bethe-salpeter approach and lepton-, hadron- deuteron scattering v.v.burov s.g.bondarenko,...
TRANSCRIPT
Bethe-Salpeter approach and lepton-, hadron-deuteron scattering
V.V.BurovS.G.Bondarenko, E.P.Rogochaya, M.V.Rzjanin, G.I Smirnov– JINR, Dubna
A.A.Goy, V.N.Dostovalov, K.Yu.Kazakov, A.V.Molochkov, D.Shulga, S.E.Suskov – FESU, Vladivostok, Russia
S.M.Dorkin- Dubna Univ., A.V.Shebeko – Kharkov, M.Beyer – RU, Rostock, W.-Y Pauchy Hwang – NTU Taipei, Taiwan,
N.Hamamoto, A.Hosaka, Y.Manabe, H.Toki –RCNP, Osaka, Japan
1. Introduction2. Basic Definitions.3. Separable Interactions 4. Summary
Introduction Study of static and dynamic electromagnetic properties of light
nuclei enables us to understand more deeply a nature of strong interactions and, in particular, the nucleon - nucleon interaction.
Urgency of such researches is connected to a large amount of experimental data, and also with planned new experiments, which will allow to move in region of the large transfer momenta in elastic, inelastic, and deep-inelastic lepton - nucleus reactions.
At such energies an assumptions of nucleus as a nucleon system is not well justified. For this reason the problems to study in intermediate energy region the nonnucleonic degrees of freedom (Δ-isobars, quarks etc.) and Mesonic Exchange Currents (MEC) are widely discussed.
20/09/2012
Introduction However, in spite of the significant progress being
achieved in this way, the relativistic effects (which a priori are very important at large transfer momenta) are needed to be included.
Other actively discussed problem is the extraction of the information about the structure bound nucleons from experiments with light nuclei . Such tasks require to take into account relativistic kinematics of reaction and dynamics of NN interaction. For this reason const-ruction of covariant approach and detailed analysis of relativistic effects in electromagnetic reactions with light nuclei are very important and interesting.
Bethe - Salpeter approach give a possibility to take into account relativistic effects in a consistent way.
20/09/2012
Bethe –Salpeter Formalism Let us define full two particle Green Function:
Bethe –Salpeter Equation for G:
where
, ; , 1 2 1 2 1 2 1 2G , ; , 0 0 ,x x y y T x x y y
, ; ,, ; , 1 2 1 2 1 2 1 2
4
, ; , 1 2 1 21
, ; , 1 2 3 4 , ; , 3
0
4
0
1 2
, ; , , ; ,
, ; ,
, ; , , ; ,
G
G
G
G ,
kk
K
x x y y x x y y
i dw x x w w
w w w w w w y y
1 2, ; , 1 2 1 2 1 2 2
01, ;G , ,F Fx x y y S x x S y y
20/09/2012
Let us make Fourier transformation of :
where is total, are relative 4-momentum
The expressions for and are similar.
0, ,K G G
1 2 1 2 1 2 1 2
1 2 1 21 2 1 2
, ; , ; ,
exp ,2 2
p p P dx dx dy dy x x y y
x x y yiP ip x x ip y y
V K
p pP
1 2 1
1 2 2
2
/ 2 2
P q q q P p
p q q q P p
G
1q
2q
1q
2q
p p
0G
20/09/2012
Full Green function for two particle system is:
The full one particle Green function is:
1 2 4;
1 2; ;4
, ;2 2
, ; , ; .2 2
G
G2
F F
F F
P Pp p P S p S p p p
P P dkiS p S p p k P k p PV
1 1
.0FS p
p pm i
We will use propagators without mass operator:
FS p S p
Mass operator
20/09/2012
T-matrix
0GV TGLet us introduce T-matrix:
; ; ;4
1 2;
, ; , ; , ;2
, ; .2 2
dkp p P p p P i p k P
P PS k
T
T
V
S k
V
k p P
The BSE for T-matrix is:
20/09/2012
Thus a bound state corresponds to a pole in a
T-matrix at (M is the mass of the bound state):
2 2P M
2 2; ;, ; , ,, ,
;p p P R p pP p p
P MT
PP
; , ;R p p P is regular at 2 2P M function,
,P p is a vertex function.
20/09/2012
Vertex function of BSE Let us write the vertex function of BSE:
One can express it by the BS Amplitude:
1 21 2 1 2
1 2
, exp2
0 ,
x xP p dx dx iP ip x x
T x x D P
denotes a state of the deuteron with total momenta
,D P .P
1 2, , .2 2
P PP p S p S p P p
20/09/2012
We can obtain the vertex function of BSE using that T- matrix
for bound state has pole at :2 2P M
;4
1 2
, , ;2
, .2 2
dkP p i p k P
P PS k S k k
V
P
BSE for vertex function , .P p
,P p ,P k
20/09/2012
The normalization condition follows from: , 0 , 2D P J D P iP
2 2
1 2
42 , , .2 22 P M
dk P PP i P k S k S k P k
P
BS equation for Amplitude:
1 2
;4, , ; , .2 2 2
P P dkP p iS p S p p k P PV k
1. E.E. Salpeter and H.A.Bethe, Phys.Rev. C84(1951) 12322. S. Mandelstam, Proc.Roy.Soc. 233A (1955) 248.3. S.Bondarenko et.al, Prog.Part.Nucl.Phys. 48(2002)449;4. S.Bondarenko et.al, NP, A832(2010)233; NP, A848
(2010) 75; NP, B219-220c (2011) 216; FBS, 49 (2011) 121; PLB, 705(2011)264; JETP Letters, 94(2011)800.
20/09/2012
Solution of BS Equation Separable Kernel of Interaction
– BSE for T-matrix after partial expansion can be written as:
– Separable anzats:
20 0 0 0 02
0 0 0 0 0
, , , ; , , , ;2
, , , ; , ; , , , ; .
ip p p p s p p p p s dq q d q
p p q q s
T
TS q q s q q p
V
p sV
0 0 0 01
, , , ; , , ,N
ij i j ij jiij
V p p p p s g p p g p p
20/09/2012
Then for T – matrix we can write:
00 01
0, ,; .,, ,N
ij i jij
s g p pp p pp s gpT p
Substitution V , T in BSE for T–matrix we can find : ij s 1 1 ,ijij ijs H s
where the can be written as: ijH s
2 0 02
0 0 , ; .2
, ,ij i j
idq q d q S q q s g q q gH s q q
Then radial part of BSA has following form:
00 0, ; ,, ,iij jg cpp p s spp S p
N
i,j=1
where coefficients satisfy the equation: jc s
, 1
0.N
i ik kj jk j
c s H s c s
20/09/2012
NN-scattering Let us consider NN-scattering in -channel ( -
notation). In this case nucleons are on mass shell:
and T-matrix can be parameterized as:
Here are phase shifts of waves, - is
mixing parameter. For low energy NN – scattering we can express phase shift through scattering length a, effective radius of interaction :
3 31 1S D 2 1S
JL
* 20 0 0, / 4 / 2,labp p p p p s m m
= = E
20
* 2
cos 2 1 sin 22.
sin 2 cos 2 1
S DS
S D D
iis
i i
e i eiT
p s i e e
S D
2 3* * *01cot .
2S
rp s p O p
a
3 31 1S D
0r
20/09/2012
Covariant Graz-II kernel of interaction As a starting point we will use for channels: 3 3
1 1S D
221 0
1 0 222 20 11
220
2 0 222 20 12
2 22 20 2 0
3 0 22 22 2 2 20 21 0 22
1 0 2 0 3 0
1, ,
, ,
1, ,
, , , 0
S
S
D
D D S
p pg p p
p p
p pg p p
p p
p p p pg p p
p p p p
g p p g p p g p p
20/09/2012
Solution of BSE The solution of BSE with separable potential can be written as:
Properties of the deuteron and low energy NN-scattering .
31
31
2 3
1 1
3
1
0 0
0 03 3
, ,
, ,
;
;
Sij ij
i
j
S
jD
D
j
j
g p p g p p
g p
c
p g p
s
c s p
%
NR 4 2.225 0.2499 0.8565 0.0241 1.786 5.419
RIA 4.82 2.225 0.2812 0.8522 0.0274 1.78 5.420
Exp. 2.2246
0.286 0.8574 0.0263 1.759 5.424
Dp
31S
D2D MeVDQ
2fm / 2e m fm fmD /D S 0r a
20/09/2012
Vertex function 31
0 4 , .S
g p p p p
± 1± 0.6
± 0.2 0 0.2 0.4 0.6 0.8 1p4 (G eV )
00.2
0.40.6
0.81
p (G eV )
0
0.2
0.4
0.6
0.8
1
20/09/2012
Vertex function 31
0 4 , .D
g p p p p
± 2± 1
01
2
p 4 ( G e V )
0 0 . 2 0 . 4 0 . 6 0 . 8 1 1 . 2 1 . 4 1 . 6 1 . 8 2
p ( G e V )
0
0 . 0 5
0 . 1
0 . 1 5
0 . 2
0 . 2 5
0 . 3
20/09/2012
19
Relativistic description
220
22 pp pp
Ps
pPpQ
22
1|)(|
ppgYamaguchi
0
11)(
2220
22 ipg
massofcenter
p
ppp
2222
11)(
pg
massofcenter
QpQ
0220 ipg p p
Qg No poles
422220 )(
1)(
pg p p
p
Y. Avishai, T. Mizutani, Nucl. Phys. A 338 (1980) 377-412
K. Schwarz, J. Frohlich, H.F.K. Zingl, L. Streit, Acta Phys. Austr. 53 (1981) 191-202
20/09/2012
EMIN-2012 20
At 0:1) Poles do not cross the counter2) Good limit
ip Esp 2/)2,1(0
222)4,3(0 ip p
222)6,5(0 ip p
R.E. Cutkosky, P.V. Landshoff, D.I. Olive, J.C. Polkinghorne, Nucl. Phys. B 12 (1969) 281-30020/09/2012
EMIN-2012 21
Form factors of the separable kernel
41
221
220
220][
1 )()(
p
pg
p
ppP
The uncoupled channels
242
222
220
2202
3220][
2 ))((
)()()(
p
pppg c
p
pppP
3P0,1P1,3P
1:
1S0
:
41
221
220
2201][
1 )(
)()(
p
pg c
p
pppS
242
222
220
22202
220][
2 ))((
))(()(
p
ppg c
p
ppppS
43
223
220
220][
3 )(
)()(
p
pg
p
ppS
20/09/2012
EMIN-2012 22
The coupled channel 3S1-3D1
41
221
220
2201][
1 )(
)()(
p
pg c
p
pppS
242
222
220
22202
220][
2 ))((
))(()(
p
ppg c
p
ppppS
)))(()((
))(()(
432
2232
220
431
2231
220
22203
220][
3
pp
ppg c
pp
ppppD
44
224
220
220][
4 )(
)()(
p
pg
p
ppD
0)()()()( ][2
][1
][4
][3 pppp DDSS gggg
)()(
)()()(
][2244233222111
][1144133122111
13
pcccc
pccccp
S
S
g
ggS
)()(
)()()(
][4444343242141
][3344333232131
13
pcccc
pccccp
D
D
g
ggD
The vertex functions of the deuteron
220
2
20
04 ))02((
|)]|,()[2(||
)2(2 kEM
kMEddk
Mp 2
i
kgkk
i
kd
ldk
dl
The normalization
20/09/2012
EMIN-2012 23
1P1+,3P1
+
consts ijij )(
1S0+,3P
0+
ijij )()( 0 sss
3S1+-
3D1+:
20
)(ms
s
ijij
0|)(|det 1
dij Ms
The calculation scheme
20/09/2012
EMIN-2012 24
Р-waves:
n
i 1
2exp2exp2 ))(())()(( iii sss
1S0+: 2exp2exp
1
2exp2exp2 )()())(())()(( aaasss iii
n
i
3S1+-3D1
+:
2exp2exp2expexp
1
2exp2exp2exp2exp2
)()())(())()((
))(())()(())(())()((
aaasss
ssssss
iii
iDiDiDiSiSiS
n
i
The Minimization procedure
20/09/2012
EMIN-2012 25
as (fm) r0s (fm)
MY3 -23.750 2.70
MYQ3 -23.754 2.78
Experiment -23.748(10) 2.75(5)
pd(%) at(fm) r0t(fm) Ed(MeV)
MY4 6 5.417 1.75 2.2246
MYQ4 6 5.417 1.75 2.2246
CD-Bonn 4.85 5.4196 1.751 2.224575
Graz II 4.82 5.42 1.78 2.225
Experiment - 5.424(4) 1.759(5) 2.224644(46)
1S0+
:
3S1+-
3D1+:
O. Dumbrajs et al., Nucl Phys. B 216 (1983) 277
20/09/2012
EMIN-2012 26
Inelasticity!
20/09/2012
EMIN-2012 2720/09/2012
EMIN-2012 2820/09/2012
EMIN-2012 29
SAID (http://gwdac.phys.gwu.edu)CD-Bonn: R. Machleidt, Phys. Rev. C 63 (2001)
024001SP07: R.A. Arndt et al., Phys. Rev. C 76 (2007)
025209
20/09/2012
EMIN-2012 3020/09/2012
EMIN-2012 31
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
20
40
60
TL ab
(G eV )
-60
-40
-20
0
20 M Y 2S P 07M Y I2
(1P
1+)
(deg
)(1
P1
+)
(deg
)
20/09/2012
EMIN-2012 3220/09/2012
EMIN-2012 3320/09/2012
EMIN-2012 34
0.0 0.5 1.0 1.5 2.0 2.5 3.00
20
40
60
80
TL ab
(G eV )
-60
-40
-20
0 M Y 2S P 07M Y I2
(3P
0+)
(deg
)(3
P0
+)
(deg
)
20/09/2012
EMIN-2012 35
0 1 2 3
0.0
0.2
0.4
0.6
0.8(
MY
I2)2
-(
exp
)2
TL ab
(G eV )
B re it-W ig n er R es o n an c e fit
TL a b ,1
=0.872 G eV , M *1=2.27 G eV ,
1=0.199 G eV ;
TL a b ,2
=1.595 G eV , M *2=2.55 G eV ,
2=1.335 G eV ;
F u ll f it
20/09/2012
EMIN-2012 3620/09/2012
EMIN-2012 3720/09/2012
EMIN-2012 38
0.0 0.5 1.0 1.5 2.0 2.5 3.00
20
40
60
80
TL ab
(G eV )
-80
-60
-40
-20
0M Y 2S P 07M Y I2
(3P
1+)
(deg
)(3
P1
+)
(deg
)
20/09/2012
EMIN-2012 39
Graz II: L. Mathelitsch, W. Plessas, M. Schweiger, Phys. Rev. C 26 (1982) 65
20/09/2012
EMIN-2012 4020/09/2012
EMIN-2012 41
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
20
40
60
TL ab
(G eV )
-80
-40
0
40 M Y 6S P 07M Y I6
(1S
0+)
(deg
)(1
S0
+)
(deg
)
20/09/2012
EMIN-2012 4220/09/2012
EMIN-2012 4320/09/2012
EMIN-2012 4420/09/2012
EMIN-2012 45
20/09/2012
EMIN-2012 46
0 1 2 3
0
20
40
60
80
TL ab
(G eV )
-120-80-40
04080
120
M Y 6S P 07M Y I6-n ewS P 00,F G A
(3S
1+)
(deg
)(3
S1
+)
(deg
)
20/09/2012
EMIN-2012 47
0 1 2 3-80
-60
-40
-20
0
TL ab
(G eV )
-80-60-40-20
02040
M Y 6S P 07M Y I6-n ewS P 00,F G A(3
D1+
)(d
eg)
(3D
1
+)
(deg
)
20/09/2012
EMIN-2012 48
Deuteron “Wave function”
0.0 0.5 1.0 1.5 2.0 2.5 3.010 -3
10 -2
10 -1
10 0
10 1
10 2
|
S|(
GeV
-3/2
)
p (G eV /c )
M Y Q 6 M Y 6 G raz II (N R ) G raz II P a r is
20/09/2012
EMIN-2012 49
Deuteron “Wave function”
0.0 0.5 1.0 1.5 2.0 2.5 3.010 -3
10 -2
10 -1
10 0
|
D|(
GeV
-3/2
)
p (G eV /c )
M Y Q 6 M Y 6 G raz II (N R ) G raz II P a r is
20/09/2012
EMIN-2012 50
Summary BS approach
– is full covariant descriptions of two body system;– allows to build the multirank covariant separable
potential MYN and MYIN of the neutron-proton interaction for coupled and uncoupled partial-waves states with the total angular momentum J=0,1,2 till the kinetic energy 3GeV.• The description of the phases and inelasticity parameter with
MYN and MYIN is very good.• Deuteron MYN wave functions are very close to
nonrelativistic one at small momenta less then 0.7 GeV/c.• Dibaryon resonances are proposed.
20/09/2012
EMIN-2012 51
Summary BS approach:
– can give very reasonable explanation structure functions, form factors and tensor polarization of deuteron in elastic eD-scattering;
– gives in one iteration approximation pair mesonic currents– gives foundations of light cone dynamics approaches;– gives good instrument to study polarization phenomena in
elastic, inelastic, deep-inelastic lepton deuteron scattering;– is a powerful tool for investigation of the reactions with the
deuteron (as well as reactions with the few-body systems).
20/09/2012
EMIN-2012 52
Plans To investigate the influence of the complex part of the
interaction kernel (namely, influence of the inelasticity parameter) to the exclusive cross section and polarization characteristics of the deuteron electrodisintegration for several kinematic conditions (Sacle, JLab).
To calculate the observables in the photo- and hadron-deuteron reactions.
20/09/2012
EMIN-2012 5320/09/2012
Evolution of Nucleon Structure in Nuclei Let us consider Deep Inelastic Scattering (DIS) leptons from
nuclei:
Cross section can be written as:
Lepton tensor has form:
Hadron tensor we write as:
l A l X
2
4.,,L k Wd
qk P p
1, .
2s s s s
ss
L k k u k u k u k u k
4 41, 2 .
2 nn
W P p P j n n j P P q p
EMIN-2012 5420/09/2012
Structure functions in DIS Hadron tensor can be related to amplitude for forward Compton
scattering T-matrix by means of the unitary relation:
Using Gauge invariance condition:
we can write ( =n q0 is the photon energy):
1, Im , .
2W P q T P q
, 0,q W P q
222
1 2 2 2 2
,, ,
W qq q P q P qW P q W q g P q P q
q M q q
EMIN-2012 5520/09/2012
In Bjorken limit
we can write the hadron tensor in following form:
Here are scale invariant structure functions (SF).
2 2
21 1
22 2
2
, ,
, ,
, ,
2
q Q
MW q F x
W q F x
qx
M
1 22 2 2
1,
q q P q P qW P q g F x P q P q F x
q P q q q
1 2,F x F x
EMIN-2012 5620/09/2012
Basic Approximations There are three basic groups of models for
explanation of the EMC effect by taking into account:– Nucleon separation energy, relativistic fermi-motion, NN-
correlations– Non-nucleon degrees of freedom;– The quark confinement radius changes.
Basic Approximations:– The one boson approximation in the bound state equation;– Treatment of the DIS amplitude as an incoherent sum of
amplitudes on individual constituents;– Representation of the hadron tensor of the bound nucleon in
the same form as for free nucleon
EMIN-2012 5720/09/2012
The first assumptions allows us to use BSE. The second assumptions allows to treat the squared amplitude of
DIS on the nucleus as the sum of the squared amplitudes for scattering on individual constituents.
The available experimental data for DIS on nuclei is mainly in the region x>10-3 and Q2>1GeV2, and shows that the ratio FA
2/FD2
is independent of Q2. In the calculations we shall restrict ourselves to the Bjorken limit, where the first and second approximations are well justified.
The third assumptions which allows the hadron tensor of a virtual nucleon to be represented through SF of free nucleon. But this representation is valid when the nontrivial differences between scattering on free and bound nucleon are small. There are three such differences or so called of shell effects: – Impossibility of using the condition of gauge invariance for the bound
nucleon; – The contribution of antinucleon degrees of freedom;– The unsynchronous of bound nucleons.
EMIN-2012 5820/09/2012
Nuclear Compton Amplitude Nuclear Compton amplitude can be written as:
where , relative time is:
Bethe-Salpeter vertex function is:
4, , 0 , ,A iqxT P q i d xe A P T j x j A P , ,2 1, 0 , , , ,A A
P PnA P T j x j A P dZdZ Z G Z x Z Z
1, 1,n nZ z z dZ dz dz ;
, 2 ,, , .A AP n PndZdZ S Z G Z Z Z
0 0.1
1 n
i j ij
z zn
EMIN-2012 5920/09/2012
The kernel of the integral BS equation is:
The kernel is the anzats of the theory:– One bozon exchange kernel:
– Separable form of the kernel:
– BS vertex in the momentum space is:
1 12 2, , , .n nnG Z Z S Z Z G Z Z
1 12
,
, , ;n m i m j i ji j m
G Z Z z z z z
2,
, .n ij i ji j
G Z Z g Z g Z
14 41 , 1, , .
n
j jj
i k xA
n P nnS P K P K dx dx e x x
EMIN-2012 6020/09/2012
The BS Amplitude of Compton scattering for deuteron
EMIN-2012 6120/09/2012
Structure functions of deuteron Using Mandelstam technique and neglecting
terms of order 1/Q2 and (MD – 2E)2 we arrive to expression for structure function of deuteron:
0 /2
3 23
3 232 2
2
0
2
2
2
2
3
2
2
2
22,
2
4
,
.,D
D
D
D
D ND N
NN
N
D
D
D
D D
ND
D
NN
E M
D
k
M E
M E
M
F M k
M k
x
E
M
E kd k m
M ME
xM
F x
dF
E k
M
x
M E
d
k
x
F x k
EMIN-2012 6220/09/2012
Normalization conditions The momentum sum rule is:
The baryon sum rule is:
0 0
3 2
3 3
2
2
0
2 ,22
,2
2
2
2
4
n
D D
D
DD
D
D
k
D
k
D
d k m E E
M ME
M E
M EM k
MM M
kE
M k
0 0
3 2
3 220
2 2 1.,2
,4 22 nDD k k
DD
D
DMd k m
M kE
M Ek
M M Ek M
EMIN-2012 6320/09/2012
Nonrelativistic limit Let us expand the enegry of the bound nucleon in power of p2/m2 :
where T=2E-2m is nucleon kinetic energy and e=M-2m is the binding energy, and analog of nonrelativistic function is:
The normalization condition has the form:
22
33
2 22
3 1,
22
N
NN
ND ND N
k dF xF x F x
dx
d k Txk k
m m
0 / 2
2
22 2
3.
4 2,
DD
E MD kD
k MME
kM E
m
3
32 1.
2
kk
d
EMIN-2012 64
EMC – effect (1983)Ratio structure functions Fe/D
20/09/2012
1.4
1.3
1.2
1.1
1.0
EMIN-2012 65
European Muon CollaborationData for the ratio of iron and deuterium structure functions are from the EMC [Aubert J.J. e.al. PL, 123B, 275(1983)]
( □ ) and from the SLAC [Arnold R.G. at al., PRL, 52,727(1984)] (•) experiments. Theory [Akulinichev et al.
Preprint INR P-0382(1984)]: the values V= -50Mev, PF= 270 Mev/c have been used in numerical calculations
20/09/2012
Wrong!!!
EMIN-2012 6620/09/2012
In Quasipotential (QP) approach with synchronous nucleons:
33
32 2
2 2
1.
22
NDD N
D ND
D
Tkd kx
m
dFk
xF x F x
dxm
Fermi motion
NRlimit
QP
EMIN-2012 6720/09/2012
56
2 2/Fe DF x F x 4
2 2/He DF x F x
EMC - effect
EMIN-2012 6820/09/2012
Ratio of SF’s in BS approach
EMIN-2012 6920/09/2012
EMIN-2012 7020/09/2012
Nuclear effects for the ratio of SF’s.Universal description for all A.
EMIN-2012 7120/09/2012
Summary BS approach:
– is full covariant descriptions of two body system;– allows to describe the properties of deuteron with separable
potential;– can give very reasonable explanation structure functions,
form factors and tensor polarization of deuteron in elastic eD-scattering;
– gives in one iteration approximation pair mesonic currents– gives foundations of light cone dynamics approaches;– gives good instrument to study polarization phenomena in
elastic, inelastic, deep-inelastic lepton deuteron scattering;
EMIN-2012 7220/09/2012
Summary BS approach:
– allows by the model-independently the SF of light nuclei to be calculated in terms of SF of nuclear fragments and three-dimensional momentum distribution;
– gives the good explanation of the behavior for SF’s ratios of the light nuclei to the SF of the free nucleon;
– indicates that the modification of the nucleon structure of lightest nuclei is a manifestation of unsynchronous behavior of bound nucleon;
– gives new understanding fundamental properties of nucleon, mainly its time deformation in relativistic bound system.