Role of three-nucleon forces in neutron-richnuclei beyond 132 Sn
Luigi Coraggio
Istituto Nazionale di Fisica Nucleare - Sezione di Napoli

June, 6th 2014

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

I A. Covello (University of Naples and INFN)
I A. Gargano (INFN)
I N. Itaco (University of Naples and INFN)
I L. C. (INFN)

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

Motivations

I What is the balance between the role of 2NF and 3NF?
I Neutron-rich nuclei above 132 Sn provide a valid laboratory to

study this topic
I To investigate the influence of three-body correlations on themonopole components of the shell-model hamiltonian

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

Our framework: the realistic shell model
I First step: choose a realistic nucleon-nucleon potential andrenormalize short-range correlations
I Second step: choose a convenient model space
I Third step: derive an effective shell-model hamiltonian Heff by

way of the many-body perturbation theory
I Fourth step: diagonalize the shell-model hamiltonian in thechosen model space

L. C., A. Covello, A. Gargano, N. Itaco, and T. T. S. Kuo, Prog. Part. Nucl. Phys. 62(2009) 135

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

The shell-model effective hamiltonian
A versatile way to derive Heff is the time-dependent perturbative
approach as developed by Kuo and his co-workers in the 1970s (seeT. T. S. Kuo and E. Osnes, Lecture Notes in Physics vol. 364 (1990))

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

The shell-model effective hamiltonian
A versatile way to derive Heff is the time-dependent perturbative
approach as developed by Kuo and his co-workers in the 1970s (seeT. T. S. Kuo and E. Osnes, Lecture Notes in Physics vol. 364 (1990))
In this approach the effective hamiltonian Heff is expressed as

Heff = Q̂ − Q̂0Z
Q̂ + Q̂

0

Z

Z
Q̂

Q̂ − Q̂

0

Z

Z
Q̂

Z
Q̂

Q̂ · · · ,I The so-called Q̂-box is a collection of irreducible valence-linked

diagrams
I The integral sign represents a generalized folding operation

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

The renormalization of the NN potential

Nowadays there are two approaches to the renormalization of theshort-range correlations:

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

The renormalization of the NN potential

Nowadays there are two approaches to the renormalization of theshort-range correlations:
I to renormalize the VNN integrating out the high-momentum

components of the potential - Vlow−k or SRG approaches
I to resort to realistic potential derived from the chiral perturbation

theory and defined only for momenta below a cutoff Λ

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

The renormalization of the NN potential

Both ways are rooted in the EFT, providing a suitable way to deal withmeson theory and QCD, respectively

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

The renormalization of the NN potential

Both ways are rooted in the EFT, providing a suitable way to deal withmeson theory and QCD, respectively
Both pictures need to include many-body terms, aside the 2NF

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

The renormalization of the NN potential

Both ways are rooted in the EFT, providing a suitable way to deal withmeson theory and QCD, respectively
Both pictures need to include many-body terms, aside the 2NF
Many-body forces recover what has been left out when constructing a
nucleon-nucleon potential below a certain energy scale

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

Low-momentum nucleon-nucleon potentials: Vlow−k
Inspiration to renormalize VNN :I Effective field theory (EFT)I Renormalization group (RG)

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

Low-momentum nucleon-nucleon potentials: Vlow−k
Inspiration to renormalize VNN :I Effective field theory (EFT)I Renormalization group (RG)

from EFT: we restrict the configurations of VNN (k , k 0 ) to those withk , k 0 < kcutoff = Λ
k’

k
R2

R1

R0
Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

I Input VNN : Vlow−k derived from the high-precision NN CD-Bonnpotential with two different cutoffs: Λ = 2.1, 2.6 fm−1 .
I Heff obtained calculating the Q-box up to the 3rd order in Vlow−k .
I Model spaces:
I
I

For protons: 0g7/2 , 1d5/2 , 1d3/2 , 2s1/2 , 0h1/2
For neutrons: 0h9/2 , 1f7/2 , 1f5/2 , 2p3/2 , 2p1/2 , 0i13/2

I Single-particle energies are taken from the experiment: this will

help to stress the role played by 3NF forces on the two-bodyresidual interaction

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

One step backwards...
LETTER

doi:10.1038/nature12226

LETTER

doi:10.1038/nature12522

Masses of exotic calcium isotopes pin down
nuclear forces

Evidence for a new nuclear ‘magic number’ from thelevel structure of 54Ca

F. Wienholtz1, D. Beck2, K. Blaum3, Ch. Borgmann3, M. Breitenfeldt4, R. B. Cakirli3,5, S. George1, F. Herfurth2, J. D. Holt6,7,
M. Kowalska8, S. Kreim3,8, D. Lunney9, V. Manea9, J. Menéndez6,7, D. Neidherr2, M. Rosenbusch1, L. Schweikhard1,
A. Schwenk7,6, J. Simonis6,7, J. Stanja10, R. N. Wolf1 & K. Zuber10

D. Steppenbeck1, S. Takeuchi2, N. Aoi3, P. Doornenbal2, M. Matsushita1, H. Wang2, H. Baba2, N. Fukuda2, S. Go1, M. Honma4,
J. Lee2, K. Matsui5, S. Michimasa1, T. Motobayashi2, D. Nishimura6, T. Otsuka1,5, H. Sakurai2,5, Y. Shiga7, P.-A. Söderström2,
T. Sumikama8, H. Suzuki2, R. Taniuchi5, Y. Utsuno9, J. J. Valiente-Dobón10 & K. Yoneda2

The properties of exotic nuclei on the verge of existence play afundamental part in our understanding of nuclear interactions1.
Exceedingly neutron-rich nuclei become sensitive to new aspects ofnuclear forces2. Calcium, with its doubly magic isotopes 40Ca and48
Ca, is an ideal test for nuclear shell evolution, from the valley ofstability to the limits of existence. With a closed proton shell, thecalcium isotopes mark the frontier for calculations with threenucleon forces from chiral effective field theory3–6. Whereas predictions for the masses of 51Ca and 52Ca have been validated bydirect measurements4, it is an open question as to how nuclear
masses evolve for heavier calcium isotopes. Here we report the mass
determination of the exotic calcium isotopes 53Ca and 54Ca, using
the multi-reflection time-of-flight mass spectrometer7 of ISOLTRAP
at CERN. The measured masses unambiguously establish a prominent shell closure at neutron number N 5 32, in excellent agreement with our theoretical calculations. These results increase ourunderstanding of neutron-rich matter and pin down the subtle
components of nuclear forces that are at the forefront of theoreticaldevelopments constrained by quantum chromodynamics8.
Exotic nuclei with extreme neutron-to-proton asymmetries exhibit
shell structures generated by unexpected orderings of shell occupations. Their description poses enormous challenges, because mosttheoretical models have been developed for nuclei at the valley ofstability. It is thus an open question how well they can predict new
magic numbers emerging far from stability9–11. This is closely linked to
our understanding of the different components of the strong force
between neutrons and protons, such as the spin–orbit or tensor interactions, which modify the gaps between single-particle orbits12, and of
three-body forces, which are pivotal in calculations of extreme neutron-rich systems based on nuclear forces2,13,14. The resulting magic
numbers, as well as the strength of the corresponding shell closures,are critical for global predictions of the nuclear landscape15, and thus
for the successful modelling of matter in astrophysical environments.
Three-body forces arise naturally in chiral effective field theory8,
which provides a systematic basis for nuclear forces connected via
its symmetries to the underlying theory of quarks and gluons, namely
quantum chromodynamics. Owing to the consistent description in

effective field theory, there are only two undetermined low-energy
couplings in chiral three-nucleon forces at leading and sub-leading
orders. These are constrained by the properties of light nuclei 3Hand 4He only, so that all heavier elements are predictions in chiraleffective field theory. The present frontier of three-nucleon forces islocated in the calcium isotopes, where the structural evolution is dominated by valence neutrons due to the closed proton shell at atomic
number Z 5 20 (refs 3, 5). These predictions withstood a recent challenge from direct Penning-trap mass measurements of 51Ca and 52Caat TITAN/TRIUMF4, which have established a substantial change
from the previous mass evaluation and leave completely open how
nuclear masses evolve past 52Ca. This region is also very exciting
because of evidence of a new magic neutron number N 5 32 from
nuclear spectroscopy16–18, with a high 21 excitation energy in 52Ca
(refs 19, 20). These results are accompanied by successful theoreticalstudies based on phenomenological shell-model interactions21,22,
which are similar for the excitation spectra at N 5 32 but disagree
markedly in their predictions for 54Ca and further away from stability.
Here we present the first mass measurements of the exotic calcium
isotopes 53Ca and 54Ca. These provide key masses for all theoreticalmodels, and unambiguously establish a strong shell closure, in excellent agreement with the predictions including three-nucleon forces.
The mass of a nucleus provides direct access to the binding energy,
the net result of all interactions between nucleons. Penning traps have
proven to be the method of choice when it comes to high-precisionmass determination of exotic nuclei23,24. The mass m of an ion ofinterest with charge q stored in a magnetic field B is determined bycomparing its cyclotron frequency nC 5 qB/(2pm) to that of a wellknown reference ion, nC,Ref. The frequency ratio rICR 5 nC,Ref/nC (ICR,
ion cyclotron resonance) then yields the mass ratio directly and thus
the atomic mass of the isotope.
We have made a critical step towards determining the pivotal calcium
masses by introducing a new method of precision mass spectrometry forshort-lived isotopes. The developments and measurements were performed with ISOLTRAP25, a high-resolution Penning-trap mass
spectrometer at the ISOLDE/CERN facility. This method was used toconfirm and even improve the accuracy of the recent mass measurements
Towards
Penning traps

Reference ion source

RFQ cooler and buncher

MR-TOF mass spectrometer

TOF detector

ISOLDE ion beam

1

Figure 1 | Experimental set-up.
Main components relevant for the
53,54
Ca study: incoming ISOLDE ion
beam, reference ion source, radiofrequency quadrupole (RFQ)buncher, multi-reflection time-offlight (MR-TOF) mass spectrometerand (removable) time-of-flight ion
detector.

Ernst-Moritz-Arndt-Universität Greifswald, Institut für Physik, Felix-Hausdorff-Strasse 6, D-17489 Greifswald, Germany. 2GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1,
D-64291 Darmstadt, Germany. 3Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany. 4Instituut voor Kern- en Stralingsfysica, Katholieke Universiteit, Celestijnenlaan
200d – bus 2418, B-3001 Heverlee, Belgium. 5University of Istanbul, Department of Physics, 34134 Istanbul, Turkey. 6Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt,
Germany. 7ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt, Germany. 8CERN, Geneva 23, CH-1211 Geneva, Switzerland. 9CSNSM-IN2P3CNRS, Université Paris-Sud, 91405 Orsay, France. 10Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Zellescher Weg 19, D-01069 Dresden, Germany.

3 4 6 | N AT U R E | VO L 4 9 8 | 2 0 J U N E 2 0 1 3©2013 Macmillan Publishers Limited. All rights reserved

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

Atomic nuclei are finite quantum systems composed of two distinct
types of fermion—protons and neutrons. In a manner similar tothat of electrons orbiting in an atom, protons and neutrons in a
nucleus form shell structures. In the case of stable, naturally occurring nuclei, large energy gaps exist between shells that fill completely
when the proton or neutron number is equal to 2, 8, 20, 28, 50, 82 or
126 (ref. 1). Away from stability, however, these so-called ‘magic
numbers’ are known to evolve in systems with a large imbalance of
protons and neutrons. Although some of the standard shell closures
can disappear, new ones are known to appear2,3. Studies aiming to
identify and understand such behaviour are of major importance inthe field of experimental and theoretical nuclear physics. Here we
report a spectroscopic study of the neutron-rich nucleus 54Ca (abound system composed of 20 protons and 34 neutrons) using
proton knockout reactions involving fast radioactive projectiles.
The results highlight the doubly magic nature of 54Ca and provide
direct experimental evidence for the onset of a sizable subshell closure at neutron number 34 in isotopes far from stability.
The shell structure of the atomic nucleus was first successfully
described more than 60 years ago1. However, the question of how
robust the standard magic numbers are in unstable nuclei with a large
excess of neutrons—often referred to as ‘exotic’ nuclei—has been oneof the main driving forces behind recent nuclear structure studies that
focus on changes in the shell structure, called ‘shell evolution’. A noteworthy example is the disappearance of the N 5 28 (neutron number28) standard magic number in 42Si (ref. 4), a nucleus that lies far fromthe stable isotopes on the Segrè chart. On the contrary, exotic oxygenisotopes3 provide evidence for the onset of a new shell closure at
N 5 16, one that is not observed in stable nuclei. In both cases, thetensor force, a non-central component of the nuclear force, has a keyrole in describing the experimental spectra5.
The region of the Segrè chart around exotic calcium isotopes has also
contributed valuable input to the understanding of nuclear shell evolution over recent years owing to experimental advances. Enhanced
excitation energies of first JP 5 21 states (spin, J; parity, P) and reduced
c-ray transition probabilities, which are good indicators of nuclear shellgaps, for 52Ca (refs 6, 7), 54Ti (refs 8, 9) and 56Cr (refs 10, 11) provide
substantial evidence for the onset of a sizable energy gap at N 5 32. This
result was recently confirmed by high-precision mass measurements onneutron-rich Ca isotopes12. In the framework of tensor-force-driven
shell evolution5, the N 5 32 subshell closure is a direct consequence of
the weakening of the attractive nucleon–nucleon interaction between
protons (p) and neutrons (n) in the pf7/2 and nf5/2 single-particle orbitals(SPOs) as the number of protons in the pf7/2 SPO is reduced and themagnitude of the pf7/2–nf5/2 energy gap increases (Fig. 1a–c).
A question that has been asked frequently over recent years iswhether or not the onset of another subshell gap occurs in exotic

N 5 34 isotones, which was suggested qualitatively more than a decadeago13 on the basis of the general properties of nuclear forces. The onsetof an appreciable subshell closure at N 5 34 is illustrated in Fig. 1d,
indicating an energy gap between the np1/2 and nf5/2 SPOs in 54Ca thatis comparable to the separation of the np3/2 and np1/2 spin–orbit partners, which is also implied by recent theoretical results; see, forexample, ref. 14. We stress, however, that no N 5 34 subshell closure
was reported in the experimental investigations of 56Ti (refs 9, 15) or58
Cr (refs 11, 16), and notable doubt on this magic number for Ca
isotopes has been raised17,18. Indeed, as indicated in Fig. 2a, theoreticalpredictions of the energy of the first JP 5 21 state for 54Ca vary considerably, ranging from ,1 MeV in some cases to as high as ,4 MeV
in others14–16,19–24, despite exhibiting close agreement for lighter isotopes; for example, the predictions of the same theories lie within only
0.4 MeV of the empirical result for 52Ca. Such stark discrepancies at
N 5 34 reflect the need for direct experimental input on the matter.
To address this issue, we report on an experimental study of 54Ca toclarify the strength of the N 5 34 subshell gap in nuclei farther fromstability. The energies of nuclear excited states were investigated using
proton knockout reactions involving 55Sc and 56Ti projectiles on a Be
target at the Radioactive Isotope Beam Factory, Japan, operated by the
RIKEN Nishina Center and the Center for Nuclear Study, Universityof Tokyo. Experimental details are provided in Methods Summary.
Particle identification plots indicating the radioactive species transported through the BigRIPS separator and ZeroDegree spectrometer25,
which were used to select and tag radioactive beam projectiles andreaction products, are presented in Fig. 3a and Fig. 3b, respectively.
We emphasize that the intensity of the radioactive beam reported here,
which was critical to the success of the experiment, is unique to theRadioactive Isotope Beam Factory. Excited-state energies were deduced
using the technique of in-beam c-ray spectroscopy.
The c-rays measured in coincidence with 54Ca projectiles produced
through the one- and two-proton knockout reaction channels arepresented in Fig. 4a. The c-ray energies measured in the laboratory
frame of reference have been corrected for Doppler shifts, and so thetransitions appear at the energies they would in the rest frame of thenucleus. The most intense c-ray line in the 54Ca spectrum, the peak at
2,043(19) keV (error, 1 s.d.) in Fig. 4a, is assigned as the transition from1
the first 21 state (2z1 ) to the 0 ground state. In addition, two weakertransitions are located at 1,656(20) and, respectively, 1,184(24) keV.
Figure 4b shows a c-ray spectrum obtained with the condition of aprompt coincidence (#10 ns) with the 2,043-keV c-ray, indicatingthat the weaker transitions were emitted in decay sequences involving
1
R
0
ground-statetransition.
On the basis of the c-ray relative
the 2z1intensities, the 1,656-keV transition is proposed to depopulate a levelat 3,699(28) keV, as presented in the 54Ca level scheme in the lowerright section of Fig. 4a. Placement of the 1,184-keV transition in the1

Center for Nuclear Study, University of Tokyo, Hongo, Bunkyo, Tokyo 113-0033, Japan. 2RIKEN Nishina Center, 2-1, Hirosawa, Wako, Saitama 351-0198, Japan. 3Research Center for Nuclear Physics,
University of Osaka, Ibaraki, Osaka 567-0047, Japan. 4Center for Mathematical Sciences, Aizu University, Aizu-Wakamatsu, Fukushima 965-8580, Japan. 5Department of Physics, University of Tokyo,
Hongo, Bunkyo, Tokyo 113-0033, Japan. 6Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan. 7Department of Physics, Rikkyo University, Toshima, Tokyo 171-8501, Japan.
Department of Physics, Tohoku University, Sendai, Miyagi 980-8578, Japan. 9Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan. 10Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali diLegnaro, Legnaro 35020, Italy.

8

1 0 O C T O B E R 2 0 1 3 | VO L 5 0 2 | N AT U R E | 2 0 7©2013 Macmillan Publishers Limited. All rights reserved

INFN, Napoli

Results for the calcium isotopes+

21 excitation energy [MeV]

4.0
3.5

Expt.
–1
Λ=2.1 fm–1
Λ=2.6 fm (2009)

3.0
2.5
2.0
1.5
1.0
20
22

22

24

26

28

30

32

34

36

30

32

34

36

N

20

S2n [MeV]

18
16
14
12
10

Expt.
–1
Λ=2.1 fm–1
Λ=2.6 fm (2009)

8
6
4
20

22

24

26

28
N

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

Single-particle states in 133 Sb

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

Effective single-particle energies of N=82 isotones
4.0

2.0

Λ = 2.1 fm–1

ESPE [MeV]

0.0

h11/2
s1/2
d3/2
d5/2
g7/2

–2.0

–4.0

–6.0

–8.0

–10.0
48 50 52 54 56 58 60 62 64 66 68 70 72
Z
Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

Effective single-particle energies of N=82 isotones
4.0

2.0

–1

Λ = 2.1 fm
Λ = 2.6 fm–1

ESPE [MeV]

0.0

h11/2
s1/2
d3/2
d5/2
g7/2

–2.0

–4.0

–6.0

–8.0

–10.0
48 50 52 54 56 58 60 62 64 66 68 70 72
Z
Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

2+
1 energies in N=82 isotones
2.8

2.0

1.6

1.2

+

21 excitation energy [MeV]

2.4

0.8
Expt.
–1
CD–Bonn Λ=2.1 fm–1
CD–Bonn Λ=2.6 fm

0.4

0.0
50

52

54

56

58

60

62

64

66

68

70

72

74

Z

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

2+
1 energies in N=82 isotones: theoretical s.p.e.
2.8

2.0

1.6

1.2

+

21 excitation energy [MeV]

2.4

0.8
Expt.
–1
CD–Bonn Λ=2.1 fm–1
CD–Bonn Λ=2.6 fm

0.4

0.0
50

52

54

56

58

60

62

64

66

68

70

72

74

Z

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

Two-proton separation energies of N=82 isotones
20

16

S2p [MeV]

12

8
Expt.
–1
CD–Bonn Λ=2.1 fm–1
CD–Bonn Λ=2.6 fm

4

0

–4
50

52

54

56

58

60

62

64

66

68

70

72

74

Z

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

Single-particle states in 133 Sn

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

Effective single-particle energies of tin heavy isotopes
i13/2
p1/2
p3/2
f5/2
f7/2
h9/2

6.0

ESPE [MeV]4.0

Λ = 2.1 fm

–1

2.0

0.0

–2.0

–4.0
80

82

84

86

88

90

92

94

96

98

100

N
Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

Effective single-particle energies of tin heavy isotopes
i13/2
p1/2
p3/2
f5/2
f7/2
h9/2

6.0

ESPE [MeV]

4.0

–1

Λ = 2.1 fm
Λ = 2.6 fm

–1

2.0

0.0

–2.0

–4.0
80

82

84

86

88

90

92

94

96

98

100

N
Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

2+
1 energies in heavy tin isotopes

1.2
1.0
0.8
0.6
0.4

+

21 excitation energy [MeV]

1.4

0.2

Expt.
–1
CD–Bonn Λ=2.1 fm–1
CD–Bonn Λ=2.6 fm

0.0
82

84

86

88

90

92

N

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

Two-neutron separation energies of heavy tin isotopes

7.0
6.5

S2n [MeV]

6.0
5.5
5.0

Expt.
–1
CD–Bonn Λ=2.1 fm–1
CD–Bonn Λ=2.6 fm

4.5
4.0
82

84

86

88

90

92

N

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

Cutoff (in fm−1 )PD (in %)

2.1
2.6
∞

3.96
4.49
4.85

INFN, Napoli

Summary

I Monopole components of the shell-model hamiltonian areaffected by the lack of the inclusion of 3NF
I This seems to be far less important for model spaces built

up by full HO major shells
I In nuclei above 132 Sn nucleon-nucleon potentials with alarger cutoff may reduce the role played by 3NF
I The latter effect is probaly connected to the tensor

component of the input nucleon-nucleon potential

Luigi Coraggio
ARIS 2014, June 1-6 2014, Tokyo

INFN, Napoli