Two-nucleon transfer reactions
R.A. Broglia, A. Idini, E. Vigezzi
Milano University and INFN
The Niels Bohr Institute, Copenhagen
F. Barranco, G. Potel
Sevilla University
G. Baym, Fi+y years of BCS theory , Denver, March 2007 Pairing correlations enhance two-nucleon transfer cross sections
Nuclear Physics 33 (1962) 685--692; ~
North-Holland Publishing Co., Amsterdam
Not to be reproduced by photoprint or microfilm without written permission from the publisher
NOTE ON THE TWO-NUCLEON
STRIPPING REACTION
S H I R O YOSHIDA t
Radiation Laboratory, University o/ Pittsburgh, Pittsburgh, Pennsylvania tt
Received 9 February 1962
A b s t r a c t : The magnitude of the two-nucleon stripping reactions is calculated using the pairing
interaction model. The calculation also is applied to final states of collective type. F o r some
types of reaction a collective enhancement of the reaction cross section is predicted.
Recently much attention has been directed to reactions like (6, d), (He 8, n),
(t, p) (or their reverse reactions), for which the two-nucleon stripping process
is believed to be important when the residual nucleus is excited at low energy.
Many investigations of these reactions have been published l-e) ttt, but most
Form factor for the transfer of a J=0 pair
theoretical investigations are concerned with the calculation of the angular
distribution rather than of the magnitude of the cross section.
In the case of the one-nucleon stripping reaction the magnitude of the cross
section is governed by the "spectroscopic factor", and it has been shown that
the study of this factor is very important for nuclear spectroscopy 7, s). We
expect that the two-nucleon stripping process also is useful for nuclear spectroscopy and that in some cases it may give new information which was not
obtainable from the one-nucleon stripping process. Our attempt in this note is
to study the two-nucleon stripping (or pick-up) reaction from the viewpoint
of nuclear structure and to try to find its usefulness in nuclear spectroscopy.
The two-nucleon spectroscopic factor is calculated using the pairing
interaction model, and this is applied also to the collective states. For some
types of reaction collective enhancement is predicted, which is not found in
Review of two-neutron transfer
experiments; pairing rotations and
pairing vibrations
2nd order DWBA: Sequential and
simultaneous contributions
PHYSICS REPORTS (Review Section of Physics Letters) 199, No. 1(1991)1—72. North-Holland
TWO-NUCLEON TRANSFER REACTION MECHANISMS
Masamichi IGARASHI*
Department of Physics, Tokyo Medical College, Shinjuku, Sinjuku-ku, Tokyo 160, Japan
Ken-ichi KUBO
Department of Physics, Tokyo Metropolitan University. Fukazawa. Setagaya-ku, Tokyo 158, Japan
and
Kohsuke YAGI
Institute of Physics and Tandem Accelerator Center, University of Tsukuba, Tsukuba, Ibaraki 305, Japan
Editor: G.E. Brown
Received April 1990
Contents:
1. Introduction
.1. Review of previous studies
1.2. Aim of this work
2. Formulation and method of calculation
2.1. The first- and second-order distorted wave Born ap-
3
3
6
6
3.1. The measurement of (p, t) analyzing powers and cross
sections
3.2. Experimental results for (p t) analyzing powers and
cross sections
3.3. Experimental studies of the (p, d) and (d, t) reactions
38
39
39
Coupled channel effects
Semiclassical theory
INSTITUTE OF PHYSICS PUBLISHING
Rep. Prog. Phys. 64 (2001) 1247–1337
REPORTS ON PROGRESS IN PHYSICS
PII: S0034-4885(01)98206-5
Pairing correlations of nucleons and multi-nucleon
transfer between heavy nuclei
W von Oertzen1,2 and A Vitturi3
1
2
3
Hahn-Meitner-Institut Berlin, Glienicker Strasse 100, D-14109 Berlin, Germany
Fachbereich Physik, Freie Universität Berlin, Germany
Dipartimento di Fisica, Universitá di Padova, and INFN, Padova, Italy
Received 20 April 2001
Published 28 September 2001
Online at stacks.iop.org/RoPP/64/1247
A. Vi?uri, Kyoto, DCEN 2011 Abstract
h?p://www2.yukawa.kyoto-­‐u.ac.jp/~ykis2011/
This review presents the status of the field of two-nucleon and multi-nucleon transfer reactions
dcen/slide/workshop4/vi?uri.pdf induced by heavy ions. The role of the pairing interaction in nuclei as a finite quantum system
is illustrated. These reactions serve as a unique tool for the study of the dynamical aspects
of pairing correlations in nuclei in particular for the cases of nuclear superfluidity. The new
possibilities offered by the development of experimental techniques, e.g. the large gammaray detectors combined with charged particle detectors are presented, which allows the study
of the enhanced pair transfer between well selected states, and the problem of the expected
quenching of pairing correlation at high spin. Further, the new possibilities offered by the
advent of radioactive beam facilities are discussed.
50 years of nuclear BCS ,eds. R.A. Broglia and V. Zeelvinsky, World ScienUfic, to be published [Phys. Rev. Lett. 107, 092501 (2011)]
Pairing rotaUonal band A.
in sIdini,
uperfluid Un iR.
sotopes G. Potel,
F. Barranco,
F. Marini,
E. Vigezzi,
A. Broglia
(Dated: Received 31 May 2011; published 22 August 2011)
•  Static deformation of the pair field
•  Rotational-like spectrum formed by a sequence of ground states of even-N
systems
PACS numbers: 25.40.Hs, 25.70.Hi, 74.20.Fg, 74.50.+r
hould be substituted
by
1
EN =
(N − N0 )2
2J
p.v. g.s. Pairing Vibrations
E − λ(N − N0 ) (MeV)
(Nobel Lecture, Ben R. Mottelson, 1975)
2y x y y x 2x •  Near closed shell nuclei (like 208Pb) no static deformation of pair field
•  Vibrational-like excitation spectrum.
•  Enhanced pair-addition and pair-removal cross-sections seen in (t,p) and
(p,t) reactions (indicated by arrows).
Two-­‐neutron transfer is the specific probe of pairing correlaUons In superfluid nuclei, +
α0 =< BCS|P |BCS >=
�
ν>0
Uν Vν ∼ ∆/G
dσ/dΩ(A, g.s.− > A + 2, g.s) ∼ α02
In normal nuclei, dσ/dΩ ∼
α0 = 0
< (α − α0 )2 >= [< 0|P + P |0 > + < 0|P P + |0 >]/2
A wise opinion (John Schiffer)
Simple ways of treating data can allow us to extract essential structural
information, even if reaction theorists are not completely happy.
One hopes that a new generation will be able to start from what was
Learned, and build on it, and not get bogged down with the fascinating
sophistries of reaction theories. We need not have to rediscover all
the blind alleys (of two-step processes, coupled channels … etc) that
obscured simple underlying information
All experiments should be feasible, exciting and interpretable,
but they most rarely enjoy more than two of the three properties,
frequently failing the interpretability test (V. Telegdi)
Some recent 2-­‐nucleon transfer experiment t(30Mg,32Mg)p K. Wimmer et al. ,PRL 105 (2011) 252501 p(11Li, 9Li)t I. Tanihata et al., PRL 100 (2008) 192502 p(8He,6He)t N. Keeley et al., PLB 646 (2007) 222 121Sb(p,t)119Sb P. Guazzoni et al., J.Phys.G 34 (2007)2665 120Sn(p,t)118Sn P. Guazzoni et al., PRC 78 (2008)064608 134Ba(p,t)132Ba S. Pascu et al., PRC 81 (2010)014304 65Cu(6He ,4He)67Cu A. Cha?erjee et al., PRL 101 (2008) 032701 9Be (18O,16O)11Be M. Cavallaro et al., J. Phys G Conf. Ser. 312(2011)092020 40Ca(96Zr,94Zr)42Ca L. Corradi et al. , PRC 84(2011)034603 112Sn(p,t)110Sn “Standard procedure”: first order DWBA
0+ P. GUAZZONI et al.
10
4
10
3
2+ PHYSICAL REVIEW C 74, 054605 (2006)
2
10
1
10
2
10
1
1.212
10
2.545
1
≈
10
3
≈
≈
G.S.
10
10
10
10
10
10
2
1
2.742
10
1
10
0
10
1
10
1
10
0
≈
2
1
3.183
0
10
1
10
0
0
20
40
θc.m. (deg)
60
FIG. 2. Differential cross sections for the excitation of 0+ states
110
112 Sn(p,t)1102.857
Sn
reaction, Ep = 26 MeV
(Guazzoni et al. PRC Note 74 054605
change o(2006))
f scale 2.965
with first order DWBAof one
obtains
cross secUons the
and of distribuUons angular distribution ofangular the angular
3.083
between 0+ and 2+ differential cross section
3.421
absolute normalization
⇒ relative cross
sections
3.751
10
1
10
0
10
-1
112
0
≈
2.573
≈
10
10
≈
1
1
≈
10
dσ/dΩ (µb/sr)
10
2
≈
dσ/dΩ (µb/sr)
≈
2.309
10
-1
SystemaUc high-­‐quality A+2Sn(p,t)ASn angular distribuUons for 112 < A <124: Guazzoni et al., PRC 60 054603 (1999); 74 054605 (2006); ecc. 3.812
0
20
40
θ c.m. (deg)
60
FIG. 3. Differential cross sections for the excitation of 2+ states
by the 112 Sn(p, t)110 Sn reaction. The dots represent the experimental
Fits obtained using normalizaUon factors and assuming dineutron transfer (one step); angular distribuUons are well described. 2-­‐body spect. ampl. T =
(2)
�
ji jf
Bjf (B, A)Bji (a, b)T (1) (jf , ji )
Ujf Vjf +Cjf (B, F )Cjf (F, A)
Cji (a, f )Cji (f, b)
(2)
× [Tsucc (jf , ji ) − TN O (jf , ji )]
Ujf x Vjf 1-­‐body spect. ampl. Both successive and simultaneous terms are coherent
CalculaUon of absolute two-­‐nucleon transfer cross secUon by finite-­‐range DWBA calculaUon Gotz
ci al., Reaction mechanism of two.nucleon transfer between heavy ions
/
‘\
-
U
4 r©
/
r2f
/
/
r2b
/
r
2,5
/\
~/
I
I
rib
/
/
/
I
~
/
r?a
/
r~A
B
//
/
/
/
I
I
/
rf~
/
F
/
r~
b
r0~
r5~
B.F. Bayman and J. Chen, Phys. Rev. C 26 (1982) 1509 G. Potel et al., arXiv:0906.4298 Simultaneous transfer
Simultaneous transfer
T (1) (ji , jf ) = 2
��
(−)∗
drfF drb1 drA2 [Ψjf (rA1 , σ1 )Ψjf (rA2 , σ2 )]0∗
0 χbB (rbB )
σ1 σ2
(+)
× v (rb1 )[Ψji (rb1 , σ1 )Ψji (rb2 , σ2 )]00 χaA (raA )
U
Gotz
ci al., Reaction mechanism of two.nucleon transfer between heav
/
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-
120
4 r©
eley, August 9, 2010
/
r2f
/
/
r2b
/
r
2,5
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~/
I
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rib
/
/
/
I
slide 4/
~
/
r?a
/
r~A
B
//
/
/
/
I
I
/
rf~
/
F
/
r~
b
r0~
r5~
Successive transfer
�
�
�
(2)
Tsucc (ji , jf ) = 2
drfF drb1 drA2 [Ψjf (rA1 , σ1 )Ψjf (rA2 , σ2 )]0∗
0
K ,M σ1� σ2�
σ1 σ2
×
×
�
�
�
�
�
�
�
drfF
drb1
drA2
G (rfF , rfF
)[Ψjf (rA2
, σ2� )Ψji (rb1
, σ1� )]K
M
2µfF
� U ji ci al.,� Reaction� mechanism
0 (+)
�
� 120 ji �
of (r
two.nucleon
)[Ψ
(r
,
σ
)Ψ
(r
,
σ
)]
χ
v
(r
aA ) transfer between h
A2 2
b1 1 0 aA
f2
2
�
Gotz
/
eley, August 9, 2010
‘\
-
×
(−)∗
χbB (rbB )v (rb1 )[Ψjf (rA2 , σ2 )Ψji (rb1 , σ1 )]K
M
4 r©
/
r2f
/
/
r2b
/
slide 4
r
2,5
/\
~/
I
I
rib
/
/
/
I
~
/
r?a
/
r~A
B
//
/
/
/
I
I
/
rf~
/
F
/
r~
b
r0~
r5~
Non–orthogonality term
Non orthogonal contribution
�
�
�
(2)
TNO (ji , jf ) = 2
drfF drb1 drA2 [Ψjf (rA1 , σ1 )Ψjf (rA2 , σ2 )]0∗
0
K ,M σ1� σ2�
σ1 σ2
(−)∗
× χbB (rbB )v (rb1 )[Ψjf (rA2 , σ2 )Ψji (rb1 , σ1 )]K
M
�
�
�
�
�
, σ1� )]K
, σ2� )Ψji (rb1
× drb1
drA2
[Ψjf (rA2
M
(+)
�
�
�
, σ1� )]U 00 χaA
× [Ψji (rA2
, σ2�120
)Ψji (rb1
ci al.,(r
Reaction
aA ) mechanism of two.nucleon transfer between
Gotz
/
‘\
-
keley, August 9, 2010
4 r©
/
r2f
/
/
r2b
/
r
2,5
/\
~/
I
I
rib
slide
/
/
/
I
~
/
/
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r~A
B
//
/
/
/
I
I
/
rf~
/
F
/
r~
b
r0~
r5~
Structure input for, e.g., the
Sn(p,t)
Sn reaction:
Elements of the calculaUon for the 112Sn(p,t)110Sn reacUon 0.7
0
2d5/2
−15
0
1g7/2
0.5
2d3/2
−50
1h11/2
0.4
−20
single particle wave functions
0.3
E (MeV)
real part
imaginary part
−10
E (MeV)
3s1/2
0.6
−5
−25
0.2
−30
0.1
−35
−40
optical potential
−45
−100
proton−neutron potential
−150
−200
0
−250
−0.1
−50
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
r (fm)
T =
�
−0.2
0
1
2
3
4
5
6
7
8
9
−300
0
10 11 12 13 14 15
�
0.5
1
1.5
2
2.5
3
r (fm)
r (fm)
(2)
(2)
Bj T (1) (j) + Tsucc
(j) + TN O (j)
�
plus the Bjj spectroscopic amplitudes needed to define the two–neutron
wavefunction:
Two neutron spectroscopic amplitude: � �
�0
j
j
Φ(r1 , σ1 , r2 , σ2 ) =
Bj ψ (r1 , σ1 )ψ (r2 , σ2 ) 0
Bj =< Ψ(A−2) |Pj |ΨA >j
Kyoto, October 24th, 2011
BCS (A−2)
Bj = (j + 1/2)1/2 Uj
(A)
Vj
slide 9/2
122Sn(p,t)120Sn E = 26 MeV lab
Successive Non orthogonal Simultaneous Simult.+Non orth. Sn(p,t)
Sn, results
10
dσ/dΩ (µ b/sr)
dσ/dΩ (µ b/sr)
2
10
1
10
112
112Sn(p,t)110
110Sn,
10
3
0
10
20
10
30
40
θCM
50
60
Sn(p,t)106Sn, Elab=26 MeV
30
40
50
60
10
70
0
10
20
30
40
60
70
110
18)
0
70
50
!CM
112
5/2
20
108
0
!CM
1
10
Elab=26 MeV
0
2
0
2
10
1
10
10
2
10
10
4
10
3
10
•  BCS wavefuncUons reproducing experimental pairing gaps Sn(p,t) Sn!
•  Tang-­‐Herndon wavefuncUons for the triton •  Ocross
pUcal otenUal Fig. 2. (left) The absolute differential
sectionp
for
the reaction fi?ed Sn (p,t)by Sn, calculated
making use of the BCS amplitudes (solid curve), already shown in Fig. 1, is compared to the
shell-model
Guazzoni et al Also shown is the result calculated
result obtained making use of
amplitudes.
assuming a pure (d ) configuration. (right) The theoretical differential cross section for
is decomposed into successive, simultaneous and non orthogonal
the reaction
Sn (p,t) Sn
4
10
3
d"/d# (µ b/sr)
A−2
d"/d# (µ b/sr)
A
10
20
4
10
30
40
50
108
60
70
2
106
θCM
contributions.
Also shown is the sum of non ortohogonal and successive amplitudes.
4
5000
3
10
3
10
4500
4000
3500
2
2
0
10
20
30
40
θCM
50
60
0
70
5
10
20
30
40
θCM
50
!(µ b)
10
10
3000
Comparison with the experimental
a)
b)
data available so
far for superfluid tin
isotopes
Potel et al., PRL 107, 092501 (2011)
5000
4500
4000
3500
3000
60 70
2500
2500
4
10
2000
10
2000
1500
dσ/dΩ (µ b/sr)
dσ/dΩ (µ b/sr)
3
10
2
10
1
10
0
30
1500
4
10
1000
3
10
1000
2
A
1
20
40
θCM
60
80
10
0
500
500
102 106 110 114 118 122 126 130
10
10
40
Emax
dσ/dΩ (µ b/sr)
dσ/dΩ (µ b/sr)
10
20
10
100
110 A
120
130
10 12 14 16 18 20 22 24 26 28 30
Elab (MeV)
Fig. 3. (a) The squares show the experimental values of the cross section integrated in the range
0o < θ < 80o for the two-neutron transfer reaction A Sn (p,t)A−2 Sn, (cf. Fig. 1), compared with
20 30the40theoretical
50 60 value
70
(triangles). The solid curve shows the integrated cross sections along the Sn
θCM
G. Potel et al., PRL107 (2011) 092501 The ground state is a coherent state well described by BCS calculations
constrained to reproduce the phenomenological pairing gap
E. Vigezzi, F. Barranco, R.A. Broglia, A. Idini and G. Potel
4
10
experiment
BCS
Shell Model
2
112
Sn ->
1
pure (d5/2) configuration
3
10
SHELL MODEL
BCS
3
d"/d#
(µ b/sr)
B(jj;0)
d"/d# (µ b/sr)
4
10
total
succ
sim
110
non
Sn
sim+non
2
10
10
2
10
0.5
1
10
1
10
112
112Sn(p,t)
110Sn,
Sn(p,t)110
Sn!Elab=26
MeV
00
0
10
0
10
20
30
40
!CM
50
60
70
10
0
g7/2 d5/2
s1/2 d3/2
d5/2
g7/2
s1/2 d3/2
108
Sn(p,t)106Sn, Elab=26 MeV
-10
10
20
h11/2
h11/2
-8
30
40
!CM
50
60
E (MeV)
-6
70
ig. 2. (left) The absolute differential cross section for the reaction 112 Sn (p,t)110 Sn, calculated
making use of the BCS amplitudes (solid curve), already shown in Fig. 1, is compared to the
18)
result obtained making use of shell-model amplitudes.Shell Also
shown
the resultet calculated
model : P. isGuazzoni al., 2
assuming a pure (d5/2 ) configuration. (right) The PRC theoretical
differential
74 054605 (2006 cross section for
108
106
the reaction
Sn (p,t) Sn is decomposed into successive, simultaneous and non orthogonal
contributions. Also shown is the sum of non ortohogonal and successive amplitudes.
Some challenges:
Check pair vibrational scheme around new magic nuclei
Transfer from heavy, weakly bound nuclei
Effects of core excitation
Transfer from halo nuclei
Continuum and coupled channel effects
Pair transfer as probe of shape coexistence
FIG. 3
expres
also ca
remov
6:6 Me
associa
a) and
and 26
show
134 Snðp
FIG. 2. Absolute calculated cross
parison with the experimentalrelativ
result
tional
FIG. 2. Absolute calculated cross section predictions in comE¼B
parison with the experimental results of [11–15].
Pair vibraUons around 100Sn and 132Sn in the harmonic approximaUon 092501-3
G. Potel et al., PRL107 (2011) 092501 Two –neutron transfer cross secUons for neutron-­‐rich Sn isotopes E. PLLUMBI
et al.
(zero-­‐range approximaUon) 136
10
-4
gs
Sn(p,t)
134
x=1, Ep=30 MeV
Sn
x=1, Ep=15 MeV
+
0
x=1, Ep=35 MeV
2
x=0.35, Ep=15 MeV
8
x=0.35, Ep=35 MeV
2
-5
10
CSgs /CS0+
diff. cross section (arb. units)
x=0.35, Ep=30 MeV
10
PH
-6
10
-7
-8
10 0
4
2
20
40 60 80
θc.m. (deg)
100 120
20
40 60 80
θc.m. (deg)
100 120
FIG. 4. (Color online) Left: Cross sections for the reaction
Sn(p, t)134 Sn obtained in the cases of a pure surface interaction
(x = 1) and aPllumbi mixed interaction
(x8=3 0.35).
The
transition to the
et al., PRC (2010) 034613 ground state of the final nucleus is considered and two values
of the incident proton energy are selected, Ep = 30 and 35 MeV.
136
136
134
1
15
20
FIG. 5. (Color online) R
the g.s. and to the 0+
2 trans
136
134
reaction Sn(p, t) Sn.
BCS wavefunctions are enough to calculate 2n transfer
between ground states of superfluid nuclei.
BUT
2n transfer reactions to collective surface vibrational states
may reveal the existence of shape fluctuations in the condensate
A-­‐2 A-­‐2 λ λ aj1aj2)λ + aj1aj2)λ A R.A. Broglia, C. Riedel, T. Udagawa, NPA169 (1971) 225 A Ground state correlaUons Probing 11Li halo-­‐neutrons correla4ons via (p,t) reac4on Introduction
We will try to draw information about the halo structure of 11 Li from the
reactions 1 H(11 Li,9 Li)3 H and 1 H(11 Li,9 Li∗ (2.69 MeV))3 H (I. Tanihata et
al., Phys. Rev. Lett. 100, 192502 (2008))
r Schematic depiction of
11 Li
Berkeley, August 9, 2010
F. Barranco et al., EPJ A11 (2001) 385 First excited state of 9 Li
slide 2/8
�
an1 ,n2 [ψn1 (r1 )ψn2 (r2 )]00
n1 ,n2
11Li 3 3 3 Vnp Vnp p 9Li 10Li d t 11Li(p,t)9Li g.s. 3/2-­‐ First exc. 1/2-­‐ G. Potel et al., PRL 105 (2010) 172502
InterpretaUon of direct reacUons: ex of 8He+p @ 15.6 MeV/nucleon Coupled reacUon channel (CRC) calculaUons needed: Cf 8He+p Analysis à N. Keeley, SPhN [now: univ of Varsaw] F. Skaza et al., PLB 619. 82 (’05) ; PRC 73, 044301 (’06) N. Keeley et al., PLB 646, 222(’07) 8He(p,d) E405s –GANIL-­‐MUST 8He +p @ 15.6 MeV/n 8He(p,t)6He (0+) 8He(p,p) 8He(p,t)6He (2+) Spectroscopic factors C2S from CRC: PLB 646(’07) (dσ/dΩ)theo % (dσ/dΩ)exp The transferred angular momentum Lt indicates Jπ V. Lapoux IRFU/SPhN [email protected] November 17th 2011 Challenge: radioactive target (TREX at ISOLDE)
first experiment with a Tritium target and a radioactive heavy ion beam
Two neutron transfer reaction to 32 Mg
coexistence of spherical and deformed states
deformed 2p − 2h configuration becomes ground state in 32use
Mg
where is the excited
0+
state?
of Tritium loaded Titanium
0.5 mg/cm2 Ti foil
predictions for the 0+
state in 32 Mg: 3
2
atomic ratio H/Ti
between 1.5 and 3 MeV
≈ 1.5
corresponds to 40 µ g/cm2 Trit
E. Caurier et al., NPA 693 374, T. Otsuka, EPJA 20 69,
R. Rodriguez-Guzmán et al., NPA 709 201
activity 10 GBq
this state has not been observed so far
similar particle-hole structure:
populate the excited 0+ state by a two neutron transfer reaction
Problem:
large overlap of wavefunctions
Fusion
reactionsfactor
withforthe
carrier material Ti produce protons
large spectroscopic
transfer
→
Mg,p)32beam
Mg
→t(30lower
Kathrin Wimmer
Kathrin Wimmer
energy, below Fusion barrier
ECT* workshop, Trento
ECT* workshop, Trento
The excitation energy of the 0+
2 state
E. Caurier et al., NPA 693 374, T. Otsuka, EPJA 20 69, R. Rodriguez-Guzmán et al., NPA 709 201
0+
2 state lower than predicted
long lifetime several ns
similar cross sections
simple picture
ground state 2p − 2h
excited state 0p − 0h
Kathrin Wimmer
ECT* workshop, Trento
Ground state configuration
Ground state:
two particle - two hole configuration
simple assumption: neutron pair in 1f7/2
Occupation numbers for the ground state
within the Monte Carlo SM
SDPF-M effective interaction
T. Otsuka et al., Prog. Part. Nucl. Phys. 47 319
J. R. Terry et al., Phys. Rev. C 77 014316
simple assumption (1f7/2 )2 amplitude
can not reproduce the data
Kathrin Wimmer
ECT* workshop, Trento
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