Hints of correlations beyond effective-interaction theory from HI-induced knockout - PowerPoint Presentation

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Hints of correlations beyond effective-interaction theory from HI-induced knockout

Alexandra Gade

Professor of PhysicsNSCL/FRIB Laboratory and Department of Physics and AstronomyMichigan State University

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award Number DE-SC0020451

Introduction – spectroscopic strength as indicator of correlations missing in shell-model or mean-field approaches

Reduction of spectroscopic strengths for rare isotopes from

HI-induced knockout

Challenges

Reduction of spectroscopic strength as indicator of correlations

The nuclear shell model

pictures deeply-bound states as fully occupied by nucleons. At and above the Fermi sea, configuration mixing leads to occupancies that gradually decrease to zero.

Some

correlation effects

(short-range, soft-core, and long-range) are beyond the effective interactions employed in the shell model and mean-field approaches. The picture given above will be modified depending on the strength of the correlation.

W.

Dickhoff

and C. Barbieri, PPNP 52, 377 (2004).

V. R.

Pandharipande et al, RMP 69, 981 (1997)

Figure from

Lapikas

,

Dickhoff

One-nucleon removal reactions

P. G. Hansen and J. A.

Tostevin, Annu. Rev. Nucl. Part. Sci. 53, 219 (2003) and references within

A nucleon is removed from a projectile upon fast collision with a C or Be target (>70 MeV/u)

In conjunction with reaction theory, spectroscopic strength can be assessed (eikonal and sudden approximations, folding potentials (HF distributions), bound-state wave function constrained with input from HF calculations)

A. Gade et al., PRC 77, 044306 (2008)

Final-state identification with



-ray spectroscopy

 thick targets and high luminosities (measurements can be done at a

few particles per second

)

Nuclear structure

Reaction dynamics

N=2 for sd

shell in A-dependent COM correction

Reduction close to stability

Shell M

A. Gade et al., PRC 77, 044306 (2008)

Weakly-bound systems

Shell M

A. Gade et al., PRC 77, 044306 (2008)

Strongly-bound systems

Shell M

A. Gade et al., PRC 77, 044306 (2008)

What it may mean

Minority nucleons, i.e. neutrons in a proton-rich nucleus or protons in a neutron-rich nucleus, are more correlated than the majority species

These correlations are not captured in effective shell-model interactions and they fragment spectroscopic strength to higher-lying orbitals outside of the necessarily truncated model spaces

Data today – contains data from NSCL, RIKEN, Lanzhou, Bevalac

Figure

: Jeff Tostevin’s 2017 update from

J. A. Tostevin and A. Gade, PRC 90, 057602 (2014)

The good, the bad, and the ugly …

HI-induced knockout

Consistent treatment of all data points, peripheral reaction with understood (strong) dependence on orbital radii, little dependence on OMP

Extensive sensitivity studies: A. Gade et al., PRC 77, 044306 (2008)

Thought to proceed through two processes, stripping and diffraction. Predicted ratios shown to agree with experiment for weakly- and deeply bound nucleonsD. Bazin et al., PRL 102, 232501 (2009)K. Wimmer et al., PRC 90, 064615 (2014)

Validity of

eikonal

and sudden approximation ~100MeV/u for deeply bound nucleons?

There is a min. beam energy as function of binding:

F. Flavigny et al., PRL 110, 122503 (2013)Strong reduction also observed at 240 MeV/u and 1.6 GeV/u, consistent with 80-100 MeV/uEffect of removing cross section via core excitations?Relies on “Reaction Theory with Skyrme HF input” x “Shell model”

started to put in overlaps from NCSM and VMC G. F. Grinyer, D. Bazin et al., PRL 106, 162502 (2011), PRC 86, 024315 (2012)







See also: T.

Aumann

et al.

, Prog. Part.

Nucl

. Phys. 118, 103847 (2021) – Outcome of 2018 EMMI Workshop



Data today – 2021 update

J. A. Tostevin and A. Gade, submitted (2021

), arXiv:2103.13133

Figure

: Open symbols are data taken at 240 MeV/u are 29Ne-1n, 25F-1p, 16C-1p,

30

Ne-1p, and

33

Na-1p and at 1.6 GeV/u 9C-1p, 12C-1n,

11C-1n and 10C-1n

Correlations of minority vs. majority species from low-energy nuclear theory

Truncated model spaces and soft interactions can lead to an asymmetry dependence as seen in knockout

N. K.

Timofeyuk

et al

,

PRL 103, 242501 (2009)

Trend (

not

the magnitude) of increased reduction at larger asymmetry found consistent with conclusions from dispersive optical model analyses of elastic scattering data

R. J. Charity

et al.

, PRC 76, 044314 (2007), PRL 97, 162503 (2006)

Continuum effects can introduce asymmetry dependence (example Oxygen isotopes from Coupled Cluster ab-initio type calculations)

O. Jensen

et al.

, PRL 107, 032501 (2011)

Asymmetry dependence expected for nuclear matter

T. Frick

et al.

, PRC 71, 014313 (2005)

Most predict a more modest asymmetry dependence than the slope from HI-induced knockout: Consistency with other probes?

Consistency with other probes?

The jury is still out but it appears that (p,2p) results only allow for a shallow slope

 see Stefano’s talk soon

Need more data at the extremes with (p,2p) and transfer and a critical evaluation of the reaction theory of all methods! Best would be a theoretical treatment with structure and reaction theory on the same footing!

T.

Aumann

et al.

, Prog. Part.

Nucl

. Phys. 118, 103847 (2021)

The reduction of spectroscopic strength, as encoded in cross sections of direct nuclear reactions relative to shell model and reaction theory, may indicate correlations beyond effective interaction theory and limited model spaces.

From the asymmetry dependence of the reduction and consistent with expectations from some models of nuclei and nuclear matter, the minority nucleons in an asymmetric nucleus appear more correlated than the majority nucleon species.

However, other probes, albeit limited in reach or cases, at best allow for a more shallow slope as function of

ΔS – core excitations/breakup must be explored and studying light mirror nuclei holds promise

Challenge: Any consistent, unified structure-reaction approach must be very precise on radii (0.1 fm) and binding and excitation energies (to the keV) – Sounds difficult? Yes, it is … other probes also have challenges that should be explored and discussed openly

Great opportunity for reaction theorists!

Takeaways

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award Number DE-SC0020451

To end on ….

BUT:

Forgetting about absolute spectroscopic factors for a moment, Hi-induced knockout, transfer reactions, and quasi-free scattering are powerful and complementary methods for studying the nuclear structure of rare isotopes as they seek out single-hole and particle strength, allow for determination of orbital angular momenta and possibly total angular momenta at modest beam intensities



Track shell evolution at the extremes of the nuclear chart

Thank you!

arXiv:2103.13133

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award Number DE-SC0020451

arXiv:2103.13133