About observation of the meson exchange current in inelastec electron scatteringon ⁴He nucleus
The problem of the experimental detection of meson exchange current contribution in inelastic electron scattering on ⁴He nucleus is examined. The upper limit of this contribution is finded for q = 0.75 - 1.50 fm⁻¹.
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irk-123456789-801052015-04-12T03:02:08Z About observation of the meson exchange current in inelastec electron scatteringon ⁴He nucleus Buki, A.Yu. Nuclear reactions The problem of the experimental detection of meson exchange current contribution in inelastic electron scattering on ⁴He nucleus is examined. The upper limit of this contribution is finded for q = 0.75 - 1.50 fm⁻¹. 2002 Article About observation of the meson exchange current in inelastec electron scatteringon ⁴He nucleus / A.Yu. Buki // Вопросы атомной науки и техники. — 2002. — № 2. — С. 19-21. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 21.30.+y; 25.30.Fj; 27.10.+h http://dspace.nbuv.gov.ua/handle/123456789/80105 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Nuclear reactions Nuclear reactions Buki, A.Yu. About observation of the meson exchange current in inelastec electron scatteringon ⁴He nucleus Вопросы атомной науки и техники |
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The problem of the experimental detection of meson exchange current contribution in inelastic electron scattering on ⁴He nucleus is examined. The upper limit of this contribution is finded for q = 0.75 - 1.50 fm⁻¹. |
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Article |
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Buki, A.Yu. |
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Buki, A.Yu. |
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Buki, A.Yu. |
| title |
About observation of the meson exchange current in inelastec electron scatteringon ⁴He nucleus |
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About observation of the meson exchange current in inelastec electron scatteringon ⁴He nucleus |
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About observation of the meson exchange current in inelastec electron scatteringon ⁴He nucleus |
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About observation of the meson exchange current in inelastec electron scatteringon ⁴He nucleus |
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About observation of the meson exchange current in inelastec electron scatteringon ⁴He nucleus |
| title_sort |
about observation of the meson exchange current in inelastec electron scatteringon ⁴he nucleus |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2002 |
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Nuclear reactions |
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http://dspace.nbuv.gov.ua/handle/123456789/80105 |
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About observation of the meson exchange current in inelastec electron scatteringon ⁴He nucleus / A.Yu. Buki // Вопросы атомной науки и техники. — 2002. — № 2. — С. 19-21. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT bukiayu aboutobservationofthemesonexchangecurrentininelastecelectronscatteringon4henucleus |
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2025-07-06T04:01:42Z |
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2025-07-06T04:01:42Z |
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1836868701758947328 |
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ABOUT OBSERVATION OF THE MESON EXCHANGE CURRENT IN IN-
ELASTEC ELECTRON SCATTERING ON 4He NUCLEUS
A.Yu. Buki
National Scientific Center “Kharkov Institute of Physics and Technology”
1 Akademicheskaya St., 61108 Kharkov, Ukraine
The problem of the experimental detection of meson exchange current contribution in inelastic electron scattering
on 4He nucleus is examined. The upper limit of this contribution is finded for q = 0.75 - 1.50 fm−1.
PACS: 21.30.+y; 25.30.Fj; 27.10.+h
1. INTRODUCTION
As it is known, the strong interaction of nucleons oc-
curs through the interchange of virtual mesons. The mo-
tion of these mesons is called the meson exchange cur-
rent (MEC). In the case of charged mesons their current
produces the magnetic field that accompanies the strong
interaction. So the magnetic field of MEC has to influ-
ence on the electromagnetic structure of the atomic nuc-
leus, that is the association of strongly interacting nucle-
ons.
The experimental investigation of MEC is complic-
ated by the fact that the assumed influence of these cur-
rents on the nuclear structure is not large relatively to
the nucleon charge interaction and strong interaction it-
self. So, the MEC contribution to the calculated form-
factor of the ground and the excited nuclear states is ∼1÷
10% and is summed up with a number of other contribu-
tions of such order. Therefore, even if such multicom-
ponent calculation agrees with the experimental data this
maybe the casual consent only, i.e. this assent relates to
the sum of contributions one of which is MEC but does-
n't prove definitely the reality of MEC.
For more definite determination of MEC contribu-
tion the studding of electronuclear sum rule calculations
[1] is very attractive.
2. MEC AND SUM RULES FOR
4He NUCLEUS
The double-differential cross section d2σ(E,ω,θ) for
electron scattering can be separated into the transverse
and the longitudinal components according to the polar-
ization of the virtual photons and can be represent by the
transverse RT(q,ω) and the longitudinal RL(q,ω) response
functions correspondingly.
d2σ(E,ω,θ) (σM(E,θ) G2(Q2))−1 = λ2RL(q,ω) + [λ/2 +
tan2(θ/2)]RT(q,ω), (1)
where E and θ are the initial energy and the scattering
angle of electron, ω is the energy transferred to the nuc-
leus, σM(E,θ) is the Mott cross section, G(Q2) is proton
electric form factor, q and Q are three and four mo-
mentum transferred correspondingly, λ = Q2/q2. The in-
tegral
∫
∞
ωω=
0
T/LT/L ),()( dqRqS , (2)
not including itself the form factor of the ground state of
the nucleus, is called the inelastic zero moment of re-
sponse function.
The moments ST(q) and SL(q) of 4He, according to
[1], can be represented with accuracy of about 1% as
ST(q) = ST
QES(q) + ST
PCC(q) + ST
MEC(q) and (3a)
SL(q) = SL
QES(q), (3b)
where ST
QES(q) and SL
QES(q) are the contributions of the
quasi-elastic scattering (QES) of electrons on the nucle-
ar nucleons, ST
PCC(q) is the contribution of the scattering
on the proton convention currents (PCC) and ST
MEC(q) is
the contribution of the scattering on MEC. In this article
the expressions for calculation of ST
QES(q), ST
PCC(q) and
SL
QES(q) was found. Let us denote the calculation of the
sum ST
QES(q) + ST
PCC(q) as Sth(q), and the experimental
value of moment ST(q) as ST
exp(q). Following expression
(3a) we have
ST
MEC(q) = ST
exp(q) − Sth(q), (4a)
or
ST
MEC(q) = (D(q) − 1) Sth(q). (4b)
in Sth(q) units. Here the quantity D(q) = ST
exp(q)/Sth(q).
3. THE EXPERIMENTAL DETERMINATION
OF MEC CONTRIBUTION
In article [2], using the method described in p. 2 and
the experimental data of [3], the value of D for 4He nuc-
leus was found at the range of q = 1.5-2.5 fm−1:
1.1 ≤ D ≤ 1.2. In our article [4] ST
exp(q) for 4He nucleus
is measured at the range of q = 0.75 - 1.5 fm−1. Let us
consider these data.
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2002, № 2.
Series: Nuclear Physics Investigations (40), p. 19-21. 19
As the measurements are always limited by some
maximum value of the transferred energy ωmax
, the ex-
perimental moment of the response function is written in
the form:
∫∫
∞
ω
ω
ωω+ωω=
max
extr
T/L
max
0
exp
T/L
exp
T/L d),(d),()( qRqRqS ,(5)
where ),(exp
T/L ωqR is the experimental value of the re-
sponse function, ),(extr
T/L ωqR is its extrapolation for
ω > ωmax . In article [4] it was used the extrapolating
form:
ωα−=ω eqCq,R )()( T/L
extr
T/L , (6)
where CT/L(q) is the parameter for the adjustment to the
experimental response function, α is parameter, which,
according to article [5], is independent from the transfer
momentum and it is almost independent from the atomic
number of nucleus. At the time when article [4] was
published it was supposed that value of α = 3 − 4 (see
[5]), and so there the value of ST
exp(q) for α = 3 and
α = 4 was presented. Since later it was found that α ≅ 3
(article [6]), we use ST
exp(q) for this value of parameter
for calculation of D.
Article [1] proposes calculations of ST/L
QES(q) with
using the unmodel sum rules (the term of this article) for
q ≤ 1.5 fm−1 and the realistic nucleon potentials for
q > 1.7 fm−1. According to [1] the accuracy of first cal-
culation is about 1%.
The calculation of ST
PCC(q) is not unequivocal be-
cause it contains the averaged kinetic energy < T > of the
intranuclear proton as a multiplier, and the diapason of
well-known values of this characteristic is 56 - 78 MeV.
Nevertheless as the contribution of ST
PCC(q) to Sth(q) is
little and it decreases monotonously with the increasing
of the transfer momentum (about 17% for q = 1 fm−1 and
1% for q = 2 fm−1) the uncertainty of the value of Sth(q)
connected with the quantity of ST
PCC(q) has not vital im-
portance for the examining problem.
Table shows the values of the experimental and the
calculated transverse moment. One can see that the ratio
of these quantities D equal to 1 with accuracy to the ex-
perimental errors.
In order to determine the possible difference of D
from unity, we have calculated the average value of
these quantities at some interval of the transfer moment
q1÷q2: ∑−
− = iDnqqD 1
21 and
∑ ∆+∆=∆ −
i
iqq D
n
DD 2
S21 )(1
sist , (7)
where ∆sDi is the statistical error of Di , ∆sistD is the sys-
tematic (non-statistical) error, which is common for all n
values of D. For the data of article [4] the error ∆
sistD = 0.05 D.
So, from the data of table one can find that 5.175.0 −
D
= 1.03 ÷1.07 ± 0.08. Here the first value corresponds to
the calculation where <T> = 78 MeV, and the second
one is for <T> = 56 MeV.
The errors of D values in article [2] are ∆
Di = 0.10 ÷ 0.15. Let us estimate the error for the aver-
aged value of quantity D that was found in this article.
The systematic error of ST
exp(q) in article [3] is not smal-
ler than 3%. Hence, we assume ∆sistD = 0.03 D and ∆
SDi = ∆Di − ∆sistD for quantities Di from [2], and using
Eq. (7b) find ∆ 5.25.1 −
D = ± 0.09.
Table. Moment of transverse response function 4He: ST
exp ± ∆SST
exp is experimental data from [4], S th is calcula-
tion on the basis of [1] (minus MEC contribution) and D ± ∆SD is theirs relation. First columns of ST
exp and D val-
ues correspond to calculation with <T> = 56 MeV, second columns of theirs correspond to calculation with <T> = 78 MeV
q fm−1 ST
exp ∆SST
exp S th D ∆SD
0.750 0.158 0.014 0.153 0.168 1.033 0.940 0.087
0.875 0.266 0.028 0.237 0.252 1.122 1.056 0.115
1.000 0.403 0.027 0.347 0.363 1.161 1.110 0.076
1.125 0.507 0.041 0.486 0.502 1.043 1.010 0.083
1.250 0.659 0.053 0.651 0.667 1.012 0.988 0.080
1.375 0.863 0.071 0.839 0.855 1.029 1.009 0.084
1.500 1.153 0.100 1.047 1.062 1.101 1.086 0.095
4. DISCUSSION OF S QEL(q)
CALCULATION
20
As one can see from Eq. (4a, 4b), the accuracy of de-
tection of MEC contribution depends on the accuracy of
Sth(q) calculation. In the last one the contribution from
QES dominates. I.e. the accuracy of Sth(q) is mainly de-
pends on the accuracy of ST
QES(q). As the equations for
ST
QES(q) and SL
QES(q) are similar, we may consider the
accuracy of the calculations with them to be equal.
In accordance with expression (2b), SL(q) moment
contains one contribution only. Therefore the calculation
of this moment can be examined by the comparison with
the experimental value SL
exp(q).
The latest SL(q) measurements on 4He [7] were real-
ized in wide diapason of transfer energy. Therefore the
extrapolation correction (second integral in Eq. (5)) for
these data is little and its amount is estimated by us as
3% for q < 2 fm−1 and 5% for q ≥ 2 fm−1. These data
with the mentioned estimation are shown in the figure.
The curves calculated according to the equations of [1]
are represented here too. One can see that these calcula-
tions agree badly with the experimental data for
q > 2 fm−1.
Inelastic moment of longitudinal response function
4He: the experimental data from [7]; solid and dashed
lines are calculation on the basis of [1] for the unmodel
sum rules and for the realistic nucleon potentials cor-
respondingly; dotted line is the calculation of [8] in-
cluding NM effect
The possible cause of this is the effect of nucleon
modification (NM), which was not accounted these cal-
culations. The confirmation of this assumption is the
agreement of the calculation (Eq. (12) of article [8]),
which accounts NM effect, with the experimental data
(see fig.). We have not the analogous calculation for
ST
QES(q). However, as NM effect is small for SL
QES(q)
calculation for q < 1.7 fm−1 and as it decreases propor-
tionally of exp(−q2) (following [8]) we may think that
ST
QES(q) calculation used by us is enough exact for
q ≤ 1.5 fm−1.
5. CONCLUSION
1. The accuracy of modern data is not enough for
sure detection of MEC contribution in the electron scat-
tering on 4He nucleus.
2. Within the limits of approximation of Eq. (3a),
value of D +∆ D =1.15 determines the upper limit of
MEC contribution for q = 0.75 - 1.5 fm−1 by means of
Eq. (4b): th15.0MEC
T
SS = .
ACKNOWLEDGMENT
Author heartily thanks to N.G. Shevchenko and
V.V. Denyak for their helpful remarks.
REFERENCES
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2. V.D. Efros. The contribution of meson ex-
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4He // VAN & T. Ser.: jad.-fiz. issled. M. CNIIaom-
inform 1992, №2, p. 28-29 (in Russian).
3. K.F. von Reden et al. Quasielastic electron
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4. A.Yu. Buki, N.G. Shevchenko, V.N. Pol-
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213.
21
PACS: 21.30.+y; 25.30.Fj; 27.10.+h
|