On some problems in describing ⁴He(e,e′) reaction
Inelastic ⁴He(e,e′) energy spectra and response functions together with realistic calculations are considered. It
 was found that at the threshold region models predict far less cross section and response functions strength than are
 experimentally observed. Аналізуються непружні е...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2004 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2004
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| Цитувати: | On some problems in describing ⁴He(e,e′) reaction / E.L. Kuplennikov, A.A. Nemashkalo, Yu.N. Ranyuk // Вопросы атомной науки и техники. — 2004. — № 5. — С. 55-57. — Бібліогр.: 11 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860249058260549632 |
|---|---|
| author | Kuplennikov, E.L. Nemashkalo, A.A. Ranyuk, Yu.N |
| author_facet | Kuplennikov, E.L. Nemashkalo, A.A. Ranyuk, Yu.N |
| citation_txt | On some problems in describing ⁴He(e,e′) reaction / E.L. Kuplennikov, A.A. Nemashkalo, Yu.N. Ranyuk // Вопросы атомной науки и техники. — 2004. — № 5. — С. 55-57. — Бібліогр.: 11 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Inelastic ⁴He(e,e′) energy spectra and response functions together with realistic calculations are considered. It
was found that at the threshold region models predict far less cross section and response functions strength than are
experimentally observed.
Аналізуються непружні енергетичні спектри та респонс функції реакції ⁴He(е,е′) сумісно з реалістичними
розрахунками. Знайдено, що у поріговій області моделі передбачають значно менші величини перерізу і
респонс-функцій, ніж спостерігаються в експерименті.
Анализируются неупругие энергетические спектры и респонс-функции реакции ⁴He(е,е′) совместно с
реалистическими расчетами. Показано, что в пороговой области модели предсказывают существенно
меньшие величины сечения и респонс-функций, чем наблюдается экспериментально.
|
| first_indexed | 2025-12-07T18:40:40Z |
| format | Article |
| fulltext |
ON SOME PROBLEMS IN DESCRIBING 4He(e,e′) REACTION
E.L. Kuplennikov, A.A. Nemashkalo, Yu.N. Ranyuk
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
e-mail: kupl@kipt.kharkov.ua
Inelastic 4He(e,e′) energy spectra and response functions together with realistic calculations are considered. It
was found that at the threshold region models predict far less cross section and response functions strength than are
experimentally observed.
PACS: 25.30.Fj
1. INTRODUCTION
A striking feature observed in inelastic (e,e′)
electron scattering spectra from nuclear targets is the
broad “quasifree” peak (QFP), which results from the
scattering of electron from a single nucleon, moving
within the nucleus. The QFP maximum position would
occur at a scattered electron energy loss ωmax∼qµ
2/2M*
(qµ- 4- momentum transfer, M*- nucleon effective mass)
and the observed width of the peak can be attributed to
the Fermi motion of the nucleons inside the nucleus.
If Lorenz covariance, parity invariance and current
conservation are assumed, the (e,e′) cross section
depends [1] on only two response functions: the L-
longitudinal (RL) and T- transverse (RT). When using
unpolarized targets and electrons the response functions
depend on two independent variables: 3- momentum
transfer q = |q| and ω. In this approximation the
differential cross section contains a mixture of L- and
T- contributions. The QFP cross section value, shape
and location are determined by the sum of the L- and
T- parts of the cross sections. All these take the
opportunity to investigate the quasifree cross sections
both with the point of view of d2σ/dωdΩ cross sections
and in terms of RL(q,ω) and RT(q,ω) that contain all the
nuclear structure information.
The goal of this paper is to look for the “white
spots” in (e,e′) scattering from 4He target in the QFP
region. By other words we investigate kinematical
conditions with weak or contradictory experimental
ensuring, problems in describing full cross sections or
L- and T- response functions. Besides a presentation of
the experimental results the work concentrates on a
description of the scattering results within the modern
nuclear models.
2. EXPERIMENTAL DATA.
COMPARISON WITH CALCULATIONS
First of all we have considered the double
differential cross sections obtained at forward (θ<90°)
scattering angles. Accurate results for inclusive electron
scattering in 4He for initial energy E=465.3; 596.8 MeV
in the QFP region at θ=60° (q in the QFP maximum
qmax=425, 535 MeV/c respectively) were obtained in [2].
The data were compared with the simple quasifree
prediction and realistic model calculations. In the first
case expressions for the cross section are given in terms
of integrals over the nucleon momentum distribution.
Realistic momentum densities were used. Second
version is a direct connection with the single-nucleon
spectral function for the A(e,e′N)B reaction. The
spectral function for 4He was calculated separately for
each possible final state: (ppnn), p3H, n3He, pnd, dd).
The (e,e′) cross section is obtained by integrating over
both nucleon momentum and removal energy. Both
models used the plane wave impulse approximation in
the final state (PWIA). The comparison shows that
theoretical predictions for all q at ω<ωmax lie
systematically below experimental points.
More complex model calculations of the 4He(e,e′)
cross sections at forward angles [1,3,4] (qmax=337…640
MeV/c) also have shown serious deviations from the
experimental points at the low ω side of the QFP.
Typical picture is displayed in Fig. 1.
0,00 0,25 0,50 0,75
0,01
0,1
1
1
3
21
d2 σ/
dω
dΩ
, µ
b
/G
e
V
s
r
Energy loss, GeV
Fig. 1. Сross section for 4He as a function of energy
loss (E=1169 MeV, θ=30°, qmax=588 MeV/c [3]).
Curves 1-3 are described in the text
The curves 1 and 2 are the results of calculations in
the framework of harmonic oscillator model and
approach [4] in which main attention is paid to
covariance and conservation of electromagnetic current
by including the vertex functions, that take into account
the structure of the 4He, for Urbana potential. It is so-
called Lorentz-Calibration-Invariable Approach (LCIA).
Curve 3- calculations with nucleon momentum
distribution derived by the variational ATMS method
[5] for Reid soft core potential. It uses a three-body
force to get the correct binding energy. Comparison
shows that there are problems in describing 4He(e,e′)
cross section at small energy loss.
Thus different simple approximations and more
fundamental theoretical approaches give a substantial
excess of the experimental cross section compared to all
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2004, № 5.
Series: Nuclear Physics Investigations (44), p. 55-57. 55
model predictions for region of interest. Apparent
violation of the impulse approximation has led to a
conclusion: other physical processes are important here.
Even more impressive picture can be seen when
comparing the experimental differential cross section of
4He(e,e′) reaction at backward θ>90° angles with model
calculations. One of the spectra [1] (qmax=530 MeV/c) is
demonstrated in Fig. 2 together with the theoretical
analysis. The dashed and dotted curves are the L- and T-
contributions [1], the solid curve is the full cross
section. The calculation sums over all possible (e,e′N)
states using the PWIA in the final state. The 4He wave
function (WF) was calculated by ATMS method [5].
Final state interactions (FSI), effects of meson exchange
currents and real pion production were not taken into
account. Note that the transverse contribution dominates
in the cross section. In addition, in Fig. 2 by the dash-
dotted curve is presented the prediction of approach [4].
Fig. 2. 4He. Cross section as a function of energy
loss at E=328 MeV, θ=134.5° [1] together with
theoretical curves (see the text)
Figs. 1,2 and the results of data interpretation [1-4]
have unequivocally showed a significant breakdown of
the quasifree picture. It proves that above mentioned
models, based on a quasifree reaction mechanism, are
rather simple ones for describing the nucleon knockout
process at low energy loss side of the QFP at
intermediate energies.
During the past few decades a series of electron
scattering experiments on 4He have been performed
with a goal of the measured double differential cross
sections separation into L- and T- response functions at
constant momentum transfers. RL(q,ω) and RT(q,ω)
response functions were extracted [1] at q=300…
500 MeV/c. Some later Rosenbluth separations into
L- and T- response functions at q=const were made for
q=300…600 MeV/c in [6]. The most accurate data for
these responses in the region of the QFP were
determined via analysis of the world’s cross section data
[7] for q=300…700 MeV/c.
It turned out that the results of different model
calculations [6] are in reasonable agreement with the
RL(q,ω) data. The best description was achieved in [8]
for q=300 and 400 MeV/c. Authors have used Green
function Monte Carlo method and realistic Hamiltonian
containing two- and three-nucleon potentials. So we
concentrated our attention on T- response functions.
T- response functions [1] at q=300…500 MeV/c and
the modern calculations results are displayed in Fig. 3.
Fig. 3. 4He. Transverse responses [1] as a function
of energy loss. Curves: PWIA [1] (dashed line), LCIA
[4] (solid line)
The data RT(q,ω) are significantly wider and there is
more strength at low ω side than what is predicted. In
general the calculations describe poorly the data. T-
responses extracted in [6] and theoretical interpretation
is presented in Fig 4.
Fig. 4. 4He. Transverse responses [6] as a function
of energy loss. Curves: PWIA (DWIA) [10,11] - dash-
dotted (solid) line; Laget calculations [9] (dotted line)
In spite of high quality of electron beams and
experimental facility in both scientific centers [1,6]
there are small differences in measured (e,e′) spectra
and obtained T- response functions. RT(q,ω) dependence
obtained at low q [1,2] is shifted to lower energy loss
and is quite asymmetric. This fact is explained by an
enhancement in these spectra from FSI or excitation of
the broad inelastic states between 20…30 MeV
excitation energies. At the same time RT(q,ω) obtained
in [6,7] shows practically smooth shape without any
anomalies. In experiment [6] at q=300 MeV/c RT(q,ω)
value is ∼10% larger. Secondly, modern theoretical
56
approaches do not describe the low energy loss side in
both cases.
T- response functions [6] have been compared to
calculations with three different models [9] and [10,11]
(two versions). In the calculations of [9] the WF of 4He
employed was determined by a variational method using
the Argonne NN potential; three-nucleon forces were
taken into account; FSI, exchange currents and pion
production are included.
In calculations [10,11] have been used two models
of the spectral function for 4He; for small nucleon
momenta (p≤300 MeV/c) the WF calculated by a
variational method and for high momenta and removal
energies the WF was obtained through a convolution
integral of the momentum distributions describing on
one hand the relative motion of the two correlated
nucleons and on the other hand the center-of-mass
motion of this correlated pair. FSI were taken into
account through an optical potential (DWIA).
The origin of the excess strength observed in the
threshold region of the transverse response functions
under different kinematical conditions q=const=300…
600 MeV/c are not convincingly explained.
3. CONCLUSIONS
When studying the 4He(e,e′) cross sections and
transverse response functions in the QFP region one
finds the kinematical region, which have weak
experimental ensuring. Besides, modern theoretical
models cannot explain the data in particular in the low
energy loss side of the QFP and T- response functions.
Without doubt this region remains interesting both for
experimentalists and theorists.
To understand reasons of such behavior of the
4He(e,e′) cross sections and RT(q,ω) dependences one
needs in additional theoretical and especially accurate
experimental studies (as it was stressed in [7] “in part,
the slow progress was due to the confusing experimental
picture, that some time obfuscated the interpretation of
the data”). At the same time pure transverse cross
sections can be obtained (not a traditional) by a direct
way - measuring the inclusive spectra at 180°.
High quality electron beam at the future NSC KIPT
Electron Accelerator, high-resolution spectrometer that
will be able to measure scattered electrons at 180°,
effective many-channel detectors will allow
measuring transverse cross sections at low energy loss
side and threshold region, avoiding measurements of the
energy spectra under different kinematical conditions
and Rosenbluth procedure of L- and T- response
functions separation. Such kind of data is practically
absent.
Another field of experimental activity may be the
resonant electroexcitation of low-lying levels, magnetic
transitions above the nucleon threshold and giant
resonances in middle weight and heavy nuclei.
REFERENSES
1. K.F. Reden, C. Alcorn, S.A. Ditman et al.
Quasifree Electron Scattering and Coulomb Sum Rule
in 4He // Phys. Rev. 1990, v. C41, № 3, p. 1084-1094.
2. S.A. Ditman, A.M. Bernstein, T.J. Pavel et al.
Inelastic Electron Scattering from 2H, 3He and 4He //
Phys. ReV. 1988, v. C38, № 2, p. 800-811.
3. E.L. Kuplennikov, А.V. Gann, А.Е. Zatserkljny et
al. Examination of the Cross Sections 4He(е,е′) Reaction
in the Quasifree, dip and ∆(1232)-Resonance Region //
Yad. Piz. 1994, v. 57, p. 771-776 (in Russian).
4. А.А. Zayats, V.А. Zolenko, Y.А. Kasatkin et al.
Electrodisintegration of 4Не: 4Не(е,е′N)T // Yad. Fiz.
1992, v. 55, № 2, p. 325-344 (in Russian).
5. Y. Akaishi. Random Number Methods in Few
Body Calculation // Nucl. Phys. 1984, v. A416, p. 409-
420.
6. A. Zghiche, J.F. Danel, M. Bernheim et al.
Longitudinal and Transverse Responses in Quasi-Elastic
Electron Scattering from 208Pb and 4He // Nucl. Phys.
1994, v. A572, p. 513-559.
7. J. Carlson, J. Jourdan, R. Schiavilla and I. Sick.
Longitudinal and Transverse Quasi-Elastic Response
Functions on Light Nuclei // Phys. Rev. 2002, v. C65,
№ 2, p. 4002-4042.
8. J. Carlson and R. Shiavilla. Euclidean Proton
Response in Light Nuclei // Phys. Rev. Lett. 1992, v. 68,
p. 3682-3687.
9. J.M. Laget. Modern Topics in Electron
Scattering, Singapore: “World Scientific”, 1991, 290 p.
10. C. Ciofi Degli Atti et al. Two-Nucleon Corre-
lations and Structure of the Nucleon Spectral Function
at High Values of Momentum and Removal Energy //
Phys. Rev. 1991, v. C44, № 1, p. R7-R11.
11. S. Simula and C. Ciofi Degli Atti, 1993 (private
communication).
57
О НЕКОТОРЫХ ПРОБЛЕМАХ ОПИСАНИЯ РЕАКЦИИ 4He(e,e′)
Э.Л. Купленников, А.А. Немашкало, Ю.Н. Ранюк
Анализируются неупругие энергетические спектры и респонс функции реакции 4He(е,е′) совместно с
реалистическими расчетами. Показано, что в пороговой области модели предсказывают существенно
меньшие величины сечения и респонс-функций, чем наблюдается экспериментально.
ПРО ДЕЯКІ ПРОБЛЕМИ ОПИСУ РЕАКЦІЇ 4He(e,e′)
Е.Л. Купленніков, А.А. Немашкало, Ю.М. Ранюк
Аналізуються непружні енергетичні спектри та респонс функції реакції 4He(е,е′) сумісно з реалістичними
розрахунками. Знайдено, що у поріговій області моделі передбачають значно менші величини перерізу і
респонс-функцій, ніж спостерігаються в експерименті.
58
REFERENSES
1. K.F. Reden, C. Alcorn, S.A. Ditman et al. Quasifree Electron Scattering and Coulomb Sum Rule in 4He // Phys. Rev. 1990, v. C41, № 3, p. 1084-1094.
2. S.A. Ditman, A.M. Bernstein, T.J. Pavel et al. Inelastic Electron Scattering from 2H, 3He and 4He // Phys. ReV. 1988, v. C38, № 2, p. 800-811.
3. E.L. Kuplennikov, А.V. Gann, А.Е. Zatserkljny et al. Examination of the Cross Sections 4He(е,е) Reaction in the Quasifree, dip and (1232)-Resonance Region // Yad. Piz. 1994, v. 57, p. 771-776 (in Russian).
4. А.А. Zayats, V.А. Zolenko, Y.А. Kasatkin et al. Electrodisintegration of 4Не: 4Не(е,еN)T // Yad. Fiz. 1992, v. 55, № 2, p. 325-344 (in Russian).
5. Y. Akaishi. Random Number Methods in Few Body Calculation // Nucl. Phys. 1984, v. A416, p. 409-420.
6. A. Zghiche, J.F. Danel, M. Bernheim et al. Longitudinal and Transverse Responses in Quasi-Elastic Electron Scattering from 208Pb and 4He // Nucl. Phys. 1994, v. A572, p. 513-559.
7. J. Carlson, J. Jourdan, R. Schiavilla and I. Sick. Longitudinal and Transverse Quasi-Elastic Response Functions on Light Nuclei // Phys. Rev. 2002, v. C65, № 2, p. 4002-4042.
8. J. Carlson and R. Shiavilla. Euclidean Proton Response in Light Nuclei // Phys. Rev. Lett. 1992, v. 68, p. 3682-3687.
9. J.M. Laget. Modern Topics in Electron Scattering, Singapore: “World Scientific”, 1991, 290 p.
10. C. Ciofi Degli Atti et al. Two-Nucleon Correlations and Structure of the Nucleon Spectral Function at High Values of Momentum and Removal Energy // Phys. Rev. 1991, v. C44, № 1, p. R7-R11.
11. S. Simula and C. Ciofi Degli Atti, 1993 (private communication).
|
| id | nasplib_isofts_kiev_ua-123456789-80509 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:40:40Z |
| publishDate | 2004 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Kuplennikov, E.L. Nemashkalo, A.A. Ranyuk, Yu.N 2015-04-18T16:29:17Z 2015-04-18T16:29:17Z 2004 On some problems in describing ⁴He(e,e′) reaction / E.L. Kuplennikov, A.A. Nemashkalo, Yu.N. Ranyuk // Вопросы атомной науки и техники. — 2004. — № 5. — С. 55-57. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 25.30.Fj https://nasplib.isofts.kiev.ua/handle/123456789/80509 Inelastic ⁴He(e,e′) energy spectra and response functions together with realistic calculations are considered. It
 was found that at the threshold region models predict far less cross section and response functions strength than are
 experimentally observed. Аналізуються непружні енергетичні спектри та респонс функції реакції ⁴He(е,е′) сумісно з реалістичними
 розрахунками. Знайдено, що у поріговій області моделі передбачають значно менші величини перерізу і
 респонс-функцій, ніж спостерігаються в експерименті. Анализируются неупругие энергетические спектры и респонс-функции реакции ⁴He(е,е′) совместно с
 реалистическими расчетами. Показано, что в пороговой области модели предсказывают существенно
 меньшие величины сечения и респонс-функций, чем наблюдается экспериментально. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Ядерная физика и элементарные частицы On some problems in describing ⁴He(e,e′) reaction Про деякі проблеми опису реакції ⁴He(e,e′) О некоторых проблемах описания реакции ⁴He(e,e′) Article published earlier |
| spellingShingle | On some problems in describing ⁴He(e,e′) reaction Kuplennikov, E.L. Nemashkalo, A.A. Ranyuk, Yu.N Ядерная физика и элементарные частицы |
| title | On some problems in describing ⁴He(e,e′) reaction |
| title_alt | Про деякі проблеми опису реакції ⁴He(e,e′) О некоторых проблемах описания реакции ⁴He(e,e′) |
| title_full | On some problems in describing ⁴He(e,e′) reaction |
| title_fullStr | On some problems in describing ⁴He(e,e′) reaction |
| title_full_unstemmed | On some problems in describing ⁴He(e,e′) reaction |
| title_short | On some problems in describing ⁴He(e,e′) reaction |
| title_sort | on some problems in describing ⁴he(e,e′) reaction |
| topic | Ядерная физика и элементарные частицы |
| topic_facet | Ядерная физика и элементарные частицы |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/80509 |
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