Quasielastic electron scattering on ⁶³Cu in the giant resonance energy region
The result of the extraction of the quasielastic part from the electron scattered spectra on ⁶³Cu is reported. The position of the peak maximum was determined for each quasielastic spectrum and the momentum transfer dependence of its shift with respect to the case of scattering on a free nucleon is...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2009 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/111150 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Quasielastic electron scattering on ⁶³Cu in the giant resonance energy region / V.V. Denyak, V.M. Khvastunov, S.A. Paschuk, H.R. Schelin // Вопросы атомной науки и техники. — 2009. — № 3. — С. 24-27. — Бібліогр.: 2 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859685166159495168 |
|---|---|
| author | Denyak, V.V. Khvastunov, V.M. Paschuk, S.A. Schelin, H.R. |
| author_facet | Denyak, V.V. Khvastunov, V.M. Paschuk, S.A. Schelin, H.R. |
| citation_txt | Quasielastic electron scattering on ⁶³Cu in the giant resonance energy region / V.V. Denyak, V.M. Khvastunov, S.A. Paschuk, H.R. Schelin // Вопросы атомной науки и техники. — 2009. — № 3. — С. 24-27. — Бібліогр.: 2 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The result of the extraction of the quasielastic part from the electron scattered spectra on ⁶³Cu is reported. The position of the peak maximum was determined for each quasielastic spectrum and the momentum transfer dependence of its shift with respect to the case of scattering on a free nucleon is presented in the momentum transfer range of q = 0.5...1.2 fm⁻¹.
Представлено результат виділення квазіпружної частини перерізу з спектрів розсіяних на ⁶³Cu електронів. У кожному з отриманих квазіпружних спектрів визначено положення максимуму та представлено залежність зсуву його енергетичного положення відносно кінематики розсіяння на вільному нуклоні в диапазоні переданих імпульсів q = 0.5...1.2 фм⁻¹.
Представлен результат выделения квазиупругой части сечения из спектров рассеянных на ⁶³Cu электронов. В каждом из полученных квазиупругих спектров определено положение максимума и представлена зависимость сдвига его энергетического положения относительно кинематики рассеяния на свободном нуклоне в диапазоне переданных импульсов q = 0.5...1.2 фм⁻¹.
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| first_indexed | 2025-11-30T21:53:07Z |
| format | Article |
| fulltext |
QUASIELASTIC ELECTRON SCATTERING ON 63Cu IN THE
GIANT RESONANCE ENERGY REGION
V.V. Denyak1∗, V.M. Khvastunov1, S.A. Paschuk2, H.R. Schelin2
1National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
2Federal University of Technology - Parana, Curitiba, 80230-901, Brazil
(Received May 30, 2008)
The result of the extraction of the quasielastic part from the electron scattered spectra on 63Cu is reported. The
position of the peak maximum was determined for each quasielastic spectrum and the momentum transfer dependence
of its shift with respect to the case of scattering on a free nucleon is presented in the momentum transfer range of
q = 0.5 ... 1.2 fm−1.
PACS: 25.30.Fj
1. INTRODUCTION
The method of the separation of the resonance and
quasielastic parts of the spectrum of scattered elec-
trons elaborated recently [1] opens possibility to in-
vestigate the properties of the qusielastic electron
scattering process at small momentums transfer. In
this work we are continuing to elaborate the proposed
method. The last one was used to obtain the spectra
of quasielastically scattered electrons on 63Cu nuclei
in the momentum transfer range q = 0.5 ... 1.2 fm−1.
Obtained pure quasielastic spectra were analyzed
by means of three phenomenological methods to de-
termine the position of the quasielastic peak maxi-
mum and its shift with respect to the peak of elastic
scattering on a proton.
2. EXPERIMENT
The spectra under consideration were measured at
electron initial energy of E0 = 150 MeV for scatter-
ing angles of θ = 39◦ and 46◦and at E0 = 225 MeV
in the angular range θ = 34◦ ... 74◦ .
The experimental equipment and the procedure
used for data processing are described in [1] and ref-
erences therein. The principal idea of the method
applied consists in the simultaneous multipole analy-
sis of the mixture of resonance and quasielastic parts
with their subsequent separation in the obtained mul-
tipole spectra.
3. QUASIELASTIC SPECTRA
The result of such analysis applied to the spectra of
scattered on 63Cu electrons is shown in Fig.1. The
uncertainty of each point of the reconstructed qua-
sielastic cross section should be treated as the confi-
dence interval. The points themselves are not statis-
tically independent that follows from the reconstruc-
tion method.
As in the case of 65Cu quasielastic cross section
is practically absent at excitations energies below
20 MeV .
4. SHIFT OF THE QUSIELASTIC PEAK
ENERGY POSITION
The shift (ε0) of the quasielastic peak maximum with
respect to that in the kinematics of scattering on a
free nucleon at the same momentum transfer was de-
termined for each quasielastic spectrum according to
the formula:
εmax =
q2
2M
− q2
2AM
+ ε0, (1)
where εmax - the energy position of the quasielastic
peak maximum, A - the atomic number of the ele-
ment, M - the nucleon mass.
To determine the energy position of the quasi-
elastic peak maximum the quasiellastic spectra were
transformed into spectra with statistically indepen-
dent points. The value of the quasielastic cross sec-
tion at given energy was determined with Gauss ran-
dom number generator considering its value in pri-
mary quasielastic spectrum as a maximum of Gauss
distribution and the error of this value as a Gauss
half-width.
As can be seen from Fig.1 in some spectra the
reconstruction errors are not small enough to give
distinct maximum position. Therefore three differ-
ent methods were used to find the quasielastic peak
maxim in the transformed spectra.
∗Corresponding author E-mail address: denyak@gmail.com
24 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2009, N3.
Series: Nuclear Physics Investigations (51), p.24-27.
Fig.1. Differential cross section of scattered electrons. Closed circles - measured spectrum. Open circles -
reconstructed quasielastic part of the spectrum. Line - result of the log-normal curve fitting
25
In the first method the peak maximum was ap-
proximated by the Gauss function. Taking into con-
sideration essential asymmetry of the quasielastic
cross section, only points, where this maximum may
be located with the probability corresponding to
two standard deviations, participated in the fitting
process - points between line 1 and line 2 in Fig.2. It
means that points that have the upper limit of the
error bar lower than the highest bottom limit among
all points were excluded from the adjustment.
Fig.2. Choice of points for the Gauss function
fitting. Numbers 1 and 2 indicates upper and bottom
limits of the peak maximum position. Line - result
of the log-normal curve fitting
In the second method all points of the spectrum par-
ticipated in fitting process but the fitting curve was
chosen as log-normal function:
y = A(1)exp(−
ln2( x
A(2) )
2A(3)2
), (2)
where A(1), A(2), A(3) - fitting parameters. As it
can be see from Fig. 1 this curve describes the ex-
perimental points quite enough.
In the third method the Gauss function was also
used but only points from the low energy front of the
spectrum took part in fitting as it is shown in Fig.3.
Fig.3. Choice of points for third method. Line -
result of the Gauss function fitting
The result of the determination of the energy posi-
tion shift is presented in Fig.4. Fist two methods
gives similar results and shows distinctly that shift
value has maximum at the momentum transferred
q ∼ 0.8 ... 1.0 fm−1. The third method doesn’t show
such maximum.
Fig.4. Sift of the quasielastic peak maximum energy position with respect to that for kinematics of scattering
on free nucleon: a) All methods used. Closed circles - Gauss function fitting, open circles - log-normal
function fitting, open squares - fitting to the front of spectrum. Curves 1 and 2 - upper and bottom limits
correspondingly, obtained from the energy position of the points that participated in the Gauss function
fitting. b) Average of three methods
26
In is necessary to mentioned that such dependence
of the shift value is based on the idea that quasi-
elastic cross section energy dependence has distinct
maximum. Such idea is rather probable but was not
proved in this momentum transfer region.
The value of the shift of quasielastic peak
maximum averaged over the hole interval of q is
28.6 ± 0.6 MeV . This value is somewhat smaller
than for 65Cu - 25.4 ± 1.6 MeV [1]. According to
the investigation presented in [2] it is unlikely that
63Cu and 65Cu has such big difference in ε0. More
probably that such difference shows the accuracy of
the method of the electron spectrum division into
resonance and quasielastic parts.
5. CONCLUSION
The carried out investigation shows that as in
the case of 65Cu in the excitation energy range
10 ... 30 MeV the quasielastic cross section in consid-
erably smaller than that previously used in the stud-
ding of giant resonances.
There is an indication that the momentum trans-
fer dependence of the shift of the quasielastic peak
energy position has maximum at q ∼ 0.8 ... 1.0 fm−1.
The estimated value of the error of the absolute
value of the quasielastic peak shift is about 3 MeV .
References
1. V.V. Denyak, V.M. Khvastunov, S.A. Paschuk,
H.R. Schelin. Qusielastic Electron Scattering in
the Giant-Resonance Energy Region // Physics
of Atomic Nuclei. 2007, v.70, p.1985-1990.
2. R.R. Whitney, I Sick, J.R. Ficenec, et al. Quasi-
elastic electron scattering //Phys.Rev. 1974, C9,
p.2230-2235.
КВАЗИУПРУГОЕ РАССЕЯНИЕ ЭЛЕКТРОНОВ НА 63Cu В ОБЛАСТИ ЭНЕРГИЙ
ГИГАНТСКИХ РЕЗОНАНСОВ
В.В. Деняк, В.М. Хвастунов, С.А. Пащук, У.Р.Счелин
Представлен результат выделения квазиупругой части сечения из спектров рассеянных на 63Cu
электронов. В каждом из полученных квазиупругих спектров определено положение максимума и
представлена зависимость сдвига его энергетического положения относительно кинематики рассеяния
на свободном нуклоне в диапазоне переданных импульсов q = 0.5 ... 1.2фм−1.
КВАЗIПРУЖНЕ РОЗСIЯННЯ ЕЛЕКТРОНIВ НА 63Cu В ОБЛАСТI ЕНЕРГIЙ
ГIГАНТСЬКИХ РЕЗОНАНСIВ
В.В. Деняк, В.М. Хвастунов, С.А. Пащук, У.Р.Счелiн
Представлено результат видiлення квазiпружної частини перерiзу з спектрiв розсiяних на 63Cu
електронiв. У кожному з отриманих квазiпружних спектрiв визначено положення максимуму та пред-
ставлено залежнiсть зсуву його енергетичного положення вiдносно кiнематики розсiяння на вiльному
нуклонi в диапазонi переданих iмпульсiв q = 0.5 ... 1.2фм−1.
27
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| id | nasplib_isofts_kiev_ua-123456789-111150 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-30T21:53:07Z |
| publishDate | 2009 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Denyak, V.V. Khvastunov, V.M. Paschuk, S.A. Schelin, H.R. 2017-01-08T16:07:17Z 2017-01-08T16:07:17Z 2009 Quasielastic electron scattering on ⁶³Cu in the giant resonance energy region / V.V. Denyak, V.M. Khvastunov, S.A. Paschuk, H.R. Schelin // Вопросы атомной науки и техники. — 2009. — № 3. — С. 24-27. — Бібліогр.: 2 назв. — англ. 1562-6016 PACS: 25.30.Fj https://nasplib.isofts.kiev.ua/handle/123456789/111150 The result of the extraction of the quasielastic part from the electron scattered spectra on ⁶³Cu is reported. The position of the peak maximum was determined for each quasielastic spectrum and the momentum transfer dependence of its shift with respect to the case of scattering on a free nucleon is presented in the momentum transfer range of q = 0.5...1.2 fm⁻¹. Представлено результат виділення квазіпружної частини перерізу з спектрів розсіяних на ⁶³Cu електронів. У кожному з отриманих квазіпружних спектрів визначено положення максимуму та представлено залежність зсуву його енергетичного положення відносно кінематики розсіяння на вільному нуклоні в диапазоні переданих імпульсів q = 0.5...1.2 фм⁻¹. Представлен результат выделения квазиупругой части сечения из спектров рассеянных на ⁶³Cu электронов. В каждом из полученных квазиупругих спектров определено положение максимума и представлена зависимость сдвига его энергетического положения относительно кинематики рассеяния на свободном нуклоне в диапазоне переданных импульсов q = 0.5...1.2 фм⁻¹. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Ядерная физика и элементарные частицы Quasielastic electron scattering on ⁶³Cu in the giant resonance energy region Квазіпружне розсіяння електронів на ⁶³Cu в області енергій гігантських резонансів Квазиупругое рассеяние электронов на ⁶³Cu в области энергий гигантских резонансов Article published earlier |
| spellingShingle | Quasielastic electron scattering on ⁶³Cu in the giant resonance energy region Denyak, V.V. Khvastunov, V.M. Paschuk, S.A. Schelin, H.R. Ядерная физика и элементарные частицы |
| title | Quasielastic electron scattering on ⁶³Cu in the giant resonance energy region |
| title_alt | Квазіпружне розсіяння електронів на ⁶³Cu в області енергій гігантських резонансів Квазиупругое рассеяние электронов на ⁶³Cu в области энергий гигантских резонансов |
| title_full | Quasielastic electron scattering on ⁶³Cu in the giant resonance energy region |
| title_fullStr | Quasielastic electron scattering on ⁶³Cu in the giant resonance energy region |
| title_full_unstemmed | Quasielastic electron scattering on ⁶³Cu in the giant resonance energy region |
| title_short | Quasielastic electron scattering on ⁶³Cu in the giant resonance energy region |
| title_sort | quasielastic electron scattering on ⁶³cu in the giant resonance energy region |
| topic | Ядерная физика и элементарные частицы |
| topic_facet | Ядерная физика и элементарные частицы |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/111150 |
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