Nuclear reactions studies in Spain: a theorist's perspective

Nuclear reactions studies in Spain:

Nuclear reactions studies in Spain:

a theorist's perspective a theorist's perspective

Antonio M. Moro Muñoz

Universidad de Sevilla, Spain

Outline:

●

Some questions being addressed by current nuclear physics studies.

●

A flavour on recent research activities

✔

Developments in nuclear reaction theory

✔

Collaborations with experimental groups

●

Challenges for the near future

Some questions addressed by current Nuclear Physics studies

 What are the limits of stability of nuclear matter?

 Novel structures in this exotic (and rich!) region?

 How do the “magic numbers” change along the nuclear chart?

 What are the mechanisms governing the collisions for these exotic nuclei?

Heavy elements abundances and shell closures

Most neutron-rich isotopes of elements heavier than nickel are produced, by the beta decay of very radioactive matter synthesized during the r process

USE

UHU USE

Madrid

Nuclear Reactions in Spain

Theory:

- Madrid (IEM, UCM) - Huelva (UHU)

- Sevilla (USE)

Santiago

Valencia

Experiments:

- Madrid (IEM) - Huelva

- Santiago de Comp.

- Sevilla (USE/CNA) - Valencia

The Spanish nuclear physics community is contributing to these studies very actively from both the theoretical and experimental sides.

Radioactive beam facilities in Europe

➔ In Europe

- GANIL (France)

- ISOLDE/CERN (Switzerland) - GSI (Germany)

➔ ...and outside Europe - RNCP, RIKEN (Japan)

- MSU, Notre Dame (USA) - RIBRAS (Brasil)

Switzerland

Energy regimes for nuclear reactions

A) “Very low” (astrophysical) energies (<< 1 MeV) - Dominated by Coulomb interaction

- Few open channels

- Eg.: radiative capture: ⁷Be(p,γ)⁸B (Solar neutrino problem!) B) “Low” energies (Coulomb barrier) (~ 1-10 MeV/u)

- Interplay between Coulomb and nuclear

- Many open channels (inelastic, transfer, breakup...) - Strong dynamical effects

C) “Intermediate” energies (~10²-10³ MeV) - Dominated by nuclear forces

- Classical-like trayectories

- More violent processes (eg. knock-out)

-

E

+

Competition between (attractive) nuclear and (repulsive) Coulomb interactions give rise to different physics depending on incident energies

(A) “Very low” energy reactions (A) “Very low” energy reactions

 Questions to be addressed

- Identification of astrophysical processes leading to the formation of elements (r-, s-, rp-processes, etc)

- Rates of relevant processes? Good knowledge of shell → structure and reaction mechanisms

 Observables measured - Capture (n,γ), (n,f)

- Sub-Coulomb tunneling

 Theoretical tools - R-matrix

- Faddeev - RGM

8Be is unbound

After the core collapse, the

temperature increases, and for T ~ 10⁸ K …

...

the appearance in the Universe of heavy nuclei

An example: the triple alpha reaction An example: the triple alpha reaction

The p-p chains are the main source of energy in young stars.

The star accumulates ⁴He in the core.

None of the A=5 nuclei is bound

Direct versus sequential capture mechanism

Direct

α + α + α →

C + γ Sequential (Hoyle, 1954)

(1) α + α →

Be* + γ (2)

Be

+α →

C

3-body problem scattering problem!

A direct capture mechanism can increase the reaction rate up to 7 orders of magnitude at low temperatures!!

Results of the IEM group (Madrid) for the triple-alpha process

(E. Garrido et al,

Eur.Phys.J. A 47, 102 (2011))

 Solve the Faddeev Equations in coordinate space.

 Hypersherical harmonic adiabatic expansion method.

 Continuum discretization with a box boundary condition.

(B) “Low” energy reactions (few MeV/nucleon) (B) “Low” energy reactions (few MeV/nucleon)

 Questions to be addressed

- Shell evolution (eg. magic numbers)

- Study of novel nuclear structures: haloes, skins, etc - Nucleus-nucleus interaction

- Investigation of new dynamical phenomena

 Observables measured

- Direct reactions: elastic, transfer, breakup, etc - Fusion

 Theoretical tools

- Faddeev (when possible) - Optical Model

- Coupled-channels formalisms - ...

Nuclear haloes Nuclear haloes

➔ Nuclei close to drip-lines (Sn~0 or Sp~0)

➔ 1 or 2 loosely bound nucleons moving far away from a compact core.

✔ 1n haloes: ¹¹Be

✔ 2n haloes (Borromean): ⁶He, ¹¹Li

✔ 1p haloes: ⁸B, ¹⁷Ne.

➢ Large reaction cross sections

➢ Narrow momentum distributions of fragments arising from breakup

➢ Large B(E1) strengths

Reactions

11

Li

Reactions induced by halo nuclei Reactions induced by halo nuclei

1N halo + target → 3-body problem

2N halo + target → 4-body problem

Faddeev eqns

d+¹⁴C p+→ ¹⁵C

Deltuva, PRC79, 054603 (2009)

➢ Pioneering applications of Faddeev eqns to nuclear reactions by the Lisbon group.

Faddeev eqns?

Limitations of Faddeev method and the need for Limitations of Faddeev method and the need for

alternative methods alternative methods

 Virtues of Faddeev method:

✔ Provides the “exact” solution for a given 3-body Hamiltonian

✔ Treats elastic, transfer and breakup on equal footing

 Drawbacks:

✗ Numerically very demanding

✗ Non-trivial disentanglement between reaction and structure

✗ Difficult to include fragments d.o.f. (eg. “core” excitations)

✗ Coulomb is difficult to include ( limited to light systems so far)→

Alternative methods are required for

the analysis of experiments

Alternatives to the Faddeev eqns:

Continuum Discretized Coupled-Channels (CDCC) formalism

➔ Two-body projectile effective 3-body model→ Eg: ¹¹Be+p =(¹⁰Be+n)+p

➔3-body WF expanded in projectile states {ϕ_n(r)}

➔ Continuum states represented by a discrete set of states

➔ Projectile breakup treated as excitation to continuum states

➔ Schrodinger eq. Coupled Channels eqns →

r , R=₀r₀ R

∑

n=1 N

_n r_n R

(similar approaches are used in atomic, particle physics,etc)

Lisbon-Sevilla collaboration:

A. Deltuva, PRC76, 064602 (2007)

CDCC vs Faddeev benchmark calculations for

C(d,pn)

C

 Inclusion of core excitation in the scattering of two-body halo nuclei with deformed core.

 Scattering of 3-body (eg Borromean) nuclei require:

➔3-body description of the projectile

➔Four-body scattering framework (4b-CDCC)

Extensions of the CDCC method

(Sevilla-Surrey collaboration)

Sevilla-Lisbon collaboration

Theory support to experimental collaborations



Sevilla-Madrid-Huelva collaboration (~40): scattering of exotic nuclei in international RNB facilities (Louvain-la- Neuve, ISOLDE/CERN, TRIUMF, GANIL)



REX-ISOLDE (CERN) (~50):

Low energy reactions with radioactive beams



RIBRAS (Sao Paulo, Brasil) (~25)



Notre Dame (USA) (~25)



Next goal further involvement in the experimental →

activities at GANIL/SPIRAL2 and GSI/FAIR

Deviations from Rutherford formula in sub-Coulomb nuclear scattering

➢ Sub-Coulomb elastic scattering of tightly bound nuclei is consistent with V(r)~1/r

(Rutherford formula)

➢ Weakly-bound nuclei will be polarized in the strong Coulomb field of a heavy target, giving rise to a dipole correction in V(r)

➢Deviations in the elastic scattering relative to the Rutherford (or Mott) formula → α

V ( r)≈ Z₁Z₂e²

r −αZ₁Z₂e²

2r⁴ Rodning et al, PRL49,909 (1982)

→ α=0.70( 5) fm³

d+²⁰⁸Pb elastic scattering

Study of ⁶He,¹¹Li+²⁰⁸Pb (Sevilla-Huelva-Madrid collaboration)

Strong Coulomb dipole polarizability effect predicted in

11Li+²⁰⁸Pb elastic scattering (Andrés et al, '96)

6He⁺²⁰⁸Pb experiments performed at Louvain-la- Neuve (2002,2004) (2 PhD theses)

- Development of 4-body CDCC method (1 PhD thesis)

- Development of transfer-to-the continuum method (α's) (1 PhD)

11

Li+

Pb elastic scattering: the largest deviation from Rutherford formula ever observed

- ¹¹Li very weakly-bound (S_2n=370 KeV)

- ¹¹Li structure highly distorted by the electric field of a Pb target - Large breakup yield (⁹Li)

Accessing unbound nuclei:

Li spectroscopy from

2

H(

Li,p)

Li transfer reaction.

➔ Unbound exotic nuclei can be studied via transfer reactions.

➔ Extensions of the DWBA approach for unbound final states developed and applied to ⁹Li(d,p)¹⁰Li (ISOLDE)

➔ Spectroscopic information: resonances, virtual states

➔ Confirmation of parity inversion in ¹⁰Li

Intermediate energies (~10² MeV/u)

- Dominated by nuclear forces but Coulomb still important at small → scattering angles (large impact parameters)

Observables:

- Momentum distributions nuclear sizes and single-particle → contents (l,s,j)

- Angle-integrated cross sections spectroscopic factors→

(A) (A-1)

Extracting physical information from knockout experiments

New reactions and the need for new theory

1 + N

(R3B collaboration at GSI with participation of Santiago group

- Due to strong absorption, knockout experiments provide information only on surface (weakly-bound nucleons).

- Leading facilities (GANIL, GSI) are starting to measure new observables whose interpretation will demand new theoretical approaches.

- Example: Kinematical complete measurements of quasi-free scattering

CH

p/n

A A-1

p

Need to calculate things like:

dσ/dΩ_N1dΩ_cdΩ_NddΕ_Ν1dΕ_Ν2 A challenge for theorists!

(Faddeev, DWIA?)

Spectroscopy from Coulomb and nuclear breakup

Eg.: ¹¹Be+¹²C at RIKEN (70 MeV/nucleon)

- DWBA calculations including valence and core excitation mechanisms

- Identification and spin assignment os resonances, spectroscopic factors, etc

Nuclear response

Coulomb response (E1)

Beta decay Charge Exchange Reaction

B(GT) = 1

2 ψ_f

∑

∑

B(F) = 1

2 ψ_f τ^± ψ_i ²

Spin-isospin response: charge-exchange reactions

➢ Complementary to beta-decay experiments

➢ No restriction in excitation energies of final states

➢ Probes the spin-isospin part of the nuclear interaction (Gamow-Teller and Fermi strengths)

d 

d   q , ≃  

 q ,  B  GT  d 

d   q , ≃  

 q ,  B  F 

2461 1+ 2699 1+ 2978 1+ 3535 1+ 3610 1+ 3870 1+

2459.8 1+ 2466.3 1+ 2697.4 1+ 2977.8 1+ 3867 1+

Reaction

Beta-decay

Charge-exchange vs. beta-decay

(IFIC-Valencia in collaboration with RCNP-Osaka and GANIL)

Concluding remarks

 Physics of exotic nuclei constitutes a very active and exciting field

to which Spanish groups are contributing from both experimental and theoretical sides.

 These studies have very applealing direct or indirect byproducts (astrophysics, medical physics,etc) but, the fact that we are

learning about completely unexplored regions of the nuclear chart, should be a sufficient justification to keep working (and investing) in these kind of research.