Elastic scattering of deuterons by deuterons at Ed ≤ 85 MeV
The differential cross sections of elastic dd-scattering at Ed = 36.9 MeV in the angular range 30° ≤ Θ c.m. ≤ 116° are measured. For describing of main peak at Θc.m. ≤ 60° we used the diffraction nuclear model taking into account the structure of the colliding nuclei. Satisfactory agreement of the p...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2011
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| Назва видання: | Вопросы атомной науки и техники |
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| Цитувати: | Elastic scattering of deuterons by deuterons at Ed ≤ 85 MeV / O.O. Beliuskina, V.I. Grantsev, K.K. Kisurin, S.E. Omelchuk, G.P. Palkin, Yu.S. Roznyuk, B.A. Rudenko, V.S. Semenov, L.I. Slusarenko, B.G. Struzhko // Вопросы атомной науки и техники. — 2011. — № 5. — С. 10-15. — Бібліогр.: 18 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1114652025-02-09T16:47:00Z Elastic scattering of deuterons by deuterons at Ed ≤ 85 MeV Пружне розсiяння дейтронiв на дейтронах при Ed ≤ 85 MeB Упругое рассеяние дейтронов на дейтронах при Ed ≤ 85 MэB Beliuskina, O.O. Grantsev, V.I. Kisurin, K.K. Omelchuk, S.E. Palkin, G.P. Roznyuk, Yu.S. Rudenko, B.A. Semenov, V.S. Slusarenko, L.I. Struzhko, B.G. Ядерная физика и элементарные частицы The differential cross sections of elastic dd-scattering at Ed = 36.9 MeV in the angular range 30° ≤ Θ c.m. ≤ 116° are measured. For describing of main peak at Θc.m. ≤ 60° we used the diffraction nuclear model taking into account the structure of the colliding nuclei. Satisfactory agreement of the present results with published data at energies of 12.1MeV ≤ Ed ≤ 85 MeV was obtained. For the theoretical interpretation of the angular distributions the identity of the colliding deuterons is taken into account. Було виміряно диференціальні перерізи пружного розсіювання дейтронів з енергією Ed = 36.9 МеВ ядрами дейтерію в діапазоні кутів 30° ≤ Θ c.m. ≤ 116°. Для опису основго максимуму Θc.m. ≤ 60° використовувалась дифракційна ядерна модель, яка враховує структуру ядер, що зіштовхуються. Отримано задовільне узгодження з експериментом для кутів Θc.m. ≤ 60° і з нашими експериментальними даними, і з даними інших робіт для енергій 12 МеВ ≤ Ed ≤ 85 МеВ. Для теоретичної інтерпретації кутових розподілів було враховано тотожність дейтронів, що зіштовхуються. Измерены дифференциальные сечения упругого рассеяния дейтронов с энергией Ed = 36.9 МэВ ядрами дейтерия в диапазоне углов 30° ≤ Θ c.m. ≤ 116°. Для описания основного максимума Θc.m. ≤ 60° использовалась дифракционная ядерная модель, учитывающая структуру сталкивающихся ядер. Получено удовлетворительное согласие с экспериментом для углов Θc.m. ≤ 60° как с нашими экспериментальными данными, так и с данными других работ для энергий 12 МэВ ≤ Ed ≤ 85 МэВ. При теоретической интерпретации угловых распределений учтена тождественность сталкивающихся дейтронов. 2011 Article Elastic scattering of deuterons by deuterons at Ed ≤ 85 MeV / O.O. Beliuskina, V.I. Grantsev, K.K. Kisurin, S.E. Omelchuk, G.P. Palkin, Yu.S. Roznyuk, B.A. Rudenko, V.S. Semenov, L.I. Slusarenko, B.G. Struzhko // Вопросы атомной науки и техники. — 2011. — № 5. — С. 10-15. — Бібліогр.: 18 назв. — англ. 1562-6016 PACS: 24.30.Cz, 13.75.Cs, 21.30.Fe, 21.60.Jz https://nasplib.isofts.kiev.ua/handle/123456789/111465 en Вопросы атомной науки и техники application/pdf 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 Beliuskina, O.O. Grantsev, V.I. Kisurin, K.K. Omelchuk, S.E. Palkin, G.P. Roznyuk, Yu.S. Rudenko, B.A. Semenov, V.S. Slusarenko, L.I. Struzhko, B.G. Elastic scattering of deuterons by deuterons at Ed ≤ 85 MeV Вопросы атомной науки и техники |
| description |
The differential cross sections of elastic dd-scattering at Ed = 36.9 MeV in the angular range 30° ≤ Θ c.m. ≤ 116° are measured. For describing of main peak at Θc.m. ≤ 60° we used the diffraction nuclear model taking into account the structure of the colliding nuclei. Satisfactory agreement of the present results with published data at energies of 12.1MeV ≤ Ed ≤ 85 MeV was obtained. For the theoretical interpretation of the angular distributions the identity of the colliding deuterons is taken into account. |
| format |
Article |
| author |
Beliuskina, O.O. Grantsev, V.I. Kisurin, K.K. Omelchuk, S.E. Palkin, G.P. Roznyuk, Yu.S. Rudenko, B.A. Semenov, V.S. Slusarenko, L.I. Struzhko, B.G. |
| author_facet |
Beliuskina, O.O. Grantsev, V.I. Kisurin, K.K. Omelchuk, S.E. Palkin, G.P. Roznyuk, Yu.S. Rudenko, B.A. Semenov, V.S. Slusarenko, L.I. Struzhko, B.G. |
| author_sort |
Beliuskina, O.O. |
| title |
Elastic scattering of deuterons by deuterons at Ed ≤ 85 MeV |
| title_short |
Elastic scattering of deuterons by deuterons at Ed ≤ 85 MeV |
| title_full |
Elastic scattering of deuterons by deuterons at Ed ≤ 85 MeV |
| title_fullStr |
Elastic scattering of deuterons by deuterons at Ed ≤ 85 MeV |
| title_full_unstemmed |
Elastic scattering of deuterons by deuterons at Ed ≤ 85 MeV |
| title_sort |
elastic scattering of deuterons by deuterons at ed ≤ 85 mev |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2011 |
| topic_facet |
Ядерная физика и элементарные частицы |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/111465 |
| citation_txt |
Elastic scattering of deuterons by deuterons at Ed ≤ 85 MeV / O.O. Beliuskina, V.I. Grantsev, K.K. Kisurin, S.E. Omelchuk, G.P. Palkin, Yu.S. Roznyuk, B.A. Rudenko, V.S. Semenov, L.I. Slusarenko, B.G. Struzhko // Вопросы атомной науки и техники. — 2011. — № 5. — С. 10-15. — Бібліогр.: 18 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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| fulltext |
ELASTIC SCATTERING OF DEUTERONS BY DEUTERONS
AT Ed ≤ 85 MeV
O.O. Beliuskina∗, V.I. Grantsev, K.K. Kisurin,
S.E. Omelchuk, G.P. Palkin, Yu.S. Roznyuk, B.A. Rudenko,
V.S. Semenov, L.I. Slusarenko, B.G. Struzhko
Institute For Nuclear Research of NAS of Ukraine, 03680, Kiev, Ukraine
(Received June 30, 2011)
The differential cross sections of elastic dd-scattering at Ed = 36.9 MeV in the angular range 30◦ ≤ θc.m. ≤ 116◦
are measured. For describing of main peak at θc.m. ≤ 60◦ we used the diffraction nuclear model taking into account
the structure of the colliding nuclei. Satisfactory agreement of the present results with published data at energies of
12.1 MeV ≤ Ed ≤ 85 MeV was obtained. For the theoretical interpretation of the angular distributions the identity
of the colliding deuterons is taken into account.
PACS: 24.30.Cz, 13.75.Cs, 21.30.Fe, 21.60.Jz
1. INTRODUCTION
The deuteron is the simplest bound nuclear system of
nucleons in which nuclear interaction takes place, and
processes with participation of deuterons are valuable
and convenient method to study some aspects of nu-
clear forces and the structure of the deuteron. Con-
taining only two nucleons it is better investigated in
many aspects in comparison with the majority of the
rest nuclei, and allows to study some more fine details
of the nuclear NN interaction, thus complementing
information got from the nucleon-nucleon scattering.
Elastic scattering of deuterons by deuterons at ener-
gies 12 ≤ Ed ≤ 100 MeV devoted a small number
of studies [1-9]. Generally the angular distributions
of elastically scattered deuterons were investigated
both experimentally and theoretically at energies up
to 25 MeV . This is conditioned by the complexity
of the theoretical interpretation of the data at Ed ≥
30 MeV , and the paucity of experimental results. In
this work experimental data on elastic scattering of
deuterons with energy Ed = 36.9 MeV by deuterons
and results of the elastic dd-scattering analysis at en-
ergies of 12 < Ed < 85 MeV are presented. We used
diffraction nuclear model with accounting of NN -
interaction for theoretical interpretation of data on
elastic scattering at angles θc.m. ≤ 60◦. Diffraction
approximation considers collisions of two deuterons
as two classical balls with accounting their identity
was used to explain structural peculiarities of angu-
lar distributions at different energies.
2. EXPERIMENT
Experimental study of dd-scattering was carried out
on the U − 240 cyclotron in the KINR of NAS
of Ukraine on the external deuteron beam with the
energy Ed = 36.9 MeV . Measurements were ful-
filled with CD2 (deuterated polyethylene) and 12C
targets. The statistical accuracy of measurements
was 1...2% and absolute values of cross sections were
determined with an accuracy of ∼ 5 percent. Mea-
surements were carried out using installation and
procedures, described earlier in works [10-12]. In the
Fig.1 our angular distributions of deuterons scattered
by deuterons in c.m. system are presented with pub-
lished data in the energy range 12 < Ed < 85 MeV .
Fig.1 Angular distributions of the elastic scattering
deuterons by deuterons at energies: 12.1 [1], 12.3 [9],
25.3 [4], 36.9 (our data) and 50...85 MeV [5] in
c.m.s. Energies of deuterons are presented in l.s.
The differential cross section at energy
Ed = 12.1 MeV reduces gradually with the growth
∗Corresponding author E-mail address: beliuskina@gmail.com
10 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2011, N5.
Series: Nuclear Physics Investigations (56), p.10-15.
of the scattering angle up to θc.m. ≈ 90◦, and then
increased also gradually with the growth of the scat-
tering angle. With the growth of the deuteron energy,
starting from Ed = 25 MeV (according available ex-
perimental data) a strong energy dependence in cross
section is observed (to up θc.m. ∼ 60◦). A structure in
angular distributions (60◦ ≤ θc.m. ≤ 120◦), i.e. indi-
cations on the minimum at θc.m. ≈ 60◦ and the broad
maximum, centered at the angle θc.m. ≈ 90◦ starts to
display. The similar trend is seen more clearly with
the further growth of incoming deuteron energy [5].
But with increasing energy up to Ed = 85 MeV no-
ticeable decrease in the cross sections observed (up to
2 mb) and structure is almost absent in the angular
range 60◦ ≤ θc.m. ≤ 120◦.
3. THEORY
At the energy of incoming deuteron in l.s. Ed ≈
40 MeV , as in our experiment, collision of two
deuterons can be considered as quasi-classical one.
In this case product of the relative wave vector k
and the radius of nuclear interaction R will exceed
a unity a few times. That is why the diffraction ap-
proximation [10, 11] for small scattering angles in l.s.
θ ≤ (kR)−1 <<1 can be used.
3.1. THE MICROSCOPIC DIFFRACTION
MODEL
The microscopic diffraction model [11, 12, 13] was
used to describe deuteron-deuteron collisions. An in-
teraction of each nucleon of the incoming deuteron
with each nucleon of the target deuteron is taken
into account. The nucleon-nucleon profile function
was chosen in the form of Gaussian:
ωij = ω (|ρij |) = α exp
(
b2ρ2
ij
)
, α = α1 − ια2 , (1)
where ~ρij is the component of vector ~rij = ~ri + ~rj
perpendicular to the incoming deuteron wave vector
~kd in l.s., while ~ri is a radius -vector for i-nucleon of
deuteron target (i = 1, 2), and ~rj is a radius-vector
of the nucleon j of the incoming deuteron (j = 3, 4).
Functions ωij are connected with appropriate scatter-
ing matrixes Ωij by a simple relation: Ωij = 1− ωij .
Values of real interaction parameters a1, a2 and b in
(1) were taken to be approximately the same as in
works [13, 14].
The deuteron-deuteron elastic scattering ampli-
tude in the diffraction approximation cab be build in
the form as it was done in [11, 12] for scattering of a
deuteron on a triton (θ is the scattering angle in the
c.m. system)
A(θ) =
∫
d(3)~r
∫
d(3)~s
∫
d(2) ~R⊥ϕ∗(~r)ϕ ~chi
∗( ~R⊥)×
×Ω13Ω14Ω23Ω24ϕ(~r)ϕ(~s)ϕ0( ~R⊥), (2)
where inner (structural) wave functions of the
deuteron-target ϕ(~r) and the incoming deuteron ϕ(~s)
depend on relative radius-vectors ~r = ~r12 = ~r1 − ~r2
and ~s = ~r34 = ~r3 − ~r4 and wave function ϕ0( ~R⊥)
and ϕ~ϕ( ~R⊥) describing the relative movement of
deuterons before and after scattering, depend on he
component ~R⊥ of the radius-vector ~R, connecting
centers of mass of the two deuterons, perpendicular
to the relative wave vector ~k = 1
2
~kd and ~χ is the
perpendicular to the vector ~k component of the mo-
mentum of the scattered deuteron, while ~χ = −~q,
where ~q is the transferred momentum [15]. So far as
the amplitude in [2] contains rather high multiplicity
of integration, we will use for calculation the wave
functions of the simplest form [11, 12, 13]
ϕ(~s) =
(
2λ2
π
)
, λ = 0.267 fm−1 , (3)
ϕ◦( ~R⊥) = 1 , ϕ~χ( ~R⊥) = ei~χ ~R⊥ , ~χ = −~q ,
χ = 2k sin
θ
2
. (4)
For our incoming deuteron energy the dd-scattering
will take place in the c.m. system mainly in small
angles range θ ≤ 600 (for l.s. θ ≤ 300). There-
fore, to calculate amplitudes and cross sections for
kinematical conditions of our experiment we can use
the impulse approximation, which will be proved to
be correct, when comparing calculated cross sections
with our experimental data. Then the substitution of
(1), (3) and (4) in (2) for diffraction elastic scatter-
ing of the deuteron by the deuteron we will get the
expression in the explicit form:
A(θ) =
4πa
b2
exp
[
−χ2
(
1
4b2
+
1
16λ2
)]
, χ = 2k sin
θ
2
,
(5)
and for the appropriate cross section of the diffraction
scattering we will get formula
dσ
dΩ
=
k2
(2π)2
| A(θ) |2= 4 | a |2 k2
b4
×
× exp
[
−2k2
(
1
b2
+
1
4λ2
)
sin2 θ
2
]
. (6)
Accounting the identity of colliding deuterons we
need to take the superposition of amplitude A(θ) and
A(θ) [16] instead of the amplitude A(θ) in (5) and the
cross section (for integer spins equal 1, as in our case)
will be now
dσ
dΩ
=
k2
(2π)2
{| A(θ) |2 + | A(π − θ) |2 +
+
3
2
Re[A(θ)A∗(π − θ)]}, (7)
that leads to the following formula for the deuteron
elastic scattering cross section
dσ
dΩ
=
4 | a |2 k2
b4
{exp
[
−2k2
(
1
b2
+
1
4λ2
)
sin2 θ
2
]
+
+ exp
[
−2k2
(
1
b2
+
1
4λ2
)
cos2
θ
2
]
+
+
2
3
exp
[
−k2
(
1
b2
+
1
4λ2
)]
}, k2 = MEd ,
(8)
11
where M is nucleon mass. The way it should be, cross
section is symmetric in the c.m. system relatively the
angle θ = 90◦, in particular, the values of cross sec-
tion at angles θ=0◦ and θ = 180◦ will be equal.
The first term in the right part of the formula
(8) is the cross section of elastic scattering (6) of
the incoming deuteron by the deuteron-target and as
k2( 1
b2 + 1
4λ2 ) >> 1, it gives the main contribution in
the cross section (8) only for small angles of scatter-
ing θ ≤ 60◦. The second terms in (8) is the cross sec-
tion of the deuteron-target knocking-out, and it con-
tributes significantly only for angles θ near to 180◦,
i.e. when θ ≥ 120◦. The third terms in (8) for our
model wave functions (3) and (4) does not depend
on the angle θ and is an interference (quantum me-
chanical) term and, as it has to be in quasi-classical
approximation, it is negligibly small for our energy,
thus we can retain in the cross section (8) only the
first two (classical) terms in a good approximation.
As our measurements of cross sections were limited
only by angles θ < 120◦, the second term in (8) will
have also only limited application for the description
of the experiment for such scattering angles.
3.2 THE NON PENETRATING SPHERES
APPROXIMATION
The behavior of the observed cross section of dd-
scattering for angles θ >> (kR)−1 in the diffraction
approximation is not longer described with model
functions (3) and (4), that is why for angles 60◦ ≤
θ ≤ 120◦, where the observed cross section is very
small, one can try to use a version of quasi-classical
approximation, in which deuterons are treated as two
identical non penetrating collided balls [11, 12, 17]. In
this approximation one can describe qualitatively the
cross section for whole angle region 60◦ ≤ θ ≤ 180◦.
At kR >> 1 for all angles θc.m. ≤ 180◦ the quasi-
classical amplitude of two colliding identical particles
will look like:
F (θ) = i
R
2 sin θ
2
J1
(
2kR sin
θ
2
)
−
− iR
2
exp
(
−2ikR sin
θ
2
)
, (9)
F1(π − θ) = i
R
2 cos θ
2
J1
(
2kR cos
θ
2
)
−
− iR
2
exp
(
−2ikR cos
θ
2
)
, (10)
where first part - diffraction quantum amplitude
fdif (θ), second - amplitude of classical isotropic scat-
tering. The differential scattering cross section can
be written as
dσ
dΩ
= (| F1(θ) |)2 +
+
2
3
Re
[
F (θ)
(| F1(θ) |)2
F1(θ)
]
. (11)
For small angle interval θ << (kR)−
1
3 the
module of diffractional part of the amplitude
fdif (θ) exceeds significantly the classical one
fcl : | fdif (θ) |>>| fcl(θ) |, and for the angular
interval θ >> (kR)
1
3 , on the contrary,
| fcl(θ) |>>| fdif (θ) |. For the small angle region near
θ ≈ (kR)−
1
3 amplitudes fdif (θ) and fcl(θ) are of the
same order of magnitude and to find simple and ex-
plicit expression for the amplitude is not easy, but
the contribution for this angular region to the inte-
gral cross section is negligibly small for kR >> 1.
The explicit expression for amplitudes fdif (θ) and
fcl(θ) were received in [17] for different conditions,
that is why it is worth to examine separately dif-
ferential cross sections of elastic scattering for two
mentioned angular regions, not to sum up amplitudes
fdif (θ) and fcl(θ). Then the cross section of diffrac-
tion scattering, taking into account (9) and (10) can
be written as
dσ
dΩ
=
R2
4
{
J2
1 (2kR sin θ
2 )
sin2 θ
2
+
J2
1 (2kR cos θ
2 )
cos2 θ
2
+
+
2
3
J1(2kR sin θ
2 )
sin θ
2
J1(2kR cos θ
2 )
cos θ
2
}
. (12)
In the quasi-classical approximation kR >> 1 the
first term in the braces of (12) gives the main con-
tribution for θ ≤ (kR)
1
3 , the second term contributes
for θ ≥ π − (kR)
1
3 , the third term, as a rule, can
be neglected as being an interference quantum con-
tribution in this approximation [18]. The classical
cross section describes the isotropic distribution of
scattered particles and has a very simple form
dσcl
dΩ
=
R2
4
. (13)
4. RESULTS OF CALCULATIONS AND
COMPARISON WITH EXPERIMENTAL
DATA
Experimental dependencies of angular distributions
dσ
dΩ of scattered deuterons in dd- collisions in the c.m.
system for a number of incoming deuteron energies
Ed in laboratory system, presented in the Fig.1 and
Fig.2, give the possibility to determine the general
structure of the distributions, some trends and, in
particular, the influence of incoming energy Ed on
them. Diffraction nuclear model that takes into ac-
count NN -interaction between the nucleons and the
identity of the colliding deuterons as two identical
bosons was used for theoretical description of elas-
tic dd-scattering angular distributions in the region
of the main peak. Calculations were carried out for
energy of incoming deuterons 12.1 ≤ Ed ≤ 85 MeV .
In follow we presented the results of our calculations
of elastic dd-scattering differential cross sections dσ
dΩ
for energies of incoming deuterons 12.1, 36.9, 60 and
70 MeV which reflects the most characteristic fea-
tures of angular distributions in this energy range.
The theoretical curves obtained using a microscopic
diffraction model by formulae (1) - (8) are shown in
Fig.2 (as a thick solid curve 1).
12
Fig.2. Comparison experimental and theoretical angular distributions of elastic dd-scattering at energies:
12 MeV [1, 8, 9], 36.9 MeV (our data), 60 and 70 MeV [5]. Points - experiment. Curves 1 - calculation
by microscopic diffraction model: (a) α1 = 0.7, α2 = 0.5, b2 = 0.355fm−2; (b)α1 = 0.5, α2 = 0.5, b2 =
0.45fm−2; (c)α1 = 0.6, α2 = 0.6, b2 = 0.52fm−2; (d)α1 = 0.45, α2 = 0.49, b2 = 0.49fm−2; curves 2 -
diffraction scattering: (a) R=5.5, (b) R=3.8 (2a - R=4.4), (c) R=3.32, (d) R=3.0; curves 3 - calculation
by classical approximation: (a) R=2.79, (b) R=5.5; curve 4–calculation by formula take into account
interference of diffraction and classical amplitudes: (a) R=5.5
According to mentioned above, such model when
using wave function (3) and (4) can lead to ade-
quate description of experiments only for compara-
tively small deuteron scattering angles in the c.m.
system θ ≤ (kR)−
1
3 ≤ 60◦, i.e. in the region of
the main (by height) first maximum of the cross sec-
tion at θ = 0◦. If the deuterons (recoils) would be
registered in experiments also for angles θ > 120◦,
than, as it was marked earlier, we would have also
the second observed high maximum at θ = 180◦,
which would be same in the high (and the form)
as the maximum at θ = 0◦ due to identity of
colliding deuterons. That is why, as it could be
expected, satisfactory agreement with experimen-
tal distributions of scattered deuterons for all men-
tioned energies of incoming deuterons was achieved
for angle θ ≤ (kR)−
1
3 ≈ 60◦. Good agreement is ob-
served also for angle interval 110◦ ≤ θc.m. ≤ 145◦ at
deuteron energy Ed = 12 MeV . For angle inter-
val 60◦ ≤ θc.m. ≤ 120◦, where this model should not
work, qualitative description of the experiment is ob-
served, i.e. the shape of experimental angular dis-
tribution is reproduced. As follows from fig.1 mini-
mum near θc.m. = 60◦ is observed both for our mea-
sured angular distribution of deuterons scattered by
deuterons at Ed = 36.9 MeV and for other data at
Ed = 25.3 MeV and Ed = 50...85 MeV . But for
the lowest energies (12.1...12.3 MeV ) such structure
in angular distribution is not seen. Characteristic
peculiarities of behavior of cross sections of elastic
dd-scattering for different energies can be also quali-
tatively described with the help of diffraction model
of two colliding nonstructural hard balls-deuterons
with the account of their identity. The angular dis-
tributions of the scattering cross section dσdif
dΩ were
calculated by the formula (12) for all energies and
are shown in Fig.2 by dashed curves. Here as well as
for the microscopic diffraction model, conditions of
model approximations can be satisfied only for angles
60◦ ≤ θc.m. ≤ 120◦ and 120◦ ≤ θc.m. ≤ 180◦. The
theoretical cross sections calculated by the formula
(12) lead to almost the same satisfactory description
13
of the experiment, as well as microscopic diffraction
model in this angular region. This model clearly
shows the presence of extremums in angular distribu-
tions at θ ≈ 60◦ and θ ≈ 120◦ for energies of incoming
deuterons Ed ≥ 25 MeV , and for smaller energies this
model describes the change of angular dependence for
angular interval 60◦ ≤ θc.m. ≤ 120◦. Positions of ex-
tremums in the angular distribution of cross sections
are qualitatively connected with the value of a bound-
ary angle θ ≈ (kR)−
1
3 (see (9) and (10), and as well
[17]), being dependent weakly on deuteron energy Ed
for energy interval 25.3 MeV ≤ Ed ≤ 51.5 MeV . In
the intermediate region of angles 60◦ ≤ θc.m. ≤ 120◦,
where conditions of applicability of the model are al-
ready violated to some extent, not only qualitative
but also quantitative description of the experiment
is achieved for Ed = 36.9...70 MeV for the region of
small by height secondary diffraction maximum. As
in the region of medium angles 60◦ ≤ θc.m. ≤ 120◦
conditions of applicability of used approximations
for our deuteron energies are still violated than to
describe cross sections in this wide angular region,
where cross sections are getting very small almost
permanent values, we used the simplified phenom-
enological model for colliding nonpenetrating balls
(with isotropic distributions of particles over angles)
[1, 11, 12, 17]. According to this model observed cross
sections are described approximately by the formula
(13) with the radius of nuclear interaction R [10, 12]
depending on energy. Appropriate dependences of
cross sections at the energy Ed = 36.9 MeV are given
in the Fig.2 by dense solid line 3. Analyzing the the-
oretical angular distribution of elastic dd-scattering
at Ed = 12, 1 (12, 3)MeV , we can note that the mi-
croscopic (8) and diffraction (12) models qualitatively
describe the shape of the angular distribution and in-
dicate the presence of a minimum at θc.m. = 90◦ (and
its absence at θc.m. = 60◦). Analyzing the experi-
mental angular distributions (see Fig.1), we can note
that the cross section at the minimum ( θc.m. = 90◦)
at Ed = 12, 1 MeV roughly an order of magnitude
higher then the cross sections in the secondary maxi-
mum (θc.m. = 90◦) at energies Ed ≥ 36, 9 MeV . Cal-
culations of the elastic scattering were carried out
by the formula (11) taking into account interference
of classical and diffraction amplitudes. The results
are shown in Fig.2 (a) by dotted curve. Interfer-
ence term in expression (11), which is usually ignored,
was significant at low energies Ed, that perhaps ex-
plains the nature of the appearance of a minimum
at θc.m. = 90◦ at a given energy. It follows from
the above analysis that both for our measured angu-
lar distribution of deuterons scattered by deuterons
at Ed = 36.9 MeV and for data of other works at
Ed = 25.3 MeV [4] and Ed = 50...85 MeV [5] a mini-
mum is observed near the angle θc.m. = 60◦. Position
of this minimum is in accord with given earlier formu-
lae for differential cross sections dσ
dΩ . It has a diffrac-
tion nature for energies Ed ≈ 25...50 MeV as well as
the secondary not strictly expressed diffraction maxi-
mum at θc.m. ≈ 90◦. Eerier (see, for example, [8]) the
arising of the mentioned structure in cross sections
dσ
dΩ was treated theoretically by methods sometimes
being some artificial and not very evident, while the
observed extremums in cross sections, as we think,
arise and are explained naturally with the help of
simple diffraction mechanism.
5. SUMMARY
1.The angular distribution of deuterons scattered
by deuterons at energy Ed = 36.9 MeV in the angle
interval in the c.m. system 30◦ ≤ θc.m. ≤ 116◦ was
measured.
2. Comparison of the present results with pub-
lished data on elastic scattering of deuterons by
deuterons at energies of 12.1 MeV ≤ Ed ≤ 85 MeV
was conducted. It is shown that the energy depen-
dence of angular distributions of dd-scattering char-
acterized by decreasing cross sections with increasing
energy Ed and by noticeable structural changes.
3.Diffraction nuclear model which takes into ac-
count NN -interaction between the nucleons and the
diffraction model of two colliding structureless hard
spheres-deuterons were used to describe the angular
distributions of elastic dd-scattering. Both mod-
els take into account the identity of the colliding
deuterons, which naturally explains the observed
symmetry of the differential cross sections for the
angle θc.m. = 90◦.
4.Our experimental data, as well as measured
differential cross sections of elastic scattering from
other works for energies of incoming deuterons
12.1 MeV ≤ Ed ≤ 85 MeV were satisfactory de-
scribed with the help of microscopic diffraction nu-
clear model which takes into account NN -interaction
between the nucleons.
5. Structural peculiarities of angular dependences
of elastic dd-scattering cross sections were qualita-
tively explained with the help of the diffraction model
of two colliding hard balls-deuterons with the ac-
count of their identity and qualitative and quanti-
tative explanation of the diffraction structure of the
cross sections was achieved for scattering angles of
60◦ ≤ θc.m. ≤ 120◦ at energies of 12.1 MeV ≤ Ed ≤
85 MeV .
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УПРУГОЕ РАССЕЯНИЕ ДЕЙТРОНОВ НА ДЕЙТРОНАХ ПРИ Ed ≤ 85МэВ
О.О. Белюскина, В.И. Гранцев, К.К. Кисурин, С.Е. Омельчук, Г.П. Палкин,
Ю.С. Рознюк, Б.А. Руденко, В.С. Семенов, Л.И. Слюсаренко, Б.Г. Стружко
Измерены дифференциальные сечения упругого рассеяния дейтронов с энергией Ed = 36, 9МэВ яд-
рами дейтерия в диапазоне углов 30◦ ≤ θc.m. ≤ 116◦. Для описания основного максимума θc.m. ≤ 60◦
использовалась дифракционная ядерная модель, учитывающая структуру сталкивающихся ядер. По-
лучено удовлетворительное согласие с экспериментом для углов θc.m. ≤ 60◦ как с нашими эксперимен-
тальными данными, так и с данными других работ для энергий 12МэВ≤ Ed ≤ 85МэВ. При теорети-
ческой интерпретации угловых распределений учтена тождественность сталкивающихся дейтронов.
ПРУЖНЕ РОЗСIЯННЯ ДЕЙТРОНIВ НА ДЕЙТРОНАХ ПРИ Ed ≤ 85МеВ
О.О. Белюскiна, В.I. Гранцев, К.К. Кiсурiн, С.Є. Омельчук, Г.П. Палкiн,
Ю.С. Рознюк, Б.А. Руденко, В.С. Семенов, Л.I. Слюсаренко, Б.Г. Стружко
Було вимiряно диференцiальнi перерiзи пружного розсiювання дейтронiв з енергiєю Ed = 36, 9МеВ
ядрами дейтерiю в дiапазонi кутiв 30◦ ≤ θc.m. ≤ 116◦. Для опису основго максимуму θc.m. ≤ 60◦ вико-
ристовувалась дифракцiйна ядерна модель, яка враховує структуру ядер, що зiштовхуються. Отри-
мано задовiльне узгодження з експериментом для кутiв θc.m. ≤ 60◦ i з нашими експериментальними
даними, i з даними iнших робiт для енергiй 12МеВ≤ Ed ≤ 85МеВ. Для теоретичної iнтерпретацiї
кутових розподiлiв було враховано тотожнiсть дейтронiв, що зiштовхуються.
15
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