INTERNATIONAL SEMINAR
ISINNISINN-- 2017 2017
Dubna, Russia, May 22 – 26, 2017
STUDY OF nn-INTERACTION IN nd- AND dd-REACTIONS
E.Konobeevski1, A.Kasparov1, V.Lebedev2, M.Mordovskoy1, A.Spassky2, S.Zuyev1
1Institute for Nuclear Research, Russian Academy of Sciences 2Skobeltsyn Institute of Nuclear Physics, Moscow State University
2
NNNN--InteractionInteraction
pp and np Interaction
A huge amount of data on pp and np interactions has been accumulated. Careful analysis of these data led to constructing NN interaction potentials describing vast majority of experimental data.
nn Interaction
The situation around neutron–neutron interaction is more ambiguous. Because of the absence of neutron target, data on this interaction are obtained primarily from reactions with two neutrons in the final state. But in many cases, there are serious discrepancies between available experimental data and the results of the current precise calculations on the basis of Faddeev equations.
3
Unresolved Problems in Unresolved Problems in NdNd--breakupbreakup
nd- and pd-breakup in SS-configuration nn-quasifree scattering
Experimental CS for nn-QFS exceed theoretical estimates by about 18%. At the same time, the theory describes well the CS obtained for np QFS
Experimental CS for pd- and nd- breakup differ greatly while the theoretical CS are almost identical
and do not agree with the experimental data
The analysis performed by several authors showed that theoretical results remain quite stable using different standard NN-potentials and
introducing modern three-nucleon forces
4
ProtonProton--protonproton scatteringscattering lengthlength isis determineddetermined fromfrom thethe pppp--
scatteringscattering ((aapppp==--1717..33±±00..44 fmfm));; itsits accuracyaccuracy isis mainlymainly connectedconnected
withwith modelmodel--dependentdependent correctionscorrections ofof CoulombCoulomb effectseffects
NeutronNeutron -- neutronneutron scatteringscattering lengthlength isis determineddetermined usingusing mostlymostly
n+dn+dp+n+np+n+n andand --++dd ++nn++nn reactionsreactions andand investigatinginvestigating thethe regionregion ofof
thethe nn--nn FSIFSI wherewhere twotwo neutronsneutrons flyfly togethertogether withwith smallsmall relativerelative energyenergy
The results obtained by now testify significant uncertainty of The results obtained by now testify significant uncertainty of aannnn
values which are clustered near values which are clustered near --16.316.3±±0.40.4 (Bonn) and (Bonn) and --18.518.5±±0.40.4
fmfm (TUNL, LAMPF), so there is even uncertainty about the sign of (TUNL, LAMPF), so there is even uncertainty about the sign of
the difference the difference aannnn--aapppp which is a measure of CSBwhich is a measure of CSB
Data on protonData on proton--proton and neutronproton and neutron--neutron neutron
scattering lengthsscattering lengths
5
33He(ppn) and He(ppn) and 33H(nnp) Systems H(nnp) Systems
Two protons in 3He are mainly in
opposite spin states
Two neutrons in 3H are also in a spin-
singlet state
Strong discrepancies observed in Nd-breakup can be
explained by a significant strengthening of nn- and pp-
correlations of attractive character in the third nucleon field.
n
p p 3He p
n n 3H
Dibaryon Model (Kukulin et al)Dibaryon Model (Kukulin et al)
New mechanism arising in the Dibaryon Model: New force – meson exchange
between the nucleon and dibaryon
In these reactions nn-correlated pair can be produced dynamically in the
intermediate state. Thus, measured nn-correlation, in particular energy of nn virtual
singlet state, may be different from those inherent for the free NN-systems.
Our plans: study of nd→p+nn, nt →d+nn and dd→pp+nn and ….
Nd or t (3He) dd → D + D → n+n+p+p
7
Determination of Determination of
nnnn--VirtualVirtual--State Energy State Energy
and Scattering Length and Scattering Length
in in n n ++ 22HH n n ++ n n ++ p p ReactionReaction
8
ndnd Breakup ReactionBreakup Reaction
Setup for Determination Setup for Determination nnnn--Scattering Length Scattering Length
Neutron beam is produced in the beam stop of INR proton accelerator
A CD2 disk (~ 100 mg cm–2) is used as the scattering target.
Registration in coincidence of one proton and two neutrons
Protons are detected by a plastic detector located at 75°6°
Neutrons are detected by a six-detector hodoscope at 30°-42°
Energies of secondary neutrons are determined by a TOF technique
Incident neutron energy and p are reconstructed from kinematics
FSI
ε=(En1+En2–2(En1En2)1/2cosΔΘ)/2
nnEd
dNWM
0
200
400
600
800
1000
1200
0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2
Experimental and simulated dependences N(Experimental and simulated dependences N() for various ) for various
values of values of EEnnnn ; ; == 6º, E6º, E0 0 = 40 = 40 ±± 5 MeV5 MeV
N, events
0
200
400
600
800
1000
1200
0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2
, MeV
The best fit is obtained for Enn = 129 ± 14 keV.
Enn = 170 keV Enn = 130 keV
Enn = 80 keV
...
2
112
2/1
2
nnn
nnnnn
nn
Emr
Em
a
10
Determination of Determination of EEnnnn from from 22 versus versus EEnnnn curve curve = 6º; E= 6º; E0 0 = 40 = 40 ±± 5 MeV5 MeV
2 value for experimental and theoretical points is given by the expression
where A is the normalization coefficient, determined as the ratio of the integrals of
the experimental and theoretical spectra over a wide range of (0–0.8 MeV),
and
is the statistical error of experimental points.
2
2
2
)(
)()(
)(
d
dN
d
dNA
d
dN
aэксп
модэксп
nn
d
dN эксп )(
2
Enn
Enn = 129 ± 14 keV ann = -16.6 ± 0.9 fm
The values of 2(Enn) are approximated by a quadratic polynomial.
The minimum of the curve determines Enn.
Statistical uncertainty Enn is given as
2min+1
Enn
2
11
Determination of Determination of
nnnn--VirtualVirtual--State Energy State Energy
and Scattering Length and Scattering Length
in in dd + + 22H H ((nnnn))SS + (+ (pppp))SS nn++nn++pp++pp
ReactionReaction
Simulation of Simulation of dd + + 22H H → → 22nnss + + 22ppss Reaction; Reaction;
EEd d = 15 MeV= 15 MeV
Output parameters: Θp1=Θp2=27°; Θn=36° (red areas)
Corresponding energies: E(2p)~6 MeV; E(2n)~4 MeV
Simulation of Simulation of dd + + 22HH→→n n ++ n n + + p p + + pp Reaction: Reaction:
EEd d = 15 MeV, = 15 MeV, p1 p1 = 27º, = 27º, p2 p2 = 27º, = 27º, n1 n1 = 36º = 36º
En1 vs En2 Enn Spectrum
Enn= [E1 + E2 – 2(E1 × E2)1/2 × CosΔΘ] / 2
For democratic breakup two neutrons can have
a relative energy in the range 0 - 1.8 MeV
14
Simulation of Simulation of dd + + 22H H →→ n n ++ n n + + p p + + pp Reaction:Reaction:
En1 vs En2 Enn Spectrum
Democratic
breakup
Democratic
breakup
Enn = 120 keV,
nn = 50 keV Enn = 120 keV,
nn = 50 keV
This structure in spectrum is due to the fact that to reach detector, installed at angle of emitting nn-system in
two-body reaction, may only breakup particles emitted in c.m. system in forward or in backward direction
15
Simulation of Simulation of dd + + 22H H →→ n n ++ n n + + p p + + pp Reaction:Reaction:
Different Energies of Singlet StateDifferent Energies of Singlet State
Enn = 50 keV,
nn = 30 keV
Enn = 200 keV,
nn = 100 keV
Enn = 120 keV,
nn = 70 keV
The distance between peaks depends on the excitation energy (excess mass of two-nucleon system over the sum of masses of its constituents)
16
Simulation of Simulation of dd + + 22H H →→ n n ++ n n + + p p + + pp Reaction:Reaction:
Different Widths of Singlet State; Different Widths of Singlet State; EEnnnn = 120 keV= 120 keV
nn = 20 keV
nn = 110 keV
nn = 70 keV
The shape of time spectra is sensitive to values of the state energy and width, that will allow us to
determine these quantities from a comparison of experimental data and simulation results
One can see that the change of the state width affects mainly on degradation of "valley" between the
peaks and on a slight shift of the peak with larger time to the middle of distribution.
Experimental: Experimental: Setup for StudySetup for Study
d d ++22H → H → p+p+n+np+p+n+n Reaction @ EReaction @ Ed d = 15 MeV= 15 MeV
Conditions: 15 MeV deuteron beam of U120 cyclotron of SINP MSU
CD2-target
p- and n-detectors are set at angles of 2p and 2n emitting
both protons are detected in one E-E telescope
n-detector at 83° was used for timing calibration in dd → 3He+n reaction
18
Experimental Experimental EE--E Plot and Simulated Plot E Plot and Simulated Plot
for Twofor Two--Proton Events Proton Events
Selecting events on p+p region and determining the neutron time of flight for these events we obtained neutron timing spectrum
19
Experimental: Experimental: Neutron TimeNeutron Time--ofof--flight Spectrumflight Spectrum
events
ns
vsvs SimulatedSimulated
20
22--Fitting on Fitting on nnnn for Different for Different EEnnnn
t
th
E
nnnn
tN
tANtNE nnnn
2exp
2exp
,2
)(
)()(),(
21
Dependence of 2 on Einn.
22--Fitting over Fitting over EEnnnn
To determine Enn the dependence of minimum value on Еnn was fitted by a quadratic
polynomial. The minimum value of 2 determines the most probable value of the
quasibound state energy.
Error in determining Enn is given as
The minimum value of the polynomial is achieved at Enn = 76 keV, Enn = ± 6 keV
)1()( 2
min
2
min nnnnnn EEE
Enn= 76 ± 6 keV ann= -22.2 ± 0.6 fm
Analysis of Analysis of aannnn
data obtained in data obtained in ndnd-- and and dddd--breakupbreakup
15
17
19
21
23
25
27
29
1 3 5 7 9
R (fm)
-an
n (
fm)
ann=(15.5+/- 0.13) + 34.3/r^1,9
Xi2/N=5.2
15
17
19
21
23
25
27
29
1 3 5 7 9
R (fm)
-an
n (
fm)
15
17
19
21
23
25
27
29
1998 2003 2008 2013 2018
Year
-an
n (
fm)
...
2
112
2/1
2
nnn
nnnnn
nn
Emr
Em
a
43
11431 ))((
MM
MEMMQEсR
For each experiment we introduced parameter R which corresponds to distance between nn pair and proton (or diproton in dd experiment) for arbitrary time interval
• The neutron-neutron 1S0 scattering length ann has been determined from a kinematically complete nd breakup experiment at En = 40 MeV.
• The values of ann = −16.6 ± 0.9 fm and Enn = 129 ± 14 keV were obtained performing the shape analysis of the FSI dependence of reaction yield on relative energy of nn pair.
For the first time, in d+2H → 2nS + 2pS → n+n+p+p reaction the energy of virtual state of 2n-system and nn-scattering length were determined - Enn = 76 ± 6 keV; ann = -22.2 ± 0.6 fm.
The obtained values of scattering lengths were compared with experimental values of 1S0 nn-scattering length obtained in nd-breakup reaction.
One can conclude that the difference in the scattering lengths obtained under different kinematic conditions can be explained by the influence of 3N-forces depending on the relative velocity between the nn-pair and the charged fragment.
ConclusionsConclusions
24
22DD--Plot EPlot E--EEfastfast E f
ast
Experimental 2DExperimental 2D--plotplot ∆∆EE--EE
dE
E
d
p p
p? d? p? d?
Summary Summary
We investigated d+2H→ 2nS + 2pS→n+n+p+p reaction, passing through a
formation in the intermediate state of dineutron and diproton singlet pairs.
For the first time, in a kinematically complete experiment the energy virtual
state of 2n-system is determined.
The energy of the state is determined by comparing the experimental TOF
spectrum of neutrons from breakup of this state with simulated spectra
depending on this energy.
The obtained value Enn = 76 ± 6 keV was compared with experimental values
of 1So nn-scattering length obtained in nd-breakup reaction.
One can conclude that the difference in the scattering lengths obtained under
different kinematic conditions can be explained by the influence of 3N-forces
depending on the relative velocity between the nn-pair and the charged
fragment.
Experimental 2DExperimental 2D--plot Eplot E--EfEf (400 μm)
1-2 – полное поглощение, 2-3 - пролет E f
ast
1
2
3 p,d
p
d
Experimental 2DExperimental 2D--plot Eplot E--EfEf (400 μm)
1-2 – полное поглощение, 2-3 - пролет E f
ast
2
3
∆E∆E--E: E: пролетный локуспролетный локус (2(2--3)3)
dE
E
Experimental 2DExperimental 2D--plot Eplot E--EfEf (400 μm)
1-2 – полное поглощение, 2-3 - пролет E f
ast
1
2
p,d
p
d
dEdE--E: E: полное поглощениеполное поглощение (1(1--2)2)
dE
p
d
E
PSD: nPSD: n--γγ разделениеразделение (EJ(EJ--301)301)
PSD
n
E
PSDPSD -- SpectrumSpectrum
PSD
N
n
Предварительные результаты по эксперименту
dpppn
• Проведено моделирование реакции dpppn
• Отлажена детектирующая система (∆E-E и n-детекторы)
• Отлажена методика выделения p+n событий
• Начат набор статистики
36
Experimental Spectrum vs SimulatedExperimental Spectrum vs Simulated
Analysis: Fitting ProcedureAnalysis: Fitting Procedure
38
Simulation of Simulation of dd + + 22HH→→n n ++ n n + + p p + + pp Reaction:Reaction:
Democratic vs Quasibound stateDemocratic vs Quasibound state
Simulated time-of-flight spectra of neutrons: 1 – for events of democratic
breakup, 2 – for events with Enn = 120 keV, nn = 50 keV. Neutron time-
of-flight base 0.79 м.
Democratic
breakup
Enn = 120 keV,
nn = 50 keV
Space Star (SS) Anomaly
• SS Anomaly was first found in 1989 in nd breakup reaction at 13 MeV.
31 August 2009 19th International IUPAP Conference on Few-Body Problems in Physics 45
Space Star
(c.m. system)
equilateral triangle
90°
nd exp.
Erlangen & TUNL
(●) (○)
nd calc.
Space Star
(1989) (1996)
J.STRATE et al., Nucl. Phys. A501 (1989) 51
H.R.Setze et al., Physics Letters B388 (1996) 229
G.RAUPRICH et al., Nucl. Phys. A535 (1991) 313
pd exp.
Koeln (1991)
EN=13 MeV
~30%
• In Star configuration, outgoing 3 nucleons have the same energy and form an equilateral triangle.
• In Space Star (SS), the star plane is perpendicular to the beam axis in c.m. system.
46
The The SearchSearch for for NNNN--Correlations in 3Correlations in 3NN--Systems Systems
In 3He neutron causes a correlation of
two protons leading to an appearance
of quasibound 1S0 diproton state
n
p p 3He
p
n n 3H
Removal of proton from 3H and/or neutron from 3He provide conditions advantageous for NN-correlations to
search
n
p p p p 2He
n n
p
2n
In 3H proton causes a correlation of two
neutrons leading to an appearance of
quasibound 1S0 dineutron state
Space Star (SS) Anomaly in pd breakup
• pd calc. were made by Deltuva et al. and by Ishikawa.
47
nd calc.
pd calc. by Deltuva et al. (2005)
pd exp.
Koeln(□)& KUTL(■)
(2002)
EN=13 MeV nd exp.
Erlangen & TUNL
(●) (○)
nd calc.
Space Star
(1989) (1996)
pd exp.
Koeln (1991)
EN=13 MeV
~30%
~15%
• At pd SS, exp. cross section is smaller than pd calc.
• At nd SS, exp. cross section is larger than nd calc.
A.Deltuva et al., PRC72,054004 (2005)
J.STRATE et al., Nucl. Phys. A501 (1989) 51
H.R.Setze et al., Physics Letters B388 (1996) 229
G.RAUPRICH et al., Nucl. Phys. A535 (1991) 313
Our Preliminary Results of d+D→Our Preliminary Results of d+D→22He+2n He+2n
Neutron TOF Spectrum @ TOF Base 1 mNeutron TOF Spectrum @ TOF Base 1 m
Tn Spectrum
N
t, ns
Experiment: 2He=27°; n=36°
Tn Spectrum
N Experiment: 2He=27°; n=36°
Simulation: Enn = 80 keV
t, ns
49
The Search for NNThe Search for NN--CorrelationsCorrelations
Результаты кинематического моделирования реакции
d + 2H→ 2ns + 2ps − двумерные диаграммы 2n-2p (a) и E2n-E2p (б),
где 2n и 2p – углы вылета, а E2n и E2p – энергии двухнейтронной и
двухпротонной систем. Красные области соответствуют вылету
системы 2ps под углом 27° ± 1.5°
50
ndnd--breakup configurations and unresolved breakup configurations and unresolved
problemsproblems
51
Modification of Modification of 11SS00 nn forcenn force
Vnn(1S0) = λ×VCDBonn(1S0)
H. Witala & W. Gloeckle suggested
H. Witala & W. Gloeckle, Phys.
Rev. C83, 034004 (2011)
=1.08
X.C.Ruan et al., Phys. Rev. C 75, 057001 (2007)
nn QFS @ 25MeV
No arguments for this modification
-40
-30
-20
-10
0
10
20
30
-50 -30 -10 10 30 50
E1-3
Kinematical curves for FSI geometry in Kinematical curves for FSI geometry in ndnd--breakupbreakup
EE00 == 4040 5 MeV, 5 MeV, nn11 = = --3636ºº , , pp = = 7575ºº
INR RAS 2012
1-neutron 3-neutron 1-neutron, 2-proton
FSI
E13=ε= (E1 + E2 – 2(E1E2)1/2cosΔΘ)/2
0, 1 ≈ 2
dSdd
d
31
3N Faddeev equation WM-approximation
0
WM
d
dN
0
5
10
15
0 5 10 15 20 25 30
E2
E1
0
5
10
15
20
25
30
35
40
0 5 10 15 20 25 30 E1
E3
-40
-30
-20
-10
0
10
20
30
-50 -30 -10 10 30 503
E1-3
FSI
0
5
10
15
20
25
30
35
40
0 5 10 15 20 25 30 E1
E3
FSI 0
5
10
15
0 5 10 15 20 25 30 E1
E2
S
nnnn-- и и pp pp --длины рассеяниядлины рассеяния
15
17
19
21
23
25
27
29
1998 2003 2008 2013 2018
Year
-an
n (
fm)
54
Charge Independence and Charge Symmetry of Nuclear Charge Independence and Charge Symmetry of Nuclear
ForcesForces
pp and np Interaction
A huge amount of data on pp and np interactions has been accumulated. Careful analysis of these data led to constructing NN interaction potentials describing vast majority of experimental data.
nn Interaction
The situation around neutron–neutron interaction is more ambiguous. Because of the absence of neutron target, data on this interaction are obtained primarily from reactions with two neutrons in the final state. But in many cases, there are serious discrepancies between available experimental data and the results of the current precise calculations on the basis of Faddeev equations.