Q-dependence of the quasifree peak maximum position in ²Н(e,e')-reaction
The problem of the quasifree peak position of energy spectra at scattering electrons in inclusive ²H(e,e')- reaction is discussed. ε(q) dependence of the lightest deuterium nucleus is investigated. The fitting experimental points are realized by a 6-th power polynomial. It is proposed the new m...
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| Published in: | Вопросы атомной науки и техники |
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| Date: | 2002 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2002
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| Cite this: | Q-dependence of the quasifree peak maximum position in ²Н(e,e')-reaction / V.V. Krasil’nikov, E.L. Kuplennikov, I.A. Levashov, Yu.N. Ranyuk // Вопросы атомной науки и техники. — 2002. — № 2. — С. 7-8. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860060457253994496 |
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| author | Krasil’nikov, V.V. Kuplennikov, E.L. Levashov, I.A. Ranyuk, Yu.N. |
| author_facet | Krasil’nikov, V.V. Kuplennikov, E.L. Levashov, I.A. Ranyuk, Yu.N. |
| citation_txt | Q-dependence of the quasifree peak maximum position in ²Н(e,e')-reaction / V.V. Krasil’nikov, E.L. Kuplennikov, I.A. Levashov, Yu.N. Ranyuk // Вопросы атомной науки и техники. — 2002. — № 2. — С. 7-8. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The problem of the quasifree peak position of energy spectra at scattering electrons in inclusive ²H(e,e')- reaction is discussed. ε(q) dependence of the lightest deuterium nucleus is investigated. The fitting experimental points are realized by a 6-th power polynomial. It is proposed the new method of finding maxima of energy spectra and its errors at the polynomial fitting.
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| first_indexed | 2025-12-07T17:04:14Z |
| format | Article |
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Q- DEPENDENCE OF THE QUASIFREE PEAK MAXIMUM POSITION
IN 2Н(e,e')- REACTION
V.V. Krasil’nikova), E.L. Kuplennikovb), I.A. Levashova), Yu.N. Ranyukb)
a)Belgorod State University, Belgorod, Russia
e-mail: kras@bsu.edu.ru
b) National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
The problem of the quasifree peak position of energy spectra at scattering electrons in inclusive 2H(e,e′)- reaction
is discussed. ε(q) dependence of the lightest deuterium nucleus is investigated. The fitting experimental points are
realized by a 6-th power polynomial. It is proposed the new method of finding maxima of energy spectra and its
errors at the polynomial fitting.
PACS: 25.30.Fj
INTRODUCTION
At large momentum transfer q, dominant feature in
the inclusive spectrum of electrons inelastically
scattered by nuclei is a wide so-called quasielastic or
quasifree peak (QFP) resulting from elastic scattering
from individual nucleons. Previous experiments have
shown that (see for example [1, 2]) the location of the
QFP ωmax on light, middle weight and heavy nuclei
differs from that of a free nucleon ωеN and shifted to the
higher energy loss ωmax > ωеN side at a certain value of ε.
The shift value is a specific function of the
kinematical conditions of measurement and cannot be
explained by the introducing an average nucleon
separation energy that must be supplied to knock the
nucleon out of the nucleus. The ε(q)- dependence has a
minimum in the momentum near the nuclear Fermi
momentum and don’t predict saturation at the large
values of q. Consequently this shift cannot be directly
related to the average nucleon separation energy. There
were difficulties in describing the experimental ε
(q)- dependences for A ≥ 3 by the different theoretical
models.
So a logical step toward understanding the observed
differences between calculations and actual behavior of
the ε(q)- dependences is the investigation of the
quasielastic 2H(e,e′) cross section over the same
kinematical region in which problems exist in
explaining results found for heavier nuclei. First of all
the deuteron is the simplest nuclear system consisting of
two nucleons. Estimates of a nuclear density show
deuteron is a friable formation enough. Therefore,
influence of residual interaction effects and dynamical
short-range NN- correlations that grow with increasing
nuclear density must be minimum. Besides, weak
nucleons couple in deuterium allows considering their
as free particles in a certain approximation, which
facilitates the theoretical interpretation of the
experimental data.
RESULTS AND DISCUSSIONS
In this work the experimental data are analyzed and
the transfer momentum dependence is obtained for the
shift of the quasifree peak maximum position on the 2Н
nucleus relatively elastic eN- peak location. The energy
spectra were taken at the Bates Linear Accelerator
Center [3, 4]. The inclusive differential cross section
was measured with high accuracy for different initial
electron energies and scattering angles of 600 and 134,5°
. All data presented have been corrected for radiative
effects. We have analyzed five energy spectra
inelastically scattered electrons from the deuteron in the
quasifree peak region at initial energies Еi = (292,8±0,4;
366,0±0,6; 465,3±0,7; 510,2±0,8; 596,8±0,9) МeV and
scattering angle 60°.
The shift value of the QFP maximum position in
2Н(е,е′)- reaction relative to the point corresponding to
free eN- kinematics is determined as
ε = ωmax - ωеN.
As the peak on a free proton wasn’t measured in the
experiments [2, 3] and the initial electron energy is
determined independently, the kinetic energy ωeN of a
recoil nucleon with its error dωeN for every concrete
spectrum are calculated as
ωeN = Ei - EH,
where EH = Ei/(1+2Ei/M Sin2 (θ/2)), M is a nucleon
mass, at the given value of the initial energy (Ei ± dEi)
and the scattering angle θ. The most value of the
absolute error ± dε is calculated by the standard
procedure of finding errors.
To increase precision of finding transferred energy
in QFP maximum and to decrease a fit error that, in
particular, is determined by a number of the points for
fitting and a fit function form the points are taken only
in vicinity of the spectrum maximum. Beforehand, the
control of a finished result dependence on the fit
function form was fulfilled. On Fig.1, it is shown the
fitting ought to the polynomial of 6-th power for one of
the spectra. It is seen that the plot describes well the
spectrum in the QFP maximum region.
It is proposed a new method for the maximum and
its error to be found in the fitting by a 6-th power
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2002, № 2.
Series: Nuclear Physics Investigations (40), p. 7-8. 7
polynomial. The method can be shortly described by the
following way. As the polynomial coefficients are
determined with their errors, it is possible to draw the
polynomial curves very much through experimental
points. So the control experimental points (xi, yi) with
their errors dyi are taken for limiting the 6-th power
polynomial set. We select only the polynomials values
of which must be equal yi ± dyi in point xi. The
maximums of different polynomials with the
coefficients within the errors of the initial polynomial
are found. The polynomial coefficients are picked up at
random. The more a number of the polynomials, the
more accurate the result we get. Among the maxima of
these random polynomials, we select two ones: one with
the most low maximum value x1max and another with the
highest value x2max. The required maximum xmax is the
arithmetical mean of these two numbers. The absolute
value of difference of xmax and x1max (or xmax and x2max) is
taken as the error of xmax. The polynomial maxima are
found by the method of half dividing.
Fig. 1. The dependence of 2Н(е,е′)- reaction cross
section on transferred energy. ■ is experimental points
for Еi = 292,8 MeV, θ = 60°. The plot is fitting by the 6-
th power polynomial
The analysis results of the experimental data at the
angle 60° are represented on Fig. 2 and in the table. The
Kinematical conditions and results of analysis
Еi,
MeV
ωmax,
MeV
ωеN,
MeV
ε,
MeV
q,
Fm-1
292,8±0,4 40,9±0,5 39,5±0,5 1,37±0,71 1,39
366,0±0,5 60,6±0,2 59,7±0,7 0,86±0,70 1,72
465,3±0,7 94,5±0,3 92,5±0,8 2,01±0,87 2,16
510,2±0,8 111,9±0,4 109,1±0,9 2,83±0,97 2,35
596,8±0,9 146,9±1,0 144,0±1,0 2,93±1,47 2,73
error of the quantity ε takes into account the
measurement error of the initial energy, the fitting error
and the error of finding the quantity ωeN. From Fig. 2, it
is seen well dynamics of the QFP maximum shift in
2Н(е,е′)- reaction relative to the peak of the elastic еN-
scattering in dependence on the kinematical conditions
of measurement. As seen from Fig. 2, polynomial fitting
experimental data points out that the shift quantity ε
increases from the value 1,37 up to 2,93 MeV with
increasing transferred momentum in the interval 1,39-
2,73 Fm-1. No obvious anomaly like a minimum appears
at low energy loss. Nevertheless, the final result is
considered not to be completely determined because of
a low number of the investigated spectra and the
relatively high experimental errors. The available data
are failed for conclusion to be reliable on behaving the
investigated dependence on the kinematical conditions
of measurement.
Fig. 2. The QFP maximum shift dependence for 2Н
nucleus relative to the peak of the elastic eN- scattering
on transferred 3- momentum. The scattering angle is
θ = 60°. is the experimental points at fitting QFP by
the 6-th polynomial. The straight line is the result of the
linear fitting
CONCLUSIONS
The shift of the QFP maximum relatively elastic eN-
kinematic increases from the value 1,37 up to 2,93 MeV
with increasing transferred momentum in the interval
1,39-2,73 Fm-1. The shift cannot be directly related to
the average nucleon separation energy.
Specific behavior of the ε(q)- dependence for
deuterium may indicate that another process is
competing with the single nucleon knockout process
and altering the perceived quasielastic peak location.
In order that progress be made in the solution of the
problem additional experimental investigations over a
large range of momentum transfer and modern
theoretical calculations are need.
REFERENCES
1. J.S. O’Connel, B. Schroder. Quasifree Electron
Scattering on Nucleons in a Momentum-Dependent
Potential // Phys. Rev. 1988, v. C38, №5, p. 2447-
2449.
2. E.L. Kuplennikov, A.Yu. Korchin, A.V. Shebeko To
Question on Maximum Position of Quasfree Peak in
(е, е')- Reaction on Atom Nuclei // Yadern. Fiz.
1984, v. 39, is. 4, p. 1047-1049 (in Russian).
3. S.A. Ditman, A.M. Bernstein, K.I. Blomqvist et al.
Inclusive Electron Scattering from 2H, 3He and 4He //
Phys. Rev. 1988, v. C38, №2, p. 800-812.
4. B.P. Quinn, A.M. Bernstein, K.I. Blomqvist et al.
Measurements of Total and Separated Response
8
9
Functions of the Deuteron Through the Quasi-
Elastic Peak Region for q∼300 - 500 MeV/c // Phys.
Rev. 1988, v. C37, № 4, p. 1609-1623.
9
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| id | nasplib_isofts_kiev_ua-123456789-80102 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:04:14Z |
| publishDate | 2002 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Krasil’nikov, V.V. Kuplennikov, E.L. Levashov, I.A. Ranyuk, Yu.N. 2015-04-11T19:09:05Z 2015-04-11T19:09:05Z 2002 Q-dependence of the quasifree peak maximum position in ²Н(e,e')-reaction / V.V. Krasil’nikov, E.L. Kuplennikov, I.A. Levashov, Yu.N. Ranyuk // Вопросы атомной науки и техники. — 2002. — № 2. — С. 7-8. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 25.30.Fj https://nasplib.isofts.kiev.ua/handle/123456789/80102 The problem of the quasifree peak position of energy spectra at scattering electrons in inclusive ²H(e,e')- reaction is discussed. ε(q) dependence of the lightest deuterium nucleus is investigated. The fitting experimental points are realized by a 6-th power polynomial. It is proposed the new method of finding maxima of energy spectra and its errors at the polynomial fitting. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Nuclear reactions Q-dependence of the quasifree peak maximum position in ²Н(e,e')-reaction Q-зависимость положения максимума квазиупругого пика в ²Н(е,е')-реакции Article published earlier |
| spellingShingle | Q-dependence of the quasifree peak maximum position in ²Н(e,e')-reaction Krasil’nikov, V.V. Kuplennikov, E.L. Levashov, I.A. Ranyuk, Yu.N. Nuclear reactions |
| title | Q-dependence of the quasifree peak maximum position in ²Н(e,e')-reaction |
| title_alt | Q-зависимость положения максимума квазиупругого пика в ²Н(е,е')-реакции |
| title_full | Q-dependence of the quasifree peak maximum position in ²Н(e,e')-reaction |
| title_fullStr | Q-dependence of the quasifree peak maximum position in ²Н(e,e')-reaction |
| title_full_unstemmed | Q-dependence of the quasifree peak maximum position in ²Н(e,e')-reaction |
| title_short | Q-dependence of the quasifree peak maximum position in ²Н(e,e')-reaction |
| title_sort | q-dependence of the quasifree peak maximum position in ²н(e,e')-reaction |
| topic | Nuclear reactions |
| topic_facet | Nuclear reactions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/80102 |
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