Correction to the electron energy in the nuclear reactions
The Coulomb correction to the electron energy in the direct electronuclear reactions is considered.
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| Veröffentlicht in: | Вопросы атомной науки и техники |
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| Datum: | 2000 |
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| Sprache: | Englisch |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2000
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| Zitieren: | Correction to the electron energy in the nuclear reactions / A.Yu. Buki // Вопросы атомной науки и техники. — 2000. — № 2. — С. 17. — Бібліогр.: 2 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859593009902911488 |
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| author | Buki, A.Yu. |
| author_facet | Buki, A.Yu. |
| citation_txt | Correction to the electron energy in the nuclear reactions / A.Yu. Buki // Вопросы атомной науки и техники. — 2000. — № 2. — С. 17. — Бібліогр.: 2 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The Coulomb correction to the electron energy in the direct electronuclear reactions is considered.
|
| first_indexed | 2025-11-27T18:12:54Z |
| format | Article |
| fulltext |
CORRECTION TO THE ELECTRON ENERGY
IN THE NUCLEAR REACTIONS
A.Yu. Buki
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
The Coulomb correction to the electron energy in the direct electronuclear reactions is considered.
PACS: 24.50+g, 24.90+d, 25.30Fj
1. When the first Born approximation is used for the
electron scattering analysis some energy Eq is added to
the initial one E0. This correction is the result of the
electron energy increasing in the nuclear Coulomb field
and taking into account this correction is alternative for
the more difficult calculation using the second Born ap-
proximation.
At first the Coulomb correction Eq was applied during
the investigation of the elastic electron scattering by nu-
clei and for light nuclei it had the form
Eq = 1.33 Ze2 <rN
2>−1/2, (1)
for medium and heavy nuclei:
Eq = 1.5 Ze2 R −1. (2)
Here <rN
2>1/2 is the mean-square nuclear radius, R = (5/3
<rN
2>)1/2 is the radius of the nuclear equivalent homoge-
neous distribution, e is the electron charge and Z is the
nuclear charge number. Expression (1) is derived from
the Gaussian charge distribution model. Expression (2)
is derived from the homogeneous distribution model.
2. Later the correction in the form (1) or (2) was
used in the research of quasi-elastic electron scattering
by nuclear nucleons [2]. One can think, that in this case,
the addition electron energy of the scattering by a proton
(p) or a neutron (n) can be presented as
E′q, p/n(r ) = E1, p/n + E2, p/n(r) , (3)
where E1,p/n is the correction for scattering by a free nu-
cleon (E1,n = 0), and E2,p/n(r) is the term taking into ac-
count the influence of the Coulomb field of the rest nu-
clear part on the energy of the electron scattering when
the distance between the electron and the nuclear center
is r. It is not difficult to see, that
E2, p/n(r) = e
Q r
r
r'
r
p n d/ ( ' )
'2
∞
∫ , (4)
where
Qp/n(r) = 4 2
0
π ρ p n d/
r
r r r( ' ) ' '∫ . (5)
The function ρp/n(r) in the case of the scattering by a
neutron is ρn(r)=ρ(r), ρ(r) is the nuclear charge density;
by the proton: ρp(r) ≈ (1−Z−1) ρ(r). Probability of the
scattering by a nucleon is proportional to ρ(r); from here
we can conclude that the nuclear volume averages Eq,
p/n(r) are:
<E′q,p> = E1, p + (1−Z−1) <E2, n>, (6)
<E2, p/n> =
4
2
2
0
π
ρ
Ze
E r r r r, / /( ) ( )p n p n d
∞
∫ . (7)
Using expression (1), we derive E1,p= 2.4 MeV. For the
homogeneous distribution model (U0 = Ze2 R −1):
E2,n(r) = [1+0.5(1− r2/R2 )] U0, r ≤R; (8)
<E′q,n> = <E2,n> = 1.2 U0, (9)
<E′q,p> = 2.4 ??? + (1−Z−1) 1.2 U0. (10)
3. We pay attention on some consequences of the ap-
proach considered.
I. Analysis of the Coulomb correction contribution
shows that using of average values of corrections in the
form (9), (10) instead of (2) leads, in some cases, to the
change of experimental values of the nuclear character-
istics by an order of magnitude of the measurement er-
ror.
II. One can see from Eq. (9) and (10) that the Coulomb
correction depends on the sort of a scattering nucleon
and from Eq. (8) this one depends on the nucleon loca-
tion inside the nucleus. From here the resulting spread of
values
∆E′q ≈ E1,p + 0.5 U0 (11)
means that the effective interaction energy Eeff =E0 +E′q
has the same spread: ∆Eeff = ∆E′q . Since, the transfer mo-
mentum is q ∝ Eeff than its amplitude of the spread is ∆
q ≈ ∆E′q/Eeff q. For example, for 208Pb at E0 = 100 ?eV ∆q
≈0.1 q. This can be important for interpretation of (e,e′)
and especially (e,e′p), (e,e′n) experiments.
III. The Coulomb nuclear field influences not only on
the energy of electron interaction but on the angle of the
electron scattering too. It can be shown, that as a result,
under electron scattering both by nucleus and by nuclear
nucleon, the interval θ = θ0 ±∆θ, where ∆θ ≈ 0.5U0/Eeff,
but in this case more than one scattering angle θ0 corre-
sponds to the single value of the transfer momentum.
Taking into account ∆θ for measurement interpretation
must lead to the very interesting results, in particular: a)
increasing of experimental values of the charge radii; b)
decreasing the EMC-effect.
In conclusion we note that all above-mentioned calcu-
lations and conclusions are related not only to the elec-
tron scattering but to any charged lepton scattering too.
In the case of scattering not by a nucleon but by a nucle-
ar cluster it is necessary to replace, in the corresponding
expressions, Eq,p value and (1−Z−1) factor by their cluster
analogies.
REFERENCES
1. H. Uberal. Electron Scattering from Complex nu-
clei. New York: “Academic”, 1971, part A, p. 162-170.
2. A. Zghiche et al. Longitudinal and transverse re-
sponses in quasi-elastic electron scattering from 208Pb
and 4He // Nucl. Phys. 1994, v. A572, p. 513-559.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000, № 2.
Серия: Ядерно-физические исследования (36), с. 17.
17
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
The Coulomb correction to the electron energy in the direct electronuclear reactions is considered.
REFERENCES
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| id | nasplib_isofts_kiev_ua-123456789-82157 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-27T18:12:54Z |
| publishDate | 2000 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Buki, A.Yu. 2015-05-25T20:36:22Z 2015-05-25T20:36:22Z 2000 Correction to the electron energy in the nuclear reactions / A.Yu. Buki // Вопросы атомной науки и техники. — 2000. — № 2. — С. 17. — Бібліогр.: 2 назв. — англ. 1562-6016 PACS: 24.50+g, 24.90+d, 25.30Fj https://nasplib.isofts.kiev.ua/handle/123456789/82157 The Coulomb correction to the electron energy in the direct electronuclear reactions is considered. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Nuclear reactions Correction to the electron energy in the nuclear reactions Поправки к энергии электрона при расчете ядерных реакций Article published earlier |
| spellingShingle | Correction to the electron energy in the nuclear reactions Buki, A.Yu. Nuclear reactions |
| title | Correction to the electron energy in the nuclear reactions |
| title_alt | Поправки к энергии электрона при расчете ядерных реакций |
| title_full | Correction to the electron energy in the nuclear reactions |
| title_fullStr | Correction to the electron energy in the nuclear reactions |
| title_full_unstemmed | Correction to the electron energy in the nuclear reactions |
| title_short | Correction to the electron energy in the nuclear reactions |
| title_sort | correction to the electron energy in the nuclear reactions |
| topic | Nuclear reactions |
| topic_facet | Nuclear reactions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/82157 |
| work_keys_str_mv | AT bukiayu correctiontotheelectronenergyinthenuclearreactions AT bukiayu popravkikénergiiélektronaprirasčeteâdernyhreakcii |