quite cold (T < 1-2 MeV) BUT, pairing effects have to vanish at high or low density. Need to apply a pairing correction factor depending on the cluster density. E. Khan, M. Grasso and J. Margueron, in PRC 80 (2009) 044328 have derived the following function from the pairing potential Vpair = V0{1- η[ρ(r)/ρ0]}δ(r1-r2) within the Hartree-Fock-Bogolioubov method: pure surface fη(<ρ>) surface + bulk

Density dependant pairing in SACA Do the pairing and shell effect affect the primary fragments? Probably yes, because: according to E. Khan et al., NPA 789 (2007) 94, pairing vanishes above T 0.5Δpairing Δpairing(ρ0) = 12 MeV/ A; ΔBpairing( 4 He)=12 MeV, ΔBpairing( 3 He)=6.9 MeV. in SACA, primary fragments are quite cold (T < 1-2 MeV) BUT, pairing effects have to vanish at high or low density. Need to apply a pairing correction factor depending on the cluster density. E. Khan, M. Grasso and J. Margueron, in PRC 80 (2009) 044328 have derived the following function from the pairing potential Vpair = V0{1- η[ρ(r)/ρ0]}δ(r1-r2) within the Hartree-Fock-Bogolioubov method: pure surface fη(<ρ>) surface + bulk

Density dependant pairing in SACA Do the pairing and shell effect affect the primary fragments? Probably yes, because: according to E. Khan et al., NPA 789 (2007) 94, pairing vanishes above T 0.5Δpairing Δpairing(ρ0) = 12 MeV/ A; ΔBpairing( 4 He)=12 MeV, ΔBpairing( 3 He)=6.9 MeV. in SACA, primary fragments are quite cold (T < 1-2 MeV) BUT, pairing effects have to vanish at high or low density. Need to apply a pairing correction factor depending on the cluster density. E. Khan, M. Grasso and J. Margueron, in PRC 80 (2009) 044328 have derived the following function from the pairing potential Vpair = V0{1- η[ρ(r)/ρ0]}δ(r1-r2) within the Hartree-Fock-Bogolioubov method: pure surface η is experimentally unknown fη(<ρ>) surface + bulk

Density dependant pairing in SACA Do the pairing and shell effect affect the primary fragments? Probably yes, because: according to E. Khan et al., NPA 789 (2007) 94, pairing vanishes above T 0.5Δpairing Δpairing(ρ0) = 12 MeV/ A; ΔBpairing( 4 He)=12 MeV, ΔBpairing( 3 He)=6.9 MeV. in SACA, primary fragments are quite cold (T < 1-2 MeV) BUT, pairing effects have to vanish at high or low density. Need to apply a pairing correction factor depending on the cluster density. E. Khan, M. Grasso and J. Margueron, in PRC 80 (2009) 044328 have derived the following function from the pairing potential Vpair = V0{1- η[ρ(r)/ρ0]}δ(r1-r2) within the Hartree-Fock-Bogolioubov method: pure surface η is experimentally unknown fη(<ρ>) surface + bulk

More detailed structure corrections to apply In order to account for all major structure effects which make the binding energy deviate from the liquid drop model, for each nucleus (N,Z), what we call «pairing» binding energy will be the difference in binding energy between experimental measurements and the Bethe-Weizäcker formula (without pairing).

More detailed structure corrections to apply In order to account for all major structure effects which make the binding energy deviate from the liquid drop model, for each nucleus (N,Z), what we call «pairing» binding energy will be the difference in binding energy between experimental measurements and the Bethe-Weizäcker formula (without pairing). ΔBpairing(N,Z,ρ0). And for a cluster at mean baryonic density <ρb>, it will be ΔBpairing(N,Z,ρ0) x fη(<ρb>)

More detailed structure corrections to apply In order to account for all major structure effects which make the binding energy deviate from the liquid drop model, for each nucleus (N,Z), what we call «pairing» binding energy will be the difference in binding energy between experimental measurements and the Bethe-Weizäcker formula (without pairing). ΔBpairing(N,Z,ρ0). And for a cluster at mean baryonic density <ρb>, it will be ΔBpairing(N,Z,ρ0) x fη(<ρb>) zoom

SACA with asymmetry energy and pairing H He η = 0.35 surface & volume pairing Li Be

SACA with asymmetry energy and pairing H He η = 1 pure surface pairing Li Be

Even in the spectator regime, we have to account correctly for isotope anisotropies Illustration: alpha particles in C+Au at 300 A.MeV - peripheral collisions γ β INDRA@GSI J. Lukasik ALaDiN-INDRA Coll. y=th -1 β//

Even in the spectator regime, we have to account correctly for isotope anisotropies Illustration: alpha particles in C+Au at 1 A.GeV - peripheral collisions INDRA@GSI J. Lukasik ALaDiN-INDRA Coll.

Even in the spectator regime, we have to account correctly for isotope anisotropies Illustration: alpha particles in C+Au at 1 A.GeV - central collisions INDRA@GSI J. Lukasik ALaDiN-INDRA Coll.