Spin-triplet transitions in (γ,p) and (γ,n) reactions of two-body ⁴He disintegration by photons of energies below 80 MeV
The simultaneous least-square fit of expressions for differential cross-sections and asymmetry to the experimental data on dσ/dΩ and Σ(θ), obtained at NSC KIPT, was realized. A set of three bilinear equations with three unknown amplitude modules | ³P₁ | E1, | ³S₁ | M1 and | ³D₁ | M1 was derived; pre...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Spin-triplet transitions in (γ,p) and (γ,n) reactions of two-body ⁴He disintegration by photons of energies below 80 MeV / Yu.P. Lyakhno, E.S. Gorbenko, I.V. Dogyust // Вопросы атомной науки и техники. — 2002. — № 2. — С. 22-24. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-801062015-04-12T03:02:00Z Spin-triplet transitions in (γ,p) and (γ,n) reactions of two-body ⁴He disintegration by photons of energies below 80 MeV Lyakhno, Yu.P. Gorbenko, E.S. Dogyust, I.V. Nuclear reactions The simultaneous least-square fit of expressions for differential cross-sections and asymmetry to the experimental data on dσ/dΩ and Σ(θ), obtained at NSC KIPT, was realized. A set of three bilinear equations with three unknown amplitude modules | ³P₁ | E1, | ³S₁ | M1 and | ³D₁ | M1 was derived; preliminary data about the magnitudes of these amplitude modules were obtained. It is shown that the ³D₁ М1 amplitude is the highest in magnitude. 2002 Article Spin-triplet transitions in (γ,p) and (γ,n) reactions of two-body ⁴He disintegration by photons of energies below 80 MeV / Yu.P. Lyakhno, E.S. Gorbenko, I.V. Dogyust // Вопросы атомной науки и техники. — 2002. — № 2. — С. 22-24. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 25.20.Dc; 29.27.Hj; 29.40. Cx http://dspace.nbuv.gov.ua/handle/123456789/80106 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
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Nuclear reactions Nuclear reactions |
| spellingShingle |
Nuclear reactions Nuclear reactions Lyakhno, Yu.P. Gorbenko, E.S. Dogyust, I.V. Spin-triplet transitions in (γ,p) and (γ,n) reactions of two-body ⁴He disintegration by photons of energies below 80 MeV Вопросы атомной науки и техники |
| description |
The simultaneous least-square fit of expressions for differential cross-sections and asymmetry to the experimental data on dσ/dΩ and Σ(θ), obtained at NSC KIPT, was realized. A set of three bilinear equations with three unknown amplitude modules | ³P₁ | E1, | ³S₁ | M1 and | ³D₁ | M1 was derived; preliminary data about the magnitudes of these amplitude modules were obtained. It is shown that the ³D₁ М1 amplitude is the highest in magnitude. |
| format |
Article |
| author |
Lyakhno, Yu.P. Gorbenko, E.S. Dogyust, I.V. |
| author_facet |
Lyakhno, Yu.P. Gorbenko, E.S. Dogyust, I.V. |
| author_sort |
Lyakhno, Yu.P. |
| title |
Spin-triplet transitions in (γ,p) and (γ,n) reactions of two-body ⁴He disintegration by photons of energies below 80 MeV |
| title_short |
Spin-triplet transitions in (γ,p) and (γ,n) reactions of two-body ⁴He disintegration by photons of energies below 80 MeV |
| title_full |
Spin-triplet transitions in (γ,p) and (γ,n) reactions of two-body ⁴He disintegration by photons of energies below 80 MeV |
| title_fullStr |
Spin-triplet transitions in (γ,p) and (γ,n) reactions of two-body ⁴He disintegration by photons of energies below 80 MeV |
| title_full_unstemmed |
Spin-triplet transitions in (γ,p) and (γ,n) reactions of two-body ⁴He disintegration by photons of energies below 80 MeV |
| title_sort |
spin-triplet transitions in (γ,p) and (γ,n) reactions of two-body ⁴he disintegration by photons of energies below 80 mev |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2002 |
| topic_facet |
Nuclear reactions |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/80106 |
| citation_txt |
Spin-triplet transitions in (γ,p) and (γ,n) reactions of two-body ⁴He disintegration by photons of energies below 80 MeV / Yu.P. Lyakhno, E.S. Gorbenko, I.V. Dogyust // Вопросы атомной науки и техники. — 2002. — № 2. — С. 22-24. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-06T04:01:46Z |
| last_indexed |
2025-07-06T04:01:46Z |
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1836868705565278208 |
| fulltext |
SPIN-TRIPLET TRANSITIONS IN (γ,p) AND (γ,n) REACTIONS OF
TWO-BODY 4He DISINTEGRATION BY PHOTONS OF ENERGIES
BELOW 80 MeV
Yu.P. Lyakhno, E.S. Gorbenko, I.V. Dogyust
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
The simultaneous least-square fit of expressions for differential cross-sections and asymmetry to the
experimental data on dσ/dΩ and Σ(θ), obtained at NSC KIPT, was realized. A set of three bilinear equations with
three unknown amplitude modules 3P1 E1, 3S1 M1 and 3D1 M1 was derived; preliminary data about the
magnitudes of these amplitude modules were obtained. It is shown that the 3D1 М1 amplitude is the highest in
magnitude.
PACS: 25.20.Dc; 29.27.Hj; 29.40. Cx
INTRODUCTION
The interest in the studies of two-body (γ,р) and (γ
,n) reactions of 4Не disintegration by low energy pho-
tons is determined by their relatively simple spin struc-
ture and a small number of particles participating in the
reaction. On the one hand, this makes possible a more
detailed theoretical calculation with a minimum of mo-
del assumptions introduced. On the other hand, the laws
of conservation of the total momentum and parity sig-
nificantly restrict the number of multipole transitions
participating in the reaction. Neglecting the contribu-
tions of higher multipoles which correspond to high to-
tal- momentum values of the photon, one can determine
to sufficient accuracy the amplitudes of the basic multi-
pole transitions. This makes possible the comparison be-
tween the theoretical calculations and the experime-
ntally measured multipole amplitudes. This comparison
is of great importance because each of the multipole
transitions can be governed by different reaction mecha-
nisms. It should be also noted that for the low particle
energy range there exist the phase-analysis data on
elastic (N,T) scattering. These data can be used for
theoretical calculations of photodisintegration reactions
on 4He.
The laws of conservation of the total momentum and
parity at two-body (γ,р) and (γ,n) disintegration of 4Не
in Е1, Е2 and М1 approximations permit six multipole
amplitudes: 1P1 Е1, 1D2 Е2, 3P1 Е1, 3D2 Е2, 3S1 М1 and
3D1 М1 (in spectroscopic notation). At present, only the
values of the first two amplitudes with ∆S=0 are deter-
mined. The analysis of experimental data has revealed
that in the low photon energy region it is the electric di-
pole E1 transition that is dominant, and the next in
prominence is the Е2 transition with ∆S=0. These
transitions occur without any change in the final-state
spin ∆S=0, the remaining four transitions take place
with changing the spin ∆S=1. Unfortunately, no evi-
dence for the amplitudes of the processes with ∆S=1,
obtained from the direct reactions, can be found in the
literature, and the data gained from the inverse reactions
are available only for low photon energies (Е
γ < 30 MeV). Moreover, most of the data are
contradictory. Wagenaar etal. [1] have investigated the
radiative capture of polarized protons of energies Tp
between 0.8 and 9 MeV by tritium nuclei. Those authors
have come to the conclusion that the cross-section for
the reaction with ∆S=1 is mainly contributed by the
magnetic dipole M1 transition. The investigation [2] of
the same reaction with a polarized proton beam at
Tр=2 MeV has led the investigators to the conclusion
that the dominant amplitude in the ∆S=1 transitions is
3P1 Е1. It has been reported in ref. [3] that the cross-
section for the M1 transition in 3Не(n,γ)4Не is extremely
low at thermal neutron energies, and also on extrapola-
tion of the data to the nucleon energy range of a
few MeV [2]. In view of this, an additional experime-
ntal information on the nature of ∆S=1 is needed. The
NSC KIPT team has obtained the most comprehensive
experimental data on both the differential cross-sections
[4] and the azimuthal cross-sectional asymmetry Σ(θ) of
(γ,р) and (γ,n) reactions [5,6], that enables one to derive
new information on the transitions with ∆S=1. In this
paper we report our preliminary results from the
multipole analysis of these data.
MULTIPOLE ANALYSIS
The differential cross-section can be expressed in
terms of multipole transition amplitudes as follows:
d
d
A
σ
θ β θ γ θ ε θ ν
Ω
= ⋅ + + + + 2 2 2
32 1[sin ( cos cos ) cos ],
(1)
where
22 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2002, № 2.
Series: Nuclear Physics Investigations (40), p. 22-24.
A P E P E D M D E
D M S M D E S M
D E D M
= − + −
− + +∗ ∗
∗
18 1 9 1 9 1 25 2
18 2 1 1 30 6 2 1 30
3 2 1
1
1
2 3
1
2 3
1
2 3
2
2
3
1
3
1
3
2
3
1
3
2
3
1
Re( ) Re( )
Re( )
(2)
β = −∗ ∗[ Re( ) Re( )]60 3 2 1 60 2 11
2
1
1
3
2
3
1D E P E D E P E A (3)
γ = −[ ]150 2 100 21
2
2 3
2
2
D E D E A (4)
ε = − − +∗ ∗
∗
[ Re( ) Re( )
Re( )]
12 6 1 1 12 3 1 1
60 2 1
3
1
3
1
3
1
3
1
3
2
3
1
S M P E D M P E
D E P E A
(5)
ν = + + + +
− −∗ ∗ ∗
[ Re
( ) Re( ) Re( )]
18 1 12 1 6 1 50 2 12 2
1 1 20 6 2 1 20 3 2 1
3
1
2 3
1
2 3
1
2 3
2
2
3
1
3
1
3
2
3
1
3
2
3
1
P E S M D M D E
D M S M D E S M D E D M A
(6)
In the approximation used here, Eqs. (2) to (6) allow the
determination of only five relationships between the
multipole transition amplitudes from the differential
cross-section.
It can be demonstrated that the azimuthal cross-
sectional asymmetry Σ(θ) is given by the expression
Σ ( )
sin ( cos cos )
sin ( cos cos ) cos
θ
θ α β θ γ θ
θ β θ γ θ ε θ ν
=
+ + +
+ + + +
2 2
2 2
1
1
, (7)
where:
α = − + + −
−
∗
∗ ∗
[ Re( )
Re( ) Re( )]
18 1 50 2 36 2 1 1 20 6
2 1 20 3 2 1
3
1
2 3
2
2 3
1
3
1
3
2
3
1
3
2
3
1
D M D E D M S M
D E S M D E D M A
(8)
Thus, the data on Σ(θ) permit the determination of
an additional relationship between the amplitudes of
multipole transitions; it is specified by expression (8).
The coefficients А, α, β, γ, ε and ν were calculated
by the least-squares method (LSM) from the fit of
expressions (1) and (7) to the experimental data histog-
rammed with a bin value of 10°. It should be noted that
for determination of cross-sections for low multipole
amplitudes some experimental errors must be taken into
account. In particular, the calculated cross-section in the
collinear geometry, entering into the coefficient ν, can
depend on the bin value of the differential cross-section,
and also on the resolution of measuring device in the
polar angle of nucleon emission. Besides, the calculated
multipole amplitude values can appear to be biased as a
result of using the LSM. Strictly speaking, this method
is applicable only with a great body of statistics in each
bin, this being not fulfilled in the case of reactions under
study in the vicinity of the angles θn∼0°, 180°. The
corresponding corrections were calculated through the
Monte-Carlo simulation of the differential cross-section.
The values of the parameters calculated by expression
(1) were used as initial. More exact values of the para-
meters were calculated by averaging over 1000 simula-
tions using the relation
L L Li i im= −2 0 , (9)
where i is the parameter number, Li0 is the parameter
value computed by the LSM, Lim is the average para-
meter value computed by the LSM.
The computed values are listed in Table 1 and
Table 2 for the 4He(γ,p)T and 4He(γ,n)3He reactions, res-
pectively.
The existing experimental data are not sufficient to
determine the cross-sections of all the mentioned tran-
sitions, and also the interference terms. In the first
variant of the analysis it was supposed that the lowest of
the ∆S=1 amplitudes under discussion is 3D2 Е2, and the
terms involving this amplitude were neglected. It is
known [7] that Е1 and М1 transitions are isovectoral.
This enables us to determine the phase differences
between 3P1 Е1, 3S1 М1 and 3D1 М1 amplitudes from the
phase analysis data for the elastic scattering of protons
by 3Не nuclei, available [8] in the energy range from 35
to 59 MeV.
Table 1. Fitting coefficients for (γ,p) reactions on
4He for three intervals of photons energy
Coef-
fic.
Eγ=34-46
MeV
Eγ=46-65
MeV
Eγ=65-90
MeV
А
β
γ
ε
ν
α
χ2
d.o.f.
87.98±1.55
0.76± 0.03
0.43±0.06
0.014±0.005
0.030±0.005
-0.16±0.09
1.2
29.91±0.75
1.15±0.05
0.85±0.10
0.008±0.006
0.018±0.006
-0.15±0.1
1.4
13.4±0.4
1.06±0.06
0.88±0.12
0.003±0.008
0.019±0.008
-0.10±0.14
1.16
Table 2. Fitting coefficients for (γ,n) reactions on
4He for three intervals of photons energy
Coef-
fic.
Eγ=34-46
MeV
Eγ=46-65
MeV
Eγ=65-90
MeV
А
β
γ
ε
ν
α
χ2
d.o.f
85.6±1.31
-0.08±0.03
0.62±0.06
0.002±0.004
0.027±0.004
-0.10±0.11
1.18
33.63±0.84
0.152±0.044
0.76±0.10
0.013±0.006
0.018±0.007
-0.28±0.11
1.26
14.9±0.46
0.35±0.06
0.83±0.13
0.008±0.008
0.027±0.009
-0.08±0.14
1.06
Thus, the coefficients А, β and γ are also used to
calculate the amplitude modules 1P1 E1 and 1D2 E2,
and also the phase differences δ(1Р1)-δ(1D2). The
remaining relationships for α, ε и ν represent a set of
three bilinear equations with three unknown amplitude
modules 3P1 E1,3S1 M1 and3D1 M1:
α δ δ= − + −[ cos( ( ) ( ))]18 1 36 2 1 13
1
2 3
1
3
1
3
1
3
1D M D M S M S D A
ε δ δ
δ δ
= − − −
−
[ cos( ( ) ( ))
cos( ( ) ( ))]
12 6 1 1 12 3 1 13
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
S M P E S P D M P E
P D A
23
ν
δ δ
= + +
−
[
cos( ( ) ( ))]
18 1 12 1 12 2 1 13
1
2 3
1
2 3
1
3
1
3
1
3
1
P E S M D M S M
S D A
(10)
The experimental data on the coefficients α0, ε0 and
ν0 have appeared such that the set (8) had no solutions.
Therefore, the set was solved for the following values of
the coefficients:
α α α
ε ε ε
ν ν ν
= +
= +
= +
0
0
0
k
k
k
∆
∆
∆
(11)
where ∆α, ∆ε and ∆ν are the statistical errors of the
corresponding coefficients, and к takes on the lowest
possible value. In this case, the set has two positive so-
lutions. However, at кmin≠0 these solutions coincide. The
solution of the set was determined in the range of one
standard deviation (k≤1). The computational results
are presented in Table 3 and Table 4 for 4Не(γ,n)3He
and 4Не(γ,p)T reactions, respectively.
It is evident from the tables that it is the 3D1 М1
amplitude that has the highest value.
In the subsequent analysis it was assumed that 3D2
E2>>3D1M1. From expression (8) it is obvious that
in this case there should be α≥0, and this does not agree
with the experimental data.
Table 3. The computed amplitude module ratios for
4Не(γ,p)T reactions for two photon energy ranges
Ratios of
amplitude
modules
Eγ=34 -46
MeV
Eγ=46 – 65
MeV
3 D 1 2 M1
1 P12E1
0.054±0.03 0.046±0.03
3 S 1 2 M1
1 P12E1
0.022±0.02 0.005±0.02
3 P 1 2 E1
1P12E1
0.010±0.02 0.008±0.02
Table 4. The computed amplitude module ratios for
4Не(γ,n)3He reactions for two photon energy ranges
Ratios of
amplitude
modules
Eγ= 34 – 46
MeV
Eγ=46 – 65
MeV
3 D 1 2 M1
1P12E1
0.051±0.03 0.092±0.04
3 S 1 2 M1
1P12E1
0.011±0.02 0.024±0.03
3 P 1 2 E1
1P12E1
0.003±0.02 0.005±0.02
CONCLUSIONS
The data on the cross-section asymmetry Σ(θ) make
it possible to derive an additional relationship between
the amplitudes of multipole transitions. A simultaneous
least-square fit of expressions for differential cross-
sections and asymmetry to the experimental data on dσ
/dΩ and Σ(θ), obtained at NSC KIPT, was realized. To
extract the information about the cross-sections of ∆S=1
transitions, a set of three bilinear equations with three
unknown amplitude modules 3P1 E1, 3S1 M1 and
3D1 M1 has been set up, and the preliminary data on the
values of these amplitude modules have been obtained.
It is shown that the 3D1 М1 amplitude is the highest in
value, and accordingly, σ(М1)>> σ(3P1 Е1). The
experimental data on the azimuthal cross-sectional
asymmetry of (γ,p) and (γ,n) reactions show that the
main contribution to the cross-section of transitions with
spin variation comes from the M1 transition. A consi-
derable cross-section of the М1 transition may be due to
the contribution of wave function components of the
4Не nucleus with nonzero orbital moments of nucleons.
ACKNOWLEDGMENT
The authors are grateful to P.V. Sorokin, L.G.
Levchuk, V.N. Gur'ev, A.F. Khodyachikh for the
discussion of present results.
REFERENCES
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24
PACS: 25.20.Dc; 29.27.Hj; 29.40. Cx
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