Possible violations of the Haeberli rules in reaction (d,p) on 1p shell nuclei at low energy
In this paper we investigate the possibility of simultaneous description of the angular distributions of the cross section, the vector polarization and the vector analyzing power with DWBA, using various modifications deuteron Z-potentials and Perey, previously experimentally observed violations of...
Збережено в:
| Дата: | 2015 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
|
| Назва видання: | Вопросы атомной науки и техники |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/112108 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Possible violations of the Haeberli rules in reaction (d,p) on 1p shell nuclei at low energy / V.D. Sarana, N.S. Lutsay, N.A. Shlyakhov // Вопросы атомной науки и техники. — 2015. — № 3. — С. 25-23. — Бібліогр.: 31 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-112108 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1121082017-01-18T03:03:26Z Possible violations of the Haeberli rules in reaction (d,p) on 1p shell nuclei at low energy Sarana, V.D. Lutsay, N.S. Shlyakhov, N.A. Ядерная физика и элементарные частицы In this paper we investigate the possibility of simultaneous description of the angular distributions of the cross section, the vector polarization and the vector analyzing power with DWBA, using various modifications deuteron Z-potentials and Perey, previously experimentally observed violations of rules Haeberli in the low-energy deuterons on the example of the reaction ⁹Be(d,p)¹⁰Be. Found that using DWBA this case can be described as a violation of the rules Haeberli at the low energy. Досліджується можливість одночасного опису кутових розподілів перерізу, векторної поляризації і векторної аналізуючої здатності в рамках БПІВ, з використанням різних модифікацій дейтонного Z-потенціалу і потенціалу Перея, раніше экспериментально спостережуваних порушень правила Хаберлі в області малих енергій дейтронів на прикладі реакції ⁹Be(d,p)¹⁰Be. Знайдено, що за допомогою БПІВ можна описати порушення правила Хаберлі при низькій енергії. Исследуется возможность одновременного описания угловых распределений сечения, векторной поляризации и векторной анализирующей способности в рамках БПИВ, с использованием различных модификаций дейтонного Z-потенциала и потенциала Перея, ранее экспериментально наблюдаемых нарушений правила Хаберли в области малых энергий дейтронов на примере реакции ⁹Be(d,p)¹⁰Be. Найдено, что с помощью БПИВ можно описать нарушение правила Хаберли при низкой энергии. 2015 Article Possible violations of the Haeberli rules in reaction (d,p) on 1p shell nuclei at low energy / V.D. Sarana, N.S. Lutsay, N.A. Shlyakhov // Вопросы атомной науки и техники. — 2015. — № 3. — С. 25-23. — Бібліогр.: 31 назв. — англ. 1562-6016 PACS: 25.40.Lw http://dspace.nbuv.gov.ua/handle/123456789/112108 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Ядерная физика и элементарные частицы Ядерная физика и элементарные частицы |
| spellingShingle |
Ядерная физика и элементарные частицы Ядерная физика и элементарные частицы Sarana, V.D. Lutsay, N.S. Shlyakhov, N.A. Possible violations of the Haeberli rules in reaction (d,p) on 1p shell nuclei at low energy Вопросы атомной науки и техники |
| description |
In this paper we investigate the possibility of simultaneous description of the angular distributions of the cross section, the vector polarization and the vector analyzing power with DWBA, using various modifications deuteron Z-potentials and Perey, previously experimentally observed violations of rules Haeberli in the low-energy deuterons on the example of the reaction ⁹Be(d,p)¹⁰Be. Found that using DWBA this case can be described as a violation of the rules Haeberli at the low energy. |
| format |
Article |
| author |
Sarana, V.D. Lutsay, N.S. Shlyakhov, N.A. |
| author_facet |
Sarana, V.D. Lutsay, N.S. Shlyakhov, N.A. |
| author_sort |
Sarana, V.D. |
| title |
Possible violations of the Haeberli rules in reaction (d,p) on 1p shell nuclei at low energy |
| title_short |
Possible violations of the Haeberli rules in reaction (d,p) on 1p shell nuclei at low energy |
| title_full |
Possible violations of the Haeberli rules in reaction (d,p) on 1p shell nuclei at low energy |
| title_fullStr |
Possible violations of the Haeberli rules in reaction (d,p) on 1p shell nuclei at low energy |
| title_full_unstemmed |
Possible violations of the Haeberli rules in reaction (d,p) on 1p shell nuclei at low energy |
| title_sort |
possible violations of the haeberli rules in reaction (d,p) on 1p shell nuclei at low energy |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2015 |
| topic_facet |
Ядерная физика и элементарные частицы |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/112108 |
| citation_txt |
Possible violations of the Haeberli rules in reaction (d,p) on 1p shell nuclei at low energy / V.D. Sarana, N.S. Lutsay, N.A. Shlyakhov // Вопросы атомной науки и техники. — 2015. — № 3. — С. 25-23. — Бібліогр.: 31 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT saranavd possibleviolationsofthehaeberlirulesinreactiondpon1pshellnucleiatlowenergy AT lutsayns possibleviolationsofthehaeberlirulesinreactiondpon1pshellnucleiatlowenergy AT shlyakhovna possibleviolationsofthehaeberlirulesinreactiondpon1pshellnucleiatlowenergy |
| first_indexed |
2025-07-08T03:24:30Z |
| last_indexed |
2025-07-08T03:24:30Z |
| _version_ |
1837047555586785280 |
| fulltext |
POSSIBLE VIOLATIONS OF THE HAEBERLI RULES IN
REACTION (d,p) ON 1p SHELL NUCLEI AT LOW ENERGY
V.D.Sarana1∗, N.S.Lutsay1, N.A.Shlyakhov2
1V.N. Karazin Kharkov National University, 61077, Kharkov, Ukraine;
2National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
(Received January 21, 2015)
In this paper we investigate the possibility of simultaneous description of the angular distributions of the cross
section, the vector polarization and the vector analyzing power with DWBA, using various modifications deuteron
Z-potentials and Perey, previously experimentally observed violations of rules Haeberli in the low-energy deuterons
on the example of the reaction 9Be(d,p)10Be. Found that using DWBA this case can be described as a violation of
the rules Haeberli at the low energy.
PACS: 25.40.Lw
1. INTRODUCTION
In previous papers [1] has been shown on the basis
of experimental data that at energies below 4 MeV
(Tab.1) is a violation of the rules Haeberli (Tab.2)
performed at energies above 7 MeV in the reactions
occurring mainly due to the direct process.
Table 1. Signs of spin observables (VAP and VP)
and slope of their angular distributions at main peak
of reactions 9Be(d,p0) jn=3/2, 9Be(d,p1)
10Be∗
(3.37MeV) jn=3/2 and 1/2 and 12C(d,p0) jn=1/2
in the problem area
Problem area <4 MeV
Spin ln...jn Ed Sign of Sign of
obser- MeV Ay(Pp) slope
vable θm<θ<2θm
1/2 2.8 − (+)
Ay 1 2.8 − +
VAP 3/2 2.5 + +
2.8 + +
1/2 3.2 − +
Pp 1
VP 3/2 2.5 + +
Table 2. Signs of spin observables (VAP) and slope
of their angular distributions at main peak
l j=l±1/2 Ay(θ at
θm<θ
<2θm
Sign of slope
Ay(θ) at θm
1 1−1/2=1/2 + +
1 1+1/2=3/2 − −
2 2−1/2=3/2 − −
2 2+1/2=5/2 + +
For the analysis of direct nuclear reactions the most
widely used method of DWBA, which is based on
the use of the optical model of elastic scattering.
However, in very light nuclei this procedure oc-
curs more difficult than for heavier nuclei. Using
phenomenological found deuteron parameter set of
the Z-potential [2] are showed an adequate descrip-
tion of the differential cross sections of the reaction
40Ca(d,p) by the local approach of the zero range dis-
torted waves method [4]. Heidelberg group [5], based
on the parameterization of Z-potential, show possibil-
ity of applicability to describe the elastic scattering
cross section and direct pick up reactions (d,t) and
(d,3He) on 1p-shell nuclei at an energy of 11.8MeV
deuterons with a slightly modified parameters (H1).
Argonne group [6] showed their applicability to de-
scribe of the cross sections striping direct reactions
(d,p) on 1p shell nuclei in the zero-range approxima-
tion using the cutoff radius RCo=4 fm. Under these
conditions of the calculation obtained spectroscopic
factors similar to those found in a shell model with
intermediate coupling [7]. Using corrections for the fi-
nite range (in the local energy approximation – LEP)
in many cases improves the agreement between the
calculated shape of the angular distribution of the
cross section with experiment and justifies the use of
the cutoff radius in the radial integral overlapping of
the wave functions for the extraction of spectroscopic
factors. However, they failed to uniquely determine
the ratio of the spectroscopic factors for mixed transi-
tions, and moreover, in case 40Ca(d,p) [4], this some-
what increases the absolute value of the spectroscopic
factors.
Continued use of Z-potential and its modifications
associated with the influence of the polarization ob-
∗Corresponding author E-mail address: sarana@univer.kharkov.ua
ISSN 1562-6016. PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2015, N3(97).
Series: Nuclear Physics Investigations (64), p.25-33.
25
servables on its parameterization and with the role of
spin-orbit interaction, at the description of the cross
section and vector polarization (VP) in the elastic
scattering of deuterons [8] the potential of Schwandt
and Haeberli (SH) (Wisconsin) as well as vector ana-
lyzing power (VAP) of the direct stripping reactions
(d,p) and (d,n) [9,10]. Found [9], that the empiri-
cal rule Haeberli, linking sign and magnitude VAP of
stripping reaction (d,p) in a certain range of angles
of emission of protons θm < θ < 2θm with the val-
ues of the transferred total angular momentum (see
Tab.2), and well reproduced by zero range DWBA
with deuteron potential type (SH) for the sd- and
2p1f-shells nuclei-targets. However, in some nuclei
1p shell (12C) this rule is violated, that the authors
of [9] is attributed to the influenced of non-optical-
model effects (formation of a compound nucleus res-
onances).
A comparison of the experimentally observed VP
− Pp(θ) and VAP − Ay(θ) at the same energy and
with a distinct picture of the direct process in the
angular distribution of the cross section for the reac-
tion 9Be(d,p)10Beg.s. shows (Figs.1a,d and in [1,9])
that in the typical range of angles θm < θ < 2θm
− the angle of the main stripping maximum) at
Edd ≥ 7 MeV for VAP Haeberli rule generally per-
formed well. For the VP sign are opposed VAP.
Fig.1. Energy dependence of the angular distri-
butions cross section, polarization (Pp) and vector
analyzing power (Ay) and their comparison with
DWBA calculations with modify Z optical-model
potential parameters for energy range from 4.0 to
8.0MeV . Experimental date for: a,d) 7...8MeV
(Y H − Be) [9,30], b,e) 5.25...5.5MeV (D2 + P6)
[11,16], c,f) 4.5...4.0MeV (D2 + P6) [11, 16]. Re-
sults calculation coincident with work [17,30]. Sign
polarization corresponds to the Basel Convention
This may indicate that in this energy region sign
rule for the VP or not performed or may be other.
Such a change in the sign confirmed by experimental
data for the VP 9Be(d,p) [30] (see Fig.1,d) and (d,n)
reactions on the target nuclei 1p1/2-shell [11], as well
as on some nuclei 1p3/2-shell [13] at low energies, in
particular for 9Be (Figs.1,e,f).
Experimentally, we found [15] what angular dis-
tributions VAP of (d,p) reaction in the interaction of
2.5- and 2.8-MeV deuteron with 9Be confirm this ex-
ception to the rule Haeberli and for VAP (see Tab.1).
Detailed analysis VP (d,n)-reactions on nuclei 1p1/2
within DWBA using the parameters of the deuteron
potential equivalent family of type 44 (classification
Meyer [12]) allows to reproduce the above rule viola-
tion Haeberli for VP in the jp=1/2 transitions, as well
as using the Z-potential in the analysis cross section
and VP (d,n0) reaction on 12C, held Wilmore and
Hodgson [14].
The aim of this work was to try to find an op-
portunity to describe the rule violation Haeberli by
optical model and DWBA using deuteron potential
parameters Z, H, and SH and their modifications and,
if possible, to find a settlement conditions in DWBA
in which these occur simultaneously qualitative ef-
fects in the angular distributions cross section, VP
and VAP, which are close to the experimentally ob-
served in the elastic scattering and reactions (d,p)
on the target nucleus of 1p3/2 shell (9Be) at energies
below 4 MeV.
2. COMPARISON OF THE DWBA WITH
OUR EXPERIMENTAL DATA AT LOW
ENERGIES
Based on the parameterization DWBA calculations
found to describe the angular distributions of the
cross section on the number of nuclei of the 1p3/2
shell at Ed=5.25 MeV [16], we repeated the calcu-
lations involving experimental data on the polariza-
tion [11] (see Figs.1,b,c,e,f), which also reproduce well
the violation of the rule Haeberli in the observed
polarization and repeat the calculation results Bon-
douk (Cairo-Bucharest) [17]. Next, we modeled the
dynamics of change in the behavior of the angular
distributions of the cross section and VAP reaction
9Be(d,p0) and elastic scattering in the transition from
a deuteron energy of 5.5 MeV to 2.8 MeV of our ex-
periment (see Figs.2,b,c).
Comparison with experimental reaction cross sec-
tion (see Fig.2,a) shows that there is a problem
with the description of the position and magni-
tude of the second peak in the reaction cross sec-
tion using zero range DWBA with spin-orbit in-
teraction. In this approximation, at low energies
there is a degeneration of the second peak with
the formation of a broad minimum between the 1-
st and 3-rd maxima in the cross section that is
clearly correlated with the disappearance of a neg-
ative minimum in the angular distribution VAP (see
Fig.2,b). So it is a significant change in the behav-
ior of the angular dependence of the cross section
for elastic scattering and polarization (see Fig.2,c)
at constant parameters of the optical potentials.
26
Fig.2. Modeling of the angular distributions of
differential cross section and V AP in the range
energies from 5.5 to 2.8MeV . a) Experimental data:
−−◦−− Ed = 5.5MeV [16]; ....• ....-Ed = 3.6MeV
[21]; − − × − −-Ed = 2.8MeV [15]. b) DWBA
zero range calculation with modify Z-potential from
[22] (D2 + P6) without energy dependence for
9Be(d, p0)10Beg.s.. jn = 3/2. c) Optical-model
calculation with modify Z-potential (D2) of the
elastic cross section σ(θ)/σR(θ) and V AP (Ay = P )
(polarization) for 9Be: -Ed = 5.5MeV ;
....-Ed = 3.6MeV ; − − −-Ed = 2.8MeV . Dashed
aria is angle aria near second pic of cross-section of
the reaction 9Be(d, p0)
10Be
First, we show the comparison results of our calcu-
lations with the above noted deuteron set of optical-
model parameters (D2, Tab.4) selected for the cal-
culation of cross sections and VAP the local zero
range DWBA with spin-orbit interaction (Fig.3) for
mixed on jn transition at a relatively low value of
Q-reaction in 9Be(d,p1)
10Be (3.37 MeV). Results of
the comparison show: a) taking into account the
contribution of the formation of the compound nu-
cleus (see Fig.3,b) joint description cross section and
VAP achieved when mixing ratio by j p2=1.85 (line
2), confirming the results of the analysis of data ob-
tained VAP at energies above 10 MeV [18]. This value
p=S3/2/S1/2, corresponds to shell model calculations
with intermediate coupling [7] and with the effective
forces of two-particle interactions (6-16)2BME. b) In
the case of p1= 0.21 (line 1) obtained a good descrip-
tion of the cross section in area of the main striping
peak, which coincides with the results of calculations
at higher energies [6,16]. However, with a complete
mismatch with the VAP data (line 1 in Fig.3) indi-
cates that preference should be given to (6-16)2BME
interaction.
In this case, the sign and shape of the an-
gular dependence of VAP does not comply with
rule Haeberli, but similar to that observed experi-
mentally VP reactions (d,n) [12] nuclei 1p1/2 shell.
Fig.3. Mixed by j transition in direct reaction
9Be(d, p1)10Be (3.339MeV ) at Ed = 2.8MeV .
Zero range DWBA theoretical calculation with
spin-orbit coupling, the potentials of D3 + P10. a -
Determination of mixing by j - p using V AP - Ay.
The solid lines correspond to the two mixing ratios
of the shell model theory: 1 - for p1 = 0.21, and 2 -
p2 = 1.85
Then, consider the comparison of predictions
DWBA both with zero range, and a mended on a
finite range (LEP) and nonlocality of optical poten-
tials, as well as the inclusion of the cutoff radius RCo
with their reflection in our experimental data for the
9Be(d,p0)
10Be (Fig.4). Comparison of calculations
with experimental data shows that: a) in the cal-
culations, as well as in the case of simulation (see
Fig.2,b) when we use the potential parameters of the
distortion waves in the entrance and exit channels
(D2+P15 or P19) (see Tab.4 and 5) in the approxi-
mation of zero range with the spin-orbit interaction
cannot properly describe the position and the size of
the 2-nd peak in the cross section, and only qualita-
tively reproduce the behavior of the polarization ob-
servables although spectroscopic factor gets close to
those given by the shell model (Tab.3); b) Inclusion
of the cutoff radius RCo=4 fm in zero range approx-
imation gives the correct position of the 2nd peak in
the cross section, but with a small amplitude. While
polarization observables are reproduced qualitatively
correctly in the forward hemisphere. c) In the case
of inclusion a finite range and no locality of opti-
cal potentials amendments to the DWBA calculations
with specially selected phenomenological parameters
of proton potentials (P15 and P19, see Tab.5) and the
modified Z-D2 potential can be simultaneous descrip-
tion of our data on the cross section, VP and VAP,
which are contrary to the rule Haeberli. However, are
somewhat inflated values of the spectroscopic factors
(see Tab.3).
27
Table 3. Comparison of spectroscopic factors found in our work with the literature data
the-
ory
[7]
2.5
MeV
[19]
2.5
MeV
[20]
2.5
MeV
[20]
5.25 MeV
[16]
0.9...3.1
MeV
[19]
2.5 MeV
our
2.8
MeV
our
2.5...2.8
MeV
our
2.8
MeV
our
2.8
MeV
our
Z+P1
No
corr.
Z
No
corr.
H+P1
with-
out
Vso
D2+P6
without
corr.
+H-F
Method
Bau-
cock for
DWBA
D2+P14
without
corr.
+H-F
D2+P15
s.o. No
corr.
average
XR+
RCO
D2+P19
corr.
+H-F
D2+
P19
corr.
2.36 1.102 1.85 1.65 2.356 2.26 2.52 2.18 2.3±25% 2.72 3.12
Allowance for the contribution of the compound
nucleus formation (Fig.5) approximates the magni-
tude of the obtained spectroscopic factors to shell-
model values [7].
Fig.4. Angular dependences 0f the cross-section , V AP
(Ay) and VP (Pp) [15] emitted protons from reaction
9Be(d, p0)
10Be at Ed = 2.5 and 2.8MeV .
a) Ed = 2.5MeV (D2 + P14),conditions of calculation:
− − −− – Rco = 4 fm; • • • • – the sum of the
corrections for the non-locality of the optical potentials
and finite range; – Zero range;
b) Ed = 2.8MeV , conditions of calculation:
– (D2 +P15), zero range; • • • • - modifications
to nonlocality and finite range (D2 + P19); − − −− –
Rco = 4 fm
Contribution to the cross section of a compound nu-
cleus by Hauser-Feshbach in the back angles at an
energy of 2.8 MeV several worsens agreement with
experiment. These results may indicate that in the
case of the reaction 9Be(d,p0) is preferably occur by
the surface direct process by transmitting one total
angular momentum j=3/2. A negative value of VP
and VAP in the front angles, near the main striping
peak (300), associated with the amendments shear-
ing the polarization observable at the front and back
angles to the range of negative values (see Fig.4 and
6), but it does not connected with rules Haeberli.
Fig.5. Allowance
for the contribution
of the formation of
the compound nu-
cleus in the reaction
9Be(d, p0)
10Be
Fig.6. Comparison of
excitation functions for the
polarization Pp [11] • - and
V AP Ay - ◦ in the reaction
9Be (d, p0)
10Beg.s. Lines
1 and 2 - average values
V AP and polarization,
respectively, for the energy
range of 2.0...3.0MeV .
< Ay >= −0.113,
< Pp >= −0.224. Con-
tinuous curve - DWBA
theoretical calculation Ay
(D2 + P19 potentials with
all corrections) for jn = 3/2
Sufficiently smooth running of the energy dependence
of VP and VAP in the energy range 2.2...3.1MeV can
also point to the prevalence of the direct process in
this energy region.
2.1. NEUTRON BOUND STATE
It is assumed that the neutron is captured on the
shell-model orbit with orbital angular momentum l
and total angular momentum j=l±1/2. We take this
orbit such that it is eigenstate in the Wood-Saxon
potential well, so that the wave function is some-
what dependent on the choice of parameters for this
well. For the calculations presented here, we assumed
that same radius (1.25A1/3 fm) and diffusivity (0.65
fm) as well as those that are commonly used for the
proton optical potential. For a more precise def-
inition was also included spin-orbit coupling is 25
times stronger than Tomason term and which cor-
responds to the force Vso≈8 MeV. These parameters
were used in all calculations. Well depth was cho-
sen such that the binding energy to give equal energy
neutron separation.
28
2.2. ENTRACE DEUTERON CHANNEL
To assess the distorted wave functions in the entrance
channel were found experimentally [22] angular dis-
tributions of the cross section and VAP elastic scat-
tering deuteron at energies 2.0, 2.3, 2.5 and 2.8 MeV.
The cross sections are in good agreement with the
data of [23] (Cairo) for energies below 2.5 MeV. Anal-
ysis of experimental data [23] conducted in the Uni-
versity of Warsaw [25] showed that one can obtain
the averaged energy parameters of the modified op-
tical potentials without spin-orbit interaction H, SH
and P (Tab.4), relating with different source lines pa-
rameterization, and about equally describing them
(Ed=1.8 MeV Figs.8-10). The first two lines corre-
spond to the parameterization of Z-potential, which
are compared with the requirements of parameteriza-
tion Perey P [26].
Fig.7 shows a comparison of our experimental
data with the calculations of the optical model, using
empirical parameters (Tab.4) what we found [24] and
other authors. With the aim of improving search con-
sent optical model calculations with experiment was
evaluated different parameterization deuteron poten-
tials. To do this, we first of all tried to do χ2 mini-
mization procedure to get an equally good description
of the cross sections and VAP for elastic scattering in
the front and back angles, using as a starting po-
tential (SH)’, that best describes of the experimen-
tal data at 2.8 MeV (Fig.9). The result of analy-
sis (Fig.7) gives the potential P4, which is good for
the description cross section and do not can describe
VAP in the back angles because there are the last two
points in the cross section data. There’s also, for com-
parison, results of the calculation with the parameters
Z-C (see Tab.4) which best describes in the potential
approach a purely shape scattering cross section of
deuterons on 12C at 2.8 MeV [3], and showing that
at correct description of the VAP in front and back
angles but the cross section shows a discrepancy with
our experimental data. Parameter set D2 by com-
parison with experiment shows that in contrast to
cases with potentials (P)‘, (SH)‘ and (H)‘ (Fig.8-10),
where under the influence of spin-orbit interaction of
the main interference minimum shifts to back angles
from the second maximum in the cross section (i.e. it
become the third minimum, where there is a strong
and destructive interference), it shows the opposite
behavior.
To compensate for this destructive interference
in the cross section were used two-mode approxi-
mation [24], taking into account the contribution
of compound nucleus formation using statistical
Hauser-Feshbach theory, which does not contribute
to VAP (Fig.11). Fig.11 shows that while mini-
mizing by χ2, the selected portion of the shape
scattering, it is possible to achieve a good de-
scription of the experimental cross section through-
out the entire range of angles, and VAP in the
back angles. ΠΠ3 potential, obtained by opti-
mizing a set of parameters of the potential (P)‘.
Fig.7. Elastic scat-
tering of deuterons at
an energy of 2.8 MeV
on 9Be. The relative
cross section σ/σR and
VAP (Ay). - - – Opti-
cal model calculation:
– χ2 minimiz-
ing the potential for
Π4; − · − · − – D2
[15] potential; − − −
–Potential Z-C [3]
Fig.8. Cross section
and VAP deuteron elas-
tic scattering on 9Be
at Ed=2.8 MeV. Optic
model calculation with
potential P – a solid line
and (P)’ with Vso=15
MeV – dot line
Fig.9. Cross section
and VAP deuteron
elastic scattering on
9Be at Ed=2.8 MeV.
Optic model calculation
with potential SH – a
solid line and (SH)’
with Vso=15 MeV –
dot line
Fig.10. Cross sec-
tion and VAP deuteron
elastic scattering on
9Be at Ed=2.8 MeV.
Optic model calculation
with potential H – a
solid line and (H)’ with
Vso=6 MeV – dot line
29
Table 4. Parameters of optical potentials with spin-orbital interaction for deuteron elastic scattering on
9Be at Ed≤2.8 MeV [46]. Surface absorption and rc=1.3 fm
Ed,
MeV
Sets of
the pa-
rameters
V0,
MeV
r0,
fm
a0,
fm
Ws,
MeV
rw,
fm
aw,
fm
Vso,
MeV
rso,
MeV
aso,
fm
Line of the param-
eterization
1.8(2.8) H (H)‘ 114.2 0.869 1.01 16.0 2.16 0.323 6.0 0.869 1.01 Hilderberg [24,25]
1.8(2.8) SH (SH)‘ 102.0 1.05 0.90 10.0 1.93 0.46 15.0 1.05 0.9 Wisconsin [24,25]
1.8(2.8) P (P)‘ 95.44 1.15 0.81 10.80 1.575 0.585 10.0 1.15 0.81 Perey [23,25,26]
8 YH-Be 89.6 1.16 0.93 18.0 1.53 0.43 15.2 1.16 0.93 [9]
5.25 D2 170.0 0.90 0.90 12.0 2.10 0.50 7.5 1.20 0.90 Powell-Robson[16]
5.25 D3 150.0 0.90 0.90 12.0 2.10 0.50 7.5 1.20 0.90 [16]
2.8 Z-C 112.5 0.90 0.90 4.25 2.861 0.493 6.0 0.90 0.90 Satchler [13]
2.8 Π4 89.6 1.05 0.931 10.0 1.80 0.60 10.0 0.90 0.60 (SH)‘→Π4 [24]
2.4 ΠΠ3 93.49 1.14 0.86 1073 1.70 0.685 9.55 0.90 0.60 P‘→ΠΠ3 [24]
The underlined values - parameters of spin-orbital of interaction added to sets
of parameters H, SH and P for 1.8MeV, proceeding from consideration Figs.8-10.
Table 5. Parameters of optical potentials with spin orbital interaction for the elastic scattering of protons
on 10Be, mentioned in the text. Surface absorption
Ep,
MeV
Sets of the
parameters
V0,
MeV
r0,
fm
a0,
fm
Ws,
MeV
rw,
fm
aw,
fm
Vso,
MeV
rso,
MeV
aso,
fm
rc,
fm
Refe-
rences
8.5 P1 52.0 1.17 0.75 5.433 1.523 0.523 6.2 1.01 0.75 1.3 [19]
P6 49.0 1.25 0.65 7.0 1.25 0.47 6.0 1.25 0.65 1.25 [16]
5.0 P10 50.0 1.38 0.65 11.9 1.50 0.37 7.3 1.35 0.33 1.33 [27]
7.0 P14 32.4 1.54 1.01 21.9 1.82 0.18 4.9 1.67 0.27 1.09 [28]
7.0 P15 48.7 1.40 0.48 10.3 1.466 0.53 8.41 1.35 0.31 1.50 [29]
8.0 P18 46.6 1.39 0.51 10.6 1.49 0.50 5.67 1.30 0.36 1.50 [28]
7.5 P19 34.0 1.49 0.9 17.5 1.755 0.22 4.9 1.625 0.28 1.09 [29]
Further research associated with the study of the
behavior of cross section, VP or VAP at energies of
4...8MeV for comparison with the results obtained
by us at energies below 3MeV. Using the parameters
deuteron potentials found in the works of other au-
thors in the two-mode analysis of elastic scattering of
9Be(d,d) and DWBA description of nuclear reaction
9Be(d,p0) [16], we modeled the angular distributions
VAP=VP shape scattering (set D3) and from the de-
scription of the direct reaction (d,p) (set D2) (Fig.12).
For purely shape scattering of deuterons the main be-
come the this interference minimum cross section at
the back angles, which masked by the contribution
from the compound nucleus formation, and, as seen
in Fig.12 (right column) associated with deep nega-
tive minimum VAP (Ay ) at θmin3 ∼ 120o, similar to
that observed in our analysis of our experiment at an
energy of 2.8MeV at θmin3 ∼ 120o (see Figs.8-11).
When the energy of 8MeV and higher the main in
cross sections is the 2-nd minimum, to which should
correspond a deep negative minimum VAP (VP) in
the same range of angles. This situation is well de-
scribed by the optical model at Ed=12MeV [18]. As
seen from Fig.12 occur shifts of the main interference
minimum, according to the calculated VAP, in the
energy region 6.5...8.0MeV. The reason for this shift
may be associated with changes in family of poten-
tials, which requires a special study.
Phenomenological analysis of our polarization
data for of elastically scattered deuterons requires in-
creased force of the spin-orbit interaction.
2.3. INFLUENCE OF SPIN-ORBIT
INTERACTION AND THE CUT OFF
RADIUS ON THE SHAPE AND
PARAMETERS OF THE ANGULAR
DEPENDENCE OF THE OBSERVED
VALUES IN THE LOCAL DWBA
In order to determine the characteristic features of
the simultaneous description of the angular depen-
dence of the cross section, VP and VAP in the stud-
ied reaction 9Be(d,p0)
10Be, having a non-standard
features, zero range DWBA modeling was conducted
with the separation of the contributions from the
spin-orbit interactions in different channels of the di-
rect reaction using the above discussed lines param-
eterization (H)’, (SH)’, (P)’ in the entrance deuteron
channel and at the same proton potential P1 (Fig.13)
which was used in the description of this reaction in
[19,25] (Warsaw).
30
Fig.11. Two-mode de-
scription averaged energy
cross section (sum) and
VAP elastic scattering on
9Be at an average energy
Ed=2.4 MeV, taking into
account the contribution
of the compound nucleus
in the statistical theory
of Hauser-Feshbach (H-F)
with the potential ΠΠ3 [24]
Fig.12. Angular dependence of the
measured elastic scattering cross sections
σ/σR and VAP (Ay(θ)) calculated using
the parameters of the optical potentials
from works: Ed=5.25MeV (D4) [16],
Ed=6.3MeV [16] and Ed=8.0 (7.8 )MeV
(YH-Be) [9,30] – a solid line in the right
column and - - - corresponds to the calcu-
lations with the parameters D2 potential at
5.25MeV that best describe (d,p) reaction
under DWBA [16]. The dot-dash line (left
column) is incoherent contribution from
the formation of a compound nucleus.
Figures – numbers lows in the angular
dependence of the cross section σ/σR
potential scattering
Fig.13. Optic model cal-
culation of cross section
and WAP elastic scatter-
ing of protons on 10Be
with potential P1 [19] at
Ep=7.5MeV – a solid
line; +++ – Experiment
for 9Be at Ep=8MeV [27]
4. CONCLUSIONS
The simulation results give: a) Taking into account
the strong spin-orbit interaction (Vso≈10...15MeV is
obtained from our polarization data of elastic scatter-
ing) separately in each channel gives a different sign
for the maximum polarization observables at θmax
(Pp, or Ay)≈ θmin (dσ/dΩ). The positive sign of the
polarization observables arises due to the spin-orbit
coupling only in the exit channel and the negative
(corresponding rule Haeberli) when the spin-orbit
coupling only in the deuteron entrance channel. b)
When using the deuteron potential (H)’ with a mean
value of the spin-orbit interaction (Vso≈5...6MeV
quite well simultaneously describing our elastic scat-
tering experimental cross section and VP data), to-
gether with the proton potential P1, we obtain the
angular dependence of the polarization observables
with behavior similar to those that match the rule
Haeberli. Inclusion of spin-orbit coupling in both
channels, in this case, does not significantly alter the
behavior of the angular dependence of the polariza-
tion observables. c) In all above mentioned cases,
the angular dependence of the cross section in area
of the 2-nd peak does not correspond to the experi-
mentally observed position. Angular dependence of
polarization observables is correlated with the spe-
cific behavior of the cross section. d) With the in-
troduction of the cutoff radius Rco in the integral of
overlap radial parts of the wave functions zero range
DWBA with spin-orbit interaction for the case b),
when it is increasing to a value close to the size of
the nucleus Rco≥3.5 fm, there is an abrupt change in
shape and sign of the polarization observables from
that which corresponds to the rule Haeberli, up to
that which qualitatively reproduces our experimen-
tal data on the VAP and the data of [10] on the VP
at an energy Ed=2.5MeV. Now the form of the an-
gular dependence cross section is changes, now the
position and shape of the 2nd peak are reproduced
(other than amplitude). A similar change occurs with
other examined deuteron potentials (SH)’ and (P)’.
This confirms the effects obtained at the description
of our and from world literature of the experimental
data using a modified Z-potential. This yields spec-
troscopic factors close to the shell-model one.
31
All this gives reason to believe that obtained by
us the experimental discrepancy with rule Haeberli
may be explained by a direct surface process de-
scribed within DWBA with the spin-orbit interaction
and corrections on the finite range and no locality of
optical potentials. The reasons for the use of ”non-
standard” parameter sets can be associated with a
change in the localization of l-space [31] what require
further theoretical study.
References
1. V.D. Sarana, N. S. Lutsay, N.A. Shlyakhov j-
dependence of the polarization observables of
striping reactions at low energies on lightweight
nuclei // Bull. KNU. Ser. ”Nuclei, Particles and
Fields”. 2013, iss.3(59), N.1059, p.29-39 (in Rus-
sian).
2. R.H.Bassel, R.M.Drisko, G.R. Satchler et al.
Elastic scattering of deuterons by 40Ca //Phys.
Rev. 1964, B136, p.960-970.
3. G.R. Satchler. An optical potential for deuteron
scattering from carbon //Nucl. Phys. 1966, v.85,
p.273-287.
4. L. L. Lee, J. P. Schiffer, B. Zeidman, et al.
40Ca(d, p)41Ca, a test of the Distortrd-Wave
Born Approximation //Phys. Rev. 1964, B136,
p.971-993.
5. W.Fitz, R. Jahr, R. Santo. Scattering and pick-
up reactions with deuterons on Be, B, C, N and
O at 11.8MeV //Nucl. Phys. 1967, A101, p.449-
459.
6. J. P. Schiffer, G.C.Morrison, R.H. Siemssen, and
B. Zeidman. Study of the (d,p) reaction in the 1p
shell //Phys. Rev. 1967, v.164, p.1274-1284.
7. S. Cohen, and D.Kurath. Spectroscopic factors
for the 1p shell //Nucl. Phys. 1967, A101, p.1-
16.
8. P. Schwandt and W.Haeberli. Optical-model
analysis of d Ca polarization and cross section
measurement from 5 to 34MeV //Nucl. Phys.
1969, A123, p.401-429.
9. T.Y.Yle, W.Haeberli. Use of polarized
deuterons to determine the total angular
momentum transfer in stripping reactions
//Nucl. Phys. 1968, A117, p.1-26.
10. D.Hilscher, J. C.Davis and P.A.Quin. Vector
analyzing power of (d,p) reactions on 11B, 12C,
14N and 15N //Nucl. Phys. 1971, A174, p.417-
425.
11. R.A.Blue, Stout and G.Marr. Polarization of
protons from the 9Be(d, p)10Be reaction //Nucl.
Phys. 1967, A90, p.601-611.
12. M.M.Meier, R. L.Walter, T.R.Donoghue, et al.
A DWBA analysis of the cross section and po-
larization data for the 14N(d, n)15O reaction at
3.5MeV //Nucl. Phys. 1970, A159, p.273-304.
13. M.M.Meier and R. L.Walter Polarization of neu-
trons from 10B+d, 11B+d and 13C+d reactions
//Nucl. Phys. 1972, A182, p.468-480.
14. P. E.Hodgson and D.Wilmore. Reactions of 1 to
5MeV deuteron on carbon //Proc. Phys. Soc.
1967, v.90, p.361-380.
15. Y. P.Antufiev, A. S.Deyneko, I. I. Zalyubovskiy,
et al. Angular distributions of differential cross
sections and vector analyzing power reactions
9Be(d, p)10Be, 9Be(d, t)8Be and 9Be(d, α)7Li at
Ed = 2.0...2.8MeV //Yad. Phys. 1984, v.40,
iss.1(7), p.53-61 (in Russian).
16. D. LPowell, G.M.Crawley, B.V.N.Rao, et al.
Deuteron-induced reactions in 6Li, 9Be and 10B
at bombarding energies of 4.5 to 6.0MeV //Nucl.
Phys. 1970, A147, p.65-80.
17. I. I. Bondouk. DWBA analysis of polarization
of protons from the 9Be(d, p0)
10Be reaction at
Ed=5.5, 13.8 and 20.5MeV: Preprint. ATKE,
bd.23, Lfg4, 1974, p.283-284.
18. O.Karban, S.Roman, G.Tungate, et al. Analyz-
ing powers of the (d,p) and (d,t) reactions in-
duced by 12MeV polarized deuterons in the 1p
shell //Nucl. Phys. 1977, A286, p.420-430.
19. D. Zwieglinski, A. Saganek, I. Sledzinska,
Z.Wilhelmi Direct and resonance processes
in 9Be(d, p0,1)
10Be and 9Be(d, t0)
8Be at low
energies //Nucl. Phys. 1975, A250, p.93-105.
20. I. I. Bondouk, F.Asfour and F.Machali. Inves-
tigation of the reactions 9Be(d, p0)
10Be and
9Be(d, p1)
10Be in the energy range 0.9...2.5MeV
//Rev. Roum. Phys. 1974, v.19, N.10, p.1053-
1061.
21. 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, p.700-702.
22. A. S.Deyneko, I. I. Zalyubovskii, V.D. Sarana, et
al. Elastic Scattering vector-polarized deuterons
on 9Be at Ed=2.0...2.8MeV //Izv. AN USSR
Physics Series 1983, v.47, N11, p.2271-2275 (in
Russian).
23. F.Machali, Z.A. Saleh, A.T.Baranik et al. Elas-
tic scattering of deuterons by 9Be and 28Si
//Atomkernenergie (ATKE). 1968, bd.13-7, H.1,
p.29-32.
24. V.D. Sarana. Parameterization of the optical
potential for elastic scattering of low-energy
deuterons on 9Be //Bull. KNU. Ser. ”Nuclei,
Particles and Fields”. 2005, v.3(28), N710, p.3-20
(in Rassian).
32
25. B. Zwieglinski, J. Piotrovski, A. Saganek, et al.
Optical model and Hauser-Feshbach analysis of
9Be+ d and 10B + p interactions at low energies
//Nucl. Phys. 1973, A209, p.348-362.
26. C.M.Perey and F.G.Perey. Deuteron optical-
model analysis in the range of 11 to 27MeV
//Nucl. Phys. 1963, v.132, p.755-773.
27. D.H. Loyd, W.Haeberli. Polarization of pro-
tons elastically scattered from beryllium //Nucl.
Phys. 1970, A148, p.236-248.
28. M.F.Werby, S. Edwards, W. J. Thompson. Opti-
cal model analysis of 9Be(p, p0)
9Be cross section
and polarizations from 6MeV to 30MeV //Nucl.
Phys. 1971, A169, p.81-94.
29. V.B.Gubin, E.A.Romanovsky. Analysis by the
optical model of the cross sections for elastic scat-
tering and polarization protons on 9Be //Izv. AN
USSR Physics Series. 1974, v.38, p.144-148 (in
Russian).
30. J.A.Green and W.C.Parkinson. Polarization of
protons in 9Be(d, p)10Be //Phys. Rev. 1962,
v.127, p.926-9282.
31. M.B.Hooper. L-space localization in deuteron
stripping reactions //Nucl. Phys. 1966, v.76,
p.449-474.
Î ÂÎÇÌÎÆÍÎÌ ÍÀÐÓØÅÍÈÈ ÏÐÀÂÈËÀ ÕÀÁÅÐËÈ Â ÐÅÀÊÖÈÈ (d,p) ÍÀ
ßÄÐÀÕ 1ð-ÎÁÎËÎ×ÊÈ ÏÐÈ ÍÈÇÊÈÕ ÝÍÅÐÃÈßÕ
Â.Ä.Ñàðàíà, Í.Ñ.Ëóöàé, H.À.Øëÿõîâ
Èññëåäóåòñÿ âîçìîæíîñòü îäíîâðåìåííîãî îïèñàíèÿ óãëîâûõ ðàñïðåäåëåíèé ñå÷åíèÿ, âåêòîðíîé ïî-
ëÿðèçàöèè è âåêòîðíîé àíàëèçèðóþùåé ñïîñîáíîñòè â ðàìêàõ ÁÏÈÂ, ñ èñïîëüçîâàíèåì ðàçëè÷íûõ
ìîäèôèêàöèé äåéòîííîãî Z-ïîòåíöèàëà è ïîòåíöèàëà Ïåðåÿ, ðàíåå ýêñïåðèìåíòàëüíî íàáëþäàåìûõ
íàðóøåíèé ïðàâèëà Õàáåðëè â îáëàñòè ìàëûõ ýíåðãèé äåéòðîíîâ íà ïðèìåðå ðåàêöèè 9Be(d,p)10Be.
Íàéäåíî, ÷òî ñ ïîìîùüþ ÁÏÈÂ ìîæíî îïèñàòü íàðóøåíèå ïðàâèëà Õàáåðëè ïðè íèçêîé ýíåðãèè.
ÏÐÎ ÌÎÆËÈÂÅ ÏÎÐÓØÅÍÍß ÏÐÀÂÈËÀ ÕÀÁÅÐËI  ÐÅÀÊÖI� (d,p) ÍÀ ßÄÐÀÕ
1ð-ÎÁÎËÎÍÊÈ ÏÐÈ ÍÈÇÜÊÈÕ ÅÍÅÐÃIßÕ
Â.Ä.Ñàðàíà, Í.Ñ.Ëóöàé, M.À.Øëÿõîâ
Äîñëiäæó¹òüñÿ ìîæëèâiñòü îäíî÷àñíîãî îïèñó êóòîâèõ ðîçïîäiëiâ ïåðåðiçó, âåêòîðíî¨ ïîëÿðèçàöi¨ i
âåêòîðíî¨ àíàëiçóþ÷î¨ çäàòíîñòi â ðàìêàõ ÁÏIÂ, ç âèêîðèñòàííÿì ðiçíèõ ìîäèôiêàöié äåéòîííîãî Z-
ïîòåíöiàëó i ïîòåíöiàëó Ïåðåÿ, ðàíiøå ýêñïåðèìåíòàëüíî ñïîñòåðåæóâàíèõ ïîðóøåíü ïðàâèëà Õàáåðëi
â îáëàñòi ìàëèõ åíåðãié äåéòðîíiâ íà ïðèêëàäi ðåàêöi¨ 9Be(d,p)10Be. Çíàéäåíî, ùî çà äîïîìîãîþ ÁÏIÂ
ìîæíà îïèñàòè ïîðóøåííÿ ïðàâèëà Õàáåðëi ïðè íèçüêié åíåðãi¨.
33
|