Calculation of the cross section for the reaction γ³He → pd at intermediate photon energies
The differential cross section and the asymmetry coefficient for the two-body photodisinteration of ³He by linearly polarized photons are calculated with wave functions for Bonn potential. Dependences of the observables on the components of the ³He wave function with the orbital angular momenta L, l...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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irk-123456789-784432015-03-18T03:01:49Z Calculation of the cross section for the reaction γ³He → pd at intermediate photon energies Kotlyar, V.V. Belyaev, A.A. Nuclear reactions The differential cross section and the asymmetry coefficient for the two-body photodisinteration of ³He by linearly polarized photons are calculated with wave functions for Bonn potential. Dependences of the observables on the components of the ³He wave function with the orbital angular momenta L, l ³ 1 are studied at photon energies Eg up to 300 MeV. 2001 Article Calculation of the cross section for the reactionγ γ³He → pd at intermediate photon energies / V.V. Kotlyar, A.A. Belyaev // Вопросы атомной науки и техники. — 2001. — № 1. — С. 50-52. — Бібліогр.: 21 назв. — англ. 1562-6016 PACS: 25.10.+s, 25.20.-x, 27.10.+h. http://dspace.nbuv.gov.ua/handle/123456789/78443 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Nuclear reactions Nuclear reactions |
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Nuclear reactions Nuclear reactions Kotlyar, V.V. Belyaev, A.A. Calculation of the cross section for the reaction γ³He → pd at intermediate photon energies Вопросы атомной науки и техники |
| description |
The differential cross section and the asymmetry coefficient for the two-body photodisinteration of ³He by linearly polarized photons are calculated with wave functions for Bonn potential. Dependences of the observables on the components of the ³He wave function with the orbital angular momenta L, l ³ 1 are studied at photon energies Eg up to 300 MeV. |
| format |
Article |
| author |
Kotlyar, V.V. Belyaev, A.A. |
| author_facet |
Kotlyar, V.V. Belyaev, A.A. |
| author_sort |
Kotlyar, V.V. |
| title |
Calculation of the cross section for the reaction γ³He → pd at intermediate photon energies |
| title_short |
Calculation of the cross section for the reaction γ³He → pd at intermediate photon energies |
| title_full |
Calculation of the cross section for the reaction γ³He → pd at intermediate photon energies |
| title_fullStr |
Calculation of the cross section for the reaction γ³He → pd at intermediate photon energies |
| title_full_unstemmed |
Calculation of the cross section for the reaction γ³He → pd at intermediate photon energies |
| title_sort |
calculation of the cross section for the reaction γ³he → pd at intermediate photon energies |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2001 |
| topic_facet |
Nuclear reactions |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/78443 |
| citation_txt |
Calculation of the cross section for the reactionγ γ³He → pd at intermediate photon energies / V.V. Kotlyar, A.A. Belyaev // Вопросы атомной науки и техники. — 2001. — № 1. — С. 50-52. — Бібліогр.: 21 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT kotlyarvv calculationofthecrosssectionforthereactiong3hepdatintermediatephotonenergies AT belyaevaa calculationofthecrosssectionforthereactiong3hepdatintermediatephotonenergies |
| first_indexed |
2025-07-06T02:32:26Z |
| last_indexed |
2025-07-06T02:32:26Z |
| _version_ |
1836863085784072192 |
| fulltext |
CALCULATION OF THE CROSS SECTION FOR THE REACTION
pdHeγ3 →
AT INTERMEDIATE PHOTON ENERGIES
V.V. Kotlyar and A.A. Belyaev
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
The differential cross section and the asymmetry coefficient for the two-body photodisintegration of 3He by line-
arly polarized photons are calculated with wave functions for Bonn potential. Dependences of the observables on the
components of the 3He wave function with the orbital angular momenta L, l ³ 1 are studied at photon energies Eg up
to 300 MeV.
PACS: 25.10.+s, 25.20.-x, 27.10.+h.
Mechanisms of the reaction g 3He®pd and proton-
deuteron radiative capture at intermediate energies were
explored in Refs. [1-9]. In these articles 3N bound state
wave functions (WFs) for realistic nucleon-nucleon po-
tentials were used and plane wave approximation for
pd-system was accepted. Role of rescattering effects
was studied only in restricted area of photon energies
Eγ≤139.1 MeV [10-12]. While calculations [1-6,9] were
performed with Hannover-Helsinki WF [13] for the Reid
soft core (RSC) potential, recent investigations [10-12]
were carried out with the rigorous solutions of the 3N
Faddeev equations for modern models of nuclear forces,
e.g., Argonne, Nijmegen and CD-Bonn potentials.
Consistency of the interaction currents and the mod-
el of nuclear forces was shown to be important [3, 4, 6, 9,
11, 12] in calculations of cross sections and polarization
observables. Thus, meson exchange currents (MEC) for
Argonne potential were used in [11,12] to respect the re-
quirement of gauge independence of the reaction ampli-
tudes.
Along with the relativistic effects originated from
meson exchange, manifestation of the spin-orbit electro-
magnetic interaction of nucleons was studied in [9,14].
It was demonstrated that inclusion of the spin-orbit current
(SOC) led to increase of Σ values reducing divergence be-
tween theory and experiment at Eγ>100 MeV.
Role of gauge invariance and Lorentz covariance
was studied in [15,16] where a model to account for a
part of MEC contributions and the pd-rescattering ef-
fects was suggested. By construction [15,16] the reac-
tion amplitudes satisfy the continuity equation. The am-
plitudes are expressed in terms of pd3He vertex function
and pd scattering phase shifts.
The aim of the present work is to extend calculations
[3, 4, 6, 9, 14] taking advantage of the precise numerical
solution of the Faddeev equations for the 3He WF ob-
tained by Bochum-Cracow group [17-19] for Bonn po-
tential and to inquire into dependence of the differential
cross section and the asymmetry coefficient on the WF
components considering the reaction at intermediate en-
ergies Eg £ 300 MeV.
The amplitudes of the reaction are calculated within
approach [3, 4, 6, 9, 14] without any multipole expansion
for the nuclear current. The contributions of the MEC
are expressed in terms of six-dimensional integrals eval-
uated numerically.
The Riska model of the π-meson exchange currents
(πEC) is used for the two-body part of the nuclear current.
The pion-nucleon form factors in MEC are taken in the
monopole form with the cut-off parameter Λπ=1.2 GeV/c.
0 50 100 150 200 250 300
-1,0
-0,5
0,0
0,5
Σ [CC;SC]
Σ [CC;π EC;SC]
Σ
Elab
γ
, MeV
10-3
10-2
10-1
100
101
102
σ [CC;π EC]+σ [SC]
σ [CC]+σ [SC]
N
α
=2
N
α
=5
N
α
=10
N
α
=34
σ,
µ
b/
sr
Fig. 1. The differential cross section cm
pdd Ω= /σσ
for 3He(γ, p)d and the asymmetry coefficient for the reac-
tion with linearly polarized photons at a proton emission
angle cm
pθ =90○. The experimental data , , , and are
taken from [20, 7 ,8, 1, 2, 5] and [21], respectively
The results obtained with Bochum-Cracow WFs
[17-19] for Bonn potential are shown in Figs. 1 and 2
for different sets of the partial wave components in the
3He WF. The number of the partial wave channels taken
into account in decomposition of the WF is Nα, where α
denotes quantum numbers in (jJ)-coupling (see, e.g.,
[19]). Two S-waves are retained in the decompositions
of the WF for Nα = 2, D-waves with the orbital angular
momenta L l=20, 02, 22 are turned on in the case of Nα
= 5, P-waves for total angular momentum in the two-
body subsystem J=0,1 are added in the set Nα = 10. The
50 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 1.
Series: Nuclear Physics Investigations (37), p. 50-52.
set Nα = 18(34) includes the components with J £2 (4)
and positive parity.
As is seen from Fig. 1, the energy dependence of the
cross section σ, obtained with convection current (CC),
spin current (SC) and S-waves in the 3He WF, has deep
minimum near lab
γE = 172 MeV. This distinctive feature
0 30 60 90 120 150 180
-1,0
-0,5
0,0
0,5
Σ [CC;SC]
Σ [CC;π EC;SC]
Σ
θ cm
p
, degrees
10-3
10-2
10-1
100
σ [CC]+σ [SC]
σ [CC;π EC]+σ [SC]
σ,
µ
b/
sr
Fig. 2. Angular distribution of the differential cross
section and the asymmetry coefficient at labEγ =
208 MeV. Notation for the curves is the same as in
Fig. 1. Points and are taken from [7] and [8]. Data
were obtained in [1, 2, 5] at labEγ = 200 MeV
of σ[CC;SC;Nα=2] is observed in the angular dependence
displayed in Fig.2 as well. Note, that in plane wave ap-
proximation σ[CC;SC]≡ σ[CC] + +σ[SC] [6,9].
MEC smooth both the energy and angular distribu-
tions of the cross section σ[CC;SC;Nα=2] filling these
minima. The appreciable difference between the values
of σ[CC;SC]=8.85∙10-4 μb/sr for Nα=2 and 9.88∙10-2 μb/sr
for Nα=34 in minimum at Eγ=172 MeV and ocm
p 90=θ
is substantially reduced when πEC are included. Really,
we have σ[CC;πEC;SC] =0.433 μb/sr and 0.384 μb/sr,
for Nα=2 and Nα=34, respectively. One can arrive at
conclusion that contributions of MEC increase the dif-
ferential cross section at ocm
p 90=θ mainly due to ab-
sorption of photons by neutron-proton pairs moving
with relative angular momentum equal to zero.
The beam asymmetry depicted in lower panels of
Figs. 1-4 is defined as Σ=(σ-σ)/(σ+σ), where the
cross section of the reaction with photons polarized in
the reaction plane (perpendicular to the plane) is de-
noted by σ(σ).
The asymmetry Σ[CC;SC] as a function of photon
energy changes qualitatively when D-wave states are
added to S-wave ones (cf. curves for Nα=2 and Nα=5 in
Fig. 1). Sensitivity of Σ to the partial waves with α>2,
unlike to the case of the cross section, survives after in-
clusion of the πEC.
Reducing to some extent the discrepancies between
calculated and measured values of the cross sections
(Figs. 1 and 2), πEC change the sign of the asymmetry
in a vide energy region that is at variance with Kharkov
[1,2,5] and Frascati [21] data.
0 30 60 90 120 150 180
-1,0
-0,5
0,0
0,5
1,0
Σ [π EC]
Σ [CC]
Σ [CC;π EC]
Σ
θ cm
p , degrees
10-5
10-4
10-3
10-2
10-1
100
σ
[π EC]
σ
[CC;π EC]
σ ||[π EC]σ
||
[CC;π EC]
σ
σ
σ , σ
, µ
b/
sr
Fig. 3. Relative role of CC and πEC in angular dis-
tributions of σ , σ and the asymmetry coefficient at
labEγ = 208 MeV
0 30 60 90 120 150 180
-0,5
0,0
0,5
σ [CC]+σ [SC]
σ [CC]+
+σ [SC;SO]
Σ
θ cmp , degrees
10-1
100
σ [CC;π EC]+
+σ [SC]
σ [CC;π EC]+
+σ [SC;SO]
σ,
µ
b/
sr
Fig. 4. The same as in Fig. 2. Shown are effects of
the spin-orbit electromagnetic interaction with nucleons
As is known [9,14] neither pionic nor seagull MEC in-
terfere with SC or SOC when final state interaction (FSI)
is neglected. Coherent contributions of CC and πEC are
plotted in Fig. 3. Influence of CC on σ⊥ is very small and σ
52
⊥ is entirely determined by πEC. Comparison of angular
distributions of σ calculated with full inclusion of the
rescattering effects [11,12] with results obtained in plane
wave approximation indicates the great importance of the
effects of FSI at energies Eγ~70-130 MeV. One can infer
that FSI compensates increase of the cross section due to
MEC. So, it can be expected that the destructive interfer-
ence of FSI and MEC can affect the asymmetry coeffi-
cient changing its behavior.
Following [9, 14], the SOC has been included into
present calculations. Inclusion of MEC results (see
Fig. 4) in considerable decrease of relative role of the
SOC effects. It turns out that influence of SOC can be
enhanced if one uses ‘soft’ pion-nucleon form factors
with cut-off parameter, e.g., Λπ=4mπ (the corresponding
curves are not shown here). However, the Riska model
of πEC with Λπ=4mπ is hardly consistent with Bonn po-
tential since Λπ=1.3 GeV/c is chosen in the later. It
should be noted that according to our calculations varia-
tions of the cut-off parameter in the interval
1.2≤Λπ≤1.3 GeV very slightly modify the values of the
observables within the energy region discussed.
In summary, it is demonstrated that πEC manifest
themselves mainly in transitions from the S-states of
3He (Nα=2) substantially increasing the cross section
values. Angular distributions of the cross section at
cm
pθ 120° are insensitive to inclusion of partial wave
components of 3He WF with the orbital angular mo-
menta L,l>0 (Nα>2).
The relative role of the states with α>2 is enhanced
in the case of the asymmetry coefficient. This observa-
tion allows one to hope that reaction pdHe3 →γ
with
linearly polarized photons provides a strict and sensitive
testing ground for exploring structure of 3N bound state.
Surely, consideration of relevant reaction mechanisms,
first of all, the rescattering in the final pd-state and
three-nucleon photoabsorption is of great interest for in-
terpretation of the data both for the cross section and the
asymmetry coefficient.
The authors would like to thank H. Kamada,
W. Glöckle, J. Golak, and H. Witała for the data on par-
tial wave components of the 3He WF for Bonn potential
and acknowledge helpful discussions with J. Jourdan.
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52
CALCULATION of the cross SECTION for the REACTION at INTERMEDIATE PHOTON ENERGIES
V.V. Kotlyar and A.A. Belyaev
REFERENCES
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