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.