The ⁹Be(d, t) nuclear reaction at low deuteron energies
Consideration is given to the possibility of describing the experimental data, earlier obtained for angular dependences of cross sections and vector analyzing powers (VAP) of the ⁹Be(d, t₀) reaction induced by vector polarized deuterons of energies between 2.5 and 2.8MeV, within the framework of the...
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Shlyakhov, N.A. 2017-01-15T11:44:50Z 2017-01-15T11:44:50Z 2013 The ⁹Be(d, t) nuclear reaction at low deuteron energies / N.A. Shlyakhov // Вопросы атомной науки и техники. — 2013. — № 3. — С. 156-161. — Бібліогр.: 16 назв. — англ. 1562-6016 PACS: 25.40.Lw, 23 20.-g https://nasplib.isofts.kiev.ua/handle/123456789/111854 Consideration is given to the possibility of describing the experimental data, earlier obtained for angular dependences of cross sections and vector analyzing powers (VAP) of the ⁹Be(d, t₀) reaction induced by vector polarized deuterons of energies between 2.5 and 2.8MeV, within the framework of the distorted wave Born approximation (DWBA), using the "measured" optical potential parameters at input/output channels without additional variations. Pairs of sets of optical potential parameters have been found, which permit simultaneous fits of the main trends in the behavior of angular distributions of cross sections and the VAP for ⁹Be(d, t₀). The direct pickup is demonstrated to be the predominant mechanism of the nuclear reaction occurrence at such low energies. It is possible that the characteristic properties of the direct process at so low energies are determined by the peculiarities of interaction between weakly coupled particles in the area of action of the thresholds of disintegration of the reacting nuclei into their fragments. Розглядається можливiсть опису ранiше знайдених експериментальних даних для кутових залежностей диференцiальних перерiзiвi векторних аналiзуючих здiбностей (ВАЗ) реакцiї ⁹Be(d, t₀), викликаних векторно поляризованими дейтронами з енергiєю 2,52...8 МеВ, в межах борнiвського наближення збурених хвиль (БНЗХ) з використанням "вимiряних" параметрiв оптичних потенцiалiв у вхiдномуi вихiдному каналах без додаткових варiацiй. Знайдено пари наборiв параметрiв оптичних потенцiалiв, що дозволяють одночасно вiдтворити основнi тенденцiї в характерi поведiнки кутових розподiлiв перетинiв i ВАЗ для ⁹Be(d, t₀). Показано, що домiнуючим механiзмом протiкання цих ядерних реакцiй при таких низьких енергiях є пряме пiдхоплення. Можливо, що характернi риси прямого процесу при таких низьких енергiях зумовленi особливостями взаємодiї слабозв’язаних частинок в областi дiї порогiв розвалу ядер, що беруть участь у процесi, на їх фрагменти. Рассматривается возможность описания ранее найденных экспериментальных данных для угловых зависимостей дифференциальных сечений и векторных анализирующих способностей (ВАСП) реакции ⁹Be(d, t₀), вызванных векторно поляризованными дейтронами с энергией 2,52...8 МэВ, в рамках борновского приближения искаженных волн (БПИВ) с использованием "измеренных" параметров оптических потенциалов во входном и выходном каналах без дополнительных вариаций. Найдены пары наборов параметров оптических потенциалов, позволяющие одновременно воспроизвести основные тенденции в характере поведения угловых распределений сечений и ВАСП для ⁹Be(d, t₀). Показано,что доминирующим механизмом протекания этих ядерных реакций при столь низких энергиях является прямой подхват. Возможно, что характерные черты прямого процесса при столь низких энергиях определяются особенностями взаимодействия слабо связанных частиц в области действия порогов развала ядер, участвующих в процессе, на их фрагменты. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Ядерная физика и элементарные частицы The ⁹Be(d, t) nuclear reaction at low deuteron energies Ядерна реакцiя ⁹Be(d, t) при низьких енергiях дейтронiв Ядерная реакция ⁹Be(d, t) при низких энергиях дейтронов Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
The ⁹Be(d, t) nuclear reaction at low deuteron energies |
| spellingShingle |
The ⁹Be(d, t) nuclear reaction at low deuteron energies Shlyakhov, N.A. Ядерная физика и элементарные частицы |
| title_short |
The ⁹Be(d, t) nuclear reaction at low deuteron energies |
| title_full |
The ⁹Be(d, t) nuclear reaction at low deuteron energies |
| title_fullStr |
The ⁹Be(d, t) nuclear reaction at low deuteron energies |
| title_full_unstemmed |
The ⁹Be(d, t) nuclear reaction at low deuteron energies |
| title_sort |
⁹be(d, t) nuclear reaction at low deuteron energies |
| author |
Shlyakhov, N.A. |
| author_facet |
Shlyakhov, N.A. |
| topic |
Ядерная физика и элементарные частицы |
| topic_facet |
Ядерная физика и элементарные частицы |
| publishDate |
2013 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Ядерна реакцiя ⁹Be(d, t) при низьких енергiях дейтронiв Ядерная реакция ⁹Be(d, t) при низких энергиях дейтронов |
| description |
Consideration is given to the possibility of describing the experimental data, earlier obtained for angular dependences of cross sections and vector analyzing powers (VAP) of the ⁹Be(d, t₀) reaction induced by vector polarized deuterons of energies between 2.5 and 2.8MeV, within the framework of the distorted wave Born approximation (DWBA), using the "measured" optical potential parameters at input/output channels without additional variations. Pairs of sets of optical potential parameters have been found, which permit simultaneous fits of the main trends in the behavior of angular distributions of cross sections and the VAP for ⁹Be(d, t₀). The direct pickup is demonstrated to be the predominant mechanism of the nuclear reaction occurrence at such low energies. It is possible that the characteristic properties of the direct process at so low energies are determined by the peculiarities of interaction between weakly coupled particles in the area of action of the thresholds of disintegration of the reacting nuclei into their fragments.
Розглядається можливiсть опису ранiше знайдених експериментальних даних для кутових залежностей диференцiальних перерiзiвi векторних аналiзуючих здiбностей (ВАЗ) реакцiї ⁹Be(d, t₀), викликаних векторно поляризованими дейтронами з енергiєю 2,52...8 МеВ, в межах борнiвського наближення збурених хвиль (БНЗХ) з використанням "вимiряних" параметрiв оптичних потенцiалiв у вхiдномуi вихiдному каналах без додаткових варiацiй. Знайдено пари наборiв параметрiв оптичних потенцiалiв, що дозволяють одночасно вiдтворити основнi тенденцiї в характерi поведiнки кутових розподiлiв перетинiв i ВАЗ для ⁹Be(d, t₀). Показано, що домiнуючим механiзмом протiкання цих ядерних реакцiй при таких низьких енергiях є пряме пiдхоплення. Можливо, що характернi риси прямого процесу при таких низьких енергiях зумовленi особливостями взаємодiї слабозв’язаних частинок в областi дiї порогiв розвалу ядер, що беруть участь у процесi, на їх фрагменти.
Рассматривается возможность описания ранее найденных экспериментальных данных для угловых зависимостей дифференциальных сечений и векторных анализирующих способностей (ВАСП) реакции ⁹Be(d, t₀), вызванных векторно поляризованными дейтронами с энергией 2,52...8 МэВ, в рамках борновского приближения искаженных волн (БПИВ) с использованием "измеренных" параметров оптических потенциалов во входном и выходном каналах без дополнительных вариаций. Найдены пары наборов параметров оптических потенциалов, позволяющие одновременно воспроизвести основные тенденции в характере поведения угловых распределений сечений и ВАСП для ⁹Be(d, t₀). Показано,что доминирующим механизмом протекания этих ядерных реакций при столь низких энергиях является прямой подхват. Возможно, что характерные черты прямого процесса при столь низких энергиях определяются особенностями взаимодействия слабо связанных частиц в области действия порогов развала ядер, участвующих в процессе, на их фрагменты.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/111854 |
| citation_txt |
The ⁹Be(d, t) nuclear reaction at low deuteron energies / N.A. Shlyakhov // Вопросы атомной науки и техники. — 2013. — № 3. — С. 156-161. — Бібліогр.: 16 назв. — англ. |
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| first_indexed |
2025-11-26T02:05:53Z |
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2025-11-26T02:05:53Z |
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| fulltext |
THE 9Be(d, t) NUCLEAR REACTION AT LOW DEUTERON
ENERGIES
N.A.Shlyakhov ∗
National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
(Received September 24, 2012)
Consideration is given to the possibility of describing the experimental data, earlier obtained for angular dependences
of cross sections and vector analyzing powers (VAP) of the 9Be(d, t0) reaction induced by vector polarized deuterons
of energies between 2.5 and 2.8 MeV , within the framework of the distorted wave Born approximation (DWBA),
using the ”measured” optical potential parameters at input/output channels without additional variations. Pairs
of sets of optical potential parameters have been found, which permit simultaneous fits of the main trends in the
behavior of angular distributions of cross sections and the VAP for 9Be(d, t0). The direct pickup is demonstrated
to be the predominant mechanism of the nuclear reaction occurrence at such low energies. It is possible that the
characteristic properties of the direct process at so low energies are determined by the peculiarities of interaction
between weakly coupled particles in the area of action of the thresholds of disintegration of the reacting nuclei into
their fragments.
PACS: 25.40.Lw, 23 20.-g
1. INTRODUCTION
A number of experiments have been made in recent
years to investigate the cross sections for deuteron-
induced reactions on the 9Be nucleus [1-2]. They
provide a more systematic approach to the analysis
of the mechanisms of nuclear reaction on this nucleus
in a rather wide incident-deuteron energy range from
1 to 15 MeV .
The existing parameterizations of one-nucleon
transfer calculations meet with difficulties stemming
from the fact that apart from the direct process con-
tribution, there arise competing mechanisms of the
reaction occurrence, which distort the angular depen-
dence shapes, of the measured observables in the ex-
periment. This sets up the problem of finding the cri-
teria for adequate description of the direct process in
the low-energy region of incident particles that would
be independent of a direct comparison with experi-
mental observables. As already stated, the compari-
son may be distorted not only by contributions from
indirect processes, but also by calculation errors due
to violations of the conditions for the fulfillment of
various assumptions included in the theoretical treat-
ments of direct processes. Besides, there is also a
problem connected with the divergence in the behav-
ior of polarization observables such as the vector ana-
lyzing power (VAP) and the polarization of outgoing
particles for the cases, where the cross-sectional an-
gular dependences show distinct features typical of
the direct process, this divergence being observed in
a wide energy range.
A detailed analysis of cross-section angular dis-
tributions as functions of energy (see ref. [3]) as well
as studies on optical potential parameterization (refs.
[4, 5]) provide good basis for investigating the pecu-
liarities of the angular distribution behavior of not
only cross sections but also of polarization observ-
ables in deuteron-induced reactions on 9Be at low
energies. The unique feature of the chosen incident-
deuteron energy range (1.5...3.0 MeV ) lies in the
fact that on the interval of less than 1 MeV there
are two thresholds of target nucleus disintegration
(n−8Be with Elab
d = 2.04 MeV , α−5He with Elab
d =
3.01 MeV ) and the threshold of incident deuteron
disintegration (n− p with Elab
d = 2.71 MeV ).
The aim of the present work has been to clarify
the possibility of simultaneous description of angu-
lar dependences of the cross section and the VAP in
the framework of the DWBA, using a phenomenolog-
ical parameterization of distorting wave functions in
the input/output channels for the one-nucleon pickup
reactions in the low-energy region of bombarding
deuterons on the 9Be nucleus. Our findings will be
compared with the results obtained at other labora-
tories of the world.
2. SPECTRA FROM A TWO-LAYER
TARGET
Simultaneous measurements of the differential cross
section dσ/dΩ and the VAP Ay(θ) for elastic scatter-
ing of vector-polarized deuterons by 9Be and 197Au,
and also, for the nuclear reactions 9Be(d, p)10Be,
9Be(d, t)8Be, 9Be(d, α)7Li were performed by the
method described in refs. [5, 6] with the use of
∗Corresponding author E-mail address: shlyahov@kipt.kharkov.ua
156 ISSN 1562-6016. PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2013, N3(85).
Series: Nuclear Physics Investigations (60), p.156-161.
two detectors, a two-component target and a po-
larized particle beam with one direction of the po-
larization vector. Figure 1 shows the charged par-
ticle spectrum measured at the interaction of po-
larized deuterons with a two-layer Be+Au target.
Fig.1. Charged particle spectrum measured at
interaction of polarized deuterons with a two-layer
(Be + Au) target at θl = 30◦ [6]
The charged particle spectra (see Fig.1) measured
with the total deuteron energy resolutions ∆E1/2 =
50...70 keV and ∆E1/2 < 40 keV for the investigated
(Be) and monitor (Au) parts of the two-layer target,
respectively, have enabled us to separate the peaks
of deuteron elastic scattering by 9Be and 197Au at
θl ≥ 30◦, and also, to separate clearly the peaks cor-
responding to the p0, p1, t0, α0, α1 particle groups.
This permits normalization of the yields of indi-
vidual groups to the yield of elastic scattering by
gold. The type of the particles and their energy
groups were identified through calculations of the re-
action kinematics: Eb = f(Ea, Ex, θb). The narrow
peaks of p1 and α2, corresponding to the reactions
9Be(d, p)10Be∗ (Ex = 3.37 MeV ) and 9Be(d, α2)7Li∗
(Ex = 4.63 MeV ) lie on a wide (Γ ∼ 1 MeV ) peak
(t1- dashed line) formed by a triton group from the re-
action 9Be(d, t1)8Be∗ (Ex = 2.94 MeV ) and by the
continuous alpha spectrum from the decay of 8Be
ground state in the reaction 9Be(d, t0)8Beo.c. → 2α
(solid line). In the angular ranges θl = 100◦...110◦
and θl = 140◦...150◦, the triton peak t0 overlaps with
the proton peaks from the reactions 12C(d, p0)13C
and 16O(d, p0)17O, respectively. The technique of
t0 peak separation in the regions of overlap with
the background has been described in ref. [7]. The
t1 group was not analyzed, as it was impossible to
identify exactly the maximum value of the wide peak.
3. THE CROSS SECTION AND VECTOR
ANALYZING POWER
Experimental results [7] for the angular dependence
of the differential cross section are presented in
Figs. 2 and 5, and the VAP energy dependence is
shown in Fig.3. The VAP energy dependence for
the 9Be(d, t)8Be reaction, measured at θ1 = 30◦ in
the region of forward-scattering angles that corre-
spond to the pickup peak at energies higher than
2.0 MeV (Ay ≈ 0), and the VAP angular depen-
dence for the 9Be(d, t0)8Be reaction (Fig.2) point t0
the predominance of the direct process. The prob-
lem lies in the presence of the third maximum at
these low energies and in the displacement of the
main pickup peak, which corresponds to the trans-
fer of the neutron having the orbital angular mo-
mentum l = 1, towards small angles (see Fig. 2).
Fig.2. Comparison of our experimental data for
the differential cross section with the data of other
authors at Ed = 2.5 MeV for the 9Be(d, t0)8Be
reaction. • - our data; - - - - differential cross
sections reconstructed with the Legendre polynomials
coefficients taken from ref. [3]; × - data of ref. [8]
Fig.3. VAP energy dependence for the
9Be(d, t0)8Be reaction, measured at θl = 30◦ (a) and
140◦ (b). Solid line represents the DWBA calculation
with D2 + T1
The angular dependences of the cross section and
the VAP at deuteron energy of 2.8 MeV are shown
in Fig. 5. They are similar to those observed at
Ed = 2.5 MeV .
4. DISTORTED WAVE ANALYSIS
For simultaneous analysis of the angular dependences
of the cross section and VAP within the framework
157
of the DWBA with the zero radius of interaction,
we have used our own program [7,9]. The program
was tested by comparing with DWUCK program
computations for angular dependences of the cross-
section and VAP of the 9Be(d, t0)8Be reaction at
the deuteron energy Ed = 15 MeV (Fig. 4) using
the optical potentials of ref. [10]. The calculation
in point is in good agreement with the experimen-
tal data for the jn = 3/2 neutron pickup [10]. The
pairs of sets of phenomenological potential parame-
ters of the input and output channel for simulta-
neous description of the cross-section and VAP of
the 9Be(d, t0)8Be reaction with jn = 3/2 were cho-
sen through comparison of the zero-range DWBA
Fig.4. Comparison of calculated angular distribu-
tions of differential cross sections and VAP for the
one-nucleon pickup reaction 9Be(d, t0)8Be at purely
vector-polarized deuteron energy Ed = 15 MeV . —-
computation by our zero-range program in the [9];
· · · · - DWUCK computation [10]
Fig.5. Comparison of measured and zero-range
DWBA-calculated angular dependences of cross-
sections and VAP for the 9Be(d, t0)8Be reaction at
Ed = 2.8 MeV for Jn = 3/2, St = 0.51 and with
different sets of optical parameters. −− - PP1+T5;
· · · · - H ′ + T4; − · −- P ′ + T4
calculated data with experimental angular distribu-
tions of the dσ(θ)/dΩ cross-sections and VAP Ae(θ),
using for this the purpose phenomenological sets of
parameters, obtained at corresponding energies for
deuterons: H ′, P ′, SH ′, PP ′ (see table 1) [5]; and
tritons: T1− T8 (see Table 1).
Table 1. Optical potential parameters with spin-orbital interaction for elastic deuteron scattering by 9Be
at Ed ≤ 2.8 MeV [5]. Surface absorption rC = 1.3 fm
Ed, Set V0 r0, a0, Ws rw, aw, Vs0, rs0, as0, χ2 χ2
c.−s. χ2
pol
MeV MeV fm fm MeV fm fm MeV fm fm
2.8 H ′ 114.2 0.869 1.01 16.0 2.16 0.323 6.0 0.869 1.01
2.8 P ′ 95.44 1.15 0.81 10.80 1.575 0.585 10.0 1.15 0.81
5.25 D2[14] 170.0 0.90 0.90 12.00 2.10 0.50 7.5 1.20 0.90
2.8 PP1 95.44 1.15 0.79 10.80 1.70 0.585 10.0 1.15 0.60 3.8 3.34 4.22
Table 2. Optical potential parameters for elastic scattering of helions and tritons, employed in the analysis
of the 9Be(d, t0)8Be reaction. Surface absorption rC = 1.4 fm
Set particle E, V0, r0, a0, Ws, Wv, rw, aw, Vs.o., rs.o., as.o., Ref.
MeV MeV fm fm MeV MeV fm fm MeV fm fm
T1 133.0 0.86 0.7 4.09 − 2.68 0.5 6.0 0.86 0.7 [16]
T4 3H +9 Be 12.0 160.5 1.40 0.63 − 16.0 1.40 0.63 5.0 1.40 0.63 [3]
T5 3He +9 Be 135.0 1.40 0.70 − 17.0 1.40 0.70 5.0 1.10 0.74 [15]
158
The calculation data and the measurement re-
sults are presented in Fig. 5. The calculated absolute
differential cross sections are shown for the spectro-
scopic factor Sn = 0.51 (close to the theoretical value
for the multiparticle shell model with the intermedi-
ate coupling - 0.58) [11].
The wave functions of the bound state of
the 9Be nucleus were calculated by a standard
method using the Woods-Saxon potential with spin-
orbital interaction. The parameters of the real
part of the potential were r0 = rs0 = 1.25 fm
and a0 = as0 = 0.65 fm with Vs0 = 6.0 MeV .
Fig.6. Spectroscopic factors S/Stheor, Stheor = 0.58
[11]. black triangles - [3]; ×- [8], ◦ and square -
present work
The depth of the real part is found through variation
until the binding energy of the neutron is obtained.
The neutron binding energy, corresponding to the
shell model with intermediate coupling [11] having
the α + 5N structure, is equal to - 6.5 MeV , whereas
for the one-particle model it equals 1.66 MeV with
V0 = 38.65 MeV , just for which all the analysis data
are shown.
Fig. 5 illustrates the possibility of simultaneous
description of the cross-section and the VAP (exper-
imentally observed at the incident deuteron energy
Ed = 2.8 MeV ) are calculated with the spectroscopic
factor close to the shell-model factor, without varying
the experimentally measured parameters of optical
potentials PP1 + T5. The PP1 potential describes
the cross-section and the VAP of elastic scattering at
Ed = 2.8 MeV .
5. DISCUSSION OF ANALYSIS DATA
The mode of behavior of the VAP, calculated at
θc.m.c.m. < 130◦, has the form corresponding to the
calculations at deuteron energies higher than 12 MeV
(see Fig. 4), and the differential cross section displays
a double-humped structure in the intensity and po-
sition of their maxima. It should be noted that the
deuteron potential parameters play an important role
in the detailed description of angular distributions
cross sections in the region of the pick-up peak, this
having a pronounced effect on the spectroscopic fac-
tor value (increasing it by factors of 2 or 3 in this
case). The set of the parameters P ′ + T4 is capa-
ble of quality reproducing both the VAP behavior
pattern in the whole angular range and the correct
cross-section in the region of the second peak, as it
has been observed at Ed = 3.6 MeV in the work of
Fulbright et al. [12].
Fig. 6 gives our calculated spectroscopic factors
in comparison with the literature data. They are lit-
tle different from the theoretical value given by the
intermediate-coupling shell model [11].
In view of the foregoing it can be stated that in the
low energy region the nuclear reaction 9Be(d, t0)8Be
proceeds mainly due to the mechanism of direct neu-
tron pickup from the neutron-enriched surface of a
weakly-bound nucleus. However, one should take
into account the peculiarity in the behavior of the
spectroscopic factor in the energy dependence of the
differential cross-section in the region of the pickup
peak maxima. The excitation function measured at
θlab = 45◦ first shows a smooth rise up to a deuteron
energy of 1.9 MeV , and from then on remains con-
stant, i.e., after 2.0 MeV the pickup peak continues
growing. Simultaneously, the second peak goes to
splitting (see Fig. 3) accompanied by the displace-
ment towards smaller angles, while the position of
the third peak remains constant. In the foregoing we
have shown that all the three peaks can be described
in the framework of the DWBA.
6. CONCLUSIONS
The analysis of the 9Be(d, t0)8Be reaction has
demonstrated the possibility of describing the exper-
imentally observed angular dependences of the differ-
ential cross-section and the VAP in the framework of
the zero-rang DWBA, using for the purpose a mod-
ified in [5] set of the parameters PP1 (initial P ′)
that describe elastic scattering at Ed = 2.8 MeV ,
and also, the helion set parameters T5 at standard
parameterization of the bound state. In such a case,
the spectroscopic factor estimated from normaliza-
tion of the calculated 1st-peak slope cross-section to
the experiment (θc.m. ∼ 30◦) (see Fig. 5) is in good
agreement with the value calculated by the many-
particle shell model with the intermediate coupling
(α + 5N) [11]. This situation may occur due to the
fact that in spite of various restrictions arising at vi-
olations of DWBA theory approximations at low en-
ergies of the particle incident on the light nucleus
and at a rather high Q = 4.592 MeV , the neutron-
binding energy is extremely low (εn = 1.665 MeV )
and this leads to the surface interaction of the reac-
tion. Besides, the reaction proceeds in the incident
deuteron energy region, which exhibits three disinte-
gration thresholds of interacting nuclei (n−8 Be with
Elab
d = 2.04 MeV , α −5 He with Elab
d = 3.01 MeV
and n− p with Elab
d = 2.71 MeV ), and it is conceiv-
able that this may also increase the contribution of
the direct process.
The peculiarities of triton potential parameteriza-
tion are the principal factors that determine the main
features of the angular dependence of cross-sections
and VAP. In our case, we have increased values of the
159
radius parameter (r0 = 1.40 fm) and the depth of
volume absorption (Wv = 17.0 MeV ). The deuteron
potential parameters have an effect on the gradient
of slope oscillations in the angular dependence of the
cross section and the magnitude of the cross-section
itself. Our parameterization enables one to reproduce
the positions and values of the 1st and 3rd maxima
in the angular distribution at low deuteron energies.
This mode of behavior of the cross-sectional angu-
lar distribution may point to the fact that the initial
motion of the deuteron is little distorted during neu-
tron transfer in the entire incident particle energy
range. This may occur provided that the reaction
has strictly a surface character. In the low energy
region, this situation is of fundamental importance
for the case when the matching condition is strongly
violated for small ri values (rapa = rbpb, where pi de-
notes relative momenta of the incident and outgoing
particles, ri corresponds to their relative distances
from centers of the target nucleus and the residual
nucleus).
The use of the parameterization D2 for the reac-
tion under study provides on the average a reliable
fit of VAP energy dependences at Ed > 2.0 MeV [13]
(see Fig. 3).
References
1. L.N. Generalov, et al. 9Be(d, p01) and 9Be(d, t−
0) reaction cross sections // Izvestiya AN SSSR.
Ser. ”Fiz.” 2000, v. 64, N3, p. 440-451 (In
Russian).
2. S.N. Abarmovich., Yu.I. Vinogradov, L.N. Gen-
eralov, et al. 9Be(d, t0)8Be reaction cross sections
// Izvestiya AN SSSR. Ser. ”Fiz.” 1995, v. 59,
N11, p. 88-91 (In Russian).
3. D. Zwieglinski, A. Saganek, I. Sledzinska,
Z. Wilhelmi Direct and Resonance processes in
9Be(d, po,1)10Be and 9Be(d, t0)8Be at low ener-
gies // Nucl. Phys. 1975, v. A250, N 1, p. 93-105.
4. B. Zwieglinska, et al. Optical model and Hauser-
Feshbach analysis of 9Be+d and 10B+p interac-
tions at low energies // Nucl. Phys. 1973, A209,
p. 348-362.
5. V.D. Sarana. Optical potential parameterization
forelastic scattering of low-energy deuterons from
9Be // Journal of Kharkov National University,
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N710, p. 3-20 (In Russian).
6. A.S. Deineko, I.I. Zalyubovsky, I.Ya. Malakhov,
V.D. Sarana, N.A. Shlyakhov. Asymmetry mea-
surements of products from polarized deuteron
reactions using the normalization to the Ruther-
ford scattering by Au. // Izvestiya AN SSSR,
ser.: Fiz., 1980, v. 44, N 11, p. 2382-2387. (In
Russian).
7. V.D. Sarana, N.A. Shlyakhov, Yu.V. Lyashko.
Polarization observables in 9Be(d, p0)10Be and
9Be(dt0)8Be reactions at low deuteron energies
and the contribution of the direct mechanism of
neutron transfer // Journal of Kharkov National
University, ser. Nuclei, Particles and Fields,
2006, iss. 3/31/ N744, p. 28-50 (In Russian).
8. Bondouk, F. Asfour, F.Machali. Investigation of
the Reaction 9Be(d, t0)8Be in the deuteron En-
ergy range 0, 9...2, 5 MeV // Ann. Phys. (Leipzig)
1975, B32, H.4, p. 255-260.
9. Yu.P. Antufyev, A.S. Deineko, V.D. Sarana,
N.A. Shlyakhov. The use of the distorted wave
method in direct nuclear reactions with polarized
particles, Kharkov, 1982, 21 p. (Preprint KhFTI
AN UkrSSR; KhFTI 82-56 (In Russian).
10. S.E.Darden, G.Murrillo, S. Sen. The
9Be(d, d)9Be, 9Be(d, p)10Be, 9Be(d, t)8Be
and 9Be(p, d)8Be reactions at 15 MeV //Nucl.
Phys. 1976, v. A266, N1, p. 29-52.
11. S. Cohen and D. Kurath. Spectroscopic factors
for the 1p shell // Nucl. Phys. 1967, v. A101,
N1, p. 1-16.
12. H.W.Fulbright, J.A. Bruner, D.A. Bromley and
L.M.Goldman. Angular distribution of protons
and tritons from deuterons- induced reactions on
9Be // Phys. Rev. 1952, v. 88, N4, p. 700-702.
13. Yu.V. Lyashko, A.S. Deineko, N.P.Dikiy,
R.P. Slabospitsky and N.A. Shlyakhov. Vec-
tor analyzing power of 9Be(d, t) and 9Be(dα)
reactions for deuteron energies up to 3 MeV .
// Izvestiya AN SSSR. Ser. ”Fiz.” 1994, v. 58,
N11, p. 184-187 (In Russian).
14. B.A. Robson. Deuteron-induced reactions in 6Li,
9Be and 10B at bombarding energies of 4.5 to
6.0 MeV . // Nucl. Phys. 1970, v. A147, p. 65-80.
15. D.J. Pullen, J.R. Rook, R. Middleton. Triton
elastic scattering from light nuclei // Nucl.Phys.
1964, v. 51, p. 88-95.
16. W.Fitz, R. Jahr and R. Santo. Scattering and
Pick-up Reactions with Deuterons on Be, B, C,
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160
ЯДЕРНАЯ РЕАКЦИЯ 9Be(d, t) ПРИ НИЗКИХ ЭНЕРГИЯХ ДЕЙТРОНОВ
Н.А.Шляхов
Рассматривается возможность описания ранее найденных экспериментальных данных для угловых
зависимостей дифференциальных сечений и векторных анализирующих способностей (ВАСП) реак-
ции 9Be(d, t0), вызванных векторно поляризованными дейтронами с энергией 2, 52...8 МэВ, в рамках
борновского приближения искаженных волн (БПИВ) с использованием "измеренных"параметров оп-
тических потенциалов во входном и выходном каналах без дополнительных вариаций. Найдены пары
наборов параметров оптических потенциалов, позволяющие одновременно воспроизвести основные тен-
денции в характере поведения угловых распределений сечений и ВАСП для 9Be(d, t0). Показано, что
доминирующим механизмом протекания этих ядерных реакций при столь низких энергиях является
прямой подхват. Возможно, что характерные черты прямого процесса при столь низких энергиях опре-
деляются особенностями взаимодействия слабо связанных частиц в области действия порогов развала
ядер, участвующих в процессе, на их фрагменты.
ЯДЕРНА РЕАКЦIЯ 9Be(d, t) ПРИ НИЗЬКИХ ЕНЕРГIЯХ ДЕЙТРОНIВ
М.А.Шляхов
Розглядається можливiсть опису ранiше знайдених експериментальних даних для кутових залежно-
стей диференцiальних перерiзiв i векторних аналiзуючих здiбностей (ВАЗ) реакцiї 9Be(d, t0), виклика-
них векторно поляризованими дейтронами з енергiєю 2, 52...8 МеВ, в межах борнiвського наближення
збурених хвиль (БНЗХ) з використанням "вимiряних"параметрiв оптичних потенцiалiв у вхiдному i
вихiдному каналах без додаткових варiацiй. Знайдено пари наборiв параметрiв оптичних потенцiалiв,
що дозволяють одночасно вiдтворити основнi тенденцiї в характерi поведiнки кутових розподiлiв пе-
ретинiв i ВАЗ для 9Be(d, t0). Показано, що домiнуючим механiзмом протiкання цих ядерних реакцiй
при таких низьких енергiях є пряме пiдхоплення. Можливо, що характернi риси прямого процесу при
таких низьких енергiях зумовленi особливостями взаємодiї слабо зв’язаних частинок в областi дiї по-
рогiв розвалу ядер, що беруть участь у процесi, на їх фрагменти.
161
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