Elastic deuteron-triton scattering AT 37MeV
Results of measurement of differential cross section of elastic scattering of deuterons by tritons at the laboratory energy of 37 MeV for the center-of-mass angles θc.m. ranging from 25° to 150° are presented. The experiment is carried out on the U-240 isochronous cyclotron of the Institute...
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| Zitieren: | Elastic deuteron-triton scattering AT 37MeV / O.O. Belyuskina, V.I. Grantsev, V.V. Davydovskyy, K.K. Kisurin, S.E. Omelchuk, G.P. Palkin, Yu.S. Roznyuk, B.A. Rudenko, L.S. Saltykov, V.S. Semenov, L.I. Slusarenko, B.G. Struzhko, V.K.Tartakovsky, V.A. Shytiuk // Вопросы атомной науки и техники. — 2009. — № 5. — С. 17-22. — Бібліогр.: 19 назв. — англ. |
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irk-123456789-963982016-03-16T03:02:38Z Elastic deuteron-triton scattering AT 37MeV Belyuskina, O.O. Grantsev, V.I. Davydovskyy, V.V. Kisurin, K.K. Omelchuk, S.E. Palkin, G.P. Roznyuk, Yu.S. Rudenko, B.A. Saltykov, L.S. Semenov, V.S. Slusarenko, L.I. Struzhko, B.G. Tartakovsky, V.K. Shytiuk, V.A. Ядерная физика и элементарные частицы Results of measurement of differential cross section of elastic scattering of deuterons by tritons at the laboratory energy of 37 MeV for the center-of-mass angles θc.m. ranging from 25° to 150° are presented. The experiment is carried out on the U-240 isochronous cyclotron of the Institute for Nuclear Research, National Academy of Science of Ukraine. Obtained experimental data is analyzed theoretically in the framework of microscopic nuclear diffraction model. Angular distributions of deuterons in a region of the main maximum (θc.m. ≤ 60° ) are described quite well at deuteron energies of 14.4, 37.0 and 39.9 MeV . An explanation of a broad secondary maximum emerging at low deuteron energies is proposed using the phenomenological quasiclassical approximation. The quasiclassical approximation allows to describe the angular distributions only qualitatively at large angles 60° < θc.m. < 150°, where the cross sections are quite small. Представлено результати вимiрювання диференцiальних перерiзiв пружного розсiяння дейтронiв з енергiєю Ed = 37, 0 МеВ на тритонах у дiапазонi кутiв розсiяння 25° ≤ θc.m. ≤ 150° . Експеримент вико- нано на iзохронному циклотронi У-240 IЯД НАН України. Проведено теоретичний аналiз отриманих експериментальних даних в межах мiкроскопiчної дифракцiйної ядерної моделi. Кутовi розподiли дей- тронiв в областi головного максимуму (θc.m. ≤ 60° ) задовiльно описуються при енергiях дейтронiв 14, 4; 37, 0 та 39, 9 МеВ. Завдяки використанню феноменологiчного квазiкласичного наближення вдалося пояснити природу появи широкого вторинного максимуму при низьких енергiях дейтронiв. Квазiкла- сичне наближення дозволяє лише якiсно описати кутовi розподiли на великих кутах 60° ≤ θc.m. ≤ 150°, де перерiзи досить малi. Представлены результаты измерений дифференциальных сечений упругого рассеяния дейтронов с энергией Ed = 37 МэВ на тритонах в диапазоне углов рассеяния 25° ≤ θc.m. ≤ 150° . Эксперимент выполнен на изохронном циклотроне У-240 ИЯИ НАН Украины. Проведен теоретический анализ по- лученных экспериментальных данных в рамках микроскопической дифракционной ядерной модели. Угловые распределения дейтронов в области главного максимума (θc.m. ≤ 60°) достаточно хорошо описываются при энергиях дейтронов 14, 4; 37, 0 та 39, 9 МэВ. Предложено с использованием феменологического квазиклассического приближения объяснение появления широкого вторичного максимума при низких энергиях дейтронов. Квазиклассическое приближение позволяет лишь качественно описать угловые распределения на больших углах 60° ≤ θc.m. ≤ 150°, где сечения уже весьма малы. 2009 Article Elastic deuteron-triton scattering AT 37MeV / O.O. Belyuskina, V.I. Grantsev, V.V. Davydovskyy, K.K. Kisurin, S.E. Omelchuk, G.P. Palkin, Yu.S. Roznyuk, B.A. Rudenko, L.S. Saltykov, V.S. Semenov, L.I. Slusarenko, B.G. Struzhko, V.K.Tartakovsky, V.A. Shytiuk // Вопросы атомной науки и техники. — 2009. — № 5. — С. 17-22. — Бібліогр.: 19 назв. — англ. 1562-6016 PACS: 24.30.Cz, 13.75.Cs, 21.30.Fe, 21.60.Jz http://dspace.nbuv.gov.ua/handle/123456789/96398 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 Belyuskina, O.O. Grantsev, V.I. Davydovskyy, V.V. Kisurin, K.K. Omelchuk, S.E. Palkin, G.P. Roznyuk, Yu.S. Rudenko, B.A. Saltykov, L.S. Semenov, V.S. Slusarenko, L.I. Struzhko, B.G. Tartakovsky, V.K. Shytiuk, V.A. Elastic deuteron-triton scattering AT 37MeV Вопросы атомной науки и техники |
| description |
Results of measurement of differential cross section of elastic scattering of deuterons by tritons at the laboratory
energy of 37 MeV for the center-of-mass angles θc.m. ranging from 25°
to 150°
are presented. The experiment is
carried out on the U-240 isochronous cyclotron of the Institute for Nuclear Research, National Academy of Science
of Ukraine. Obtained experimental data is analyzed theoretically in the framework of microscopic nuclear diffraction
model. Angular distributions of deuterons in a region of the main maximum (θc.m. ≤ 60°
) are described quite
well at deuteron energies of 14.4, 37.0 and 39.9 MeV . An explanation of a broad secondary maximum emerging
at low deuteron energies is proposed using the phenomenological quasiclassical approximation. The quasiclassical
approximation allows to describe the angular distributions only qualitatively at large angles 60° < θc.m. < 150°,
where the cross sections are quite small. |
| format |
Article |
| author |
Belyuskina, O.O. Grantsev, V.I. Davydovskyy, V.V. Kisurin, K.K. Omelchuk, S.E. Palkin, G.P. Roznyuk, Yu.S. Rudenko, B.A. Saltykov, L.S. Semenov, V.S. Slusarenko, L.I. Struzhko, B.G. Tartakovsky, V.K. Shytiuk, V.A. |
| author_facet |
Belyuskina, O.O. Grantsev, V.I. Davydovskyy, V.V. Kisurin, K.K. Omelchuk, S.E. Palkin, G.P. Roznyuk, Yu.S. Rudenko, B.A. Saltykov, L.S. Semenov, V.S. Slusarenko, L.I. Struzhko, B.G. Tartakovsky, V.K. Shytiuk, V.A. |
| author_sort |
Belyuskina, O.O. |
| title |
Elastic deuteron-triton scattering AT 37MeV |
| title_short |
Elastic deuteron-triton scattering AT 37MeV |
| title_full |
Elastic deuteron-triton scattering AT 37MeV |
| title_fullStr |
Elastic deuteron-triton scattering AT 37MeV |
| title_full_unstemmed |
Elastic deuteron-triton scattering AT 37MeV |
| title_sort |
elastic deuteron-triton scattering at 37mev |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2009 |
| topic_facet |
Ядерная физика и элементарные частицы |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/96398 |
| citation_txt |
Elastic deuteron-triton scattering AT 37MeV / O.O. Belyuskina, V.I. Grantsev, V.V. Davydovskyy, K.K. Kisurin,
S.E. Omelchuk, G.P. Palkin, Yu.S. Roznyuk, B.A. Rudenko, L.S. Saltykov, V.S. Semenov, L.I. Slusarenko, B.G. Struzhko, V.K.Tartakovsky, V.A. Shytiuk // Вопросы атомной науки и техники. — 2009. — № 5. — С. 17-22. — Бібліогр.: 19 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT belyuskinaoo elasticdeuterontritonscatteringat37mev AT grantsevvi elasticdeuterontritonscatteringat37mev AT davydovskyyvv elasticdeuterontritonscatteringat37mev AT kisurinkk elasticdeuterontritonscatteringat37mev AT omelchukse elasticdeuterontritonscatteringat37mev AT palkingp elasticdeuterontritonscatteringat37mev AT roznyukyus elasticdeuterontritonscatteringat37mev AT rudenkoba elasticdeuterontritonscatteringat37mev AT saltykovls elasticdeuterontritonscatteringat37mev AT semenovvs elasticdeuterontritonscatteringat37mev AT slusarenkoli elasticdeuterontritonscatteringat37mev AT struzhkobg elasticdeuterontritonscatteringat37mev AT tartakovskyvk elasticdeuterontritonscatteringat37mev AT shytiukva elasticdeuterontritonscatteringat37mev |
| first_indexed |
2025-07-07T03:35:41Z |
| last_indexed |
2025-07-07T03:35:41Z |
| _version_ |
1836957661315203072 |
| fulltext |
ELASTIC DEUTERON-TRITON SCATTERING AT 37MeV
O.O. Belyuskina, V.I. Grantsev, V.V. Davydovskyy∗, K.K. Kisurin,
S.E. Omelchuk, G.P. Palkin, Yu.S. Roznyuk, B.A. Rudenko,
L.S. Saltykov, V.S. Semenov, L.I. Slusarenko, B.G. Struzhko,
V.K.Tartakovsky, V.A. Shytiuk
Institute for Nuclear Research, NAS of Ukraine, 03680, Kyiv, Ukraine
(Received July 30, 2008)
Results of measurement of differential cross section of elastic scattering of deuterons by tritons at the laboratory
energy of 37 MeV for the center-of-mass angles θc.m. ranging from 25◦ to 150◦ are presented. The experiment is
carried out on the U-240 isochronous cyclotron of the Institute for Nuclear Research, National Academy of Science
of Ukraine. Obtained experimental data is analyzed theoretically in the framework of microscopic nuclear diffraction
model. Angular distributions of deuterons in a region of the main maximum (θc.m. ≤ 60◦) are described quite
well at deuteron energies of 14.4, 37.0 and 39.9 MeV . An explanation of a broad secondary maximum emerging
at low deuteron energies is proposed using the phenomenological quasiclassical approximation. The quasiclassical
approximation allows to describe the angular distributions only qualitatively at large angles 60◦ < θc.m. < 150◦,
where the cross sections are quite small.
PACS: 24.30.Cz, 13.75.Cs, 21.30.Fe, 21.60.Jz
1. INTRODUCTION
Collisions of deuterons with tritons at energies of tens
MeV still remain studied insufficiently [1-7], though
they are very informative and are of interest for in-
vestigation of both the few-nucleon nucleus structure
and the nuclear interaction. Coulomb interaction
gives negligibly small contribution (of the order of
1%) into the scattering cross section at the energies
of incident deuterons in the interval of 10 ... 40MeV .
Therefore, in considering dt-scattering we will sub-
sequently neglect the Coulomb interaction. For the
same reason, the d3He-scattering [7-9] is very much
similar to the dt-scattering.
At the deuteron energies that are being consid-
ered, the wavelength λ of the relative motion of 2H
and 3H nuclei divided by 2π appears to be a few
times less than the radius of their nuclear interac-
tion RN (approximately 4 ... 6 fm), therefore the dif-
fraction approximation can be used for a calculation
of the elastic deuteron - triton scattering cross sec-
tion. Consideration will be inherently quasiclassical
(λ ¿ RN ) when an influence of many quantum me-
chanical effects (the Pauli principle, spins of nuclei,
antisymmetrization of wave functions) becomes sub-
stantially weaker [10], which simplifies calculations
significantly. In addition, as it will be shown, the
macroscopic description of the dt-scattering process
is also possible. In present work, we consider the dt-
collision and solve the very complicated problem of
five interacting nucleons of continuous energy spec-
trum approximately in the framework of nuclear dif-
fraction model. The goal of this work is to present
the results of our experiment on elastic scattering of
deuterons with the energy Ed = 37 MeV by tritons
as well as to provide the theoretical description and
interpretation of our data together with the published
data corresponding to other energies Ed using simple
quasiclassical methods of quantum mechanics [10-15].
2. EXPERIMENT
Elastic scattering of deuterons by tritium nuclei with
energy of deuterons Ed = 37 MeV was experimen-
tally studied on Kiev isochronous cyclotron U − 240
of KINR, NAS of Ukraine. Measurements were car-
ried on self-maintained titanium-tritium target and
on pure titanium target. Ti-T target is a tritium-
loaded titanium film with activity of 7.57 Ci.
Charged particles were detected by three tele-
scopes of counters (∆E−E) placed in reaction plane.
Intensity of ion beam passed through the target was
detected with Faraday cup connected to current inte-
grator. For determination of angular distribution of
elastically scattered deuterons data on elastic scat-
tering of deuterons T (d, d)T as well as data on recoil
tritons were used. Registration was performed in an-
gular range of 15◦ ≤ θlab ≤ 58◦ for deuterons and in
angular range of 15◦ ≤ θlab ≤ 52◦ for tritons. (θlab is
an angle in laboratory system of coordinates). Statis-
tical error of measurement for inclusive spectra was
1 ... 3% depending on angle of detection. Absolute
values of cross sections were determined with accu-
racy ∼ 15%. Measurement procedure and prelimi-
nary results were published in [1,6].
∗Corresponding author E-mail address: interdep@kinr.kiev.ua, fax: (044)525-44-63, tel.: (044)525-23-49
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2009, N5.
Series: Nuclear Physics Investigations (52), p.17-22.
17
Fig.1(a) presents one-dimensional deuterons
spectra measured on Ti − T and Ti tar-
gets at angle 15◦, Fig.1(b) presents re-
coil tritons spectra at the same angle.
Fig.1. Deuteron spectra measured on Ti−T and Ti
targets for the angle of 15◦ at the deuteron energy
of 37 MeV (a); the same for recoil tritons (b)
Fig.2. Energy spectra for elastically scattered
deuterons and recoil tritons at the deuteron energy
of 37 MeV for the angle of 15◦ (a); (b) - the same
for the angle of 38◦. Solid and dashed lines corre-
spond to the calculations based on the microscopic
nuclear diffraction model [15,16]
Isolation of peaks corresponding to elastic scattering
of deuterons on tritons was carried by subtraction
of spectra derived on Ti-target from spectra ob-
tained from Ti − T target. The same approach was
used for separation of peaks of recoil tritons. En-
ergy spectra of deuterons and recoil tritons from
T (d, d)T reaction obtained at 15◦ and 38◦ are il-
lustrated on Fig.2(a,b). Analysis of energy spectra
is presented in sections 4 and 5. Dependence of
differential sections dσ/dΩ for elastic scattering of
deuterons on tritons in center-of-mass system (c.m.)
is presented on Fig.3(a). Before, the elastic scat-
tering of deuterons on tritons was studied only at
low energies (6.6 ... 14.4 MeV ) [7]. On Fig.3(a) pre-
viously published data on dt-scattering at 8.3 and
14.4 MeV are presented together with data obtained
in our experiment. Angular distributions have com-
mon typical features: sharp decrease of section with
scattering angle increasing to θc.m. ≤ 60◦ and no-
ticeable rise of cross sections at angles starting from
θc.m. ≈ 130◦. However there are considerable differ-
ences at 60◦ ≤ θc.m. ≤ 130◦ angle range. Wide max-
ima observed at θc.m. ≈ 100◦ with energies 8.3 MeV
and 14.4 MeV , disappears at our energy 37 MeV .
We made comparison with data on elastic d3He
scattering at energies 10.0, 14.4 [7], 17.49, 39.9 MeV
[7,8,9]. Comparison is presented on Fig.3(b).
Fig.3. Elastic scattering of deuterons by tritons at
the laboratory energies of 8.3 MeV [7], 14.4 MeV
[7] and 37 MeV (our data) (a); (b)- deuterons on
helions at the laboratory energies of 14.4 MeV [7],
17.49 MeV [7,8] and 39.9 MeV [9]
Nature of dependence of elastic d3He cross-
section at range of low and high angles is identical to
dependence of cross-section for elastic dt-scattering.
At angular range of 60◦ ≤ θc.m. ≤ 130◦ the similar
picture is observed: with deuterons energy increasing
the wide maximum at angle θc.m. ≈ 100◦ disappears
18
distorting with energy 39.9 MeV . Data on 3He(d, d)
scattering obtained at energy 17.49 MeV already in-
dicate maximum disappearing at angle θc.m. ≈ 100◦.
Deuterons elastic scattering on helions at energy
Ed = 39.9 MeV has practically the same dependence
as elastic scattering of deuterons on tritons at our
energy.
3. FORMALISM FOR ANGULAR
DISTRIBUTIONS OF SCATTERED
DEUTERONS
We consider the deuteron - triton scattering in the
center-of-mass frame and use the microscopic diffrac-
tion model [10,15], in which an interaction of each of
three nucleons of 3H nucleus with each of two nucle-
ons of 2H nucleus is described by the nucleon-nucleon
profile functions of Gaussian type [10,12,16]:
ωij ≡ ω(|~ρij |) = a exp(−b2ρ2
ij) , (1)
where ~ρij is the component of the vector ~rij = ~ri − ~rj
perpendicular to the incident deuteron momentum ~kd
in the laboratory frame. Here ~ri is the radius vector
of the i − th nucleon of triton (i = 1, 2, 3), ~rj is
the radius vector of the j − th nucleon of deuteron
(j = 4, 5).
The amplitude of elastic deuteron - triton scatter-
ing in the diffraction impulse approximation [11]
A(~χ) =
∫
d(3)~ρ1
∫
d(3)~r
∫
d(3)~s
∫
d(2) ~R⊥φ2
d(~s)
×φ2
t (~ρ1, ~r)ψ∗~χ(~R⊥)ψ0(~R⊥)
×(ω14 + ω15 + ω24 + ω25 + ω34 + ω35) , (2)
where
~s = ~r45, ~r = ~r23, ~ρ1 = ~r1 − ~r2 + ~r3
2
.
It describes well the corresponding diffraction cross
section
dσ =
k2
(2π)2
|A(~χ)|2 dΩ ,
k =
3
5
kd , |~χ| = 2k sin
θ
2
. (3)
In a region of the main diffraction maximum, where
the scattering angle θ ≡ θc.m. does not exceed 65◦ (in
the laboratory frame this angle does not exceed ap-
proximately 40◦), simple intrinsic wave functions of
deuteron φd(~s) and triton φt(~ρ1, ~r) in Gaussian form
[10,12,16] are used:
φd(~s) =
(
2λ2
π
)3/4
e−λ2s2
,
λ = 0, 267 fm−1, (4)
φt(~ρ1, ~r) =
33/4α3
π3/2
e−α2(ρ2
1+3r2/4),
α = 0, 375 fm−1. (5)
The relative motion of deuteron and triton before and
after scattering is described by the following wave
functions [11]:
ψ0(~R⊥) = 1, ψ~χ(~R⊥) = ei~χ~R⊥ , (6)
where ~χ is the transferred momentum (~χ~kd = 0), ~R⊥
is the component of vector ~R, which connects the
centers of mass of deuteron and triton (h̄ = c = 1),
perpendicular to ~kd.
On using the equations (1) - (6), we get the follow-
ing compact expression for the angular distribution
of deuterons in elastic scattering in explicit form:
dσ
dΩ
=
9a2k2
b4
exp
[
−χ2
(
1
2b2
+
1
9α2
+
1
16λ2
)]
,
χ = 2k sin
θ
2
, k =
2π
λ
=
6
5
√
MEd, θ ≤ 65◦, (7)
where M is the nucleon mass.
For quality description of scattering at large an-
gles (65◦ ≤ θ ≤ 180◦) in the center-of-mass frame,
where the cross section is quite small, we use qua-
siclassical expression for the scattering amplitude
of two colliding impenetrable balls, which represent
deuteron and triton, disregarding their internal struc-
ture [13]:
f(θ) = i
RN
2 sin θ
2
J1
(
2kRN sin
θ
2
)
− i
2
RN exp
(
−2ikRN sin
θ
2
)
. (8)
4. FORMALISM FOR ENERGY SPECTRA
With the help of the above formulae of the micro-
scopic diffraction model, we obtained the following
differential cross sections, which can be used to de-
scribe the energy distribution in the laboratory frame
(where tritons are in the rest before collision) versus
the energy of scattered deuterons E′
d and the recoil
energy of tritons Et at fixed deuteron angle θd and
triton escape angle θt:
dσ
dΩddE′
d
=
9M
√
EdE′
d
5π2
|A(χ)|2 ×
δ
(
5E′
d − Ed − 4
√
EdE′
d cos θd
)
, (9)
dσ
dΩtdEt
=
33/2M
√
EdE′
t
5
√
2π2
|A(χ)|2 ×
δ
(
2
√
6EdE′
t cos θt − 5Et
)
, (10)
where |A(χ)|2 is taken from (3) and (7). In addition,
the variable χ in the amplitude A(χ) should be ex-
pressed in terms of kinematic variables in the labora-
tory frame. So, we substitute the following expression
to (9):
χ =
[
4M(Ed + E′
d − 2
√
EdE′
d cos θd)
]1/2
, (11)
19
and the following expression to (10):
χ =
√
6MEt =
12
5
√
MEd cos θd, (12)
where the relationships for scattering (escape) angles
and energies of nuclei before and after collision in the
center-of mass and laboratory frames were used [14].
In calculations of the cross sections (9) and (10),
the delta-functions δ(E) were replaced with the finite
functions δΓ(E), whose narrow maxima are defined
by the finite width Γ [10,16]:
δΓ(E) =
Γ
2π
1
E2 + 1
4Γ2
, lim
Γ→0
δΓ(E) = δ(E) . (13)
5. ANGULAR AND ENERGY
DISTRIBUTIONS ANALYSIS
5.1. ANGULAR DISTRIBUTIONS
ANALYSIS
Differential cross-sections of elastic dt-scattering
dσ/dΩ in center of mass system obtained at deuterons
energy 37.0 MeV as well as published data at energy
14.4 MeV [7] and data on d3He scattering at en-
ergy 39.9 MeV [9] were used in analysis. Fig.4(a,b,c)
presents these data and corresponding theoretical cal-
culations. Curves 1-1a on Fig.4 are derived using
equation (7). As shown on Fig.4 experimental angu-
lar distributions of scattered deuterons in the vicinity
of main maximum (θc.m. ≤ 65◦) are quite well de-
scribed theoretically by (7) at energies Ed = 14.4; 37
and 39.9 MeV .
Curves 2 and 3 on Fig.4(a) and curves 2 on
Fig.4(b,c) are derived using equation (8). Curves 2a
are plotted using only first item in (8) i.e. based on
model of colliding black balls with sharp edge, and
curves 2b are plotted using only second item in (8),
which is concerned with classical isotropic scattering
(RN = 4.4 fm). Curves 3 on Fig.4(b,c) corresponds
to the same second item in (8), but with RN = 2 fm,
what better describes cross-section at θ ≥ 65◦.
Decreasing of radius of interaction RN with in-
creasing θ when energy transmission is increasing, is
in accordance with long ago observed [17-19] decreas-
ing of RN with increasing of relative energy of collid-
ing nuclei, when energy transmission is increasing.
This phenomenon was confirmed (and explained) by
optical model calculations [17].
Appearance of wide but low in height experimen-
tal maximum on Fig.4(a) for Ed = 14.4 MeV at
65◦ ≤ θ ≤ 140◦ is explained by the advent of sec-
ondary diffractive maximum due to the first item in
(8), which however is distinctly distorted by interfer-
ence of quantum and classical amplitudes in (8) and
by influence of inner structure of nuclei. This maxi-
mum disappears with increasing of energy Ed.
Phenomenological semi-classical approach can’t
describe well in angles range 25◦ ≤ θ ≤ 150◦
the observed cross-section dependence on θc.m. with-
out taking into account some number of quan-
tum effects and real structure of colliding nuclei.
In the angular range 65◦ ≤ θc.m. ≤ 150◦ only
qualitative description of cross sections is achieved.
Fig.4. Ttheoretical calculations compared with
experimental angular distributions at the following
energies: (a) - 14.4 MeV , (b) - 37 MeV , (c) -
39.9 MeV . Curves 1 and 1a - calculations based
on the microscopic nuclear diffraction model (7)
with the following parameters: (a) 1 - α = 1.30,
b2 = 0.30 fm−2; 1a - α = 0.5, b2 = 0.10 fm−2;
(b) 1 - α = 0.80; b2 = 0.31 fm−2; 1a - α = 0.65,
b2 = 0.22 fm−2; (c) 1 - α = 0.70, b2 = 0.31 fm−2.
Line 2 - calculations based on quasiclassical approx-
imation (8) with the following parameters: (a) 2 -
RN = 5.2 fm; 3 - RN = 4.15 fm, (b) RN = 4.4 fm,
(c) RN = 4.4 fm. Curve 3 on (b,cb) denotes the
cross section dσ
dΩ = 1
4R2
N for deuteron scattering
angles θd > 70◦, RN = 2 fm
5.2. ENERGY SPECTRA ANALYSIS
Experimental energy spectra at angle θlab = 15◦
for deuterons (Γ = 0.69 MeV ) and tritons (Γ =
0.92 MeV ) are represented on Fig.2(a), and Fig.2(b)
shows spectra for deuterons (Γ = 0.68 MeV ) and tri-
tons (Γ = 1.07 MeV ) at angle θlab = 38◦. Location,
width Γ, and height of maxima are well described
with curves calculated by equations (9) - (13), except
of cross section dσ/dΩtdEt at θt = 15◦ and Et in
range from 15MeV to 30 MeV (see Fig.2(a)). The
last circumstance is concerned with fact that at low
20
θt and E′
t > 15MeV impulse and energy of recoil
triton gain high values what can excite inner degrees
of freedom of colliding nuclei with its transition into
intermediate quasisteady states, majority of which
come back to bound states and we detect it in our
experiment, minority break up and we don’t detect
the decay products.
6. CONCLUSIONS
1. Differential cross sections of the elastic scatter-
ing of deuterons with the energy of 37MeV by tritons
are measured for the center-of mass scattering angles
ranging from 25◦ to 150◦.
2. The analysis of the elastic scattering of
deuterons by tritons (helions) is carried out for
deuteron energies of 14.4 MeV [7], 37 MeV (our
data) and 39.9 MeV [9] in the framework of the mi-
croscopic nuclear diffraction model. The experimen-
tal angular distributions of scattered deuterons in the
region of main maximum (θc.m. ≤ 65◦) are quite well
described theoretically for the deuteron energies of
14.4 MeV , 37 MeV and 39.9 MeV .
3. The phenomenological quasiclassical approxi-
mation cannot adequately well describe the observed
dependence of the cross section on θc.m. in the whole
range of angles 25◦ ≤ θc.m. ≤ 150◦ without taking
into account a number of quantum effects and real
structure of colliding nuclei. In the range of angles
65◦ ≤ θc.m. ≤ 150◦, only qualitative description of
the cross sections is achieved.
4. An explanation of the broad secondary max-
imum emerging in the dependence of the observed
cross section on the deuteron scattering angle in a
range 65◦ ≤ θc.m. ≤ 140◦ for the incident deuteron
energies Ed ≤ 17 MeV is proposed. It is shown
that the maximum emerges due to the diffraction
process and the interference of quantum and classi-
cal isotropic scattering amplitudes as well as to the
manifestation of the structure of colliding nuclei.
5. The analysis of measured energy spectra of
deuterons and recoil tritons from the reaction t(d, d)t
at the energy Ed = 37MeV is carried out. Our
calculations of the energy distributions, based on
the microscopic nuclear diffraction model, are in
good agreement with the experiment at width Γ =
0.68...0.69 MeV (15◦ ≤ θlab ≤ 38◦) for deuterons and
Γ = 0.92...1.07 MeV (15◦ ≤ θlab ≤ 38◦) for recoil tri-
tons.
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УПРУГОЕ dt-РАССЕЯНИЕ ПРИ ЭНЕРГИИ 37 МэВ
О.О. Белюскина, В.И. Гранцев, В.В. Давидовский, К.К. Кисурин, С.Е. Омельчук,
Г.П. Палкин, Ю.С. Рознюк, Б.А. Руденко, Л.С. Салтыков, В.С. Семенов,
Л.И. Слюсаренко, Б.Г. Стружко, В.К. Тартаковский, В.А. Шитюк
Представлены результаты измерений дифференциальных сечений упругого рассеяния дейтронов с
энергией Ed = 37 МэВ на тритонах в диапазоне углов рассеяния 25◦ ≤ θc.m. ≤ 150◦. Эксперимент
выполнен на изохронном циклотроне У-240 ИЯИ НАН Украины. Проведен теоретический анализ по-
лученных экспериментальных данных в рамках микроскопической дифракционной ядерной модели.
Угловые распределения дейтронов в области главного максимума (θc.m. ≤ 60◦) достаточно хорошо
описываются при энергиях дейтронов 14, 4; 37, 0 та 39, 9 МэВ. Предложено с использованием фемено-
логического квазиклассического приближения объяснение появления широкого вторичного максимума
при низких энергиях дейтронов. Квазиклассическое приближение позволяет лишь качественно описать
угловые распределения на больших углах 60◦ ≤ θc.m. ≤ 150◦, где сечения уже весьма малы.
ПРУЖНЕ dt-РОЗСIЯННЯ ПРИ ЕНЕРГIЇ 37 МеВ
О.О. Белюскiна, В.I. Гранцев, В.В. Давидовський, К.К. Кiсурiн, С.Є. Омельчук,
Г.П. Палкiн, Ю.С. Рознюк, Б.А. Руденко, Л.С. Салтиков, В.С. Семенов,
Л.I. Слюсаренко, Б.Г. Стружко, В.К. Тартаковський, В.А. Шитюк
Представлено результати вимiрювання диференцiальних перерiзiв пружного розсiяння дейтронiв з
енергiєю Ed = 37, 0 МеВ на тритонах у дiапазонi кутiв розсiяння 25◦ ≤ θc.m. ≤ 150◦. Експеримент вико-
нано на iзохронному циклотронi У-240 IЯД НАН України. Проведено теоретичний аналiз отриманих
експериментальних даних в межах мiкроскопiчної дифракцiйної ядерної моделi. Кутовi розподiли дей-
тронiв в областi головного максимуму (θc.m. ≤ 60◦) задовiльно описуються при енергiях дейтронiв 14, 4;
37, 0 та 39, 9 МеВ. Завдяки використанню феноменологiчного квазiкласичного наближення вдалося
пояснити природу появи широкого вторинного максимуму при низьких енергiях дейтронiв. Квазiкла-
сичне наближення дозволяє лише якiсно описати кутовi розподiли на великих кутах 60◦ ≤ θc.m. ≤ 150◦,
де перерiзи досить малi.
22
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