Analysis of ¹⁶O(γ, 4α) reaction mechanism
The mechanism of triangular and quadrangular ⁸Be and ¹²C Feynman diagrams for the ¹⁶O(γ, 4α) reaction in the field of photon energy Eg = 15...45 MeV was analyzed. The paper presents the calculation results on the peak positions in the energy dependence of total reaction cross-sections with consider...
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Guryev, V.N. 2017-01-08T16:27:02Z 2017-01-08T16:27:02Z 2009 Analysis of ¹⁶O(γ, 4α) reaction mechanism / V.N. Guryev // Вопросы атомной науки и техники. — 2009. — № 3. — С. 15-19. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 21.60.Gx, 25.20.X https://nasplib.isofts.kiev.ua/handle/123456789/111152 The mechanism of triangular and quadrangular ⁸Be and ¹²C Feynman diagrams for the ¹⁶O(γ, 4α) reaction in the field of photon energy Eg = 15...45 MeV was analyzed. The paper presents the calculation results on the peak positions in the energy dependence of total reaction cross-sections with consideration of the ⁸Be and ¹²C exitation spectra. It is shown that the radical extremes of triangular diagrams can manifest themselves in the form of "ghosts" of ⁸Be, ⁸Be* and ¹²C* nuclei in the excited states of 2α and 3α- particles in the final state. The distributions of energy correlations of two α- particle pairs in the approximation of the pole ⁸Be- diagram at Eg=20...40 MeV were calculated. Проведен анализ механизма трех- и четырехугольных ⁸Be- и ¹²C- фейнмановских диаграмм для реакции ¹⁶O(γ, 4α) в области энергии фотонов Eγ = 15...45 МэВ. Проведен расчет положения пиков в энергетической зависимости полных сечений реакции с учетом спектров возбуждения ядер ⁸Be и ¹²C. Показана возможность проявления корневых особенностей треугольных диаграмм в виде <<призраков>> ядер ⁸Be, ⁸Be* и ¹²C* в возбужденных состояниях 2α- и 3α-частиц в конечном состоянии. Проведен расчет распределений энергетических корреляций двух пар α-частиц в приближении полюсной 8Be-диаграммы при Eg = 20...40 МэВ. Проведено аналіз механізму трьох- і чотирикутних ⁸Be- і ¹²C- фейнмановських діаграм для реакції ¹⁶O(γ, 4α) в області енергій фотонів Eγ = 15...45 МеВ. Проведено розрахунок розташування піків в енергетичній залежності повних перерізів реакції з розрахунком спектрів збудження ядер ⁸Be и ¹²C. Показано можливість проявлення корінних особливостей трикутних діаграм у вигляді <<примар>> ядер ⁸Be, ⁸Be* и ¹²C* в збудженних станах 2α- і 3α-частинок в кінцевому стані. Проведено розрахунок розподілів енергетичних кореляцій двох пар α-частинок в наближенні полюсної ⁸Be- діаграми при Eg=20...40 МеВ. The author is grateful to S.N.Afanasyev for discussions of experimental problems being considered in the present paper. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Ядерная физика и элементарные частицы Analysis of ¹⁶O(γ, 4α) reaction mechanism Аналіз механізму реакціі ¹⁶O(γ, 4α) Анализ механизма реакции ¹⁶O(γ, 4α) Article published earlier |
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| title |
Analysis of ¹⁶O(γ, 4α) reaction mechanism |
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Analysis of ¹⁶O(γ, 4α) reaction mechanism Guryev, V.N. Ядерная физика и элементарные частицы |
| title_short |
Analysis of ¹⁶O(γ, 4α) reaction mechanism |
| title_full |
Analysis of ¹⁶O(γ, 4α) reaction mechanism |
| title_fullStr |
Analysis of ¹⁶O(γ, 4α) reaction mechanism |
| title_full_unstemmed |
Analysis of ¹⁶O(γ, 4α) reaction mechanism |
| title_sort |
analysis of ¹⁶o(γ, 4α) reaction mechanism |
| author |
Guryev, V.N. |
| author_facet |
Guryev, V.N. |
| topic |
Ядерная физика и элементарные частицы |
| topic_facet |
Ядерная физика и элементарные частицы |
| publishDate |
2009 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Аналіз механізму реакціі ¹⁶O(γ, 4α) Анализ механизма реакции ¹⁶O(γ, 4α) |
| description |
The mechanism of triangular and quadrangular ⁸Be and ¹²C Feynman diagrams for the ¹⁶O(γ, 4α) reaction in the field of photon energy Eg = 15...45 MeV was analyzed. The paper presents the calculation results on the peak positions in the energy dependence of total reaction cross-sections with consideration of the ⁸Be and ¹²C exitation spectra. It is shown that the radical extremes of triangular diagrams can manifest themselves in the form of "ghosts" of ⁸Be, ⁸Be* and ¹²C* nuclei in the excited states of 2α and 3α- particles in the final state. The distributions of energy correlations of two α- particle pairs in the approximation of the pole ⁸Be- diagram at Eg=20...40 MeV were calculated.
Проведен анализ механизма трех- и четырехугольных ⁸Be- и ¹²C- фейнмановских диаграмм для реакции ¹⁶O(γ, 4α) в области энергии фотонов Eγ = 15...45 МэВ. Проведен расчет положения пиков в энергетической зависимости полных сечений реакции с учетом спектров возбуждения ядер ⁸Be и ¹²C. Показана возможность проявления корневых особенностей треугольных диаграмм в виде <<призраков>> ядер ⁸Be, ⁸Be* и ¹²C* в возбужденных состояниях 2α- и 3α-частиц в конечном состоянии. Проведен расчет распределений энергетических корреляций двух пар α-частиц в приближении полюсной 8Be-диаграммы при Eg = 20...40 МэВ.
Проведено аналіз механізму трьох- і чотирикутних ⁸Be- і ¹²C- фейнмановських діаграм для реакції ¹⁶O(γ, 4α) в області енергій фотонів Eγ = 15...45 МеВ. Проведено розрахунок розташування піків в енергетичній залежності повних перерізів реакції з розрахунком спектрів збудження ядер ⁸Be и ¹²C. Показано можливість проявлення корінних особливостей трикутних діаграм у вигляді <<примар>> ядер ⁸Be, ⁸Be* и ¹²C* в збудженних станах 2α- і 3α-частинок в кінцевому стані. Проведено розрахунок розподілів енергетичних кореляцій двох пар α-частинок в наближенні полюсної ⁸Be- діаграми при Eg=20...40 МеВ.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/111152 |
| citation_txt |
Analysis of ¹⁶O(γ, 4α) reaction mechanism / V.N. Guryev // Вопросы атомной науки и техники. — 2009. — № 3. — С. 15-19. — Бібліогр.: 14 назв. — англ. |
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| first_indexed |
2025-11-24T06:09:40Z |
| last_indexed |
2025-11-24T06:09:40Z |
| _version_ |
1850844087800823808 |
| fulltext |
ANALYSIS OF 16O(γ, 4α) REACTION MECHANISM
V.N. Guryev∗
National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
(Received March 18, 2009)
The mechanism of triangular and quadrangular 8Be and 12C Feynman diagrams for the 16O(γ, 4α) reaction in the
field of photon energy Eγ = 15 ... 45 MeV was analyzed. The paper presents the calculation results on the peak
positions in the energy dependence of total reaction cross-sections with consideration of the 8Be and 12C exitation
spectra. It is shown that the radical extremes of triangular diagrams can manifest themselves in the form of ”ghosts”
of 8Be, 8Be∗ and 12C∗ nuclei in the excited states of 2α and 3α- particles in the final state. The distributions of
energy correlations of two α- particle pairs in the approximation of the pole 8Be- diagram at Eγ = 20 ... 40 MeV
were calculated.
PACS: 21.60.Gx, 25.20.X
1. INTRODUCTION
Investigation into the total α-particle photodisinte-
gration of α-cluster nuclei is of particular interest
for the study of properties of virtual α-cluster struc-
tures in nuclei and their influence on the nuclear re-
action mechanism and on the α-synthesis dynamics
in the Universe. In connection with these problems
a complex experimental and theoretical investigation
of the 16O(γ, 4α) reaction in the field of it manifes-
tation at photon energies Eγ = 14, 42 ... 50 MeV is
much promising. In earlier works [1]-[3], one has car-
ried out experimental investigations on the energy
dependence of total reaction cross-sections σt(Eγ),
energy and angular distributions of α-particles and
distributions in the excitation energies of 2α- and
3α-particles in the final state with the use of pho-
toemulsions on the bremsstrahlung photon beams in
the energy interval Eγ = 14, 42 ... 70 MeV . In later
works [4] one has carried out experimental investi-
gations on the same reaction characteristics and on
the energy and angular correlations of α-particles at
Eγ = 18 ... 48 MeV with the use of photoemulsions on
the bremsstrahlung photon beams having the maxi-
mum energy of 300 MeV . It should be noted, that
the available experimental data have a contradictory
character. So, in [1]-[4] evident discrepancies are ob-
served between the positions of maxima in σt(Eγ).
For example, in [1] (180 reaction events) the peaks at
Em
γ ∼ 23; 28; 30 and 35 MeV were observed (ibidem
presented are the findings of D.L.Livesey, C.L.Smith
(1956) at Em
γ ∼ 22; 26 ... 27; 29; 32 and 35 MeV ); in
[2] (53 events)- at Em
γ ∼ 18, 5 and 20, 5 MeV ; in [3]-
two narrow peaks at Em
γ ∼ 23 and 25 MeV and a
broad resonance with the centre at Em
γ ∼ 30 MeV ;
in [4] (540 events)-a small peak at Em
γ ∼ 20 and
a broad resonance at Em
γ ∼ 30 MeV . Also, there
are disagreements in the interpretation of the reac-
tion mechanism with taking into account a possible
realization of partial channels: γ + 16O→ 4α; α +
12C∗; 8Be(8Be∗) + 8Be(8Be∗); α + α + 8Be(8Be∗).
Besides, all the qualitative theoretical construct were
considered in the two-particle approximation without
taking into account the interaction particles in the fi-
nal state. So, in [2] one expected appearance of the
second (with the excitation energy EC∗ = 7, 7 MeV )
and the third (with EBe∗ = 3 MeV ) partial channels
at Eγ = 17, 5 ... 19, 5 MeV and higher excitatons of
8Be and 12C nuclei at Eγ = 19, 5 ... 21, 5 MeV , as
well as, a probable manifestation of the fourth par-
tial channel; in [3] a contribution of the E2-transition
up to Eγ = 40 MeV was supposed to interpret the
structures in the function of reaction excitation. In
[4] basing on the analysis of distributions by the rela-
tive energies of α-particles ηαi ≡ Eαi/(Eγ−ε) (where
i = 1 ... 4, ε is the reaction threshold) and mani-
festation of excited states of intermediate 8Be∗ and
12C∗ nuclei, it has been concluded that the mech-
anism of the statistical decay of 16O nucleus up to
Eγ = 28 MeV plays a main role. When Eγ increases
the quasi-direct interaction between the photons and
the 2α- 3α- clusters of 16O nucleus, followed by the
formation of intermediate 8Be∗ and12C∗ nuclei in the
state with Jπ= 2+, is the major mechanism. Here of
interest is the manifestation of peaks in the exper-
imental spectra of 8Be excitation at E∗
Be ∼ 3 MeV
and of 12C excitation at E∗
C ∼ 15 ... 16 MeV in both
intervals: Eγ = 18 ... 28 MeV , in the case of co-
incidence with the phase distribution, as well as,
Eγ = 28 ... 48 MeV , when the phase distribution is
distinctly displaced into the region of high excita-
tion energy E∗
x. The same independence on Eγ was
observed in the experimental relative energy distri-
bution ηα1 for the most energetic α1- particle with
the peak position at ηm
α1
' 0, 37 in energy inter-
∗Corresponding author E-mail address: guryev@kipt.kharkov.ua
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2009, N3.
Series: Nuclear Physics Investigations (51), p.15-19.
15
val Eγ = 18 ... 48MeV , as well as,in the position of
maxima in the distributions of experimental events
by the variable tαα at tαα ' 0, 05 and 0, 5, where
tαα ≡ Eαα/(Eγ − ε) and Eαα is the relative energy
of 2α-particles.
In p.2 of the present paper the above-mentioned
problems, concerning the interpretation of the peak
positions in σt(Eγ) of the 16O(γ, 4α) reaction,the
manifestation of excited, independent on Eγ , states
in the (2α) and (3α)-systems in the final states, and
the singularities in the distributions ηα1 are consid-
ered using the triangular and quadrangular 8Be and
12C Feynman diagrams at Eγ = 15 ... 45 MeV . The
equations for kinetic energies of 4α-particles, neces-
sary for the experimental verification of the trian-
gular diagrams under consideration were obtained.
The paper presents the numerical estimates of event
distributions by the variables tα1α2 and tα3α4 in the
approximation of the pole 8Be-diagram, respectively,
for 2α-particles at the photon and the spectator ver-
tices at Eγ = 20 ... 40 MeV . In p.3 the results ob-
tained are discussed.
2. METHODS AND RESULTS
In connection with experimental ambiguities in the
energy positions and in the interpretation of quantum
peak characteristics in σt(Eγ) of the 16O(γ, 4α) reac-
tion [1-4], as well as, taking into account the stable,
independent on Eγ , positions of maxima in the ex-
citation spectra of 2α and 3α-particles in the energy
interval Eγ = 18 ... 48 MeV [4], we have applied, for
calculation of this characteristics, the method in the
approximation of triangular and quadrangular Feyn-
man diagrams presented in Fig.1 and Fig.2.
α
α
α
α
α
α
γ
Fig.1. Triangular 8Be- and 12C- diagrams
for the 16O(γ, 4α) reaction
α
α
α
α
α
α
γ
Fig.2. Quadrangular 8Be- and 12C- diagrams
for the 16O(γ, 4α) reaction
The quadrangular diagrams are the detailed repre-
sentation of triangular diagrams taking into account
a probable resonance excitation of primary clusters at
the photon vertices. For three-particle photonuclear
reactions a similar approximation was considered in
[5, 6]. Near the singularities of amplitudes, presented
by the quadrangular diagrams in Fig. 2, it is pos-
sible to neglect the virtual particle going out from
the mass surface [7, 8] and to consider the resonance
processes as the processes on free particles. Then
the approximate estimates of photon energies Em
γ ,
at which the resonance peaks in σt(Eγ) arise, can be
obtained for quadrangular 8Be and 12C diagrams of
Fig.2, from equations
Em
γ (Be) = E∗
Be + 2mBe −m0, (1)
Em
γ (C) = E∗
C + mC + mHe −mO, (2)
where mHe, mBe, mC , mO and E∗
Be, E∗
C are
the masses of nuclei 4He, 8Be, 12C, 16O and
the excitation energies of 8Be∗ and 12C∗ nuclei
respectively. The calculations of Em
γ (Be) and
Em
γ (C) by (1) and (2) are given in Tables 1 and
2 with taking into account the levels of 8Be [9]
and 12C nuclei [10]. As is seen from Tables 1
and 2, the energy position of peaks in σt(Eγ)
does not contradict to the data set given in [1-4].
Table 1
E∗
Be(J
π), MeV Em
γ (Be), MeV
3.04 ± 0.03(2+) 17.66 ± 0.03
11.4 ± 0.3(4+) 26.0 ± 0.3
16 - 17(2+) 31 - 32
20.1 - 20.2(0+) 34.7 - 34.8
22.2(0+) 36.8
25.2(0+) 39.8
25.5(4+) 40.1
27.4(0+) 42.1
Table 2
E∗
C(Jπ), MeV Em
γ (C), MeV
7.65 ± 0.15(0+) 14.82 ± 0.15
10.3 ± 0.3(0+) 17.5 ± 0.3
11.16 ± 0.05(2+) 18.33 ± 0.05
14.08 ± 0.01(4+) 21.25 ± 0.01
15.44 ± 0.09(2+) 22.61 ± 0.09
17.76 ± 0.20(0+) 24.93 ± 0.02
21.6 ± 0.1(4+) 28.8 ± 0.1
On the other hand, according to the general approx-
imation in [11], the radical singularities of triangular
diagrams in Fig.1 look as extremes in the center-of-
mass system of α2, α3, α4-particles in the final state
at excitation energies
E∗
x = mHe + mBe + a− 3mHe, (3)
where x = 2α, 3α; a = 0, E∗
Be, E∗
Be,s. In (3) we have
considered, for generality, also the contribution of the
8Be∗s- cluster in the spectator channel of triangular
and quadrangular 8Be diagrams in Fig.1 and 2. Then
16
there take place a displacement by the value E∗
Be,s in
the Em
γ (Be) estimates of Table 1. In accordance with
(3) the presence in the triangular 8Be- and 12C- di-
agrams Fig.1 of a virtual 8Be(0+) cluster (at a = 0)
can manifest itself, with taking into account the en-
ergy balance, as a ”ghost” of 8Be(0+) nucleus in the
system of 2α-particles at E∗
2α = 0, 092 MeV with a
kinetic energy 0f the third α- particle in the center-
of-mass system of 3α equal to zero, or as a ”ghost” of
12C nucleus in the excited state of 3α-particles with
E∗
C,g ∼ 7, 4 ... 7, 5 MeV . The presence of exited 8Be∗
and 8Be∗s clusters, at a 6= 0 in (3), can manifest it-
self as a ”ghost” of 8Be∗ and 12C∗ nucleus with the
excitation energies E∗
Be,g and E∗
C,g respectively
E∗
Be,g = E∗
x + 2mHe −mBe = E∗
Be(E
∗
Be,s), (4)
E∗
C,g = E∗
x + 3mHe −mC =
mHe + mBe −mC + E∗
Be(E
∗
Be,s). (5)
Then, the presence of excited 8Be∗ and 8Be∗s clus-
ters in the diagrams of the Fig.1 at E∗
Be = 3, 04 MeV
can manifested itself as ”ghost” of 8Be∗ nucleus in
the system of 2α- particles with the excitation energy
E∗
Be,g = 3, 04 MeV and with the of the third α- parti-
cle close to zero, or according (5) as a ”ghost” of 12C∗
nucleus in the final excited state of 3α- particles with
E∗
C,g ' 10, 34 MeV . Then the exited state of 8Be∗
in the triangular 12C- diagram at E∗
Be ∼ 7 ... 8 MeV ,
that has been found in the 12C(α, 4α) reaction [12],
can manifest itself as a ”ghost” of 12C∗ nucleus in the
final state of 3α- particles with E∗
C,g = 15, 4 MeV ,
discussed in [4]. Real manifestation of one of two
variants of ”ghost” 8Be∗g or 12C∗g states can be ob-
served only in experiments. At that, the positions of
radical extremes of the triangular diagrams does not
depend on Eγ . Independent experimental informa-
tion about the contributions of 8Be- and 12C- trian-
gular diagrams can be obtained from the estimates of
maxima positions in the distribution by the relative
kinetic energy of α1- particle at the photon vertex
ηα1= Eα1/(Eγ-ε) and in the distributions of exper-
imental events of the reaction by the value (Eα2 +
Eα3 + Eα4 -nEα1), where n=1 and 0,5, respectively,
for these diagrams. So, from the energy balance on
the mass surface for the virtual processes in the pho-
ton and spectator vertices we have, correspondingly,
for the 8Be- and 12C- triangular diagrams
Eα1(Be) = 0, 5(Eγ − ε1 − ε2), (6)
Eα1(C) = 2(Eγ − ε− E∗
Be)/3, (7)
where ε1=2mBe + (EBe,s) - mO, ε2= 2mHe - mBe,
ε= 4mHe - mO. Note, that taking into account the
two-particle channel γ + 16O−→ 8Be + 8Be, for
which
Eα1 = 0, 25(Eγ − ε) (8)
and Eq.(6) at EBe,s= 0, we have for the aver-
age value of the relative energy 〈ηα1〉≈ 0,37, which
is followed from the distributions Eα1/(Eγ - ε) in
[4] for Eγ = 18 ... 48 MeV . For the two-particle
γ +16 O −→ α1 +12 C∗ channel we obtain
Eα1 = 3(Eγ − ε)/4 . (9)
While, taking into account (7), 0 ≤ Eα1(C)/(Eγ −
ε) ≤ 0, 4 at E∗
Be + ε ≤ Eγ ≤ 2, 5E∗
Be + ε. From
Eqs.(6,7) and from the balance of energies and pulses
on the mass surface for virtual processes in the three
vertices of triangular 8Be- and 12C- diagrams we have
respectively
Eα2+Eα3+Eα4−Eα1 = mBe−2mHe+(E∗
Be,s), (10)
Eα2+Eα3+Eα4−0, 5Eα1 = mBe−2mHe+E∗
Be. (11)
An additional possibility in the determination of the
mechanism of the reaction under consideration arises
in the experimental and theoretical analysis of en-
ergy correlation distributions of two pairs of α- par-
ticles by the variable tαiαk
≡Eαiαk
/(Eγ − ε), where
Eαiαk
is the relative energy of αi and αk- particles.
In [13] the similar problem was considered for the
analysis of the mechanism of four- particle photonu-
clear 12C(γ, pt)2α reaction in the approximation of
the pole α- cluster diagram. Thus, firstly, the general
formulas have been obtained for calculations of the
distributions of differential probabilities dΛ4/dtαiαk
in the approximation of the pole ”i”- cluster diagram
with constant vertex functions, represented in Fig.3,
for two pairs of (a, b) and (c, d)- particles in the
photon- and spectator vertices respectively
dΛ4
dtab
= C1
(1− tab)2
√
tab
[ε0/T0 + b(1− tab)]2
F (2, 3/2; 3; z), (12)
dΛ4
dtcd
= C2
(1− tcd)2
√
tcd
[ε0/T0 + b(1− b)tcd)]2
F (2, 3/2; 3; z
′
),
(13)
where C1 and C2 are the arbitrary constants,
F (α, β; γ; z) is the hypergeometric Gaussian series
[14],
z =
(b− 1)(1− tab)
ε0/T0 + b(1− tab)
, (14)
z
′
=
b(1− tcd)
ε0/T0 + b + (1− b)tcd
, (15)
b =
(ma + mb)(mi + mc + md)
mi(ma + mb + mc + md)
, (16)
ε0 = mi + mc + md −mA, (17)
T0 = Eγ − ε, (18)
ε is the reaction threshold, mk is the particle mass
”k”. Eqs. (12), (13) are obtained in the factorized
form, where the four-particle phase volume is exactly
determined
dV4
dtkn
= C3(1− tkn)2)
√
tkn. (19)
17
γ
Fig.3. Pole diagram for the photonuclear
γ + A −→ a + b + c + d reaction
γ α
γ
αα
Λ
αα
Fig.4. Energy (α, α) correlations for the
16O(γ, 4α) reaction calculated by (12) (curve 1), by
(13) (curve 2), by (23) (curve 3), by (20) (curve 4)
at mi≡mBe and ma= mb= mc= md≡mα
For comparison, we have considered also the
three-particle photonuclear γ + A−→ a + b + B re-
action in the pole ”i”- diagram with a single-particle
spectator B for which
dΛ3
dtab
= C4
√
tab(1− tab)
[εi/T0 + b′(1− tab)]2
, (20)
where
b
′
=
(ma + mb)(mi + mB)
mi(ma + mb + mB)
, (21)
εi = mi + mB −mA, (22)
and the phase volume
dV3
dtkn
= C5
√
tkn(1− tkn). (23)
In (19), (20) and (23) C3, C4, C5 are the ar-
bitrary constants. Fig.4 presents the calculations
of dΛ4/dtα1α2 (curve 1), dΛ4/dtα3α4 (curve 2) and
dV3/dtα1α2 (curve 3), dΛ3/dtα1α2 (curve 4) by (12),
(13) and (23), (20) with ma= mb= mc= md≡mα and
mi= mB≡mBe for the 16O(γ, 4α) and 16O(γ, 2α)8Be
reactions respectively at Eγ = 20 ... 40 MeV . The
calculations are made in the pole 8Be cluster ap-
proximation with normalization of all the curves on
the identical integral area. For the distributions
dΛ4/dtα1α2 and dΛ4/dtα3α4 characteristic is the po-
sition of maxima independent on Eγ at tmα1α2
≈ 0, 5
in correspondence with experimental data at Eγ =
18 ... 48 MeV [4] and with tmα3α4
≈ 0, 2, practically
coinciding with the phase volume (19). This fact
is confirmed by our calculations at Eγ = 20 ... 25,
25 ... 30 and 30 ... 40 MeV , which, almost do not dif-
fer from the given calculations of curves 1 and 2 in
Fig.4. The coincidence of calculated curves 1 and
3,as well as, the position of the maximum of curve
4 at tmαα ≈ 0, 8 in Fig.4 indicates the incorrectness
of the application of an approximation of the three-
particle 16O(γ, 2α)8Be reaction in the calculations
of energy αα-correlations in the 16O(γ, 4α) reaction.
Probably, the use of a realistic vertex function in the
spectator channel may improve the agreement with
experiment in the estimate tmα3α4
≈ 0, 05.
3.DISCUSSION
In p.2 we have demonstrated an important role of
triangular and quadrangular 8Be- and 12C-diagrams,
as well as, of a 8Be- pole diagram in interpretation
of the 16O(γ, 4α) reaction mechanism. The equa-
tions were first obtained for the calculation of peak
positions in the energy dependence of the total re-
action cross-section in the photon energy interval
Eγ = 15 ... 45 MeV with taking into account the con-
tribution of resonance 8Be∗ and 12C∗ states (see (1),
(2) and Tables 1, 2) permitting to investigate the
quantum characteristics of structure peculiarities in
the experimental function excitation of reaction. We
have offered, with taking into account (3), the in-
terpretation of the appearance of the excited states,
being independent on Eγ , in the systems of 2α and
3α-particles in the final state. They have a form of
”ghosts” of 8Be, 8Be∗ and 12C∗ nuclei, as manifesta-
tions of radical singularities of triangular diagrams,
represented in Fig.1, with 8Be, 8Be∗ clusters on the
mass surface. Unlike the reaction under our con-
sideration, in [6] the triangular 8Be-diagram for the
12C(γ, 3α) reaction has at the output an α + α −→
α + α vertex with a radical singularity E∗
x(2α) = 0.
However, the amplitude contribution of this diagram
into the cross-section will be insignificant because the
phase volume of the reaction is proportional to the
factor
√
Eαα. The authors [6] assume that such di-
agram is realized when a real excited state of 8Be∗
arises in the α+α −→ 8Be∗ −→ α+α process in the
final state. The experimental estimate of the relative
kinetic energy of α1-particles Eα1/(Eγ−ε) ≈ 0, 37 in
the energy interval Eγ = 18 ... 48 MeV [4] probably is
the evidence, according to (6) at E∗
Be,s = 0 and (8),
of some contribution also from the mechanism of the
two-particle partial γ + 16O −→ 8Be + 8Be channel.
Detailed experimental analysis of the Em
γ estimates,
given in Tables 1 and 2,the energy distributions in
(6), (7) (with taking into account (8), (9)), as well as
(10), (11),is very necessary to substantiate the mech-
anism of triangular and quadrangular 8Be- and 12C-
diagrams for the 16O(γ, 4α) reaction in the energy
interval Eγ = 14, 42 ... 50 MeV . Consideration of the
18
pole 8Be-diagram mechanism (Fig.3) opens an addi-
tional possibility (see Fig.4) for calculation of the en-
ergy correlation in the (α1, α2) and (α3, α4)-particle
systems testifying to the probable appearance of the
γ + 16O −→ 2α + 8Be, s −→ 2α + (2α)s channel
with the experimental estimate tmα3α4
≈ 0, 05. Be-
sides, it seems necessary to separate, in each of exper-
imental events, two pairs of α-particles, correspond-
ingly with maximum and minimum energies, for the
more detailed correct description of dΛ4/dtα1α2 and
dΛ4/dtα3α4- distributions. Verification of such distri-
bution independence on the energy Eγ requires to de-
crease significantly the investigated energy intervals
that is also necessary for construction of realistic pho-
ton and spectator vertex functions for the pole 8Be-
diagram. The author is grateful to S.N.Afanasyev
for discussions of experimental problems being con-
sidered in the present paper.
References
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+ z opening threshold //Yadernaya Fizika. 1987,
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АНАЛИЗ МЕХАНИЗМА РЕАКЦИИ 16O(γ, 4α)
В.Н. Гурьев
Проведен анализ механизма трех- и четырехугольных 8Be- и 12C- фейнмановских диаграмм для ре-
акции 16O(γ, 4α) в области энергии фотонов Eγ = 15 ... 45МэВ. Проведен расчет положения пиков в
энергетической зависимости полных сечений реакции с учетом спектров возбуждения ядер 8Be и 12C.
Показана возможность проявления корневых особенностей треугольных диаграмм в виде «призраков»
ядер 8Be, 8Be∗ и 12C∗ в возбужденных состояниях 2α- и 3α-частиц в конечном состоянии. Проведен
расчет распределений энергетических корреляций двух пар α-частиц в приближении полюсной 8Be-
диаграммы при Eγ = 20 ... 40МэВ.
АНАЛIЗ МЕХАНIЗМУ РЕАКЦII 16O(γ, 4α)
В.М. Гур’єв
Проведено аналiз механiзму трьох- i чотирикутних 8Be- i 12C- фейнмановських дiаграм для реакцiї
16O(γ, 4α) в областi енергiй фотонiв Eγ = 15 ... 45МеВ. Проведено розрахунок розташування пiкiв в
енергетичнiй залежностi повних перерiзiв реакцiї з розрахунком спектрiв збудження ядер 8Be и 12C.
Показано можливiсть проявлення корiнних особливостей трикутних дiаграм у виглядi «примар» ядер
8Be, 8Be∗ и 12C∗ в збудженних станах 2α- i 3α-частинок в кiнцевому станi. Проведено розрахунок
розподiлiв енергетичних кореляцiй двох пар α-частинок в наближеннi полюсної 8Be- дiаграми при
Eγ = 20 ... 40МеВ.
19
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