Analysis of the¹²C(γ, pt)2α reaction mechanism
Calculation of the (p, t) and (α, α) energy correlations in reaction¹²C(γ, pt)2α at photon energies Eγ = 27 - 140MeV is carried out using the pole a-cluster diagram with two-spectator α) particles. These energy correlations agree with experimental data at photon energies Eγ = 32 - 50MeV.
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irk-123456789-1101562016-12-31T03:01:50Z Analysis of the¹²C(γ, pt)2α reaction mechanism Guryev, V.N. Ядерная физика и элементарные частицы Calculation of the (p, t) and (α, α) energy correlations in reaction¹²C(γ, pt)2α at photon energies Eγ = 27 - 140MeV is carried out using the pole a-cluster diagram with two-spectator α) particles. These energy correlations agree with experimental data at photon energies Eγ = 32 - 50MeV. Проведено розрахунок (p, t) та (α, α) енергетичних кореляцій в реакції¹²C(γ, pt)2α з використанням полюсної α-кластерної діаграми з двомa спектаторними α--частинками при енергшї фотонів Eγ=27 - 140MeV. Ці енергетичні кореляціі узгоджуються з експериментальними даними при енергіях фотонів Eγ=32 - 50MeV. Проведен расчет (p, t) и (α, α) энергетических корреляций в реакции¹²C(γ, pt)2α с использованием полюсной α-кластерной диаграммы с двумя спектаторными α-частицами при энергии фотонов Eγ=27 - 140MeV. Эти энергетические корреляции согласуются с экспериментальными данными при энергиях фотонов Eγ=32 - 50MeV. 2007-03-04 Article Analysis of the¹²C(γ, pt)2α reaction mechanism / Guryev, V.N. // Вопросы атомной науки и техники. — 2007. — № 5. — С. 9-12. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 23.20.en, 25.20.-x http://dspace.nbuv.gov.ua/handle/123456789/110156 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Ядерная физика и элементарные частицы Ядерная физика и элементарные частицы Guryev, V.N. Analysis of the¹²C(γ, pt)2α reaction mechanism Вопросы атомной науки и техники |
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Calculation of the (p, t) and (α, α) energy correlations in reaction¹²C(γ, pt)2α at photon energies Eγ = 27 - 140MeV is carried out using the pole a-cluster diagram with two-spectator α) particles. These energy correlations agree with experimental data at photon energies Eγ = 32 - 50MeV. |
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Article |
| author |
Guryev, V.N. |
| author_facet |
Guryev, V.N. |
| author_sort |
Guryev, V.N. |
| title |
Analysis of the¹²C(γ, pt)2α reaction mechanism |
| title_short |
Analysis of the¹²C(γ, pt)2α reaction mechanism |
| title_full |
Analysis of the¹²C(γ, pt)2α reaction mechanism |
| title_fullStr |
Analysis of the¹²C(γ, pt)2α reaction mechanism |
| title_full_unstemmed |
Analysis of the¹²C(γ, pt)2α reaction mechanism |
| title_sort |
analysis of the¹²c(γ, pt)2α reaction mechanism |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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| topic_facet |
Ядерная физика и элементарные частицы |
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http://dspace.nbuv.gov.ua/handle/123456789/110156 |
| citation_txt |
Analysis of the¹²C(γ, pt)2α reaction mechanism / Guryev, V.N. // Вопросы атомной науки и техники. — 2007. — № 5. — С. 9-12. — Бібліогр.: 12 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT guryevvn analysisofthe12cgpt2areactionmechanism |
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2025-07-08T00:10:41Z |
| last_indexed |
2025-07-08T00:10:41Z |
| _version_ |
1837035364650319872 |
| fulltext |
ANALYSIS OF THE 12C(γ, pt)2α REACTION MECHANISM
V.N. Guryev∗
National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov , Ukraine
(Received March 4, 2007)
Calculation of the (p, t) and (α, α) energy correlations in reaction 12C(γ, p t)2α at photon energies Eγ = 27− 140 MeV
is carried out using the pole α-cluster diagram with two-spectator α particles. These energy correlations agree with
experimental data at photon energies Eγ = 32− 50 MeV .
PACS: 23.20.en, 25.20.− x
1. INTRODUCTION
The investigation of the many-particles photonuclear
reactions on the light nuclei opens larger possibil-
ities for the analysis of the mechanism of the in-
teractions of photons with virtual dynamic clusters
(p, d, t, h, α; A > 4) systems and of the evolution of
the nuclei cascade processes. In principle for the re-
action 12C(γ, p t)2α several mechanisms are possible
at Eγ = 27− 140 MeV : (a) one-particle interaction
γ + 12C → p + 11B
∗
, 11B
∗ → t + 8Be
∗
,
8Be
∗ → 2α ; (1)
11B
∗ → α + 7Li
∗
, 7Li
∗ → t + α ; (2)
γ + 12C → t + 9B
∗
, 9B
∗ → p + 8Be
∗
,
8Be
∗ → 2α ; (3)
γ + 12C → α + 8Be
∗
, 8Be
∗ → p + t + α ;
(4)
(b) two-particles direct production
γ + 12C → p + t + 2α
(
8Be
∗)
,
8Be
∗ → 2α; (5)
γ + 12C → p + α + 7Li
∗
, 7Li
∗ → t + α; (6)
γ + 12C → t + α + 5Li
∗
, 5Li
∗ → p + α; (7)
(c) 12C
∗ decay-schemes
γ + 12C → 12C
∗
, 12C
∗ → p + t + 8Be
∗
,
8Be
∗ → 2α; (8)
12C
∗ → t + 9B
∗
, 9B
∗ → p + 8Be
∗
,
8Be
∗ → 2α; (9)
12C
∗ → α + 8Be
∗
, 8Be
∗ → p + t + α; (10)
12C
∗ → 5Li
∗
+ 7Li
∗
, 5Li
∗ → p + α,
7Li
∗ → t + α. (11)
The 12C(γ, pt)2α reaction has been experimen-
tally studied with several methods. The photoemul-
sive method [1] was used to obtain the preliminary
data about energy dependence of the total cross sec-
tion for photons energies Eγ = 27, 5− 80 MeV , pro-
ton and triton energy distributions and proton angu-
lar distributions at Eγ < 70 MeV . The kinematical
analysis of 132 events has been carried out. Only
the channel (1) has been analyzed. As a result for
the most of the events for 12C(γ, pt)2α reaction the
manifestation of ground and 3 MeV excited states of
8Be was observed.
With the Wilson chamber method [2] there
were obtained analyzing 77 events of the reac-
tion 12C(γ, pt)2α the energy and angular correla-
tions of the proton-triton for Eγ = 40− 60 MeV and
60− 140 MeV , also the excitation spectra of the in-
termediate nuclei 11B and 9B up to 80 MeV with
the aim of studying the channels (1)-(3) and (9). Ac-
cording to experimental data [1], [2] together with
the one-proton mechanism (1),(2) the interactions of
the photons with the triton and α-clusters in the
channels (3) and (4), (5) respectively are possible.
The diffusion chamber placed in the magnetic field
has been used in [3] to measure the total cross sec-
tions of the 12C(γ, pt)2α reaction, the energy cor-
relations and mean energies distribution of the fi-
nal particles at Eγ = 27− 140 MeV . The kinemat-
ical analysis of 786 events of this reaction has been
carried out. The excitation spectra of the interme-
diate nuclei 4He, 5Li, 7Li, 8Be, 9B, 11B were ob-
tained. The results of the experiment show that at
energies of the photons Eγ > 50 MeV the dominant
mechanism of the reaction is direct interaction with
S1/2 -protons of the carbon nucleus in the channels
(1),(2). The experimental energy distributions of par-
ticles in the reaction 12C(γ, pt)2α were obtained in [4]
for Eγ = 27, 5− 150 MeV by further processing the
data of [3]. Calculations for the channel (5) carried
out in the pole α-cluster approximation [4] with and
without taking into account final state interaction in
the three-particle version of the 12C(γ, pt)8Be reac-
tion have not allowed to describe in a satisfactory way
energy distributions of protons at Eγ > 40 MeV and
∗Corresponding author. E-mail address: guryev@kipt.kharkov.ua
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2007, N5.
Series: Nuclear Physics Investigations (48), p.9-12.
9
tritons at Eγ > 32 MeV . In [5] the theoretical com-
putations of the total cross sections of the reaction
12C(γ, pt)2α in the range 15− 21 MeV of 11B
∗ exci-
tation energies have been carried out in the approx-
imation of the one-particle mechanism (1) with the
ejection of S1/2 protons. These computations, as well
as ones carried out in the α cluster model [6] for the
three-particle version of the reaction 12C(γ, pt)8Be,
are in a satisfactory agreement with the experimen-
tal data of [3] at Eγ < 80 MeV . However, calculation
results of (p, t) energy correlations in [6] turned out
to be essentially larger than experimental data [3].As
one can deduce from theoretical results of [5] and [6]
total cross sections are practically the same for both
mechanisms. Therefore, to distinguish among them
one should deal with energy and angular distributions
and correlations of the final particles. In this connec-
tion we have carried out calculation of energy (p, t)
and (α, α) correlations in approximation of the pole
(α-cluster mechanism for the channel (5) with two-
spectator α particles. In contrast to the calculation
[6] with the one-particle spectator 8Be we obtained
an essential improvement of the agreement with the
experimental data [3] of the theoretical estimations
of the energy (p, t)-correlations in the energy range
of the photons Eγ = 32− 50 MeV .
2. METHOD
We consider the four-particle photonuclear reaction
γ + A → a + b + c + d whose amplitude is described
by the pole diagram (Fig.1) of the direct production
of (a) and (b) particles, where (A) is the nuclear-
target, (c) and (d) are the two-particle spectators,
and (i) is the dynamic virtual cluster.
Fig.1. Pole diagram for the two-particles direct
production in the photonuclear reaction
γ + A → a + b + c + d
Then, the differential probability of this reaction
in the non-relativistic approximation [7] can be writ-
ten in the laboratory system, as
dΛ ≈ |Fi(~pc, ~pd)|2 |Mi|2δ(~pa + ~pb + ~pc + ~pd − ~pγ)δ(Ta + Tb + Tc + Td − T0)
|k(ε0 + Tcd) + ~p 2
cd|2
d~pad~pbd~pcd~pd, (12)
where Fi is the form-factor of the virtual de-
cay A → i + c + d; |Mi|2 is the average over the
spin states matrix element squared of the reaction
γ + i → a + b; Tn, pn, mn is the kinetic energy, the
momentum and the mass of the particle (n), ..., re-
spectively, Tcd and pcd is the relative energy and total
momentum of the particles (c) and (d),
T0 = Eγ − εc, (13)
εc = ma + mb + mc + md −mA, (14)
ε0 = mi + mc + md −mA, (15)
k =
2mi(mc + md)
mi + mc + md
, (16)
Tcd =
~q 2
cd
2mcd
, (17)
~qcd =
md~pc −mc~pd
mc + md
, (18)
mcd =
mcmd
mc + md
, (19)
~pcd = ~pc + ~pd. (20)
Since we are interested only in the manifestation of
the pole mechanism of the reaction we put |Fi| and
|Mi| to be constants [7].
Transforming Eq.(12) from variables
~pn (n = a, b, c, d) to ~pab, ~qab, ~pcd, ~qcd and integrating
over ~pab, ~pcd, ~qcd for the distributions in variables
tab = Tab/T0 and tcd = Tcd/T0 at T0 = const one can
get
dΛ
dtab
= C1
(1− tab)2
√
tab
[ε0/T0 + b(1− tab)]2
F (2, 3/2; 3; z),
(21)
dΛ
dtcd
= C2
(1− tcd)2
√
tcd
[ε0/T0 + b + (1− b)tcd]2
F (2, 3/2; 3; z′),
(22)
where C1 and C2 are the constants, F (α, β; γ; z) is the
Gauss hypergeometric series (for example Eq.(15.3.1)
[8]),
z =
(b− 1)(1− tab)
ε0/T0 + b(1− tab)
, (23)
z′ =
b(1− tcd)
ε0/T0 + b + (1− b)tcd
, (24)
b =
(ma + mb)(mi + mc + md)
mi(ma + mb + mc + md)
. (25)
Eq-s (21) and (22) have been obtained in the factor-
ized form where the distribution over variables tkn
10
for the four-particle phase volumes were separated
explicitly
dV
dtkn
= C3(1− tkn)2
√
tkn, (26)
which essentially differs from the three-particle phase
volumes
dV
dtkn
= C4
√
tkn(1− tkn). (27)
So for the reaction γ + A = a + b + B with the one-
particle spectator B from Eq.(27) [9] at T0 = const
one can get
dΛ
dtab
= C5
√
tab(1− tab)
|ε/T0 + b′(1− tab)|2
, (28)
where
b′ =
(ma + mb)(mi + mB)
mi(ma + mb + mB)
, (29)
ε = mi + mB −mA. (30)
In Eq-s (26...28) C3, C4 and C5 are the constants.
3. RESULTS
On Figs. 2 and 3 the solid curves represent the
energy correlations of the particles in the reaction
12C(γ, pt)2α which were calculated using (21) and
(22) respectively.
0,0 0,5 1,0
0,0
0,5
1,0
0,0 0,5 1,0
0,0
0,5
1,0
0,0 0,5 1,0
0,0
0,5
1,0
0,0 0,5 1,0
0,0
0,8
1,6
tpt
d
/d
t pt
, r
el
at
. u
ni
ts
a)
pt
c)
b)
d)
Fig.2. The energy (p,t) correlations for the reaction
12C(γ, pt)2α were calculated by (21) (solid curves)
and by (26) (dashed curves); for the reaction
12C(γ, pt)8Be by (28)(dot-dashed curves); (a − d)
for Eγ = 27− 32, 32− 40, 40− 50, 50− 140 MeV ,
respectively. Experimental data are taken from [3]
Here (a, b) denote (p, t) and (c, d) denote (α, α).
The dot-dashed curves show the energy (p, t)
correlations for the reaction 12C(γ, pt)8Be which
were calculated using (28). The calculated
curves are normalized accordingly to the exper-
imental data [3]. They are demonstrated with
the experimental data [3] in the energy inter-
vals Eγ = 27− 32, 32− 40, 40− 50, 50− 140 MeV .
Comparison with experimental data [3] suggests that
the α-cluster mechanism dominates in the reaction
12C(γ, pt)2α in channel (5) for the photon energy
range 32− 50 MeV (look at solid curves in Figs.2,3).
At the same time, for Eγ = 50− 140MeV (Fig.2)
the α-cluster mechanism with the one-body spectator
8Be (dot-dash curve) appears to be more preferable.
However, the results of analyzing of the experimental
data [3] shows that mechanism of reactions (1) and
(2) is dominant at these energies Eγ .
0,0 0,5 1,0
0,0
0,5
1,0
0,0 0,5 1,0
0,0
0,5
1,0
0,0 0,5 1,0
0,0
0,5
1,0
0,0 0,5 1,0
0,0
0,5
1,0
d)
t
d
/d
t
, r
el
at
. u
ni
ts
c)
b)
a)
Fig.3. The energy (α, α) correlations for the
reaction 12C(γ, pt)2α were calculated by (22)
(solid curves), by (26) (dashed curves); (a...d)
for Eγ = 27− 32, 32− 40, 40− 50, 50− 140 MeV
respectively. Experimental data are taken from [3]
4. DISCUSSION
We have shown the effect of the essential influence
of the four-particle phase volume on the energy corre-
lations of the (p, t) and (α, α) particles for the channel
(5) in the pole approximation. Taking into account
this effect allowed us to determine the energy range of
the α-cluster mechanism (Eγ = 32− 50 MeV ) on the
background of the other possible mechanisms for the
channels (1− 4, 6− 11) of the reaction 12C(γ, pt)2α.
For testing this method at Eγ = 50− 140 MeV it is
necessary to improve energy resolution of the exper-
iment. The theoretical and experimental investiga-
tions of the angular (p, t) and (α, α)- correlations
dΛ/d cos θpt, dΛ/d cos θαα for Eγ = 32− 140 MeV is
also necessary for identification of the α-cluster mech-
anism in the 12C(γ, pt)2α reaction. Such problem
was discussed in [9], [10] for the three-particles reac-
tions. Note that the analysis of the channels (1-3) be-
comes complicated because of the possible manifesta-
tion of the quasi-deuteron and α-cluster mechanisms
11
with the corresponding singularities of the triangu-
lar diagrams. Such α-cluster mechanism with rescat-
tering in the final state was analyzed in [4] only for
the energy distributions of the final particles in the
reaction 12C(γ, pt)8Be and did not give satisfactory
description of the experimental data. The analysis of
these mechanisms requires comparison of the experi-
mental data for the energy and angular distributions
and correlations of the final particles in the reactions
12C(γ, pt)2α and 12C(γ, nh)2α. Thus a solid sup-
port of the α-cluster mechanism in these reactions
at Eγ = 32− 50 MeV may be provided by experi-
mentally discovered sharp increase of the asymmetry
coefficients βp and βn in the angular distributions
of photoprotons and photoneutrons at Eγ = 40 MeV
[11]. Similar energy distributions of these parameters
(especially for βn at Eγ = 40− 50 MeV ) were found
in the 4He(γ, p)3H and 4He(γ, n)3He reactions (see
review of the experimental data [12]). Also for the
more complete analysis of the α-cluster mechanism
in the reaction 12C(γ, pt)2α the model estimations of
Fi and Mi in the formula for the differential proba-
bility (12) are required.
REFERENCES
1. V.N. Maikov. Some photo-reactions on light nu-
clei// ZhETP. 1958, v. 34, p. 1406-1419 (in Rus-
sian).
2. G.G. Taran. Photodisintegration of carbon, reac-
tions with emission of several particles // Yad.
Fiz. 1968, v. 7, p. 478-492 (in Russian).
3. V.I. Voloshchuk, I.V. Dogyust, V.V. Kirichenko,
A.F. Khodyachikh. 12C(γ, pt)2α reaction at
Eγ max = 150 MeV // Yad. Fiz. 1989, v. 49,
p.916-921 (in Russian).
4. I.V. Dogyust, V.A. Zolenko, V.V. Kirichenko.
Energy distributions in the 12C(γ, pt)2α reaction
// Yad. Fiz. 1990, v. 51, p.913-919 (in Russian).
5. V.V. Balashov, V.N. Fetisov. Role of nucleon
clasters in deep photodisintegration of light nu-
clei// Nucl.Phys. 1961, v. 27, p.337-343.
6. R.I. Jibuti, T.I. Kopaleishvilli, V.I. Ma-
masakhlisov. Nucleon clusters in light nuclei //
Nucl. Phys. 1964, v. 52, p.345-352.
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in light nuclei // Yad. Fiz. 1966, v. 3, p.729-738
(in Russian).
8. ”Handbook of mathematical functions”. Edited
by M. Abramowitz and I. Stegun. Nation. Bu-
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1979, 830 p. (Russion translation).
9. V.M. Kolybasov. Angular correlations in the cap-
ture of π-mesons by nuclei // Yad. Fiz. 1966, v.3,
p.965-973 (in Russian).
10. I.S. Shapiro. Some questions of the theory of the
nuclear reactions at high energies // Uspekhi Fiz.
Nauk. 1967, v. 92, p.549-582 (in Russian).
11. S.N. Afanas’ev, A.S. Kachan, A.F. Khodyachikh
et al. Main results on nuclear physics obtained at
IPHENP NNC KIPT during 2002-2004 years //
PAST. Ser.: Nuclear Physics Investigations(45).
2005, N6, p.3-10.
12. V.N. Guryev. 2+-resonances in the reactions of
the two-particles photodesintegration of the nu-
cleus 4He// Yad. Fiz. 1979, v. 29, p.1414-1416
(in Russian).
АНАЛИЗ МЕХАНИЗМА РЕАКЦИИ 12C(γ, pt)2α
В.Н. Гурьев
Проведен расчет (p, t) и (α, α) энергетических корреляций в реакции 12C(γ, pt)2α с использова-
нием полюсной α-кластерной диаграммы с двумя спектаторными α-частицами при энергии фотонов
Eγ = (27− 140)MэВ. Эти энергетические корреляции согласуются с экспериментальными данными
при энергиях фотонов Eγ = (32− 50)MэВ.
АНАЛIЗ МЕХАНIЗМА РЕАКЦIЇ 12C(γ, pt)2α
В.М. Гур’єв
Проведено розрахунок (p, t) та (α, α) енергетичних кореляцiй в реакцiї 12C(γ, pt)2α з використан-
ням полюсної α-кластерної дiаграми з двомa спектаторними α-частинками при енергшї фотонiв
Eγ = (27− 140)MeВ. Цi енергетичнi кореляцii узгоджуються з експериментальними даними при енер-
гiях фотонiв Eγ = (32− 50)MeВ.
12
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